In case the attachments aren't working ; here's a pure text file , within this message . LnDioGH.par AND LnDioGH.frm , together . START PARAMETER FILE======================================= Diode { reset=1821 type=formula formulafile=c:\winf1821\alndgh.frm formulaname=LnDioGH corners=-0.16588419/0.25978091/-0.15031315/0.1691023 float=y maxiter=512 logmap=yes colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<5>zNFFVF<5>zV\ FFbF<5>zbFFjF<5>zjFFrF<5>zrFFzF<5>zzFFFN<5>zFNFNN<5>zNNFVN<5>zVNFbN<5>zb\ NFjN<5>zjNFrN<5>zrNFzN<5>zzNFFV<5>zFVFNV<5>zNVFVV<5>zVVFbV<5>zbVFjV<5>zj\ VFrV<5>zrVFzV<5>zzVFFb<5>zFbFNb<5>zNbFVb<5>zVbFbb<5>zbbFjb<5>zjbFrb<5>zr\ bFzb<5>zzbFFj<5>zFjFNj<5>zNjFVj<5>zVjFbj<5>zbjFjj<5>zjjFrj<4>rrjzywccdWW\ Wz000z0zz000zz0z0zzzzz } comment { From : sciwise@ihug.co.nz July 2009 copyright c 2009 This is a model of a diode , as an electronic component . It utilizes Newton's method to solve a non-linear equation ; known as the ideal diode or Shockley equation . The very basic form of this equation is : i = Ids*(exp(Vs/(n*Vt))-1) where , Q = 1.6*(10^-19) Electronic Charge . K = 1.38*(10^-23) Boltzman's constant . T = Absolute Temperature , in Kelvins . T = 273 [K] + degreesC For degreesC = 25 , Vt ~= 0.025 [v] Ids = Saturation current . Vs = Applied , source , voltage . n = Ideality factor = ( 1 to 2 ) . Vt = K * T / Q Thermionic Voltage . A more realistic model of a diode will include the finite ohmic resistance of the leads . A parallel conductance is also modeled , as this speeds the convergence of Newton's method . Therefore the circuit we're modelling looks like this . i --> ----------------------------, ' | | -------------------, | | .---. Vs - D --- | | Gm --- /_\ |___| | |__________________| | | | .---. | | | Rs | |___| '----------------------------' Where D is represented by the ideal diode equation . Now the total current , i , flowing through this circuit is : i = Ids*(exp((Vs-i*Rs)/(n*Vt))-1) + Gm*(Vs-i*Rs) This equation needs to be solved in terms of i and be put in a form that can be readily and accurately solved through Newton's method . The steps involved are : 1) Let log(x) = (Vs-i*Rs)/(n*Vt) 2) Solve log(x) = (Vs-i*Rs)/(n*Vt) in terms of i . i = -(n*Vt*log(x)-Vs)/Rs 3) Substitute the expression for i , from (2) into i = Ids*(exp((Vs-i*Rs)/(n*Vt))-1) + Gm*(Vs-i*Rs) -(n*Vt*log(x)-Vs)/Rs = Ids*(x-1) + Gm*(Vs--((n*Vt*log(x)-Vs)/Rs)*Rs) -(n*Vt*log(x)-Vs)/Rs = Ids*(x-1) + Gm*((n*Vt*log(x)/Rs)*Rs) (Vs-n*Vt*log(x))/Rs = Ids*(x-1) + Gm*(n*Vt*log(x)) 4) Solve (3) for x , x = -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1); 5) Find the derivative of (4) in terms of x . 1 = -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x) 6) Now Newton's iteration formula is : x = x - f(x) / f '(x) , where f '(x) == d f(x) / dx . 7) For this example : f(x) = x = -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1) and f '(x) = 1 = -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x) 8) Therefore Newton's iteration formula for this example is : x = x - ( -((Gm*n*Rs*Vt+n*Vt)*log(x)-Vs-Is*Rs)/(Is*Rs),Is*Rs,1) - x )/( -(Gm*n*Rs*Vt+n*Vt)/(Is*Rs*x)-1) 9) Simplifying (8) x = x -( (-Ids*Rs-Vs)*x + Ids*Rs*x*x + (n+Gm*n*Rs)*Vt*x*log(x) ) / ( (n + Gm*n*Rs)*Vt+Ids*Rs*x ) Substitute u = Gm*n*Rs*Vt+n*Vt vr = Ids*Rs x = x-( -(Vs+vr)*x + vr*x*x + u*x*log(x) )/(vr*x+u)) In this logarithmic format overflow , and possibly underflow , is avoided . 10 ) We need to be able to convert x back to i , to do this we use the inverse of the original substitution : log(x) = (Vs-i*Rs)/(n*Vt) Solving for i , i = - ( log(x)*(n*Vt) - Vs ) / Rs Substitute Pt = n*Vt i = - ( log(x)*Pt - Vs ) / Rs Between successive iterations of Newton's formula the previous value of i is compared with the present, if the absolute difference is less than a predefined tolerance , Pd , then the iteration stops . Vs is a complex voltage source , possibly equivalent to a multi phase voltage source . This is a basic diode model and doesn't include the effects of diode junction capacitance . For small voltages a purely exponential representation of the diode model may converge quicker than the logarithmic and still remain accurate . The logarithmic model has been implemented as a BASIC language program and compared with data from a SPICE simulation , for a real voltage source , there is good agreement . For a Complex voltage source , the few samples generated from the BASIC program are in good agreement with those from MAXIMA CAS . } LnDioGH{ ; ; ; Complex Voltage - Complex Current ; Diode Characteristics . ; ; for 1N4148 silicon type . ; Level 1 model . ; ; at 25 degrees C ; ; Pd = (10^-13), Gm = 9.4*(10^-13), Ids = 2.52*(10^-09), Rs = 0.968, n = 1.752, Vt = 0.025, u = Gm*n*Rs*Vt+n*Vt, Pt = n*Vt, vr = Ids*Rs, Vs = Pixel, x = (0.1,0), x = x-((u*x*log(x)+vr*x*x-(Vs+vr)*x)/(vr*x+u)), y = -(Pt*log(x)-Vs)/Rs, tol = (1,0): u = y; x = x-((u*x*log(x)+vr*x*x-(Vs+vr)*x)/(vr*x+u)); y = -(Pt*log(x)-Vs)/Rs, tol = |u-y|, tol > Pd } comment { The floating point option needs to be selected , 512 iterations , or more , should be selected . Also a logarithmic palette . Minibrot structures aren't immediately apparent at the default parameter settings . A parameter setting of : xmin - 0.005770310598 xmax - 0.005666943901 ymin 0.000516417395 ymax 0.000594104392 shows embedded mimibrots and spirals , wether this is relevant in a real diode is unknown . You might be able to locate mimibrots elsewhere on the map . } END PARAMETER FILE========================================= ----- Original Message ----- From: JackOfTradeZ@comcast.net To: fractint@mailman.xmission.com Sent: Thursday, July 16, 2009 4:21 PM Subject: Re: [Fractint] Diode Fractal . No PAR or FRM is seen, and no attachments. Maybe it is problem on my end? I am using comcast web client email. . ------------------------------------------------------------------------------ _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint