Elliptic Curve Crypto - User contributions [en]

Crystal radio

2026-05-05T01:23:57Z

Rational Point: Spanish expression

Building a simple AM crystal radio is, or ought to be, a basic survival skill.

This circuit <ref>All About Circuits. ''Textbook // Semiconductors // Practical Analog Semiconductor Circuits // Radio Circuits.'' https://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/radio-circuits/</ref>
shows an antenna tuned with an inductor of 240μH and a variable capacitor of 365 pF.

[[File:Crystal-radio.png|frame|center|Simple crystal radio circuit]]

The resonant frequency for this tuning with the variable capacitor set at 365 pF starts at about

:''f'' = 1 / 2π√(LC) =~ 537.73472 kilohertz

If the variable capacitance is ''reduced'' to 36.5 pF, then the resonant frequency will be increased to 1700.46649 kilohertz, the other end of the popular AM broadcast radio band, which is about exactly half a decade wide, spanning a ratio of √10 on the radio spectrum.

== Notes ==

The circuit shows a ground. It would not typically be considered necessary to physically connect the circuit to the earth at that point, but, as this is an unamplified radio receiver powered solely by the energy of broadcast radio waves hitting the antenna, it may be possible and convenient to draw more power from the antenna if the circuit is physically grounded at the other end of the inductor coil. Otherwise the other pole of a dipole antenna might be connected at that point.

The listening device could be any basic earbud or one of a pair of good quality earbuds salvaged if the other is damaged or broken. Special high impedance earbuds are sold specifically for crystal radio sets.

Crystal diodes have been made out of razor blades, pencil leads, safety pins, etc. The original "crystal" was a galena (lead or silver sulfide) crystal with the anode soldered in place with an alloy of bismuth, lead, tin and cadmium called "Wood’s Metal." A normal tin-lead solder alloy or even leaded or lead-free silver-bearing solder is probably adequate, since cadmium is even more toxic than lead.

There is an expression in Spanish, “‘la ley’ o ‘el sistema’ de plata o plomo” that describes the theory of operation of these crystal diodes, although, nowadays, crystal diodes are mostly forgotten and that expression is more used as a metaphor to describe the modus operandi of organized crime cartels.

A very fine sharp wire called a “cat’s whisker” is allowed to touch the surface of the galena crystal where it will allow electrons to pass into the crystal but it will not be able to pick up any electrons from the crystal. (The solder alloy bonded to the other side of the crystal will pick up and conduct electrons freely.) Commercially available “cat’s whisker” diodes are typically encased in clear glass and sold as “fast recovery” diodes.

There are many interesting ways to make inductors and variable or fixed capacitors.

Crystal radio

2026-05-05T00:10:00Z

Rational Point: notes

Building a simple AM crystal radio is, or ought to be, a basic survival skill.

This circuit <ref>All About Circuits. ''Textbook // Semiconductors // Practical Analog Semiconductor Circuits // Radio Circuits.'' https://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/radio-circuits/</ref>
shows an antenna tuned with an inductor of 240μH and a variable capacitor of 365 pF.

[[File:Crystal-radio.png|frame|center|Simple crystal radio circuit]]

The resonant frequency for this tuning with the variable capacitor set at 365 pF starts at about

:''f'' = 1 / 2π√(LC) =~ 537.73472 kilohertz

If the variable capacitance is ''reduced'' to 36.5 pF, then the resonant frequency will be increased to 1700.46649 kilohertz, the other end of the popular AM broadcast radio band, which is about exactly half a decade wide, spanning a ratio of √10 on the radio spectrum.

== Notes ==

The circuit shows a ground. It would not typically be considered necessary to physically connect the circuit to the earth at that point, but, as this is an unamplified radio receiver powered solely by the energy of broadcast radio waves hitting the antenna, it may be possible and convenient to draw more power from the antenna if the circuit is physically grounded at the other end of the inductor coil. Otherwise the other pole of a dipole antenna might be connected at that point.

The listening device could be any basic earbud or one of a pair of good quality earbuds salvaged if the other is damaged or broken. Special high impedance earbuds are sold specifically for crystal radio sets.

Crystal diodes have been made out of razor blades, pencil leads, safety pins, etc. The original "crystal" was a galena (lead or silver sulfide) crystal with the anode soldered in place with an alloy of bismuth, lead, tin and cadmium called "Wood’s Metal." A normal tin-lead solder alloy or even leaded or lead-free silver-bearing solder is probably adequate, since cadmium is even more toxic than lead.

A very fine sharp wire called a “cat’s whisker” is allowed to touch the surface of the galena crystal where it will allow electrons to pass into the crystal but it will not be able to pick up any electrons from the crystal. (The solder alloy bonded to the other side of the crystal will pick up and conduct electrons freely.) Commercially available “cat’s whisker” diodes are typically encased in clear glass and sold as “fast recovery” diodes.

There are many interesting ways to make inductors and variable or fixed capacitors.

Mathemetical modeling and computer simulation of analog electronic circuits

2026-05-04T04:51:19Z

Rational Point: Range & accuracy

The overriding assumptions are that '''“good programs” already exist''' to solve any given problem of basic circuit simulation, and to some extent, they do <ref>LTspice: Fast • Free • Unlimited https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html</ref><ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref><ref>Circuit simulation and schematics. https://www.circuitlab.com/</ref><ref>Circuit Design and Simulation Software https://www.keysight.com/us/en/products/software/pathwave-design-software/eda-software-for-circuit-design.html</ref>.

== First-order systems of ordinary differential equations ==

Analog electronic circuit simulation problems are first-order systems of ordinary differential equations to be solved numerically or approximately.

Every node in a circuit has an electric potential, and every device carries an electric current. (Transistor base and collector currents are considered separate variables in the simulation, while the emitter current is constrained to be equal to the negative sum of them.)

The differential equations are ordinary and of the first order, because they involve these potentials and currents and their first derivatives with respect to time only.

== Problems of convergence and so-called “stiffness”==

Convergence problems <ref>LT wiki: Convergence Problems. https://ltwiki.org/index.php?title=Convergence_problems%3F</ref> have plagued many SPICE (Simulation Program with Integrated Circuit Emphasis) implementations.

During the space race, Erwin Fehlberg found that many of the Runge-Kutta methods then in use, including many he had earlier proposed himself, were too complicated, requiring too many evaluations and calculations per time step without achieving any better accuracy. The best he presented at the time of Neil Armstrong’s moon landing <ref>Erwin Fehlberg. ''Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems.'' NASA TR R-315 https://ntrs.nasa.gov/api/citations/19690021375/downloads/19690021375.pdf</ref> is a particular RK1(2) method which is little more than a modified first-order Euler-Cauchy method with a simple error estimate fed back to the algorithm to adjust the step size or time increment.

Systems of differential equations whose solutions do not converge to within an acceptable error bound using these fairly simply, naïve, elementary methods are often said to be “stiff.” We would generally prefer to avoid the math jock lingo, but that is the classic terminology from the Hippie era. “Math is hard.”

== If the easy way doesn’t work, we have to do it the hard way ==

When “non-stiff” methods of solving differential equations fail, according to the literature, we must turn to “stiff” methods <ref>Chris Rackauckas. ''Solving Stiff Ordinary Differential Equations.'' October 14th, 2020 https://book.sciml.ai/notes/09-Solving_Stiff_Ordinary_Differential_Equations/</ref>. Many of these methods have the theoretical properties of being '''A-stable''' and/or '''L-stable''' <ref>T. D. Bui. ''Some A-Stable and L-Stable Methods for the Numerical Integration of Stiff Ordinary Differential Equations.'' Journal of the ACM (JACM), Volume 26, Issue 3.
Pages 483 - 493. https://dl.acm.org/doi/10.1145/322139.322147
</ref><ref>K. Selva Kumar and K. Jason. ''L-Stable and A-Stable numerical method of order two for stiff differential equation.'' April 2022. https://www.researchgate.net/publication/367887368_L-Stable_and_A-Stable_numerical_method_of_order_two_for_stiff_differential_equation</ref>.

== Range of potentials and accuracy of floating point representation ==

There is no such thing as an “absolute” electric potential, although sometimes the earth, or an iron rod pounded into the earth and affixed with an electrical lug, is taken as such. All potentials are relative in any given circuit. If two nodes of a circuit are equal or “crossing over” in potential, there is often “interesting” behavior that may be much better modeled if the difference between those potentials is directly represented as a floating point value rather than two differences from an arbitrary ground reference. Very small numbers may be represented in floating point format with large negative exponents, whereas if all potentials are expressed as differences from an arbitrary fixed ground point, then the accuracy of representation is limited to the worst relative precision of the potentials from the fixed ground point.

On the other hand, directly representing very small potential differences without reference to an arbitrarily chosen ground point is a non-conservative approach to a conservative problem, and it introduces additional degrees of freedom which may be undesirable in some situations.

Mathemetical modeling and computer simulation of analog electronic circuits

2026-05-03T18:56:23Z

Rational Point: A-stable and/or L-stable

Mathemetical modeling and computer simulation of analog electronic circuits

2026-05-02T22:59:00Z

Rational Point: Stiffness and convergence problems

Mathemetical modeling and computer simulation of analog electronic circuits

2026-05-02T21:05:46Z

Rational Point: intro

The assumptions are that '''“good programs” already exist''' to solve any given problem of basic circuit simulation, and to some extent, they do <ref>LTspice: Fast • Free • Unlimited https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html</ref><ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref><ref>Circuit simulation and schematics. https://www.circuitlab.com/</ref><ref>Circuit Design and Simulation Software https://www.keysight.com/us/en/products/software/pathwave-design-software/eda-software-for-circuit-design.html</ref>.

Analog electronic circuit simulation problems are first-order systems of ordinary differential equations to be solved numerically or approximately.

Every node in a circuit has an electric potential, and every device carries an electric current. (Transistor base and collector currents are considered separate variables in the simulation, while the emitter current is constrained to be equal to the negative sum of them.)

The differential equations are ordinary and of the first order, because they involve these potentials and currents and their first derivatives with respect to time only.

Lead-free solder, tin whiskers and bald-faced lies

2026-04-30T03:47:03Z

Rational Point: 96.5% tin, 0.5% copper and 3% silver

The health hazards of leaded solder are probably exaggerated. Other than that, there is absolutely nothing wrong with RoHS-compliant (Restriction of Hazardous Substances) solder.

Persons who are experienced soldering by hand with leaded solder <ref>Edward Fenderson. ''ROHS vs. Non-ROHS Soldering.'' 2015-08-26 https://www.digikey.com/en/maker/blogs/rohs-vs-non-rohs-soldering</ref> may not want to change. Also, silver costs more than lead, bosses are not the ones doing that kind of work, and they don’t want to pay for silver. So hand solder jobs in the electronics industry are only for prototyping and make-work.

:"… In this case, a thorough post-solder cleaning should be done to prevent flux-related problems such as corrosion, dendritic growth, poor adhesion of the conformity coatings, and electromigration, which can cause short circuits between circuit traces. … A good lead-based solder joint will be smooth and shiny, while the lead-free joints are usually duller and grainy.…"

No. A composition of 99% tin, 0.7% copper and 0.3% silver is fine. An alloy of 96.5% tin, 0.5% copper and 3% silver is also popular. Very nice and shiny. If the guys at work don't steal it and use it at home to solder jewelry for their wives and girlfriends. Actually, do not use jewelry solder for electronics. Even so-called "extra easy" silver solder is much too hot and hard. Silver happens to be an excellent electrical conductor, and a little bit goes a long way, while lead is a rather poor conductor of electricity, but used because of its resistance to acids.

:\"Tin whiskers\" is not an imaginative, fanciful term for some aspect of electronics manufacturing. Tin whiskers are real. They are microscopic conductive fibers emanating from pure tin surfaces, and they pose a serious problem to electronics of all types. These whiskers can form electrical paths, which affect the operation of the subject device. This article discusses the problems caused by the removal of lead from electronics and describes some techniques to mitigate tin whiskers <ref>Analog Devices. ''Tin Whiskers Are Real and Complex.'' Dec 13, 2011 https://www.analog.com/en/resources/technical-articles/tin-whiskers-are-real-and-complex.html</ref>.

No. No. Just no. Absolutely not. Straight honest men shave and dress for work without talking about "tin whiskers." Nothing is wrong with silver solder.

Get serious. Cost is a consideration, but leaded solder suffers from cold solder joints and poor electrical conductivity, and ultimately those guys should have shaved for work and not robbed the jewelry store.

Lead-free solder, tin whiskers and bald-faced lies

2026-04-30T03:44:19Z

Rational Point: do not use jewelry solder

The health hazards of leaded solder are probably exaggerated. Other than that, there is absolutely nothing wrong with RoHS-compliant (Restriction of Hazardous Substances) solder.

Persons who are experienced soldering by hand with leaded solder <ref>Edward Fenderson. ''ROHS vs. Non-ROHS Soldering.'' 2015-08-26 https://www.digikey.com/en/maker/blogs/rohs-vs-non-rohs-soldering</ref> may not want to change. Also, silver costs more than lead, bosses are not the ones doing that kind of work, and they don’t want to pay for silver. So hand solder jobs in the electronics industry are only for prototyping and make-work.

:"… In this case, a thorough post-solder cleaning should be done to prevent flux-related problems such as corrosion, dendritic growth, poor adhesion of the conformity coatings, and electromigration, which can cause short circuits between circuit traces. … A good lead-based solder joint will be smooth and shiny, while the lead-free joints are usually duller and grainy.…"

No. A composition of 99% tin, 0.7% copper and 0.3% silver is fine. Very nice and shiny. If the guys at work don't steal it and use it at home to solder jewelry for their wives and girlfriends. Actually, do not use jewelry solder for electronics. Even so-called "extra easy" silver solder is much too hot and hard. Silver happens to be an excellent electrical conductor, and a little bit goes a long way, while lead is a rather poor conductor of electricity, but used because of its resistance to acids.

:\"Tin whiskers\" is not an imaginative, fanciful term for some aspect of electronics manufacturing. Tin whiskers are real. They are microscopic conductive fibers emanating from pure tin surfaces, and they pose a serious problem to electronics of all types. These whiskers can form electrical paths, which affect the operation of the subject device. This article discusses the problems caused by the removal of lead from electronics and describes some techniques to mitigate tin whiskers <ref>Analog Devices. ''Tin Whiskers Are Real and Complex.'' Dec 13, 2011 https://www.analog.com/en/resources/technical-articles/tin-whiskers-are-real-and-complex.html</ref>.

No. No. Just no. Absolutely not. Straight honest men shave and dress for work without talking about "tin whiskers." Nothing is wrong with silver solder.

Get serious. Cost is a consideration, but leaded solder suffers from cold solder joints and poor electrical conductivity, and ultimately those guys should have shaved for work and not robbed the jewelry store.

Lead-free solder, tin whiskers and bald-faced lies

2026-04-29T05:50:05Z

Rational Point: robbery at the jewelry store

The health hazards of leaded solder are probably exaggerated. Other than that, there is absolutely nothing wrong with RoHS-compliant (Restriction of Hazardous Substances) solder.

Persons who are experienced soldering by hand with leaded solder <ref>Edward Fenderson. ''ROHS vs. Non-ROHS Soldering.'' 2015-08-26 https://www.digikey.com/en/maker/blogs/rohs-vs-non-rohs-soldering</ref> may not want to change. Also, silver costs more than lead, bosses are not the ones doing that kind of work, and they don’t want to pay for silver. So hand solder jobs in the electronics industry are only for prototyping and make-work.

:"… In this case, a thorough post-solder cleaning should be done to prevent flux-related problems such as corrosion, dendritic growth, poor adhesion of the conformity coatings, and electromigration, which can cause short circuits between circuit traces. … A good lead-based solder joint will be smooth and shiny, while the lead-free joints are usually duller and grainy.…"

No. A composition of 99% tin, 0.7% copper and 0.3% silver is fine. Very nice and shiny. If the guys at work don't steal it and use it at home to solder jewelry for their wives and girlfriends.

Silver happens to be an excellent electrical conductor, while lead is very poor conductor of electricity.

:\"Tin whiskers\" is not an imaginative, fanciful term for some aspect of electronics manufacturing. Tin whiskers are real. They are microscopic conductive fibers emanating from pure tin surfaces, and they pose a serious problem to electronics of all types. These whiskers can form electrical paths, which affect the operation of the subject device. This article discusses the problems caused by the removal of lead from electronics and describes some techniques to mitigate tin whiskers <ref>Analog Devices. ''Tin Whiskers Are Real and Complex.'' Dec 13, 2011 https://www.analog.com/en/resources/technical-articles/tin-whiskers-are-real-and-complex.html</ref>.

No. No. Just no. Absolutely not. Straight honest men shave and dress for work without talking about "tin whiskers." Nothing is wrong with silver solder.

Get serious. Cost is a consideration, but leaded solder suffers from cold solder joints and poor electrical conductivity, and ultimately those guys should have shaved for work and not robbed the jewelry store.

SEPIC.tex

2026-04-24T14:13:47Z

Rational Point: /* Source code for File:SEPIC.pdf */

== Source code for [[File:SEPIC.pdf]] ==
<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@article{falco2025,
author = {Eleazar Falco},
title = {The SEPIC with coupled and uncoupled inductors},
journal = {W\"urth Elektronik},
year = {2025},
url= {https://www.we-online.com/en/support/knowledge/application-notes?d=anp135-sepic-inductors}
}
@article{zhang,
author= {Dongbing Zhang},
title = {AN-1484 Designing A SEPIC Converter},
journal = {Application Report, SNVA168E--May 2006--Revised April 2013},
url={https://www.ti.com/lit/an/snva168e/snva168e.pdf}
}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}
@article{panasonic-lc,
author = {{Panasonic}},
title = {Basic Knowledge of LC Filters},
journal = {Panasonic Industry: Optimal solution for circuit design: Basic Knowledge of LC Filters},
url = {https://industrial.panasonic.com/ww/ds/ss/technical/b4},
year = {2018}
}
@article{mp-sepic,
author = {{Monolithic Power}},
title = {SEPIC Converters},
journal = {MPScholar // Power Electronics // DC/DC Converters},
url = {https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters}
}
@article{arduino-pwm,
author = {Timothy Hirzel},
title = {Basics of PWM (Pulse Width Modulation)},
journal = {Arduino Docs},
year = {2022},
url = {https://docs.arduino.cc/learn/microcontrollers/analog-output/}
}
@misc{zd-tr,
author = {{Maker.io}},
title = {Zener Diode Regulator with Transistor Current Buffer},
year = {2015-08-26},
url = {https://www.digikey.com/en/maker/tutorials/2016/zener-diode-regulator-with-transistor-current-buffers}
}
@misc{uvlo-se,
author = {{Electronics Stack Exchange}},
title = {Undervoltage lockout},
year = {2021},
url = {https://electronics.stackexchange.com/questions/560991/undervoltage-lockout}
}
@article{uvlo-h,
author = {Pinkesh Sachdev},
title = {Adding Hysteresis for Smooth Undervoltage and Overvoltage Lockout},
journal = {Analog Dialogue},
volume = {55},
year = {Mar 2021},
url = {https://www.analog.com/en/resources/analog-dialogue/articles/adding-hysteresis-for-smooth-undervoltage-and-overvoltage-lockout.html}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED NOTES \& REFERENCES ---\\
--- WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.

Please do your own research. Fully hyperlinked references are included for convenience.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvmodule, invert, l_=$SC_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0) node[circ]{}
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\node[above left, font=\scriptsize] at (d1.left) {$A$};
\node[above right, font=\scriptsize] at (d1.right) {$K$};
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [above right, font=\scriptsize] at (Q1.S) {S};
\node [below right, font=\scriptsize] at (Q1.D) {D};
\node [above, font=\scriptsize] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (8,3) to[curved capacitor, l_=$C_3$] ++(0,-2) -- ++(0,-1) node[circ]{}
-- ++(-2,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (10,2.5) node[circ]{} -- ++(-1,0) to[curved capacitor, l_=$C_4$] ++(0,-2.5) node[circ]{};
\draw (10,2.25) node[circ]{} -- ++(-0.4,0) -- ++(0,-3) -- ++ (-5.6,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC \cite{mp-sepic} is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few as if one would have attended a conference or presentation in Las Vegas on various get-rich-quick schemes.

We are confronting a pernicious problem with obnoxious patent issuances and intellectual property lawsuits over standard, commonly taught, well-known, and legally unpatentable designs. When obnoxious patents are licensed as intellectual property, and royalties are collected, the patented inventions tend to be manufactured under paid suit-and-tie licenses and shady contracts with substandard parts and sold as consumer junk.

We have not been seeing the quality we are after, particularly the details of filtering and smoothing the power supply, including the LC filter on the output in Figure~\ref{f1}, which is omitted in most introductory diagrams, but really essential in practice \cite{panasonic-lc}, probably with some field testing.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. See \cite{falco2025}. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode {\scriptsize $A$} of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $D=\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Energy transfer per clock cycle}

The amount of energy stored in an capacitor or inductor, respectively, is:

$$
E_C = \frac 1 2 V^2C; \qquad E_L = \frac 1 2 I^2L.
$$

Zhang \cite{zhang} suggests choosing inductors of a value that will allow a 40\% ripple in current at the switching frequency. In effect, that causes perhaps 64\% of the total energy stored in an inductor to be transferred each clock cycle, which appears to be a good practical limit of tolerable ``ripple'' under conditions of light load or open circuit among other considerations.

We suggest using heavy gauge wire on a heavy iron core to carry large currents to avoid overheating and/or saturating the core. This only permits relatively few turns of wire and will not result in any excessively large inductance. However this approach limits the system to low frequencies.

The capacitors in a coupled SEPIC system are movable: their exact values and placements do not seem to be critical, and may need to be determined experimentally.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18~V and 200~W each, all connected in parallel to serve a common automotive-like 12~V electrical system for which many accessories are commonly available, as well as inverters to produce 110~VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

It is particularly important to pay attention to officially published datasheets on electronic component parts and ICs. Those are the legal contracts of technical specifications on which the chips are sold, and they contain all the information you need to know from the manufacturer on the particular product you are using. Other comments or opinions from engineers or salesmen, personal or otherwise, are ultimately irrelevant, as they have presumably already stated all of the information to which they can be held accountable on the datasheet.

Once you ``make'' or ``build,'' you are no longer a consumer but a potential competitor and arch-rival making a possibly hostile use of the firm's component parts which you are effectively taking over and re-purposing as parts of your own final product. So if you are in direct competition with that firm, you would be well advised to avoid any ``vendor lock-in'' and be prepared to find alternatives or substitutes for their component parts.

\begin{quote}
``We sell electronic component parts and chips, and we have engineers who would love to talk to you about the technical details, but (obviously) our goals and objectives are merely to protect and defend our intellectual property and if at all possible to prevent you from making or building anything in direct competition with any of our own products.''
\end{quote}

\noindent To view the published datasheet with such a jaundiced eye and jaded opinions, the Amish farmer's honesty won't permit it at all.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of a greater forward voltage drop. On the other hand, the higher gate voltage required to turn them on is a possible disadvantage of MOSFETs.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24~V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100~kHz to 2.2~MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}, although the reason high frequencies have been used for this purpose was to enable a greater power transfer through inductors and capacitors that can hold only a fixed amount of energy per clock cycle.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20~kHz to 500~kHz. These chips are older, rather outdated, and no longer under active development, but they are still in production.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20~kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation. There is no reason we cannot go as low as 400, 60 or even 50~Hz. Larger inductors and capacitors will be required in these cases, but the converter will be more efficient and may produce smoother, cleaner power.

The ``Arduino'' also has a rudimentary pulse width modulation ``analog output'' running at about 0.5~kHz \cite{arduino-pwm}, which is adequate for our purposes as long as we design and plan for the very low frequency.

\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,6) -- ++(-2,0) node[ocirc]{} to[pvmodule, invert, l_=$SC_1$] ++(0,-6) node[ocirc]{} -- ++(2,0);
\draw (2,6) node[circ]{} to[resistor, label=$R_2$] ++(0,-3) node[circ, name=qb0]{}
to[zzDo, invert, label=$D_2$] ++(0,-3) node[circ]{};
\draw (4,3) node[npn, name=q1]{$Q_2$};
\draw (qb0) -- (q1.base);
\draw (2,6) -- ++(2,0) -- (q1.collector);
\draw (2,0) -- ++(3,0) node[circ, name=j3]{} -- ++(2,0) node[circ, name=j4]{} -- ++(1,0) node[ocirc, label=$GND$]{};
\draw (q1.emitter) -- ++(1,0) node[circ, name=j1]{} to[cute inductor, inductors/coils=3, label=$L_4$]
++(2,0) node[circ, name=j2]{} -- ++(1,0) node[ocirc, label=$V_{CC}$]{};
\node[above right, font=\scriptsize] at (q1.emitter){$E$};
\node[above, font=\scriptsize] at (q1.base){$B$};
\node[below right, font=\scriptsize] at (q1.collector){$C$};
\draw (j1) to[curved capacitor, label=$C_5$] (j3);
\draw (j2) to[curved capacitor, label=$C_6$] (j4);
\end{circuitikz}
\end{center}
\caption{Logic level power supply for $PWM$}
\label{f2}
\end{figure}

\subsection{Logic level power supply}
A simple Zener diode voltage regulator with a transistor current buffer \cite{zd-tr} as depicted in Figure~\ref{f2} should be used to power logic level circuits directly from highly variable power supplies if possible. This simple circuit also has the effect of an undervoltage lockout or UVLO \cite{uvlo-se}. Some hysteresis \cite{uvlo-h} would be desirable in order to avoid an amplified chattering effect from transistor $Q_2$ when the voltage supply is barely adequate and teetering at the edge of the lockout level.

\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\cleardoublepage
\phantomsection
\addcontentsline{toc}{section}{References}
\printbibliography
\end{document}

</syntaxhighlight>

File:SEPIC.pdf

2026-04-24T14:13:19Z

Rational Point: Rational Point uploaded a new version of File:SEPIC.pdf

See [[SEPIC.tex]] for the source code for this document.

SEPIC.tex

2026-04-24T03:44:14Z

Rational Point:

== Source code for [[File:SEPIC.pdf]] ==
<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@article{falco2025,
author = {Eleazar Falco},
title = {The SEPIC with coupled and uncoupled inductors},
journal = {W\"urth Elektronik},
year = {2025},
url= {https://www.we-online.com/en/support/knowledge/application-notes?d=anp135-sepic-inductors}
}
@article{zhang,
author= {Dongbing Zhang},
title = {AN-1484 Designing A SEPIC Converter},
journal = {Application Report, SNVA168E--May 2006--Revised April 2013},
url={https://www.ti.com/lit/an/snva168e/snva168e.pdf}
}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}
@article{panasonic-lc,
author = {{Panasonic}},
title = {Basic Knowledge of LC Filters},
journal = {Panasonic Industry: Optimal solution for circuit design: Basic Knowledge of LC Filters},
url = {https://industrial.panasonic.com/ww/ds/ss/technical/b4},
year = {2018}
}
@article{mp-sepic,
author = {{Monolithic Power}},
title = {SEPIC Converters},
journal = {MPScholar // Power Electronics // DC/DC Converters},
url = {https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters}
}
@article{arduino-pwm,
author = {Timothy Hirzel},
title = {Basics of PWM (Pulse Width Modulation)},
journal = {Arduino Docs},
year = {2022},
url = {https://docs.arduino.cc/learn/microcontrollers/analog-output/}
}
@misc{zd-tr,
author = {{Maker.io}},
title = {Zener Diode Regulator with Transistor Current Buffer},
year = {2015-08-26},
url = {https://www.digikey.com/en/maker/tutorials/2016/zener-diode-regulator-with-transistor-current-buffers}
}
@misc{uvlo-se,
author = {{Electronics Stack Exchange}},
title = {Undervoltage lockout},
year = {2021},
url = {https://electronics.stackexchange.com/questions/560991/undervoltage-lockout}
}
@article{uvlo-h,
author = {Pinkesh Sachdev},
title = {Adding Hysteresis for Smooth Undervoltage and Overvoltage Lockout},
journal = {Analog Dialogue},
volume = {55},
year = {Mar 2021},
url = {https://www.analog.com/en/resources/analog-dialogue/articles/adding-hysteresis-for-smooth-undervoltage-and-overvoltage-lockout.html}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED NOTES \& REFERENCES ---\\
--- WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.

Please do your own research. Fully hyperlinked references are included for convenience.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvmodule, invert, l_=$SC_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0) node[circ]{}
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\node[above left, font=\scriptsize] at (d1.left) {$A$};
\node[above right, font=\scriptsize] at (d1.right) {$K$};
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [above right, font=\scriptsize] at (Q1.S) {S};
\node [below right, font=\scriptsize] at (Q1.D) {D};
\node [above, font=\scriptsize] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (8,3) to[curved capacitor, l_=$C_3$] ++(0,-2) -- ++(0,-1) node[circ]{}
-- ++(-2,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (10,2.5) node[circ]{} -- ++(-1,0) to[curved capacitor, l_=$C_4$] ++(0,-2.5) node[circ]{};
\draw (10,2.25) node[circ]{} -- ++(-0.4,0) -- ++(0,-3) -- ++ (-5.6,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC \cite{mp-sepic} is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few as if one would have attended a conference or presentation in Las Vegas on various get-rich-quick schemes.

We are confronting a pernicious problem with obnoxious patent issuances and intellectual property lawsuits over standard, commonly taught, well-known, and legally unpatentable designs. When obnoxious patents are licensed as intellectual property, and royalties are collected, the patented inventions tend to be manufactured under paid suit-and-tie licenses and shady contracts with substandard parts and sold as consumer junk.

We have not been seeing the quality we are after, particularly the details of filtering and smoothing the power supply, including the LC filter on the output in Figure~\ref{f1}, which is omitted in most introductory diagrams, but really essential in practice \cite{panasonic-lc}, probably with some field testing.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. See \cite{falco2025}. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode {\scriptsize $A$} of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Energy transfer per clock cycle}

The amount of energy stored in an capacitor or inductor, respectively, is:

$$
E_C = \frac 1 2 V^2C; \qquad E_L = \frac 1 2 I^2L.
$$

Zhang \cite{zhang} suggests choosing inductors of a value that will allow a 40\% ripple in current at the switching frequency. In effect, that causes perhaps 64\% of the total energy stored in an inductor to be transferred each clock cycle, which appears to be a good practical limit of tolerable ``ripple'' under conditions of light load or open circuit among other considerations.

We suggest using heavy gauge wire on a heavy iron core to carry large currents to avoid overheating and/or saturating the core. This only permits relatively few turns of wire and will not result in any excessively large inductance.

The capacitors in a coupled SEPIC system are movable, and their exact values do not seem to be critical.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18~V and 200~W each, all connected in parallel to serve a common automotive-like 12~V electrical system for which many accessories are commonly available, as well as inverters to produce 110~VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of a greater forward voltage drop. On the other hand, the higher gate voltage required to turn them on is a possible disadvantage of MOSFETs.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24~V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100~kHz to 2.2~MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}, although the reason high frequencies have been used for this purpose was to enable a greater power transfer through inductors and capacitors that can hold only a fixed amount of energy per clock cycle.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20~kHz to 500~kHz. These chips are older, rather outdated, and no longer under active development, but they are still in production.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20~kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation. There is no reason we cannot go as low as 400, 60 or even 50~Hz. Larger inductors and capacitors will be required in these cases, but the converter will be more efficient and may produce smoother, cleaner power.

The ``Arduino'' also has a rudimentary pulse width modulation ``analog output'' running at about 0.5~kHz \cite{arduino-pwm}, which is adequate for our purposes as long as we design and plan for the very low frequency.
\subsection{Logic level power supply}

\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,6) -- ++(-2,0) node[ocirc]{} to[pvmodule, invert, l_=$SC_1$] ++(0,-6) node[ocirc]{} -- ++(2,0);
\draw (2,6) node[circ]{} to[resistor, label=$R_2$] ++(0,-3) node[circ, name=qb0]{}
to[zzDo, invert, label=$D_2$] ++(0,-3) node[circ]{};
\draw (4,3) node[pnp, name=q1]{$Q_2$};
\draw (qb0) -- (q1.base);
\draw (2,6) -- ++(2,0) -- (q1.emitter);
\draw (2,0) -- ++(3,0) node[circ, name=j3]{} -- ++(2,0) node[circ, name=j4]{} -- ++(1,0) node[ocirc, label=$GND$]{};
\draw (q1.collector) -- ++(1,0) node[circ, name=j1]{} to[cute inductor, inductors/coils=3, label=$L_4$]
++(2,0) node[circ, name=j2]{} -- ++(1,0) node[ocirc, label=$V_{CC}$]{};
\node[below right, font=\scriptsize] at (q1.emitter){$E$};
\node[below, font=\scriptsize] at (q1.base){$B$};
\node[above right, font=\scriptsize] at (q1.collector){$C$};
\draw (j1) to[curved capacitor, label=$C_5$] (j3);
\draw (j2) to[curved capacitor, label=$C_6$] (j4);
\end{circuitikz}
\end{center}
\caption{Logic level power supply for $PWM$}
\label{f2}
\end{figure}

A simple Zener diode voltage regulator with a transistor current buffer \cite{zd-tr} as depicted in Figure~\ref{f2} should be used to power logic level circuits directly from highly variable power supplies if possible. This simple circuit also has the effect of an undervoltage lockout or UVLO \cite{uvlo-se}. Some hysteresis \cite{uvlo-h} would be desirable in order to avoid an amplified chattering effect from transistor $Q_2$ when the voltage supply is barely adequate and teetering at the edge of the lockout level.

\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\cleardoublepage
\phantomsection
\addcontentsline{toc}{section}{References}
\printbibliography
\end{document}

</syntaxhighlight>

File:SEPIC.pdf

2026-04-24T03:42:45Z

Rational Point: Rational Point uploaded a new version of File:SEPIC.pdf

See [[SEPIC.tex]] for the source code for this document.

Magnetic permeability

2026-04-21T15:48:48Z

Rational Point: /* Calculating the magnetic permeability of a toroid core */

== Calculating the magnetic permeability of a toroid core ==

:''L'' = ''μN''2''A'' / ''ℓ''

where ''L'' is the inductance of a winding of wire about a magnetic core, ''μ'' is the magnetic permeability of the core, ''N'' is the number of turns of wire, A is the (constant) cross-sectional area of the core and ''ℓ'' is the harmonic mean path length of magnetic flux through the core. If ''Φ'' is the outer diameter and ''φ'' is the inner diameter of a toroidal core with a rectangular cross section, then the harmonic mean path length is calculated:

:<math>\ell = \pi\cdot\frac{\Phi-\phi}{\int_{\phi}^{\Phi} \frac {dx}x} = \pi\cdot\frac{\Phi-\phi}{\log\Phi-\log\phi}</math>.

Now

:''μ'' = ''Lℓ'' / ''N''2''A''

=== Example ===

[[File:Inductor 20260412~2.jpg|thumb|alt=Measuring inductance|Measuring inductance|none]]

For this example, L=1.813mH, ''Φ''=102mm, ''φ''=65.5mm, A=18.25mm×19.5mm, and N=23.

Problem: calculate the magnetic permeability of the material of which this core is made.

=== The Biot–Savart Law for air-core inductors and coils in free space ===

...

Solar systems

2026-04-20T04:45:04Z

Rational Point: /* Charge controller */ Zener Diode Regulator with Transistor Current Buffer

It seems arrogant to talk about man-made '''solar systems''' for generating electricity for home use off-grid, as if one were to elevate one's throne above the stars of heaven as Lucifer the bearer of light to do that. Not so. The "grid" itself is that beast, the natural intellect of man, given to the industrial revolution, with the arrogance to carry man-made electricity long distances over land.

However, the set-up of solar panels themselves does depend very much on their alignment with the sun, stars and planets, and the motions of the earth and moon. A common suggestion is that solar panels should face, say, due south in the northern hemisphere, inclined from the horizontal at an angle approximately equal to one's latitude.

Conditions of partial shade and/or high latitude dictate special engineering considerations with respect to adequate insolation for generating electricity.

The maximum energy intensity of sunlight hitting the earth on a clear day may be estimated as

:''I'' = 1350 W/m² × sin ''α'' × exp(–0.30 × ''p'' / sin ''α'')

where α is the angle of elevation of the sun above the horizon, and ''p'' is the ratio of barometric pressure at the altitude of the site to that at sea level. The fist factor is the "outer space" intensity of sunlight at the Earth's distance from the Sun. The second factor accounts for the slant of the sun's rays, and the third factor accounts for the filtering and dimming of the sunlight through Earth's atmosphere.

== The war against social objections to living off the grid ==
Solar panels are often considered a "green" or environmentally sensitive alternative for generating electricity, and we neither object to that consideration nor make a religion out of it.

Technology that enables "off-grid" living reduces the attack surface for secure computer systems, banks, broker houses, and even low-budget private homes etc. by enabling redundancy and reliability even if nothing else, and if the upfront capital and ongoing maintenance costs are reasonable for a reliable electric power system, should be welcomed by Christians living a simple rural lifestyle off the grid.

However, be warned that some "Christians" are married to the grid and to the assumptions of universal vaccinations etc. on which urban lifestyles have been based for millennia with or without Christ. "There's a lady" in the worst Mafia sense of the phrase, (guns are banned and please remove your hats, gentlemen,) so if you are a male "sovereign citizen" or "freeman on the land," then you are deemed to be risking her life and the lives of your children by your simple rural lifestyle.

It's a strange and unnatural situation of religious restrictions to urban white-collar employment and indoors-only entertainment where people with horses and cows etc. are suddenly deemed to be living lives of vice and heavy sin by a certain cadre of over-educated city-dwelling churchgoers, in whose presence hunting and fishing are deemed to be mortal and unforgivable sins.

City people are at always at law and if you give them an inch they take a mile, so don't even start with them.

==Solar panels==

As of 2026, typical solar panels are available in sizes of 100 to 400 watts, costing about one dollar per watt at the lowest bulk price available from major vendors in the United States.

These solar panels typically produce electricity at a nominal 18 volts, ranging from 16 volts at full load to 20 volts at no load in full direct sunlight, designed for charging 12 volt battery systems. Common automotive accessories may be powered directly or an inverter may be used to generate 110‒250VAC if desired.

==Charge controller==
[[File:Ss-1.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI TL5001AMJG)]]
[[File:Ss-2.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI LM51561HPWPR)]]

We find that off-the-shelf charge controllers are over-rated and overpriced, and we propose building one from scratch with adequate safety margins for high household power requirements.

A Buck-Boost Converter <ref>Buck-Boost Converter: What is it? (Formula and Circuit Diagram) https://www.electrical4u.com/buck-boost-converter/</ref> or Single-Ended Primary Inductor Converter (SEPIC) <ref>SEPIC Converters https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters</ref><ref>Dongbing Zhang. "AN-1484 Designing A SEPIC Converter." Application Report SNVA168E – May 2006 – Revised April 2013. https://www.ti.com/lit/an/snva168e/snva168e.pdf </ref> is typically used for this purpose.

An inductor, coil or transformer may be wound by hand using a adequate gauge of thinly insulated Tefzel or similar wire on a used or salvaged laminated or powdered iron core. The core of a transformer or inductor, if not powdered cerrite, must be made of thin layers of soft tempered malleable iron or mild steel that will swing the needle of a compass, and it should never be "quenched" or "saturated." The laminated iron core should be "tanned" with oak gall and waxed with beeswax and/or lacquered with boiled linseed oil to form insulative layers of oxide and wax or lacquer between the layers of steel, so that the transformer will not short out between the layers of steel and melt down under load. The windings of wire on a homemade transformer or inductor should be of the purest copper, smoothly drawn, carefully annealed to a soft temper, ductile, and flexible, with the best quality of insulation that is not too thick. Take care that wire windings are smooth and not bent or creased on sharp corners.

Power capacitors of several farads in capacity are widely available and inexpensive, mostly intended for car stereos and audio systems. We suggest using wire of adequate size for the intended current-carrying capacity, while over-provisioning and de-rating cheap power electronics parts, and installing fast-blow fuses at strategic locations, taking care not to overcharge a capacitor or induce a flyback voltage in a large coil. We are not certain about quality but there are audiophiles who listen to music and demand such quality.

High-power transistors, and even several transistors in parallel, may be used to control large electric currents.

Capacitance, inductance and transistor performance characteristics, etc. of all component parts should be carefully measured and verified with appropriate field or bench test equipment.

A Zener diode with a resistor and a transistor <ref> ''Zener Diode Regulator with Transistor Current Buffer.'' 2015-08-26. https://www.digikey.com/en/maker/tutorials/2016/zener-diode-regulator-with-transistor-current-buffers</ref> may be helpful as a logic-level voltage supply for the charge controller itself to enable "wide ''Vin''" functionality for integrated circuit power directly from the solar panels under varying sunlight conditions.

=== Component selection and Bill of Materials ===

''See [[File:SEPIC.pdf]] for details.''

The heart of the controller is a Pulse Width Modulation chip <ref>Some manufacturers and corporations will not like our attitude for referring to their integrated circuits as "chips" for sure, but at pawn shops and online auction sites selling jewelry and electronics one should not be ashamed to call them that. We have no opinions on offers of free samples direct from manufacturers or wholesalers, other than that they apparently contact local cops to enforce a litany of unwritten rules and unspoken codes sometimes pertaining to "intellectual property" by which hobbyists as opposed to professionals are supposed to abide.</ref> like the Texas Instruments TL5001AMJG <ref>PWM Controller with wide input range, with ±3% tolerance on reference, operation –55°C to 125°C https://www.ti.com/product/TL5001AM</ref>. These particular integrated circuits operate in a wide range between 3 and 40 volts, and also come in radiation-hardened versions, which suggests that they were used for solar panels to power satellites launched into outer space decades ago, many of which are still in service today.

The Littelfuse/IXYS IXFN520N075T2<ref>Littelfuse/IXYS IXFN520N075T2 https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2</ref><ref>Littelfuse/IXYS IXFN520N075T2 Datasheet https://www.littelfuse.com/assetdocs/littelfuse-discrete-mosfets-ixfn520n075t2-datasheet?assetguid=8706a9d1-94c2-4e6f-8277-46cab5c71388</ref> power MOSFET "trench gate" is essentially rated to handle 480A in the on state and 75V in the off state. The Vishay VS-FC420SA10 <ref>VS-FC420SA10 Product Information https://www.vishay.com/en/product/95793/</ref><ref>Vishay VS-FC420SA10 Datasheet https://www.vishay.com/docs/95793/vs-fc420sa10.pdf</ref> is another brand of power MOSFET rated to carry 435A when on or hold 100V when off. It comes in the same form factor, an SOT-227 which looks and acts like a miniature clothes iron, and requires an excellent heat sink rated for switching losses and forward voltage drop at the rated current. It would appear that if either of these devices functions as advertised, you could easily start an automobile with the electric current they are rated for handling if you wired one of them up in place of a solenoid for the starter motor. As far as we can tell, this can actually be done, except that the high power MOSFETS require 10V to drive the gate, and the drawdown on a 12V car battery from the starting current will reduce the voltage below the gate actuation level.

Insulated-Gate Bipolar Transistors (IGBTs)<ref>Insulated-Gate Bipolar Transistors (IGBTs) https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-16.html
</ref><ref>Comparison of Forward Characteristics of IGBTs and MOSFETs
https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-21.html</ref> are another option for the high power current switching needed for the Buck-Boost or SEPIC controllers that need to be used for regulating the voltage from variably sunlit photovoltaic cells to a usable level.

[[Category:Electronics]]

== Batteries ==
tbd ...

FM radio

2026-04-20T03:27:05Z

Rational Point: start article

Various circuits exist for building simple FM radio receivers <ref>''Simple FM Radio.'' https://electronics-diy.com/simple-fm-radio.php</ref><ref>D. Prabakaran. ''Designing Simple FM Radio Receiver Circuit.'' August 16, 2023. https://www.electronicsforu.com/electronics-projects/simple-fm-receiver </ref><ref>''LEAP #476: Simplest Direct FM Receiver.'' https://leap.tardate.com/radio/fm/simplestdirectreceiver/</ref><ref>''How to Build a Simple FM Radio Receiver on a Breadboard.'' https://en.eeworld.com.cn/circuit/view/105092</ref>.

This one <ref>Boris Landoni. ''DiY FM Micro Receiver.'' https://www.open-electronics.org/diy-fm-micro-receiver/</ref> has stereo output and uses an integrated circuit.

File:Crystal-radio.png

2026-04-19T18:00:12Z

Rational Point: Rational Point uploaded a new version of File:Crystal-radio.png

Basic Crystal radio circuit
https://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/radio-circuits/

Crystal radio

2026-04-19T17:56:42Z

Rational Point: minor edits

Crystal radio

2026-04-19T17:53:12Z

Rational Point: Simple crystal radio circuit

Building a simple crystal radio is, or ought to be, a basic survival skill.

This circuit <ref>All About Circuits. ''Textbook // Semiconductors // Practical Analog Semiconductor Circuits // Radio Circuits.'' https://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/radio-circuits/</ref>
shows an antenna tuned with an inductor of 240μH and a variable capacitor of 365pF.

[[File:Crystal-radio.png|frame|center|Simple crystal radio circuit]]

The resonant frequency for this tuning will be about

:''f'' = 1 / 2π√(LC) =~ 537.73472 kilohertz

If the variable capacitance is reduced to 36.5pF, then the resonant frequency will be increased to 1700.46649 kilohertz, the other end of the popular AM broadcast radio band, which is about exactly half a decade wide, spanning a ratio of √10 on the radio spectrum.

File:Crystal-radio.png

2026-04-19T17:51:38Z

Rational Point:

Basic Crystal radio circuit
https://www.allaboutcircuits.com/textbook/semiconductors/chpt-9/radio-circuits/

File:SEPIC.pdf

2026-04-17T05:55:16Z

Rational Point: Rational Point uploaded a new version of File:SEPIC.pdf

See [[SEPIC.tex]] for the source code for this document.

SEPIC.tex

2026-04-17T05:54:51Z

Rational Point: Arduino

<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@article{falco2025,
author = {Eleazar Falco},
title = {The SEPIC with coupled and uncoupled inductors},
journal = {W\"urth Elektronik},
year = {2025},
url= {https://www.we-online.com/en/support/knowledge/application-notes?d=anp135-sepic-inductors}
}
@article{zhang,
author= {Dongbing Zhang},
title = {AN-1484 Designing A SEPIC Converter},
journal = {Application Report, SNVA168E--May 2006--Revised April 2013},
url={https://www.ti.com/lit/an/snva168e/snva168e.pdf}
}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}
@article{panasonic-lc,
author = {{Panasonic}},
title = {Basic Knowledge of LC Filters},
journal = {Panasonic Industry: Optimal solution for circuit design: Basic Knowledge of LC Filters},
url = {https://industrial.panasonic.com/ww/ds/ss/technical/b4},
year = {2018}
}
@article{mp-sepic,
author = {{Monolithic Power}},
title = {SEPIC Converters},
journal = {MPScholar // Power Electronics // DC/DC Converters},
url = {https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters}
}
@article{arduino-pwm,
author = {Timothy Hirzel},
title = {Basics of PWM (Pulse Width Modulation)},
journal = {Arduino Docs},
year = {2022},
url = {https://docs.arduino.cc/learn/microcontrollers/analog-output/}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvsource, invert, l_=$V_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0) node[circ]{}
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [right, font=\tiny] at (Q1.S) {S};
\node [right, font=\tiny] at (Q1.D) {D};
\node [above, font=\tiny] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (8,3) to[curved capacitor, l_=$C_3$] ++(0,-2) -- ++(0,-1) node[circ]{}
-- ++(-2,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (10,2.5) node[circ]{} -- ++(-1,0) to[curved capacitor, l_=$C_4$] ++(0,-2.5) node[circ]{};
\draw (10,2.25) node[circ]{} -- ++(-0.4,0) -- ++(0,-3) -- ++ (-5.6,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC \cite{mp-sepic} is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few as if one would have attended a conference or presentation in Las Vegas on various get-rich-quick schemes.

We are confronting a pernicious problem with obnoxious patent issuances and intellectual property lawsuits over standard, commonly taught, well-known, and legally unpatentable designs. When obnoxious patents are licensed as intellectual property, and royalties are collected, the patented inventions tend to be manufactured under paid suit-and-tie licenses and shady contracts with substandard parts and sold as consumer junk.

We have not been seeing the quality we are after, particularly the details of filtering and smoothing the power supply, including the LC filter on the output in Figure~\ref{f1}, which is omitted in most introductory diagrams, but really essential in practice \cite{panasonic-lc}, probably with some field testing.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. See \cite{falco2025}. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Energy transfer per clock cycle}

The amount of energy stored in an capacitor or inductor, respectively, is:

$$
E_C = \frac 1 2 V^2C; \qquad E_L = \frac 1 2 I^2L.
$$

Zhang \cite{zhang} suggests choosing inductors of a value that will allow a 40\% ripple in current at the switching frequency. In effect, that causes perhaps 64\% of the total energy stored in an inductor to be transferred each clock cycle, which appears to be a good practical absolute maximum possible amount of energy that can be effectively transferred through the SEPIC per clock cycle, if that degree of ``ripple'' is tolerable among other considerations.

We suggest using heavy gauge wire on a heavy iron core to carry large currents to avoid overheating and/or saturating the core. This only permits relatively few turns of wire and will not result in any excessively large inductance.

The capacitors in a coupled SEPIC system are movable, and their exact values do not seem to be critical.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18~V and 200~W each, all connected in parallel to serve a common automotive-like 12~V electrical system for which many accessories are commonly available, as well as inverters to produce 110~VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``'ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of a greater forward voltage drop. On the other hand, the higher gate voltage required to turn them on is a possible disadvantage of MOSFETs.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24~V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100~kHz to 2.2~MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}, although the reason high frequencies have been used for this purpose was to enable a greater power transfer through inductors and capacitors that can hold only a fixed amount of energy per clock cycle.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20~kHz to 500~kHz. These chips are older, rather outdated, and no longer under active development, but they are still in production.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20~kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation. There is no reason we cannot go as low as 400, 60 or even 50~Hz. Larger inductors and capacitors will be required in these cases, but the converter will be more efficient and may produce smoother, cleaner power.

The ``Arduino'' also has a rudimentary pulse width modulation ``analog output'' running at about 0.5~kHz \cite{arduino-pwm}, which is adequate for our purposes as long as we design and plan for the very low frequency.

\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\printbibliography
\end{document}

</syntaxhighlight>

File:SEPIC.pdf

2026-04-17T05:16:21Z

Rational Point: Rational Point uploaded a new version of File:SEPIC.pdf

See [[SEPIC.tex]] for the source code for this document.

SEPIC.tex

2026-04-17T05:15:27Z

Rational Point: something is missing

<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@article{falco2025,
author = {Eleazar Falco},
title = {The SEPIC with coupled and uncoupled inductors},
journal = {W\"urth Elektronik},
year = {2025},
url= {https://www.we-online.com/en/support/knowledge/application-notes?d=anp135-sepic-inductors}
}
@article{zhang,
author= {Dongbing Zhang},
title = {AN-1484 Designing A SEPIC Converter},
journal = {Application Report, SNVA168E--May 2006--Revised April 2013},
url={https://www.ti.com/lit/an/snva168e/snva168e.pdf}
}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}
@article{panasonic-lc,
author = {{Panasonic}},
title = {Basic Knowledge of LC Filters},
journal = {Panasonic Industry: Optimal solution for circuit design: Basic Knowledge of LC Filters},
url = {https://industrial.panasonic.com/ww/ds/ss/technical/b4},
year = {2018}
}
@article{mp-sepic,
author = {{Monolithic Power}},
title = {SEPIC Converters},
journal = {MPScholar // Power Electronics // DC/DC Converters},
url = {https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvsource, invert, l_=$V_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0) node[circ]{}
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [right, font=\tiny] at (Q1.S) {S};
\node [right, font=\tiny] at (Q1.D) {D};
\node [above, font=\tiny] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (8,3) to[curved capacitor, l_=$C_3$] ++(0,-2) -- ++(0,-1) node[circ]{}
-- ++(-2,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (10,2.5) node[circ]{} -- ++(-1,0) to[curved capacitor, l_=$C_4$] ++(0,-2.5) node[circ]{};
\draw (10,2.25) node[circ]{} -- ++(-0.4,0) -- ++(0,-3) -- ++ (-5.6,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC \cite{mp-sepic} is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few as if one would have attended a conference or presentation in Las Vegas on various get-rich-quick schemes.

We are confronting a pernicious problem with obnoxious patent issuances and intellectual property lawsuits over standard, commonly taught, well-known, and legally unpatentable designs. When obnoxious patents are licensed as intellectual property, and royalties are collected, the patented inventions tend to be manufactured under paid suit-and-tie licenses and shady contracts with substandard parts and sold as consumer junk.

We have not been seeing the quality we are after, particularly the details of filtering and smoothing the power supply, including the LC filter on the output in Figure~\ref{f1}, which is omitted in most introductory diagrams, but really essential in practice \cite{panasonic-lc}, probably with some field testing.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. See \cite{falco2025}. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Energy transfer per clock cycle}

The amount of energy stored in an capacitor or inductor, respectively, is:

$$
E_C = \frac 1 2 V^2C; \qquad E_L = \frac 1 2 I^2L.
$$

Zhang \cite{zhang} suggests choosing inductors of a value that will allow a 40\% ripple in current at the switching frequency. In effect, that causes perhaps 64\% of the total energy stored in an inductor to be transferred each clock cycle, which appears to be a good practical absolute maximum possible amount of energy that can be effectively transferred through the SEPIC per clock cycle, if that degree of ``ripple'' is tolerable among other considerations.

We suggest using heavy gauge wire on a heavy iron core to carry large currents to avoid overheating and/or saturating the core. This only permits relatively few turns of wire and will not result in any excessively large inductance.

The capacitors in a coupled SEPIC system are movable, and their exact values do not seem to be critical.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18~V and 200~W each, all connected in parallel to serve a common automotive-like 12~V electrical system for which many accessories are commonly available, as well as inverters to produce 110~VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``'ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of a greater forward voltage drop. On the other hand, the higher gate voltage required to turn them on is a possible disadvantage of MOSFETs.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24~V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100~kHz to 2.2~MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}, although the reason high frequencies have been used for this purpose was to enable a greater power transfer through inductors and capacitors that can hold only a fixed amount of energy per clock cycle.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20~kHz to 500~kHz. These chips are older, rather outdated, and no longer under active development, but they are still in production.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20~kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation. There is no reason we cannot go as low as 400, 60 or even 50~Hz. Larger inductors and capacitors will be required in these cases, but the converter will be more efficient may produce smoother, cleaner power.

\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\printbibliography
\end{document}

</syntaxhighlight>

SEPIC.tex

2026-04-14T04:09:05Z

Rational Point: new section; more refs

<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@article{falco2025,
author = {Eleazar Falco},
title = {The SEPIC with coupled and uncoupled inductors},
journal = {W\"urth Elektronik},
year = {2025},
url= {https://www.we-online.com/en/support/knowledge/application-notes?d=anp135-sepic-inductors}
}
@article{zhang,
author= {Dongbing Zhang},
title = {AN-1484 Designing A SEPIC Converter},
journal = {Application Report, SNVA168E--May 2006--Revised April 2013},
url={https://www.ti.com/lit/an/snva168e/snva168e.pdf}
}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvsource, invert, l_=$V_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0)
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [right, font=\tiny] at (Q1.S) {S};
\node [right, font=\tiny] at (Q1.D) {D};
\node [above, font=\tiny] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (10,2.5) -- ++(-1,0) to[curved capacitor, l_=$C_3$] ++(0,-2.5) node[circ]{}
-- ++(-3,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (9,2.5) node[circ]{} -- ++(-1.33,0) -- ++(0,-3.25) -- ++ (-3.67,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. See \cite{falco2025}. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Energy transfer per clock cycle}

The amount of energy stored in an capacitor or inductor, respectively, is:

$$
E_C = \frac 1 2 V^2C; \qquad E_L = \frac 1 2 I^2L.
$$

Zhang \cite{zhang} suggests choosing inductors of a value that will allow a 40\% ripple in current at the switching frequency. In effect, that causes perhaps 64\% of the total energy stored in an inductor to be transferred each clock cycle, which appears to be a good practical absolute maximum possible amount of energy that can be effectively transferred through the SEPIC per clock cycle, if that degree of ``ripple'' is tolerable among other considerations.

We suggest using heavy gauge wire on a heavy iron core to carry large currents to avoid overheating and/or saturating the core. This only permits relatively few turns of wire and will not result in any excessively large inductance.

The capacitors in a coupled SEPIC system are movable, and their exact values do not seem to be critical.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18V and 200W each, all connected in parallel to serve a common automotive-like 12V electrical system for which many accessories are commonly available, as well as inverters to generate 110VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``'ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of the forward voltage drop. Power MOSFETs may also require a higher gate voltage to turn on.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24 V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100 kHz to 2.2 MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20 kHz to 500 kHz.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20 kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation.
\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\printbibliography
\end{document}

</syntaxhighlight>

File:SEPIC.pdf

2026-04-14T04:08:09Z

Rational Point: Rational Point uploaded a new version of File:SEPIC.pdf

See [[SEPIC.tex]] for the source code for this document.

File:SEPIC.pdf

2026-04-13T23:53:04Z

Rational Point: source code

See [[SEPIC.tex]] for the source code for this document.

SEPIC.tex

2026-04-13T23:51:20Z

Rational Point: source code

<syntaxhighlight lang="latex" line="">
\documentclass{article}
\usepackage{currfile}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{tikz}
\usepackage[american]{circuitikz}
\usepackage[backend=biber, style=numeric]{biblatex}
\usepackage{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=blue,
filecolor=magenta,
urlcolor=cyan,
pdftitle={Controlling and Driving the SEPIC}
}
\begin{filecontents}[overwrite,nosearch]{\currfilebase.bib}
@misc{IXFN520N075T2,
author = {{Littelfuse/IXYS}},
title = {IXFN520N075T2: DiscMSFT NChTrenchGateGen2 SOT-227B(mini | Series: Gen2},
url = {https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2}
}
@misc{VS-FC420SA10,
author = {{Vishay Semiconductors}},
title = {VS-FC420SA10 PRODUCT INFORMATION:
SOT-227 Power Module Single Switch - Power MOSFET, 420 A},
url = {https://www.vishay.com/en/product/95793/}
}
@misc{STPS200170TV1,
author={{ST Microelectronics}},
title={STPS200170TV1: 170 V, 200 A dual Power Schottky Rectifier},
url={https://www.st.com/en/diodes-and-rectifiers/stps200170tv1.html}
}
@misc{VS-203CNQ100PbF,
author = {{Vishay Semiconductors}},
title = {VS-203CNQ100PbF PRODUCT INFORMATION:
High Performance Schottky Rectifier, 200 A},
url = {https://www.vishay.com/en/product/94155/}
}
@misc{apmcap,
author = {{Absolute Pro Music}},
title = {Search for ``capacitor'' ...},
url = {https://absolutepromusic.com/search?q=capacitor}
}
@misc{bossaudiocap,
author = {{Boss Audio}},
title = {Search for ``capacitor'' ...},
url = {https://bossaudio.com/collections/sale?q=capacitor}
}
@misc{LM5155,
author = {{Texas Instruments}},
title = {LM5155: 2.2-MHz wide VIN, 1.5-A MOSFET driver, non-synchronous boost controller},
url = {https://www.ti.com/product/LM5155}
}
@misc{LM51551,
author={{Texas Instruments}},
title = {LM51551: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with hiccup},
url = {https://www.ti.com/product/LM51551}
}
@misc{LM5156H,
author = {{Texas Instruments}},
title = {LM5156H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with dual random spread spectrum},
url = {https://www.ti.com/product/LM5156H}
}
@misc{LM51561,
author = {{Texas Instruments}},
title = {LM51561: 2.2MHz Wide Input Nonsynchronous Boost, SEPIC, Flyback Controller with Spread Spectrum},
url = {https://www.ti.com/product/LM51561}
}
@misc{LM51561H,
author = {{Texas Instruments}},
title = {LM51561H: 2.2-MHz wide VIN nonsynchronous boost, flyback, {\&} SEPIC controller with spread spectrum and hiccup},
url = {https://www.ti.com/product/LM51561H}
}
@misc{TL5001,
author = {{Texas Instruments}},
title = {TL5001: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001}
}
@misc{TL5001A,
author = {{Texas Instruments}},
title = {TL5001A: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --20\textdegree C to 85\textdegree C},
url = {https://www.ti.com/product/TL5001A}
}
@misc{TL5001M,
author = {{Texas Instruments}},
title = {TL5001M: PWM Controller with wide input range, with \textpm 5{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001M}
}
@misc{TL5001AM,
author = {{Texas Instruments}},
title = {TL5001AM: PWM Controller with wide input range, with \textpm 3{\%} tolerance on reference, operation --55\textdegree C to 125\textdegree C},
url = {https://www.ti.com/product/TL5001AM}
}
@misc{LM555,
author = {{Texas Instruments}},
title = {LM555: Highly Stable 555 Timer},
url = {https://www.ti.com/product/LM555}
}

\end{filecontents}
\addbibresource{\currfilebase.bib}
%opening
\title{Controlling and Driving the SEPIC}
\author{--- NON-PUBLISHED WORK-IN-PROGRESS ---}

\begin{document}

\maketitle

\begin{abstract}
Investigating the ``Single Ended Primary Inductor Converter'' for use with residential, rooftop, commercial or industrial solar panels. The purpose of this study is to gain a more thorough understanding of the theory of operation of switching power supplies and ``charge controllers'' for solar panel systems before putting it in practice.
\end{abstract}
\tableofcontents
\begin{figure}
\begin{center}
\begin{circuitikz}
\draw (2,3) -- ++(-2,0) to[pvsource, invert, l_=$V_1$] ++(0,-3) -- ++(2,0);
\draw (2,3) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_1$, name=l1] ++(2,0) node[circ]{}
to[curved capacitor, label=$C_2$] ++(2,0) node[circ]{}
to[sDo, label=$D_1$, name=d1] ++(2,0)
to[cute choke, inductors/coils=3, label=$L_3$] ++(2,0) -- ++(0,-0.5) node[circ]{}
to[european resistor, label=$R_1$] ++(0,-2.5) -- ++(-2,0);
\draw (2,3) to[curved capacitor, l_=$C_1$] ++(0,-3) node[circ]{}
-- ++(2,0) node[circ]{};
\draw (4,1.5) node[nigfete, solderdot](Q1){$Q_1$};
\node [right, font=\tiny] at (Q1.S) {S};
\node [right, font=\tiny] at (Q1.D) {D};
\node [above, font=\tiny] at (Q1.G) {G};
\draw (Q1.D) -- (4,3); \draw (Q1.S) -- (4,0);
\draw (4,0) -- ++(2,0) node[circ]{} to[cute inductor, inductors/coils=5, l_=$L_2$, name=l2] ++(0,3);
\path (l1.lr dot) node[circ]{} (l2.lr dot) node[circ]{};
\draw[thick, double] (l1.core west) -- (l1.core east);
\draw[thick, double] (l2.core west) -- (l2.core east);
\draw (10,2.5) -- ++(-1,0) to[curved capacitor, l_=$C_3$] ++(0,-2.5) node[circ]{}
-- ++(-3,0);
\draw (Q1.G) --++ (0,-1) to[square voltage source, l_=$PWM$] ++(0,-2) node[ground]{};
\draw (10,0) node[circ]{} -- ++(0,-1.75) node[ground]{};
\draw (9,2.5) node[circ]{} -- ++(-1.33,0) -- ++(0,-3.25) -- ++ (-3.67,0) node[vcc, rotate=90, label={\qquad\qquad feedback}]{};
\end{circuitikz}
\end{center}
\caption{SEPIC circuit diagram}
\label{f1}
\end{figure}

\section{Introduction}

The SEPIC is one of a number of regulated switching power supply topologies, among which are included various versions of Buck, Boost, Buck--Boost, Flyback, Zeta and \'Cuk\footnote{Named after the prolific Serbo-Croatian--American inventor Slobodan \'Cuk of the California Institute of Technology.} DC-to-DC converters, to name a few.

\section{Discussion of the SEPIC topology}

If the inductors $L_1$ and $L_2$ in Figure~\ref{f1} are coupled, or wound on the same iron core as indicated by the black dots in the diagram, then the capacitors $C_1$ and $C_2$ are essentially placed in parallel, and one or the other may be removed without affecting the circuit much, because the inductance in canceled out for any electric current flowing through $L_1$ and back the opposite way through $L_2$. Nevertheless, the capacitors $C_1$ and $C_2$ as placed serve to protect the power MOSFET $Q_1$ from transient ``spikes'' in the inductive windings.

When $Q_1$ is switched on by the $PWM$, the current through $L_1$ increases, and when $Q_1$ is switched off, the remaining magnetic flux in the iron core forces the current through the other winding $L_2$ past the diode $D_1$ to keep the capacitor $C_3$ charged and continue supplying power to the load resistance $R_1$. This is omitting $C_2$ from consideration, and depending on mutual inductance alone.

However the circuit will still function if the inductors $L_1$ and $L_2$ are \textit{not} coupled and $C_2$ is present. In this case, $C_2$ is discharged by current flowing through $L_2$ when $Q_1$ is switched on, and additional supply current is admitted through $L_1$. Now when $Q_1$ is switched off, $C_2$ is charged again by current continuing through $L_1$, and the current that was flowing through $L_2$ as $C_2$ was discharging is suddenly switched and forced through the diode $D_1$ instead.

When the inductors $L_1$ and $L_2$ are coupled, and $C_2$ is present, there is additional redundancy, stability, and reliability for the circuit.

\section{Calculating the duty cycle of the PWM}

A simple way to figure out the duty cycle of the pulse width modulator needed to produce the desired potential at the output is to consider that the mean potential at the drain of $Q_1$ over the switching cycle must be equal to the input potential $V_1$, and that potential is equal to zero, or the forward voltage drop of the transistor during the time when it is on, which we want as small as possible. That potential must then be high enough during the time when the transistor is off to average out to the correct value over the entire clock cycle $T$. Let $\tau$ be the pulse width, or the time when the power transistor $Q_1$ is turned on and conducting electricity between its source and drain:

$$
\overline{V_Q} = V_1; \qquad V_{Q_\textrm{on}}=0;
\qquad V_{Q_\textrm{off}} = \frac{TV_1}{T-\tau}.
$$

Now consider the operating potential $V_P$ at the anode of diode $D_1$. At all times, $V_P$ is less than the potential $V_Q$ at the transistor drain by a difference equal to the input potential $V_1$.

$$
V_P = V_Q - V_1.
$$

So

$$
\overline{V_P} = 0; \qquad V_{P_\textrm{on}}=-V_1;
\qquad V_{P_\textrm{off}} = \frac{\tau V_1}{T-\tau}.
$$

Increasing the duty cycle $\tau/T$ will increase the potential $V_{P_\textrm{off}}$ which is available at the output less the forward drop through the diode $D_1$, but it will correspondingly decrease the clock-cycle-averaged current available at the increased potential. A Pulse Width Modulator with a feedback loop will assist in maintaining a stable output potential from a variable input potential from solar panels.

\section{Size and scale of systems proposed}

We propose off-grid solar electric power systems for use by ``sovereign citizens'' or ``freemen on the land'' (or even banks or broker houses that desire back-up power and money savings at the city electric meter) with about a dozen solar panels rated at 18V and 200W each, all connected in parallel to serve a common automotive-like 12V electrical system for which many accessories are commonly available, as well as inverters to generate 110VAC if desired.

\section{Selection of components and bill of materials}

The selection of components is based on how much ``'ripple voltage'' and possible overheating of components we are willing to tolerate versus how much money we can afford and are willing to spend on bigger and better components for reliability and smoothness of the power supply system.

\subsection{Power MOSFETs or IGBTs}

For $Q_1$ in Figure~\ref{f1}, the Littelfuse/IXYS IXFN520N075T2 \cite{IXFN520N075T2} or the Vishay VS-FC420SA10 \cite{VS-FC420SA10} might be useful. IGBTs are better than MOSFETs for higher frequency switching but are much less desireable for a low-voltage system because of the forward voltage drop. Power MOSFETs may also require a higher gate voltage to turn on.

\subsection{Power Schottky rectifier diodes}

The ST Microelectronics STPS200170TV1 \cite{STPS200170TV1} and the Vishay VS-203CNQ100PbF \cite{VS-203CNQ100PbF} are likely candidates.

\subsection{Power audio capacitors}

We suggest using power audio capacitors from a music supply store \cite{apmcap,bossaudiocap} for the capacitors $C_1$, $C_2$ and $C_3$ in Figure~\ref{f1}, and certainly for that matter our proposed system will be capable of powering the high-end stereo systems offered at those stores. Check ratings carefully for use with 18--24 V. It may be possible to use two identical capacitors in series to double the voltage rating. Some care will be needed to switch them on to avoid a short-circuit inrush current.

\subsection{Heavy iron inductors and power chokes}

Inductors and chokes are to be wound by hand with varnished magnet wire of adquate gauge on suitably heavy toroidal cores of laminated mild electrical steel or ferrite to prevent saturation in normal use. The use of closed toroidal cores reduces radio and audio systems interference.

\subsection{Pulse Width Modulators}

We suggest a Texas Instruments line-up of pulse width modulators depending on the desired frequency.

\subsubsection{High frequency}

The LM515xx series \cite{LM5155,LM51551,LM5156H,LM51561,LM51561H} of pulse width modulators offer a dynamically programmable switching frequency ranging from 100 kHz to 2.2 MHz. Switching in the megahertz range for our application may incur excessive power losses and inefficiency in the large power MOSFETs \cite{STPS200170TV1,VS-203CNQ100PbF}.

\subsubsection{Medium frequency}

The TL5001xx series PWMs \cite{TL5001,TL5001A,TL5001M,TL5001AM} operate in the range of 20 kHz to 500 kHz.

\subsubsection{Low frequency}

The LM555 \cite{LM555} or similar ICs from many manufacturers may be used for frequencies below 20 kHz, but the 555 is a general purpose timer which will require additional customization and circuitry to use specifically for pulse width modulation.
\subsection{The feedback loop}

There needs to be a stable and reliable automated method of adjusting the duty cycle of the PWM up and down between certain limits based on the difference between the desired correct output voltage and the actual output voltage measured.

\printbibliography
\end{document}

</syntaxhighlight>

Solar systems

2026-04-13T23:45:28Z

Rational Point: link

It seems arrogant to talk about man-made '''solar systems''' for generating electricity for home use off-grid, as if one were to elevate one's throne above the stars of heaven as Lucifer the bearer of light to do that. Not so. The "grid" itself is that beast, the natural intellect of man, given to the industrial revolution, with the arrogance to carry man-made electricity long distances over land.

However, the set-up of solar panels themselves does depend very much on their alignment with the sun, stars and planets, and the motions of the earth and moon. A common suggestion is that solar panels should face, say, due south in the northern hemisphere, inclined from the horizontal at an angle approximately equal to one's latitude.

Conditions of partial shade and/or high latitude dictate special engineering considerations with respect to adequate insolation for generating electricity.

The maximum energy intensity of sunlight hitting the earth on a clear day may be estimated as

:''I'' = 1350 W/m² × sin ''α'' × exp(–0.30 × ''p'' / sin ''α'')

where α is the angle of elevation of the sun above the horizon, and ''p'' is the ratio of barometric pressure at the altitude of the site to that at sea level. The fist factor is the "outer space" intensity of sunlight at the Earth's distance from the Sun. The second factor accounts for the slant of the sun's rays, and the third factor accounts for the filtering and dimming of the sunlight through Earth's atmosphere.

== The war against social objections to living off the grid ==
Solar panels are often considered a "green" or environmentally sensitive alternative for generating electricity, and we neither object to that consideration nor make a religion out of it.

Technology that enables "off-grid" living reduces the attack surface for secure computer systems, banks, broker houses, and even low-budget private homes etc. by enabling redundancy and reliability even if nothing else, and if the upfront capital and ongoing maintenance costs are reasonable for a reliable electric power system, should be welcomed by Christians living a simple rural lifestyle off the grid.

However, be warned that some "Christians" are married to the grid and to the assumptions of universal vaccinations etc. on which urban lifestyles have been based for millennia with or without Christ. "There's a lady" in the worst Mafia sense of the phrase, (guns are banned and please remove your hats, gentlemen,) so if you are a male "sovereign citizen" or "freeman on the land," then you are deemed to be risking her life and the lives of your children by your simple rural lifestyle.

It's a strange and unnatural situation of religious restrictions to urban white-collar employment and indoors-only entertainment where people with horses and cows etc. are suddenly deemed to be living lives of vice and heavy sin by a certain cadre of over-educated city-dwelling churchgoers, in whose presence hunting and fishing are deemed to be mortal and unforgivable sins.

City people are at always at law and if you give them an inch they take a mile, so don't even start with them.

==Solar panels==

As of 2026, typical solar panels are available in sizes of 100 to 400 watts, costing about one dollar per watt at the lowest bulk price available from major vendors in the United States.

These solar panels typically produce electricity at a nominal 18 volts, ranging from 16 volts at full load to 20 volts at no load in full direct sunlight, designed for charging 12 volt battery systems. Common automotive accessories may be powered directly or an inverter may be used to generate 110‒250VAC if desired.

==Charge controller==
[[File:Ss-1.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI TL5001AMJG)]]
[[File:Ss-2.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI LM51561HPWPR)]]

We find that off-the-shelf charge controllers are over-rated and overpriced, and we propose building one from scratch with adequate safety margins for high household power requirements.

A Buck-Boost Converter <ref>Buck-Boost Converter: What is it? (Formula and Circuit Diagram) https://www.electrical4u.com/buck-boost-converter/</ref> or Single-Ended Primary Inductor Converter (SEPIC) <ref>SEPIC Converters https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters</ref><ref>Dongbing Zhang. "AN-1484 Designing A SEPIC Converter." Application Report SNVA168E – May 2006 – Revised April 2013. https://www.ti.com/lit/an/snva168e/snva168e.pdf </ref> is typically used for this purpose.

An inductor, coil or transformer may be wound by hand using a adequate gauge of thinly insulated Tefzel or similar wire on a used or salvaged laminated or powdered iron core. The core of a transformer or inductor, if not powdered cerrite, must be made of thin layers of soft tempered malleable iron or mild steel that will swing the needle of a compass, and it should never be "quenched" or "saturated." The laminated iron core should be "tanned" with oak gall and waxed with beeswax and/or lacquered with boiled linseed oil to form insulative layers of oxide and wax or lacquer between the layers of steel, so that the transformer will not short out between the layers of steel and melt down under load. The windings of wire on a homemade transformer or inductor should be of the purest copper, smoothly drawn, carefully annealed to a soft temper, ductile, and flexible, with the best quality of insulation that is not too thick. Take care that wire windings are smooth and not bent or creased on sharp corners.

Power capacitors of several farads in capacity are widely available and inexpensive, mostly intended for car stereos and audio systems. We suggest using wire of adequate size for the intended current-carrying capacity, while over-provisioning and de-rating cheap power electronics parts, and installing fast-blow fuses at strategic locations, taking care not to overcharge a capacitor or induce a flyback voltage in a large coil. We are not certain about quality but there are audiophiles who listen to music and demand such quality.

High-power transistors, and even several transistors in parallel, may be used to control large electric currents.

Capacitance, inductance and transistor performance characteristics, etc. of all component parts should be carefully measured and verified with appropriate field or bench test equipment.

=== Component selection and Bill of Materials ===

''See [[File:SEPIC.pdf]] for details.''

The heart of the controller is a Pulse Width Modulation chip <ref>Some manufacturers and corporations will not like our attitude for referring to their integrated circuits as "chips" for sure, but at pawn shops and online auction sites selling jewelry and electronics one should not be ashamed to call them that. We have no opinions on offers of free samples direct from manufacturers or wholesalers, other than that they apparently contact local cops to enforce a litany of unwritten rules and unspoken codes sometimes pertaining to "intellectual property" by which hobbyists as opposed to professionals are supposed to abide.</ref> like the Texas Instruments TL5001AMJG <ref>PWM Controller with wide input range, with ±3% tolerance on reference, operation –55°C to 125°C https://www.ti.com/product/TL5001AM</ref>. These particular integrated circuits operate in a wide range between 3 and 40 volts, and also come in radiation-hardened versions, which suggests that they were used for solar panels to power satellites launched into outer space decades ago, many of which are still in service today.

The Littelfuse/IXYS IXFN520N075T2<ref>Littelfuse/IXYS IXFN520N075T2 https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2</ref><ref>Littelfuse/IXYS IXFN520N075T2 Datasheet https://www.littelfuse.com/assetdocs/littelfuse-discrete-mosfets-ixfn520n075t2-datasheet?assetguid=8706a9d1-94c2-4e6f-8277-46cab5c71388</ref> power MOSFET "trench gate" is essentially rated to handle 480A in the on state and 75V in the off state. The Vishay VS-FC420SA10 <ref>VS-FC420SA10 Product Information https://www.vishay.com/en/product/95793/</ref><ref>Vishay VS-FC420SA10 Datasheet https://www.vishay.com/docs/95793/vs-fc420sa10.pdf</ref> is another brand of power MOSFET rated to carry 435A when on or hold 100V when off. It comes in the same form factor, an SOT-227 which looks and acts like a miniature clothes iron, and requires an excellent heat sink rated for switching losses and forward voltage drop at the rated current. It would appear that if either of these devices functions as advertised, you could easily start an automobile with the electric current they are rated for handling if you wired one of them up in place of a solenoid for the starter motor. As far as we can tell, this can actually be done, except that the high power MOSFETS require 10V to drive the gate, and the drawdown on a 12V car battery from the starting current will reduce the voltage below the gate actuation level.

Insulated-Gate Bipolar Transistors (IGBTs)<ref>Insulated-Gate Bipolar Transistors (IGBTs) https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-16.html
</ref><ref>Comparison of Forward Characteristics of IGBTs and MOSFETs
https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-21.html</ref> are another option for the high power current switching needed for the Buck-Boost or SEPIC controllers that need to be used for regulating the voltage from variably sunlit photovoltaic cells to a usable level.

[[Category:Electronics]]

== Batteries ==
tbd ...

File:SEPIC.pdf

2026-04-13T23:43:33Z

Rational Point:

Main Page

2026-04-12T23:41:33Z

Rational Point: Alan Turing straight and narrow

[[Image:Elliptic-curve-1.png|frame|right|The elliptic curve
<math>y^2=x^3-x^2+\frac 12</math>.]]
There is cryptography here, the rudimentary framework of it.

* [[TO DO]]: Reminders, work in progress ...

However, life gets in the way. Life is about punishing our enemies, and making them pay for all the trouble and sorrow they have caused us and continue to cause us. The Pagans had a creed, "I will kill all my enemies." Once, having accomplished this, they accepted Christianity, but for a long time now, there is no peace, no rest on Sunday, since others we had thought to be friends and believed to be friends invited our enemies into our churches and usual places of worship to spite us. Perhaps they were ignorant, and perhaps in their ignorance they thought it was some small matter or another for which they could act as "peacemakers" — but no, those enemies really are our enemies, and they really are here to kill us, as that is their creed, on their side of the battle. Some of them wanted others to assume that we were all friends together, but that is not and cannot be the case. No. They bear malice which can no longer be concealed, and that is what bursts forth in open anger once ignorance is ruled out as a cause of their continual troublemaking.

As an example of troublemaking one might consider the case of Alan Turing's dishonorable bosses and associates who insisted he was gay and tortured him to death on that account. All indications are that Alan Turing was simply much too straight and narrow for that "sort of nonsense up with which we will not put" to paraphrase Winston Churchill.

== Introduction ==

[[Elliptic curve]]s over <math>\mathbb R</math>, the field of real numbers, are visually appealing and readily depicted as plots of cubic curves, or curves of degree three on ''x''-''y'' planes with Cartesian coördinates, which serve as a graphical aid for understanding algebraic operations on them. The terminology is somewhat vague and confusing to the uninitiated, because actual ellipses are [[:Category:Conic section cryptography|conic section]]s or quadratic curves, having a degree of two, whereas [[quartic point group operation|quartic]] or [[quintic point group operation|quintic]] curves, of degree four or five, or curves of even higher degree are often called “[https://hyperelliptic.org/ hyperelliptic],” with respect to algebraic degree rather than “genus” or other topological properties.

And again, without respect of “gender” as such, this is an area of high school algebra level “math jocks,” girls chewing bubble gum and teasing, “Math is hard!” etc., etc. and then one has to deal with overeducated college “frat boys” and “sorry girls.” In other words, there is a great deal of [[bad curves and weak crypto|deliberate stupidity]] that needs to be confronted head-on.

== Rational points ==

Finding the '''rational points''' on elliptic curves determined by equations with rational coefficients in the third degree in two variables has long been the object of much pure mathematical study for the sake of its own beauty.

[[Mordell’s theorem]], that all the rational points on an elliptic curve, even infinitely many of them, may be generated by only a finite number of them with a certain algebraic [[point group operation]], is the starting point for this study.

== Finite fields ==

[[Quotient group]]s among the rational points on an elliptic curve have led naturally to the study of elliptic curves over [[finite field]]s. The idea is akin to finding a large prime number to serve as a “least common denominator” of sorts for a group of rational points, and then considering only the numerators of proper fractions with respect to that denominator, using modular arithmetic, with the [[extended Euclidean algorithm]] among other multiple precision arithmetic operations on big integers.

[[Hasse’s theorem|Helmut Hasse proved]] Emil Artin’s conjecture that the '''number of points on an elliptic curve over a finite field of ''q'' elements''', <nowiki>[</nowiki>i.e., modulo the prime ''q'' or the finite field ''GF''(''q''=''p''''k''),<nowiki>]</nowiki> is between <math>q + 1 - 2\sqrt q</math> and <math>q + 1 + 2\sqrt q</math> inclusive. (André Weil [[Hasse–Weil bound|generalized]] the result to range between <math>q + 1 - 2g\sqrt q</math> and <math>q + 1 + 2g\sqrt q</math> inclusive for hyperelliptic curves of genus ''g''>1.)

It is in general a very difficult problem to calculate the exact number of points on an algebraic curve over a finite field within this range. The security of all elliptic curve cryptographic schemes is based on the discrete [[logarithm problem]] with respect to the [[point group operation]], which is in turn dependent on and closely related to the difficulty of this calculation of the number of points, if it is not defeated by the use of weak or trivially reducible curves in cryptographic applications.

[[Schoof's point counting algorithm]] is supposed to run in polynomial time, but information is  REDACTED  in published ex-pat or non-U.S. sources. 🎗

== Cryptographic applications ==

Elliptic curves over finite fields have serious applications to public key cryptography, the first widely implemented example of such being [[Ed25519]], still in use today despite being somewhat controversial because of the use of a non-elliptic curve of degree four reducible to two, a slew of associated intellectual property patent claims and a very strong association of college frat boys, academia and higher education in general with communism, communist spies, and people who just don’t mind their own business or respect industry, privacy or private property; hence the very need for [[strong cryptography]] rather than [[bad curves and weak crypto]]. “The Powers That Be” <ref>Jeff Larson. “Revealed: The NSA's Secret Campaign to Crack, Undermine Internet Security.” ''ProPublica'', Sept. 5, 2013. https://www.propublica.org/article/the-nsas-secret-campaign-to-crack-undermine-internet-encryption</ref><ref>Christopher Wray, Director
Federal Bureau of Investigation. “Finding a Way Forward on Lawful Access: Bringing Child Predators out of the Shadows:
Remarks as delivered.” ''Department of Justice Lawful Access Summit,'' Washington, D.C. October 4, 2019. https://www.fbi.gov/news/speeches/finding-a-way-forward-on-lawful-access</ref><ref>Zack Whittaker. “US attorney general William Barr says Americans should accept security risks of encryption backdoors.” ''TechCrunch,'' July 23, 2019. https://techcrunch.com/2019/07/23/william-barr-consumers-security-risks-backdoors/</ref> unfortunately punted on freedom, and offered deliberately middling to weak security with fake elliptic curves for consumers on official recommendations <ref>RFC 7748 https://archive.org/details/rfc7748</ref>.

Such official recommendations are the product of a self-serving federal government only interested in defending itself with its own hired military capabilities, with a progressive reinterpretation of the term “National Security” to mean security of the government, for the government and by the government, never mind the people who actually are the nation.

== Unsolved problems ==

[[Dirichlet L-functions]] <ref>Dirichlet L-function. ''Encyclopedia of Mathematics.'' https://encyclopediaofmath.org/wiki/Dirichlet_L-function</ref> are the elliptic curve finite-field analogs of the [[Riemann ζ-function]] <ref>Riemann Zeta Function. ''Wolfram Mathworld.'' https://mathworld.wolfram.com/RiemannZetaFunction.html</ref>, closely related to two of CMI’s [[:Category:Unsolved Millennium problems|Millennium problems]], the [[Birch and Swinnerton-Dyer conjecture]] and the [[Riemann hypothesis]].

Main Page

2026-04-12T23:01:29Z

Rational Point: Ignorance or malice?

[[Image:Elliptic-curve-1.png|frame|right|The elliptic curve
<math>y^2=x^3-x^2+\frac 12</math>.]]
There is cryptography here, the rudimentary framework of it.

* [[TO DO]]: Reminders, work in progress ...

However, life gets in the way. Life is about punishing our enemies, and making them pay for all the trouble and sorrow they have caused us and continue to cause us. The Pagans had a creed, "I will kill all my enemies." Once, having accomplished this, they accepted Christianity, but for a long time now, there is no peace, no rest on Sunday, since others we had thought to be friends and believed to be friends invited our enemies into our churches and usual places of worship to spite us. Perhaps they were ignorant, and perhaps in their ignorance they thought it was some small matter or another for which they could act as "peacemakers" — but no, those enemies really are our enemies, and they really are here to kill us, as that is their creed, on their side of the battle. Some of them wanted others to assume that we were all friends together, but that is not and cannot be the case. No. They bear malice which can no longer be concealed, and that is what bursts forth in open anger once ignorance is ruled out as a cause of their continual troublemaking.

== Introduction ==

[[Elliptic curve]]s over <math>\mathbb R</math>, the field of real numbers, are visually appealing and readily depicted as plots of cubic curves, or curves of degree three on ''x''-''y'' planes with Cartesian coördinates, which serve as a graphical aid for understanding algebraic operations on them. The terminology is somewhat vague and confusing to the uninitiated, because actual ellipses are [[:Category:Conic section cryptography|conic section]]s or quadratic curves, having a degree of two, whereas [[quartic point group operation|quartic]] or [[quintic point group operation|quintic]] curves, of degree four or five, or curves of even higher degree are often called “[https://hyperelliptic.org/ hyperelliptic],” with respect to algebraic degree rather than “genus” or other topological properties.

And again, without respect of “gender” as such, this is an area of high school algebra level “math jocks,” girls chewing bubble gum and teasing, “Math is hard!” etc., etc. and then one has to deal with overeducated college “frat boys” and “sorry girls.” In other words, there is a great deal of [[bad curves and weak crypto|deliberate stupidity]] that needs to be confronted head-on.

== Rational points ==

Finding the '''rational points''' on elliptic curves determined by equations with rational coefficients in the third degree in two variables has long been the object of much pure mathematical study for the sake of its own beauty.

[[Mordell’s theorem]], that all the rational points on an elliptic curve, even infinitely many of them, may be generated by only a finite number of them with a certain algebraic [[point group operation]], is the starting point for this study.

== Finite fields ==

[[Quotient group]]s among the rational points on an elliptic curve have led naturally to the study of elliptic curves over [[finite field]]s. The idea is akin to finding a large prime number to serve as a “least common denominator” of sorts for a group of rational points, and then considering only the numerators of proper fractions with respect to that denominator, using modular arithmetic, with the [[extended Euclidean algorithm]] among other multiple precision arithmetic operations on big integers.

[[Hasse’s theorem|Helmut Hasse proved]] Emil Artin’s conjecture that the '''number of points on an elliptic curve over a finite field of ''q'' elements''', <nowiki>[</nowiki>i.e., modulo the prime ''q'' or the finite field ''GF''(''q''=''p''''k''),<nowiki>]</nowiki> is between <math>q + 1 - 2\sqrt q</math> and <math>q + 1 + 2\sqrt q</math> inclusive. (André Weil [[Hasse–Weil bound|generalized]] the result to range between <math>q + 1 - 2g\sqrt q</math> and <math>q + 1 + 2g\sqrt q</math> inclusive for hyperelliptic curves of genus ''g''>1.)

It is in general a very difficult problem to calculate the exact number of points on an algebraic curve over a finite field within this range. The security of all elliptic curve cryptographic schemes is based on the discrete [[logarithm problem]] with respect to the [[point group operation]], which is in turn dependent on and closely related to the difficulty of this calculation of the number of points, if it is not defeated by the use of weak or trivially reducible curves in cryptographic applications.

[[Schoof's point counting algorithm]] is supposed to run in polynomial time, but information is  REDACTED  in published ex-pat or non-U.S. sources. 🎗

== Cryptographic applications ==

Elliptic curves over finite fields have serious applications to public key cryptography, the first widely implemented example of such being [[Ed25519]], still in use today despite being somewhat controversial because of the use of a non-elliptic curve of degree four reducible to two, a slew of associated intellectual property patent claims and a very strong association of college frat boys, academia and higher education in general with communism, communist spies, and people who just don’t mind their own business or respect industry, privacy or private property; hence the very need for [[strong cryptography]] rather than [[bad curves and weak crypto]]. “The Powers That Be” <ref>Jeff Larson. “Revealed: The NSA's Secret Campaign to Crack, Undermine Internet Security.” ''ProPublica'', Sept. 5, 2013. https://www.propublica.org/article/the-nsas-secret-campaign-to-crack-undermine-internet-encryption</ref><ref>Christopher Wray, Director
Federal Bureau of Investigation. “Finding a Way Forward on Lawful Access: Bringing Child Predators out of the Shadows:
Remarks as delivered.” ''Department of Justice Lawful Access Summit,'' Washington, D.C. October 4, 2019. https://www.fbi.gov/news/speeches/finding-a-way-forward-on-lawful-access</ref><ref>Zack Whittaker. “US attorney general William Barr says Americans should accept security risks of encryption backdoors.” ''TechCrunch,'' July 23, 2019. https://techcrunch.com/2019/07/23/william-barr-consumers-security-risks-backdoors/</ref> unfortunately punted on freedom, and offered deliberately middling to weak security with fake elliptic curves for consumers on official recommendations <ref>RFC 7748 https://archive.org/details/rfc7748</ref>.

Such official recommendations are the product of a self-serving federal government only interested in defending itself with its own hired military capabilities, with a progressive reinterpretation of the term “National Security” to mean security of the government, for the government and by the government, never mind the people who actually are the nation.

== Unsolved problems ==

[[Dirichlet L-functions]] <ref>Dirichlet L-function. ''Encyclopedia of Mathematics.'' https://encyclopediaofmath.org/wiki/Dirichlet_L-function</ref> are the elliptic curve finite-field analogs of the [[Riemann ζ-function]] <ref>Riemann Zeta Function. ''Wolfram Mathworld.'' https://mathworld.wolfram.com/RiemannZetaFunction.html</ref>, closely related to two of CMI’s [[:Category:Unsolved Millennium problems|Millennium problems]], the [[Birch and Swinnerton-Dyer conjecture]] and the [[Riemann hypothesis]].

Magnetic permeability

2026-04-12T15:01:22Z

Rational Point: Example problem

File:Inductor 20260412~2.jpg

2026-04-12T14:46:03Z

Rational Point:

Magnetic permeability

2026-04-11T22:37:14Z

Rational Point: harmonic mean path length

555

2026-04-08T15:32:28Z

Rational Point: /* Notes */

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

== Clocking the 555 ==
The simple demonstration circuit depicted above right is probably the simplest external clock for the 555. Below we have hastily constructed a true precision “clock” using four off-the-shelf bipolar transistors and some auxiliary resistors.

This circuit below operates by charging capacitor C1 through resistor R5 only up to the trigger level of 2/3 the supplied voltage, and then discharging the same capacitor down to the threshold value of 1/3 the supplied voltage through resistor R2 only.

[[File:555-op-amp-ctl-clock.svg|frameless|none]]

=== Notes ===

Transistors Q1 and Q4 operating in parallel appear redundant, and it would seem desirable to simplify the circuit to eliminate one of them. We have not determined the best way to do this with a simulated design, however.

R9 is an arbitrary load resistor for the output, probably less than desirable.

We have produced a simulated oscilloscope trace using Ngspice <ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref> and/or LTspice <ref>“LTspice® is a powerful, fast, and free SPICE simulator software…” https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html</ref> on KiCad <ref>KiCad: A Cross Platform and Open Source PCB Design Suite https://www.kicad.org/</ref>.

[[File:Plot555-2026-04-06.png|frameless|none]]

[[Category:Electronics]]

555

2026-04-08T15:06:26Z

Rational Point: /* Clocking the 555 */

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

== Clocking the 555 ==
The simple demonstration circuit depicted above right is probably the simplest external clock for the 555. Below we have hastily constructed a true precision “clock” using four off-the-shelf bipolar transistors and some auxiliary resistors.

This circuit below operates by charging capacitor C1 through resistor R5 only up to the trigger level of 2/3 the supplied voltage, and then discharging the same capacitor down to the threshold value of 1/3 the supplied voltage through resistor R2 only.

[[File:555-op-amp-ctl-clock.svg|frameless|none]]

=== Notes ===

Transistors Q1 and Q4 operating in parallel appear redundant, and it would seem desirable to simplify the circuit to eliminate one of them. We have not determined the best way to do this with a simulated design, however.

R9 is an arbitrary load resistor for the output, probably less than desirable.

We have produced a simulated oscilloscope trace using Ngspice <ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref> on KiCad <ref>KiCad: A Cross Platform and Open Source PCB Design Suite https://www.kicad.org/</ref>.

[[File:Plot555-2026-04-06.png|frameless|none]]

[[Category:Electronics]]

555

2026-04-08T15:05:49Z

Rational Point: /* Clocking the 555 */ phrase

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

== Clocking the 555 ==
The simple demonstration circuit depicted above right is probably the simplest external clock for the 555. Below we have hastily constructed a true precision “clock” using four off-the-shelf bipolar transistors and some auxiliary resistors.

This circuit operates by charging capacitor C1 through resistor R5 only up to the trigger level of 2/3 the supplied voltage, and then discharging the same capacitor down to the threshold value of 1/3 the supplied voltage through resistor R2 only.

[[File:555-op-amp-ctl-clock.svg|frameless|none]]

=== Notes ===

Transistors Q1 and Q4 operating in parallel appear redundant, and it would seem desirable to simplify the circuit to eliminate one of them. We have not determined the best way to do this with a simulated design, however.

R9 is an arbitrary load resistor for the output, probably less than desirable.

We have produced a simulated oscilloscope trace using Ngspice <ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref> on KiCad <ref>KiCad: A Cross Platform and Open Source PCB Design Suite https://www.kicad.org/</ref>.

[[File:Plot555-2026-04-06.png|frameless|none]]

[[Category:Electronics]]

555

2026-04-08T15:04:30Z

Rational Point: /* Notes */ refs

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

== Clocking the 555 ==
The simple demonstration circuit depicted above right is probably the simplest external clock for the 555. Below we have hastily constructed a true precision “clock” using four off-the-shelf bipolar transistors and some auxiliary resistors.

This circuit operates by charging capacitor C1 through resistor R5 only up to the trigger level of 2/3 the supplied voltage, and then discharging the same capacitor down to the threshold value of 1/3 the supplied voltage through resistor R2 only down to the threshold voltage.

[[File:555-op-amp-ctl-clock.svg|frameless|none]]

=== Notes ===

Transistors Q1 and Q4 operating in parallel appear redundant, and it would seem desirable to simplify the circuit to eliminate one of them. We have not determined the best way to do this with a simulated design, however.

R9 is an arbitrary load resistor for the output, probably less than desirable.

We have produced a simulated oscilloscope trace using Ngspice <ref>ngspice - open source spice simulator https://ngspice.sourceforge.io/</ref> on KiCad <ref>KiCad: A Cross Platform and Open Source PCB Design Suite https://www.kicad.org/</ref>.

[[File:Plot555-2026-04-06.png|frameless|none]]

[[Category:Electronics]]

555

2026-04-08T15:01:17Z

Rational Point: clock / notes

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

== Clocking the 555 ==
The simple demonstration circuit depicted above right is probably the simplest external clock for the 555. Below we have hastily constructed a true precision “clock” using four off-the-shelf bipolar transistors and some auxiliary resistors.

This circuit operates by charging capacitor C1 through resistor R5 only up to the trigger level of 2/3 the supplied voltage, and then discharging the same capacitor down to the threshold value of 1/3 the supplied voltage through resistor R2 only down to the threshold voltage.

[[File:555-op-amp-ctl-clock.svg|frameless|none]]

=== Notes ===

Transistors Q1 and Q4 operating in parallel appear redundant, and it would seem desirable to simplify the circuit to eliminate one of them. We have not determined the best way to do this with a simulated design, however.

R9 is an arbitrary load resistor for the output, probably less than desirable.

We have produced a simulated oscilloscope trace using NGSPICE on KiCad.

[[File:Plot555-2026-04-06.png|frameless|none]]

[[Category:Electronics]]

File:Plot555-2026-04-06.png

2026-04-08T14:57:03Z

Rational Point:

File:555-op-amp-ctl-clock.svg

2026-04-08T14:32:11Z

Rational Point:

Main Page

2026-04-04T14:45:04Z

Rational Point: TO DO

[[Image:Elliptic-curve-1.png|frame|right|The elliptic curve
<math>y^2=x^3-x^2+\frac 12</math>.]]

* [[TO DO]]: Reminders, work in progress ...

== Introduction ==

[[Elliptic curve]]s over <math>\mathbb R</math>, the field of real numbers, are visually appealing and readily depicted as plots of cubic curves, or curves of degree three on ''x''-''y'' planes with Cartesian coördinates, which serve as a graphical aid for understanding algebraic operations on them. The terminology is somewhat vague and confusing to the uninitiated, because actual ellipses are [[:Category:Conic section cryptography|conic section]]s or quadratic curves, having a degree of two, whereas [[quartic point group operation|quartic]] or [[quintic point group operation|quintic]] curves, of degree four or five, or curves of even higher degree are often called “[https://hyperelliptic.org/ hyperelliptic],” with respect to algebraic degree rather than “genus” or other topological properties.

And again, without respect of “gender” as such, this is an area of high school algebra level “math jocks,” girls chewing bubble gum and teasing, “Math is hard!” etc., etc. and then one has to deal with overeducated college “frat boys” and “sorry girls.” In other words, there is a great deal of [[bad curves and weak crypto|deliberate stupidity]] that needs to be confronted head-on.

== Rational points ==

Finding the '''rational points''' on elliptic curves determined by equations with rational coefficients in the third degree in two variables has long been the object of much pure mathematical study for the sake of its own beauty.

[[Mordell’s theorem]], that all the rational points on an elliptic curve, even infinitely many of them, may be generated by only a finite number of them with a certain algebraic [[point group operation]], is the starting point for this study.

== Finite fields ==

[[Quotient group]]s among the rational points on an elliptic curve have led naturally to the study of elliptic curves over [[finite field]]s. The idea is akin to finding a large prime number to serve as a “least common denominator” of sorts for a group of rational points, and then considering only the numerators of proper fractions with respect to that denominator, using modular arithmetic, with the [[extended Euclidean algorithm]] among other multiple precision arithmetic operations on big integers.

[[Hasse’s theorem|Helmut Hasse proved]] Emil Artin’s conjecture that the '''number of points on an elliptic curve over a finite field of ''q'' elements''', <nowiki>[</nowiki>i.e., modulo the prime ''q'' or the finite field ''GF''(''q''=''p''''k''),<nowiki>]</nowiki> is between <math>q + 1 - 2\sqrt q</math> and <math>q + 1 + 2\sqrt q</math> inclusive. (André Weil [[Hasse–Weil bound|generalized]] the result to range between <math>q + 1 - 2g\sqrt q</math> and <math>q + 1 + 2g\sqrt q</math> inclusive for hyperelliptic curves of genus ''g''>1.)

It is in general a very difficult problem to calculate the exact number of points on an algebraic curve over a finite field within this range. The security of all elliptic curve cryptographic schemes is based on the discrete [[logarithm problem]] with respect to the [[point group operation]], which is in turn dependent on and closely related to the difficulty of this calculation of the number of points, if it is not defeated by the use of weak or trivially reducible curves in cryptographic applications.

[[Schoof's point counting algorithm]] is supposed to run in polynomial time, but information is  REDACTED  in published ex-pat or non-U.S. sources. 🎗

== Cryptographic applications ==

Elliptic curves over finite fields have serious applications to public key cryptography, the first widely implemented example of such being [[Ed25519]], still in use today despite being somewhat controversial because of the use of a non-elliptic curve of degree four reducible to two, a slew of associated intellectual property patent claims and a very strong association of college frat boys, academia and higher education in general with communism, communist spies, and people who just don’t mind their own business or respect industry, privacy or private property; hence the very need for [[strong cryptography]] rather than [[bad curves and weak crypto]]. “The Powers That Be” <ref>Jeff Larson. “Revealed: The NSA's Secret Campaign to Crack, Undermine Internet Security.” ''ProPublica'', Sept. 5, 2013. https://www.propublica.org/article/the-nsas-secret-campaign-to-crack-undermine-internet-encryption</ref><ref>Christopher Wray, Director
Federal Bureau of Investigation. “Finding a Way Forward on Lawful Access: Bringing Child Predators out of the Shadows:
Remarks as delivered.” ''Department of Justice Lawful Access Summit,'' Washington, D.C. October 4, 2019. https://www.fbi.gov/news/speeches/finding-a-way-forward-on-lawful-access</ref><ref>Zack Whittaker. “US attorney general William Barr says Americans should accept security risks of encryption backdoors.” ''TechCrunch,'' July 23, 2019. https://techcrunch.com/2019/07/23/william-barr-consumers-security-risks-backdoors/</ref> unfortunately punted on freedom, and offered deliberately middling to weak security with fake elliptic curves for consumers on official recommendations <ref>RFC 7748 https://archive.org/details/rfc7748</ref>.

Such official recommendations are the product of a self-serving federal government only interested in defending itself with its own hired military capabilities, with a progressive reinterpretation of the term “National Security” to mean security of the government, for the government and by the government, never mind the people who actually are the nation.

== Unsolved problems ==

[[Dirichlet L-functions]] <ref>Dirichlet L-function. ''Encyclopedia of Mathematics.'' https://encyclopediaofmath.org/wiki/Dirichlet_L-function</ref> are the elliptic curve finite-field analogs of the [[Riemann ζ-function]] <ref>Riemann Zeta Function. ''Wolfram Mathworld.'' https://mathworld.wolfram.com/RiemannZetaFunction.html</ref>, closely related to two of CMI’s [[:Category:Unsolved Millennium problems|Millennium problems]], the [[Birch and Swinnerton-Dyer conjecture]] and the [[Riemann hypothesis]].

TO DO

2026-04-04T14:43:45Z

Rational Point: TO DO stuff moved off front page

== TO DO: ==
'''It's a total show-stopper: Get rid of the third-party equation-running services.'''
=== Example error message when editing equations ===
<big><nowiki>Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E=mc^2}</nowiki></big>

* <tt>[https://wikimedia.org/api/rest_v1/ "https://wikimedia.org/api/rest_v1/"]</tt> Huh? What's that for?


Example workaround code is here: <big>'''[[Pure HTML Math]]'''</big> for equations without 3rd-party SaaS or equation-running malware. Please take a look and experiment yourself.


Mathjax and Mathoid or Restbase or related services or funky MathML browser plugins are notorious for containing malicious code and spyware, and hidden calls to third party API services.

Math equations cannot be made up “beautiful” or spread “all over the web” or ripped off or dynamically rendered on other people’s websites. Math equations are highly technical, and they need to be left alone on people's websites, precisely as is, without any extraneous garbage dependencies or third party API services or pop-ups or dollar-sign script-runners or other javascript nonsense called in to dynamically render or display them.

The math jerks and the malicious software math equation web APIs gotta go. Stop running off with all the math equations out the back door!

* https://www.etsy.com/market/hippity_hoppity_get_off_my_property_sign
* https://www.mysecuritysign.com/funny-hippity-hoppity-get-off-my-property-frog-sign/sku-s2-5588
* https://highceeaerials.com/hippity-hoppity-get-off-of-my-property/
* https://threeinfive.com/hippity-hoppity-get-off-my-property-kermit/

Main Page

2026-04-04T14:42:37Z

Rational Point:

[[Image:Elliptic-curve-1.png|frame|right|The elliptic curve
<math>y^2=x^3-x^2+\frac 12</math>.]]

[[TO DO]]

== Introduction ==

[[Elliptic curve]]s over <math>\mathbb R</math>, the field of real numbers, are visually appealing and readily depicted as plots of cubic curves, or curves of degree three on ''x''-''y'' planes with Cartesian coördinates, which serve as a graphical aid for understanding algebraic operations on them. The terminology is somewhat vague and confusing to the uninitiated, because actual ellipses are [[:Category:Conic section cryptography|conic section]]s or quadratic curves, having a degree of two, whereas [[quartic point group operation|quartic]] or [[quintic point group operation|quintic]] curves, of degree four or five, or curves of even higher degree are often called “[https://hyperelliptic.org/ hyperelliptic],” with respect to algebraic degree rather than “genus” or other topological properties.

And again, without respect of “gender” as such, this is an area of high school algebra level “math jocks,” girls chewing bubble gum and teasing, “Math is hard!” etc., etc. and then one has to deal with overeducated college “frat boys” and “sorry girls.” In other words, there is a great deal of [[bad curves and weak crypto|deliberate stupidity]] that needs to be confronted head-on.

== Rational points ==

Finding the '''rational points''' on elliptic curves determined by equations with rational coefficients in the third degree in two variables has long been the object of much pure mathematical study for the sake of its own beauty.

[[Mordell’s theorem]], that all the rational points on an elliptic curve, even infinitely many of them, may be generated by only a finite number of them with a certain algebraic [[point group operation]], is the starting point for this study.

== Finite fields ==

[[Quotient group]]s among the rational points on an elliptic curve have led naturally to the study of elliptic curves over [[finite field]]s. The idea is akin to finding a large prime number to serve as a “least common denominator” of sorts for a group of rational points, and then considering only the numerators of proper fractions with respect to that denominator, using modular arithmetic, with the [[extended Euclidean algorithm]] among other multiple precision arithmetic operations on big integers.

[[Hasse’s theorem|Helmut Hasse proved]] Emil Artin’s conjecture that the '''number of points on an elliptic curve over a finite field of ''q'' elements''', <nowiki>[</nowiki>i.e., modulo the prime ''q'' or the finite field ''GF''(''q''=''p''''k''),<nowiki>]</nowiki> is between <math>q + 1 - 2\sqrt q</math> and <math>q + 1 + 2\sqrt q</math> inclusive. (André Weil [[Hasse–Weil bound|generalized]] the result to range between <math>q + 1 - 2g\sqrt q</math> and <math>q + 1 + 2g\sqrt q</math> inclusive for hyperelliptic curves of genus ''g''>1.)

It is in general a very difficult problem to calculate the exact number of points on an algebraic curve over a finite field within this range. The security of all elliptic curve cryptographic schemes is based on the discrete [[logarithm problem]] with respect to the [[point group operation]], which is in turn dependent on and closely related to the difficulty of this calculation of the number of points, if it is not defeated by the use of weak or trivially reducible curves in cryptographic applications.

[[Schoof's point counting algorithm]] is supposed to run in polynomial time, but information is  REDACTED  in published ex-pat or non-U.S. sources. 🎗

== Cryptographic applications ==

Elliptic curves over finite fields have serious applications to public key cryptography, the first widely implemented example of such being [[Ed25519]], still in use today despite being somewhat controversial because of the use of a non-elliptic curve of degree four reducible to two, a slew of associated intellectual property patent claims and a very strong association of college frat boys, academia and higher education in general with communism, communist spies, and people who just don’t mind their own business or respect industry, privacy or private property; hence the very need for [[strong cryptography]] rather than [[bad curves and weak crypto]]. “The Powers That Be” <ref>Jeff Larson. “Revealed: The NSA's Secret Campaign to Crack, Undermine Internet Security.” ''ProPublica'', Sept. 5, 2013. https://www.propublica.org/article/the-nsas-secret-campaign-to-crack-undermine-internet-encryption</ref><ref>Christopher Wray, Director
Federal Bureau of Investigation. “Finding a Way Forward on Lawful Access: Bringing Child Predators out of the Shadows:
Remarks as delivered.” ''Department of Justice Lawful Access Summit,'' Washington, D.C. October 4, 2019. https://www.fbi.gov/news/speeches/finding-a-way-forward-on-lawful-access</ref><ref>Zack Whittaker. “US attorney general William Barr says Americans should accept security risks of encryption backdoors.” ''TechCrunch,'' July 23, 2019. https://techcrunch.com/2019/07/23/william-barr-consumers-security-risks-backdoors/</ref> unfortunately punted on freedom, and offered deliberately middling to weak security with fake elliptic curves for consumers on official recommendations <ref>RFC 7748 https://archive.org/details/rfc7748</ref>.

Such official recommendations are the product of a self-serving federal government only interested in defending itself with its own hired military capabilities, with a progressive reinterpretation of the term “National Security” to mean security of the government, for the government and by the government, never mind the people who actually are the nation.

== Unsolved problems ==

[[Dirichlet L-functions]] <ref>Dirichlet L-function. ''Encyclopedia of Mathematics.'' https://encyclopediaofmath.org/wiki/Dirichlet_L-function</ref> are the elliptic curve finite-field analogs of the [[Riemann ζ-function]] <ref>Riemann Zeta Function. ''Wolfram Mathworld.'' https://mathworld.wolfram.com/RiemannZetaFunction.html</ref>, closely related to two of CMI’s [[:Category:Unsolved Millennium problems|Millennium problems]], the [[Birch and Swinnerton-Dyer conjecture]] and the [[Riemann hypothesis]].

Solar systems

2026-04-03T15:55:01Z

Rational Point: /* Component selection and Bill of Materials */

It seems arrogant to talk about man-made '''solar systems''' for generating electricity for home use off-grid, as if one were to elevate one's throne above the stars of heaven as Lucifer the bearer of light to do that. Not so. The "grid" itself is that beast, the natural intellect of man, given to the industrial revolution, with the arrogance to carry man-made electricity long distances over land.

However, the set-up of solar panels themselves does depend very much on their alignment with the sun, stars and planets, and the motions of the earth and moon. A common suggestion is that solar panels should face, say, due south in the northern hemisphere, inclined from the horizontal at an angle approximately equal to one's latitude.

Conditions of partial shade and/or high latitude dictate special engineering considerations with respect to adequate insolation for generating electricity.

The maximum energy intensity of sunlight hitting the earth on a clear day may be estimated as

:''I'' = 1350 W/m² × sin ''α'' × exp(–0.30 × ''p'' / sin ''α'')

where α is the angle of elevation of the sun above the horizon, and ''p'' is the ratio of barometric pressure at the altitude of the site to that at sea level. The fist factor is the "outer space" intensity of sunlight at the Earth's distance from the Sun. The second factor accounts for the slant of the sun's rays, and the third factor accounts for the filtering and dimming of the sunlight through Earth's atmosphere.

== The war against social objections to living off the grid ==
Solar panels are often considered a "green" or environmentally sensitive alternative for generating electricity, and we neither object to that consideration nor make a religion out of it.

Technology that enables "off-grid" living reduces the attack surface for secure computer systems, banks, broker houses, and even low-budget private homes etc. by enabling redundancy and reliability even if nothing else, and if the upfront capital and ongoing maintenance costs are reasonable for a reliable electric power system, should be welcomed by Christians living a simple rural lifestyle off the grid.

However, be warned that some "Christians" are married to the grid and to the assumptions of universal vaccinations etc. on which urban lifestyles have been based for millennia with or without Christ. "There's a lady" in the worst Mafia sense of the phrase, (guns are banned and please remove your hats, gentlemen,) so if you are a male "sovereign citizen" or "freeman on the land," then you are deemed to be risking her life and the lives of your children by your simple rural lifestyle.

It's a strange and unnatural situation of religious restrictions to urban white-collar employment and indoors-only entertainment where people with horses and cows etc. are suddenly deemed to be living lives of vice and heavy sin by a certain cadre of over-educated city-dwelling churchgoers, in whose presence hunting and fishing are deemed to be mortal and unforgivable sins.

City people are at always at law and if you give them an inch they take a mile, so don't even start with them.

==Solar panels==

As of 2026, typical solar panels are available in sizes of 100 to 400 watts, costing about one dollar per watt at the lowest bulk price available from major vendors in the United States.

These solar panels typically produce electricity at a nominal 18 volts, ranging from 16 volts at full load to 20 volts at no load in full direct sunlight, designed for charging 12 volt battery systems. Common automotive accessories may be powered directly or an inverter may be used to generate 110‒250VAC if desired.

==Charge controller==
[[File:Ss-1.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI TL5001AMJG)]]
[[File:Ss-2.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI LM51561HPWPR)]]

We find that off-the-shelf charge controllers are over-rated and overpriced, and we propose building one from scratch with adequate safety margins for high household power requirements.

A Buck-Boost Converter <ref>Buck-Boost Converter: What is it? (Formula and Circuit Diagram) https://www.electrical4u.com/buck-boost-converter/</ref> or Single-Ended Primary Inductor Converter (SEPIC) <ref>SEPIC Converters https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters</ref><ref>Dongbing Zhang. "AN-1484 Designing A SEPIC Converter." Application Report SNVA168E – May 2006 – Revised April 2013. https://www.ti.com/lit/an/snva168e/snva168e.pdf </ref> is typically used for this purpose.

An inductor, coil or transformer may be wound by hand using a adequate gauge of thinly insulated Tefzel or similar wire on a used or salvaged laminated or powdered iron core. The core of a transformer or inductor, if not powdered cerrite, must be made of thin layers of soft tempered malleable iron or mild steel that will swing the needle of a compass, and it should never be "quenched" or "saturated." The laminated iron core should be "tanned" with oak gall and waxed with beeswax and/or lacquered with boiled linseed oil to form insulative layers of oxide and wax or lacquer between the layers of steel, so that the transformer will not short out between the layers of steel and melt down under load. The windings of wire on a homemade transformer or inductor should be of the purest copper, smoothly drawn, carefully annealed to a soft temper, ductile, and flexible, with the best quality of insulation that is not too thick. Take care that wire windings are smooth and not bent or creased on sharp corners.

Power capacitors of several farads in capacity are widely available and inexpensive, mostly intended for car stereos and audio systems. We suggest using wire of adequate size for the intended current-carrying capacity, while over-provisioning and de-rating cheap power electronics parts, and installing fast-blow fuses at strategic locations, taking care not to overcharge a capacitor or induce a flyback voltage in a large coil. We are not certain about quality but there are audiophiles who listen to music and demand such quality.

High-power transistors, and even several transistors in parallel, may be used to control large electric currents.

Capacitance, inductance and transistor performance characteristics, etc. of all component parts should be carefully measured and verified with appropriate field or bench test equipment.

=== Component selection and Bill of Materials ===

The heart of the controller is a Pulse Width Modulation chip <ref>Some manufacturers and corporations will not like our attitude for referring to their integrated circuits as "chips" for sure, but at pawn shops and online auction sites selling jewelry and electronics one should not be ashamed to call them that. We have no opinions on offers of free samples direct from manufacturers or wholesalers, other than that they apparently contact local cops to enforce a litany of unwritten rules and unspoken codes sometimes pertaining to "intellectual property" by which hobbyists as opposed to professionals are supposed to abide.</ref> like the Texas Instruments TL5001AMJG <ref>PWM Controller with wide input range, with ±3% tolerance on reference, operation –55°C to 125°C https://www.ti.com/product/TL5001AM</ref>. These particular integrated circuits operate in a wide range between 3 and 40 volts, and also come in radiation-hardened versions, which suggests that they were used for solar panels to power satellites launched into outer space decades ago, many of which are still in service today.

The Littelfuse/IXYS IXFN520N075T2<ref>Littelfuse/IXYS IXFN520N075T2 https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2</ref><ref>Littelfuse/IXYS IXFN520N075T2 Datasheet https://www.littelfuse.com/assetdocs/littelfuse-discrete-mosfets-ixfn520n075t2-datasheet?assetguid=8706a9d1-94c2-4e6f-8277-46cab5c71388</ref> power MOSFET "trench gate" is essentially rated to handle 480A in the on state and 75V in the off state. The Vishay VS-FC420SA10 <ref>VS-FC420SA10 Product Information https://www.vishay.com/en/product/95793/</ref><ref>Vishay VS-FC420SA10 Datasheet https://www.vishay.com/docs/95793/vs-fc420sa10.pdf</ref> is another brand of power MOSFET rated to carry 435A when on or hold 100V when off. It comes in the same form factor, an SOT-227 which looks and acts like a miniature clothes iron, and requires an excellent heat sink rated for switching losses and forward voltage drop at the rated current. It would appear that if either of these devices functions as advertised, you could easily start an automobile with the electric current they are rated for handling if you wired one of them up in place of a solenoid for the starter motor. As far as we can tell, this can actually be done, except that the high power MOSFETS require 10V to drive the gate, and the drawdown on a 12V car battery from the starting current will reduce the voltage below the gate actuation level.

Insulated-Gate Bipolar Transistors (IGBTs)<ref>Insulated-Gate Bipolar Transistors (IGBTs) https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-16.html
</ref><ref>Comparison of Forward Characteristics of IGBTs and MOSFETs
https://toshiba.semicon-storage.com/us/semiconductor/knowledge/e-learning/discrete/chap3/chap3-21.html</ref> are another option for the high power current switching needed for the Buck-Boost or SEPIC controllers that need to be used for regulating the voltage from variably sunlit photovoltaic cells to a usable level.

[[Category:Electronics]]

== Batteries ==
tbd ...

555

2026-04-03T04:50:59Z

Rational Point: demo

The '''555''' is a ubiquitous "timer" chip used by electronics hobbyists and experimenters.

[[File:555-op-amp-ctl.svg|thumb|alt=555 op amp demo|Simple Demonstration Circuit]]

[[Category:Electronics]]

File:555-op-amp-ctl.svg

2026-04-03T04:47:50Z

Rational Point:

File:Ss-2.svg

2026-04-02T16:46:31Z

Rational Point: /* Summary */

== Summary ==
Another model using the LM51561H

Very sketchy. We have not had success running the official SPICE simulation distributed with this product.

It is a very delicate surface mount chip about 5mm×6mm with 14 pins spaced at a 0.65mm pitch, and requiring a heat sink. Another version is 2mm×3mm and has 12 surface mount solder pads with a 0.5mm spacing.

We are not dealing with very high frequencies and we would prefer to avoid chips that are so tiny and delicate.

However, for those who know what they are doing and have the knowledge and experience to make these things work, they might be just fine, assuming they do function as documented.

Solar systems

2026-04-02T16:34:05Z

Rational Point: /* Component selection and Bill of Materials */ alternative power MOSFET

It seems arrogant to talk about man-made '''solar systems''' for generating electricity for home use off-grid, as if one were to elevate one's throne above the stars of heaven as Lucifer the bearer of light to do that. Not so. The "grid" itself is that beast, the natural intellect of man, given to the industrial revolution, with the arrogance to carry man-made electricity long distances over land.

However, the set-up of solar panels themselves does depend very much on their alignment with the sun, stars and planets, and the motions of the earth and moon. A common suggestion is that solar panels should face, say, due south in the northern hemisphere, inclined from the horizontal at an angle approximately equal to one's latitude.

Conditions of partial shade and/or high latitude dictate special engineering considerations with respect to adequate insolation for generating electricity.

The maximum energy intensity of sunlight hitting the earth on a clear day may be estimated as

:''I'' = 1350 W/m² × sin ''α'' × exp(–0.30 × ''p'' / sin ''α'')

where α is the angle of elevation of the sun above the horizon, and ''p'' is the ratio of barometric pressure at the altitude of the site to that at sea level. The fist factor is the "outer space" intensity of sunlight at the Earth's distance from the Sun. The second factor accounts for the slant of the sun's rays, and the third factor accounts for the filtering and dimming of the sunlight through Earth's atmosphere.

== The war against social objections to living off the grid ==
Solar panels are often considered a "green" or environmentally sensitive alternative for generating electricity, and we neither object to that consideration nor make a religion out of it.

Technology that enables "off-grid" living reduces the attack surface for secure computer systems, banks, broker houses, and even low-budget private homes etc. by enabling redundancy and reliability even if nothing else, and if the upfront capital and ongoing maintenance costs are reasonable for a reliable electric power system, should be welcomed by Christians living a simple rural lifestyle off the grid.

However, be warned that some "Christians" are married to the grid and to the assumptions of universal vaccinations etc. on which urban lifestyles have been based for millennia with or without Christ. "There's a lady" in the worst Mafia sense of the phrase, (guns are banned and please remove your hats, gentlemen,) so if you are a male "sovereign citizen" or "freeman on the land," then you are deemed to be risking her life and the lives of your children by your simple rural lifestyle.

It's a strange and unnatural situation of religious restrictions to urban white-collar employment and indoors-only entertainment where people with horses and cows etc. are suddenly deemed to be living lives of vice and heavy sin by a certain cadre of over-educated city-dwelling churchgoers, in whose presence hunting and fishing are deemed to be mortal and unforgivable sins.

City people are at always at law and if you give them an inch they take a mile, so don't even start with them.

==Solar panels==

As of 2026, typical solar panels are available in sizes of 100 to 400 watts, costing about one dollar per watt at the lowest bulk price available from major vendors in the United States.

These solar panels typically produce electricity at a nominal 18 volts, ranging from 16 volts at full load to 20 volts at no load in full direct sunlight, designed for charging 12 volt battery systems. Common automotive accessories may be powered directly or an inverter may be used to generate 110‒250VAC if desired.

==Charge controller==
[[File:Ss-1.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI TL5001AMJG)]]
[[File:Ss-2.svg|alt=Solar Cell System with Charge Controller and Battery|thumb|Solar Cell System with Charge Controller and Battery (using TI LM51561HPWPR)]]

We find that off-the-shelf charge controllers are over-rated and overpriced, and we propose building one from scratch with adequate safety margins for high household power requirements.

A Buck-Boost Converter <ref>Buck-Boost Converter: What is it? (Formula and Circuit Diagram) https://www.electrical4u.com/buck-boost-converter/</ref> or Single-Ended Primary Inductor Converter (SEPIC) <ref>SEPIC Converters https://www.monolithicpower.com/en/learning/mpscholar/power-electronics/dc-dc-converters/sepic-converters</ref><ref>Dongbing Zhang. "AN-1484 Designing A SEPIC Converter." Application Report SNVA168E – May 2006 – Revised April 2013. https://www.ti.com/lit/an/snva168e/snva168e.pdf </ref> is typically used for this purpose.

An inductor, coil or transformer may be wound by hand using a adequate gauge of thinly insulated Tefzel or similar wire on a used or salvaged laminated or powdered iron core. The core of a transformer or inductor, if not powdered cerrite, must be made of thin layers of soft tempered malleable iron or mild steel that will swing the needle of a compass, and it should never be "quenched" or "saturated." The laminated iron core should be "tanned" with oak gall and waxed with beeswax and/or lacquered with boiled linseed oil to form insulative layers of oxide and wax or lacquer between the layers of steel, so that the transformer will not short out between the layers of steel and melt down under load. The windings of wire on a homemade transformer or inductor should be of the purest copper, smoothly drawn, carefully annealed to a soft temper, ductile, and flexible, with the best quality of insulation that is not too thick. Take care that wire windings are smooth and not bent or creased on sharp corners.

Power capacitors of several farads in capacity are widely available and inexpensive, mostly intended for car stereos and audio systems. We suggest using wire of adequate size for the intended current-carrying capacity, while over-provisioning and de-rating cheap power electronics parts, and installing fast-blow fuses at strategic locations, taking care not to overcharge a capacitor or induce a flyback voltage in a large coil. We are not certain about quality but there are audiophiles who listen to music and demand such quality.

High-power transistors, and even several transistors in parallel, may be used to control large electric currents.

Capacitance, inductance and transistor performance characteristics, etc. of all component parts should be carefully measured and verified with appropriate field or bench test equipment.

=== Component selection and Bill of Materials ===

The heart of the controller is a Pulse Width Modulation chip <ref>Some manufacturers and corporations will not like our attitude for referring to their integrated circuits as "chips" for sure, but at pawn shops and online auction sites selling jewelry and electronics one should not be ashamed to call them that. We have no opinions on offers of free samples direct from manufacturers or wholesalers, other than that they apparently contact local cops to enforce a litany of unwritten rules and unspoken codes sometimes pertaining to "intellectual property" by which hobbyists as opposed to professionals are supposed to abide.</ref> like the Texas Instruments TL5001AMJG <ref>PWM Controller with wide input range, with ±3% tolerance on reference, operation –55°C to 125°C https://www.ti.com/product/TL5001AM</ref>. These particular integrated circuits operate in a wide range between 3 and 40 volts, and also come in radiation-hardened versions, which suggests that they were used for solar panels to power satellites launched into outer space decades ago, many of which are still in service today.

The Littelfuse/IXYS IXFN520N075T2<ref>Littelfuse/IXYS IXFN520N075T2 https://www.littelfuse.com/products/power-semiconductors-control-ics/mosfets-si-sic/n-channel-trench-gate/gen2/ixfn520n075t2</ref><ref>Littelfuse/IXYS IXFN520N075T2 Datasheet https://www.littelfuse.com/assetdocs/littelfuse-discrete-mosfets-ixfn520n075t2-datasheet?assetguid=8706a9d1-94c2-4e6f-8277-46cab5c71388</ref> power MOSFET "trench gate" is essentially rated to handle 480A in the on state and 75V in the off state. The Vishay VS-FC420SA10 <ref>VS-FC420SA10 Product Information https://www.vishay.com/en/product/95793/</ref><ref>Vishay VS-FC420SA10 Datasheet https://www.vishay.com/docs/95793/vs-fc420sa10.pdf</ref> is another brand of power MOSFET rated to carry 435A when on or hold 100V when off. It comes in the same form factor, an SOT-227 which looks and acts like a miniature clothes iron, and requires an excellent heat sink rated for switching losses and forward voltage drop at the rated current. It would appear that if either of these devices functions as advertised, you could easily start an automobile with the electric current they are rated for handling if you wired one of them up in place of a solenoid for the starter motor.

== Batteries ==
tbd ...