Ranjelin at 23:28, 25 January 2025

2025-01-25T23:28:26Z

←Older revision		Revision as of 23:28, 25 January 2025
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	[[Image:Diode.jpg\|850px]]		[[Image:Diode.jpg\|850px]]
		+	[[Image:Cyclic.jpg\|850px]]
	<pre>		<pre>
	function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision) %from Convex Optimization & Euclidean Distance Geometry		function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision) %from Convex Optimization & Euclidean Distance Geometry

Ranjelin at 06:33, 17 January 2025

2025-01-17T06:33:04Z

←Older revision		Revision as of 06:33, 17 January 2025
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	isR = is(RsRl/(Rs + Rl) + Rd);		isR = is(RsRl/(Rs + Rl) + Rd);

-	% circuit.nb
	dvd = 1000*randn(size(vi)); %perturbation of derivative proves that iteration converges to same median capacitance		dvd = 1000*randn(size(vi)); %perturbation of derivative proves that iteration converges to same median capacitance
	for i=1:5 %3 iterations will introduce randomness into mean impedance calculation		for i=1:5 %3 iterations will introduce randomness into mean impedance calculation

Ranjelin: New page: 850px

 function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision)  %from Convex Optimization & Euclidean Distance Geometry    mp.Digi...

2025-01-16T23:51:32Z

New page: 850px <pre> function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision) %from Convex Optimization & Euclidean Distance Geometry mp.Digi...

New page

[[Image:Diode.jpg|850px]]
<pre>
function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision) %from Convex Optimization & Euclidean Distance Geometry
mp.Digits(precision); %Advanpix MCT
k = 1.380649e-23; %boltzmann constant % https://www.nist.gov/si-redefinition/kelvin-boltzmann-constant
T = 298; %temperature kelvin %Neudeck p.5
q = 1.602176634e-19; %electron charge %NIST
is = 76.9e-12; %circuitlab diodeInduced
eta = 1.45; %circuitlab diodeInduced
tau = 4.32e-6; %transport time. max exponent (observed) e-4. Increasing capacitance observes more nonlinearity in vL FFT.
Rd = 0.042; %diode internal resistance
nVt = eta*k*T/q; %[V] thermal voltage for particular diode characterized by eta
isR = is*(Rs*Rl/(Rs + Rl) + Rd);

% circuit.nb
dvd = 1000*randn(size(vi)); %perturbation of derivative proves that iteration converges to same median capacitance
for i=1:5 %3 iterations will introduce randomness into mean impedance calculation
Lw = exp((isR + vi*Rl/(Rl + Rs))/nVt)*isR.*(1 + tau*dvd/nVt)/nVt;
vd = isR - nVt*Lambert_W(Lw) + vi*Rl/(Rl + Rs);
dvd = [vd(2)-vd(end); vd(3:end)-vd(1:end-2); vd(1)-vd(end-1)]/2; %approximate the derivative first time around, otherwise dvd becomes near 0. Assumes periodicity.
if verbose
Cd = tau*is*exp(vd/nVt)/nVt;
Cdmed = median(Cd);
disp([num2eng(Cdmed,false,false,false,16) ' farad']);
end
end
if verbose
Cdmax = max(Cd);
Cdmin = min(Cd);

figure(20); plot(0:numel(Cd)-1, Cd);
title('Cd over time'); xlabel('sample number'); ylabel('Farad'); set(get(gca,'ylabel'),'rotation',0);
drawnow
else
Cd = tau*is*exp(vd/nVt)/nVt;
end
iC = Cd.*dvd*Fs; %diffusion capacitor current. Normalization by Fs makes current independent of sample rate
id = is*(exp(vd/nVt) - 1); %ideal Shockley equation. This is already independent of Fs.
vl = (id + iC)*Rd + vd;

if verbose
figure(21); plot(0:numel(iC)-1, iC);
title('Cd current'); xlabel('sample number'); ylabel('Amp'); set(get(gca,'ylabel'),'rotation',0);
figure(22); plot(0:numel(id)-1, id);
title('diode current'); xlabel('sample number'); ylabel('Amp'); set(get(gca,'ylabel'),'rotation',0);
idx = find(iC ~= 0);
disp(['mean capacitor impedance = ' num2str(orosumvec(vd(idx)./iC(idx),1)/numel(idx),'%3.4e')])
% disp(['mean capacitor |impedance| = ' num2str(orosumvec(abs(vd(idx)./iC(idx)),1)/numel(idx),'%3.4e')])
t = median(vd./iC);
if t < 0, spc=[]; else spc=' '; end
disp(['median capacitor impedance =' spc num2str(t)]) %median impedance is always far smaller than mean despite mp.Digits precision
medcapimp = median(abs(vd./iC));
disp(['median capacitor |impedance| = ' num2str(medcapimp,'%3.4e')])
disp(['empirical constant c = ' num2str(medcapimp*(2*pi*fundfreq*Cdmed),'%3.15e')])

figure(23);
histogram(Cd,50,'Normalization','probability'); %for book illustration
% histogram(Cd,round(3.25*48000)); %for counting smallest diffusion capacitors
title('histogram C_d'); xlabel('bin'); ylabel('relative count'); %set(get(gca,'ylabel'),'rotation',0);
drawnow
end
end

% https://www.mathworks.com/matlabcentral/fileexchange/43419-the-lambert-w-function
function w = Lambert_W(x,branch)
% Lambert_W Functional inverse of x = w*exp(w).
% w = Lambert_W(x), same as Lambert_W(x,0)
% w = Lambert_W(x,0) Primary or upper branch, W_0(x)
% w = Lambert_W(x,-1) Lower branch, W_{-1}(x)
%
% See: http://blogs.mathworks.com/cleve/2013/09/02/the-lambert-w-function/

% Effective starting guess
if nargin < 2 || branch ~= -1
w = ones(size(x)); % Start above -1
else
w = -2*ones(size(x)); % Start below -1
end
v = inf*w;

% Halley's method
c = 0;
limit = 100;
while any(abs(w - v)./abs(w) > 1e-15) && c < limit %changed magic tolerance. Was 1e-8. -JonD
v = w;
e = exp(w);
f = w.*e - x; % Iterate, to make this quantity zero
w = w - f./((e.*(w+1) - (w+2).*f./(2*w + 2)));
c = c + 1;
end
if c >= limit
disp('%%%%%%%%%%%%%%%%%%%%%% Warning: Lambert limit reached %%%%%%%%%%%%%%%%%%%%%')
end
end
</pre>

Diode Circuit Analysis - Revision history

Ranjelin at 23:28, 25 January 2025

Ranjelin at 06:33, 17 January 2025

Ranjelin: New page: 850px
function [vl Cdmax Cdmin Cdmed] = diodeMap(vi, Rs, Rl, verbose, fundfreq, Fs, precision) %from Convex Optimization & Euclidean Distance Geometry mp.Digi...