/********** Copyright 1990 Regents of the University of California. All rights reserved. Author: 1988 Jaijeet S Roychowdhury **********/ #include "ngspice/ngspice.h" #include "ngspice/cktdefs.h" #include "bjtdefs.h" #include "ngspice/const.h" #include "ngspice/distodef.h" #include "ngspice/sperror.h" #include "ngspice/devdefs.h" #include "ngspice/suffix.h" /* * This function initialises the Taylor coeffs for the * BJT's in the circuit */ /* actually load the current resistance value into the sparse matrix * previously provided */ int BJTdSetup(GENmodel *inModel, CKTcircuit *ckt) { BJTmodel *model = (BJTmodel*)inModel; BJTinstance *here; double arg; double c2; double c4; double lcapbe1, lcapbe2, lcapbe3; double lcapbx1, lcapbx2, lcapbx3; double cb = 0.0; double cbc; double cbcn; double cbe; double cben; double cdis; double csat; double ctot; double czbc; double czbcf2; double czbe; double czbef2; double czbx; double czbxf2; double czcs; double evbc; double evbcn; double evbe; double evben; double f1; double f2; double f3; double fcpc; double fcpe; double gbb1 = 0.0; double gbc; double gbcn; double gbe; double gbe2, gbe3; double gbc2,gbc3; double gben2,gben3; double gbcn2,gbcn3; double gben; double gbb2 = 0.0, gbb3 = 0.0; double oik; double oikr; double ovtf; double pc; double pe; double ps; double q1; double q2; double qb; double rbpi; double rbpr; double sarg; double sqarg; double tf; double tr; double vbc; double vbe; double vbx; double vsc; double vt; double vtc; double vte; double vtn; double xjrb; double xjtf; double xmc; double xme; double xms; double xtf; double vbed; double vbb; double lcapbc1 = 0.0; double lcapbc2 = 0.0; double lcapbc3 = 0.0; double lcapsc1 = 0.0; double lcapsc2 = 0.0; double lcapsc3 = 0.0; double ic; double dummy; Dderivs d_p, d_q, d_r; Dderivs d_dummy, d_q1, d_qb, d_dummy2; Dderivs d_arg, d_sqarg, d_ic, d_q2; Dderivs d_z, d_tanz, d_vbb, d_ibb, d_rbb; Dderivs d_ib, d_cbe, d_tff, d_qbe; d_p.value = 0.0; d_p.d1_p = 1.0; d_p.d1_q = 0.0; d_p.d1_r = 0.0; d_p.d2_p2 = 0.0; d_p.d2_q2 = 0.0; d_p.d2_r2 = 0.0; d_p.d2_pq = 0.0; d_p.d2_qr = 0.0; d_p.d2_pr = 0.0; d_p.d3_p3 = 0.0; d_p.d3_q3 = 0.0; d_p.d3_r3 = 0.0; d_p.d3_p2q = 0.0; d_p.d3_p2r = 0.0; d_p.d3_pq2 = 0.0; d_p.d3_q2r = 0.0; d_p.d3_pr2 = 0.0; d_p.d3_qr2 = 0.0; d_p.d3_pqr = 0.0; EqualDeriv(&d_q, &d_p); d_q.d1_q = 1.0; d_q.d1_p = 0.0; EqualDeriv(&d_r, &d_p); d_r.d1_r = 1.0; d_r.d1_p = 0.0; /* loop through all the models */ for( ; model != NULL; model = model->BJTnextModel ) { /* loop through all the instances of the model */ for (here = model->BJTinstances; here != NULL ; here=here->BJTnextInstance) { vt = here->BJTtemp * CONSTKoverQ; /* * dc model paramters */ csat=here->BJTtSatCur*here->BJTarea * here->BJTm; rbpr=here->BJTtminBaseResist/(here->BJTarea * here->BJTm); rbpi=here->BJTtbaseResist/(here->BJTarea * here->BJTm)-rbpr; oik=here->BJTtinvRollOffF/(here->BJTarea * here->BJTm); c2=here->BJTtBEleakCur*here->BJTarea * here->BJTm; vte=here->BJTtleakBEemissionCoeff*vt; oikr=here->BJTtinvRollOffR/(here->BJTarea * here->BJTm); c4=here->BJTtBCleakCur * here->BJTm; if (model->BJTsubs == VERTICAL) c4 *= here->BJTareab; else c4 *= here->BJTareac; /* lateral transistor */ vtc=here->BJTtleakBCemissionCoeff*vt; xjrb=here->BJTtbaseCurrentHalfResist*here->BJTarea * here->BJTm; /* * initialization */ vbe= model->BJTtype*(*(ckt->CKTrhsOld + here->BJTbasePrimeNode) - *(ckt->CKTrhsOld + here->BJTemitPrimeNode)); vbc= model->BJTtype*(*(ckt->CKTrhsOld + here->BJTbaseNode) - *(ckt->CKTrhsOld + here->BJTcolPrimeNode)); vbx=model->BJTtype*( *(ckt->CKTrhsOld+here->BJTbaseNode)- *(ckt->CKTrhsOld+here->BJTcolPrimeNode)); vsc=model->BJTtype*( *(ckt->CKTrhsOld+here->BJTsubstNode)- *(ckt->CKTrhsOld+here->BJTcolPrimeNode)); vbb=model->BJTtype*( *(ckt->CKTrhsOld+here->BJTbaseNode) - *(ckt->CKTrhsOld+here->BJTbasePrimeNode)); vbed = vbe; /* this is just a dummy variable * it is the delayed vbe to be * used in the delayed gm generator */ /* ic = f1(vbe,vbc,vbed) + f2(vbc) + f3(vbc) * * we shall calculate the taylor coeffs of ic wrt vbe, * vbed, and vbc and store them away. the equations f1 f2 * and f3 are given elsewhere; we shall start off with f1, * compute derivs. upto third order and then do f2 and f3 * and add their derivatives. * * Since f1 above is a function of three variables, it * will be convenient to use derivative structures to * compute the derivatives of f1. For this computation, * p=vbe, q=vbc, r=vbed. * * ib = f1(vbe) + f2(vbc) (not the same f's as above, in * case you are wondering!) the gbe's gbc's gben's and * gbcn's are convenient subsidiary variables. * * irb = f(vbe, vbc, vbb) - the vbe & vbc dependencies * arise from the qb term. * * qbe = f1(vbe,vbc) + f2(vbe) * * derivative structures will be used again in the above * two equations. p=vbe, q=vbc, r=vbb. * * qbc = f(vbc) ; qbx = f(vbx) * * qss = f(vsc) */ /* * determine dc current and derivitives */ vtn=vt*here->BJTtemissionCoeffF; if(vbe > -5*vtn){ evbe=exp(vbe/vtn); cbe=csat*(evbe-1)+ckt->CKTgmin*vbe; gbe=csat*evbe/vtn+ckt->CKTgmin; gbe2 = csat*evbe/vtn/vtn; gbe3 = gbe2/vtn; /* note - these are actually derivs, not Taylor * coeffs. - not divided by 2! and 3! */ if (c2 == 0) { cben=0; gben=gben2=gben3=0; } else { evben=exp(vbe/vte); cben=c2*(evben-1); gben=c2*evben/vte; gben2=gben/vte; gben3=gben2/vte; } } else { gbe = -csat/vbe+ckt->CKTgmin; gbe2=gbe3=gben2=gben3=0; cbe=gbe*vbe; gben = -c2/vbe; cben=gben*vbe; } vtn=vt*here->BJTtemissionCoeffR; if(vbc > -5*vtn) { evbc=exp(vbc/vtn); cbc=csat*(evbc-1)+ckt->CKTgmin*vbc; gbc=csat*evbc/vtn+ckt->CKTgmin; gbc2=csat*evbc/vtn/vtn; gbc3=gbc2/vtn; if (c4 == 0) { cbcn=0; gbcn=0; gbcn2=gbcn3=0; } else { evbcn=exp(vbc/vtc); cbcn=c4*(evbcn-1); gbcn=c4*evbcn/vtc; gbcn2=gbcn/vtc; gbcn3=gbcn2/vtc; } } else { gbc = -csat/vbc+ckt->CKTgmin; gbc2=gbc3=0; cbc = gbc*vbc; gbcn = -c4/vbc; gbcn2=gbcn3=0; cbcn=gbcn*vbc; } /* * determine base charge terms */ /* q1 is a function of 2 variables p=vbe and q=vbc. r= * anything */ q1=1/(1-here->BJTtinvEarlyVoltF*vbc-here->BJTtinvEarlyVoltR*vbe); dummy = (1-here->BJTtinvEarlyVoltF*vbc- here->BJTtinvEarlyVoltR*vbe); EqualDeriv(&d_dummy, &d_p); d_dummy.value = dummy; d_dummy.d1_p = - here->BJTtinvEarlyVoltR; d_dummy.d1_q = - here->BJTtinvEarlyVoltF; /* q1 = 1/dummy */ InvDeriv(&d_q1, &d_dummy); /* now q1 and its derivatives are set up */ if(oik == 0 && oikr == 0) { qb=q1; EqualDeriv(&d_qb, &d_q1); } else { q2=oik*cbe+oikr*cbc; EqualDeriv(&d_q2, &d_p); d_q2.value = q2; d_q2.d1_p = oik*gbe; d_q2.d1_q = oikr*gbc; d_q2.d2_p2 = oik*gbe2; d_q2.d2_q2 = oikr*gbc2; d_q2.d3_p3 = oik*gbe3; d_q2.d3_q3 = oikr*gbc3; arg=MAX(0,1+4*q2); if (arg == 0.) { EqualDeriv(&d_arg,&d_p); d_arg.d1_p = 0.0; } else { TimesDeriv(&d_arg,&d_q2,4.0); d_arg.value += 1.; } sqarg=1; EqualDeriv(&d_sqarg,&d_p); d_sqarg.value = 1.0; d_sqarg.d1_p = 0.0; if(arg != 0){ sqarg=sqrt(arg); SqrtDeriv(&d_sqarg, &d_arg); } qb=q1*(1+sqarg)/2; dummy = 1 + sqarg; EqualDeriv(&d_dummy, &d_sqarg); d_dummy.value += 1.0; MultDeriv(&d_qb, &d_q1, &d_dummy); TimesDeriv(&d_qb, &d_qb, 0.5); } ic = (cbe - cbc)/qb; /* cbe is a fn of vbed only; cbc of vbc; and qb of vbe and vbc */ /* p=vbe, q=vbc, r=vbed; now dummy = cbe - cbc */ EqualDeriv(&d_dummy, &d_p); d_dummy.d1_p = 0.0; d_dummy.value = cbe-cbc; d_dummy.d1_r = gbe; d_dummy.d2_r2 = gbe2; d_dummy.d3_r3 = gbe3; d_dummy.d1_q = -gbc; d_dummy.d2_q2 = -gbc2; d_dummy.d3_q3 = -gbc3; DivDeriv(&d_ic, &d_dummy, &d_qb); d_ic.value -= cbc/here->BJTtBetaR + cbcn; d_ic.d1_q -= gbc/here->BJTtBetaR + gbcn; d_ic.d2_q2 -= gbc2/here->BJTtBetaR + gbcn2; d_ic.d3_q3 -= gbc3/here->BJTtBetaR + gbcn3; /* check this point: where is the f2(vbe) contribution to ic ? */ /* ic derivatives all set up now */ /* base spread resistance */ if ( !((rbpr == 0.0) && (rbpi == 0.0))) { cb=cbe/here->BJTtBetaF+cben+cbc/here->BJTtBetaR+cbcn; /* we are calculating derivatives w.r.t cb itself */ /* gx=rbpr+rbpi/qb; */ if (cb != 0.0) { if((xjrb != 0.0) && (rbpi != 0.0)) { /* p = ib, q, r = anything */ dummy=MAX(cb/xjrb,1e-9); EqualDeriv(&d_dummy, &d_p); d_dummy.value = dummy; d_dummy.d1_p = 1/xjrb; SqrtDeriv(&d_dummy, &d_dummy); TimesDeriv(&d_dummy, &d_dummy, 2.4317); /* dummy2=(-1+sqrt(1+14.59025*MAX(cb/xjrb,1e-9))); */ EqualDeriv(&d_dummy2, &d_p); d_dummy2.value = 1+14.59025*MAX(cb/xjrb,1e-9); d_dummy2.d1_p = 14.59025/xjrb; SqrtDeriv(&d_dummy2, &d_dummy2); d_dummy2.value -= 1.0; DivDeriv(&d_z, &d_dummy2, &d_dummy); TanDeriv(&d_tanz, &d_z); /* now using dummy = tanz - z and dummy2 = z*tanz*tanz */ TimesDeriv(&d_dummy, &d_z, -1.0); PlusDeriv(&d_dummy, &d_dummy, &d_tanz); MultDeriv(&d_dummy2, &d_tanz, &d_tanz); MultDeriv(&d_dummy2, &d_dummy2, &d_z); DivDeriv(&d_rbb , &d_dummy, &d_dummy2); TimesDeriv(&d_rbb,&d_rbb, 3.0*rbpi); d_rbb.value += rbpr; MultDeriv(&d_vbb, &d_rbb, &d_p); /* power series inversion to get the conductance derivatives */ if (d_vbb.d1_p != 0) { gbb1 = 1/d_vbb.d1_p; gbb2 = -(d_vbb.d2_p2*0.5)*gbb1*gbb1; gbb3 = gbb1*gbb1*gbb1*gbb1*(-(d_vbb.d3_p3/6.0) + 2*(d_vbb.d2_p2*0.5)*(d_vbb.d2_p2*0.5)*gbb1); } else printf("\nd_vbb.d1_p = 0 in base spread resistance calculations\n"); /* r = vbb */ EqualDeriv(&d_ibb, &d_r); d_ibb.value = cb; d_ibb.d1_r = gbb1; d_ibb.d2_r2 = 2*gbb2; d_ibb.d3_r3 = 6.0*gbb3; } else { /* rbb = rbpr + rbpi/qb; ibb = vbb /rbb; = f(vbe, vbc, vbb) */ EqualDeriv(&d_rbb,&d_p); d_rbb.d1_p = 0.0; if (rbpi != 0.0) { InvDeriv(&d_rbb, &d_qb); TimesDeriv(&d_rbb, &d_rbb,rbpi); } d_rbb.value += rbpr; EqualDeriv(&d_ibb,&d_r); d_ibb.value = vbb; DivDeriv(&d_ibb,&d_ibb,&d_rbb); } } else { EqualDeriv(&d_ibb,&d_r); if (rbpr != 0.0) d_ibb.d1_r = 1/rbpr; } } else { EqualDeriv(&d_ibb,&d_p); d_ibb.d1_p = 0.0; } /* formulae for base spread resistance over! */ /* ib term */ EqualDeriv(&d_ib, &d_p); d_ib.d1_p = 0.0; d_ib.value = cb; d_ib.d1_p = gbe/here->BJTtBetaF + gben; d_ib.d2_p2 = gbe2/here->BJTtBetaF + gben2; d_ib.d3_p3 = gbe3/here->BJTtBetaF + gben3; d_ib.d1_q = gbc/here->BJTtBetaR + gbcn; d_ib.d2_q2 = gbc2/here->BJTtBetaR + gbcn2; d_ib.d3_q3 = gbc3/here->BJTtBetaR + gbcn3; /* ib term over */ /* * charge storage elements */ tf=here->BJTttransitTimeF; tr=here->BJTttransitTimeR; czbe=here->BJTtBEcap*here->BJTarea * here->BJTm; pe=here->BJTtBEpot; xme=here->BJTtjunctionExpBE; cdis=model->BJTbaseFractionBCcap; ctot=here->BJTtBCcap * here->BJTm; if (model->BJTsubs == VERTICAL) ctot *= here->BJTareab; else ctot *= here->BJTareac; czbc=ctot*cdis; czbx=ctot-czbc; pc=here->BJTtBCpot; xmc=here->BJTtjunctionExpBC; fcpe=here->BJTtDepCap; czcs=model->BJTcapSub * here->BJTm; if (model->BJTsubs == VERTICAL) czcs *= here->BJTareac; else czcs *= here->BJTareab; ps=model->BJTpotentialSubstrate; xms=model->BJTexponentialSubstrate; xtf=model->BJTtransitTimeBiasCoeffF; ovtf=model->BJTtransitTimeVBCFactor; xjtf=here->BJTttransitTimeHighCurrentF*here->BJTarea * here->BJTm; if(tf != 0 && vbe >0) { EqualDeriv(&d_cbe, &d_p); d_cbe.value = cbe; d_cbe.d1_p = gbe; d_cbe.d2_p2 = gbe2; d_cbe.d3_p3 = gbe3; if(xtf != 0){ if(ovtf != 0) { /* dummy = exp ( vbc*ovtf) */ EqualDeriv(&d_dummy, &d_q); d_dummy.value = vbc*ovtf; d_dummy.d1_q = ovtf; ExpDeriv(&d_dummy, &d_dummy); } else { EqualDeriv(&d_dummy,&d_p); d_dummy.value = 1.0; d_dummy.d1_p = 0.0; } if(xjtf != 0) { EqualDeriv(&d_dummy2, &d_cbe); d_dummy2.value += xjtf; DivDeriv(&d_dummy2, &d_cbe, &d_dummy2); MultDeriv (&d_dummy2, &d_dummy2, &d_dummy2); } else { EqualDeriv(&d_dummy2,&d_p); d_dummy2.value = 1.0; d_dummy2.d1_p = 0.0; } MultDeriv(&d_tff, &d_dummy, &d_dummy2); TimesDeriv(&d_tff, &d_tff, tf*xtf); d_tff.value += tf; } else { EqualDeriv(&d_tff,&d_p); d_tff.value = tf; d_tff.d1_p = 0.0; } /* qbe = tff/qb*cbe */ /* dummy = tff/qb; */ /* these are the cbe coeffs */ DivDeriv(&d_dummy, &d_tff, &d_qb); MultDeriv(&d_qbe, &d_dummy, &d_cbe); } else { EqualDeriv(&d_qbe, &d_p); d_qbe.value = 0.0; d_qbe.d1_p = 0.0; } if (vbe < fcpe) { arg=1-vbe/pe; sarg=exp(-xme*log(arg)); lcapbe1 = czbe*sarg; lcapbe2 = 0.5*czbe*xme*sarg/(arg*pe); lcapbe3 = czbe*xme*(xme+1)*sarg/(arg*arg*pe*pe*6); } else { f1=here->BJTtf1; f2=model->BJTf2; f3=model->BJTf3; czbef2=czbe/f2; lcapbe1 = czbef2*(f3+xme*vbe/pe); lcapbe2 = 0.5*xme*czbef2/pe; lcapbe3 = 0.0; } d_qbe.d1_p += lcapbe1; d_qbe.d2_p2 += lcapbe2*2.; d_qbe.d3_p3 += lcapbe3*6.; fcpc=here->BJTtf4; f1=here->BJTtf5; f2=model->BJTf6; f3=model->BJTf7; if (vbc < fcpc) { arg=1-vbc/pc; sarg=exp(-xmc*log(arg)); lcapbc1 = czbc*sarg; lcapbc2 = 0.5*czbc*xmc*sarg/(arg*pc); lcapbc3 = czbc*xmc*(xmc+1)*sarg/(arg*arg*pc*pc*6); } else { czbcf2=czbc/f2; lcapbc1 = czbcf2*(f3+xmc*vbc/pc); lcapbc2 = 0.5*xmc*czbcf2/pc; lcapbc3 = 0; } if(vbx < fcpc) { arg=1-vbx/pc; sarg=exp(-xmc*log(arg)); lcapbx1 = czbx*sarg; lcapbx2 = 0.5*czbx*xmc*sarg/(arg*pc); lcapbx3 = czbx*xmc*(xmc+1)*sarg/(arg*arg*pc*pc*6); } else { czbxf2=czbx/f2; lcapbx1 = czbxf2*(f3+xmc*vbx/pc); lcapbx2 = 0.5*xmc*czbxf2/pc; lcapbx3 = 0; } if(vsc < 0){ arg=1-vsc/ps; sarg=exp(-xms*log(arg)); lcapsc1 = czcs*sarg; lcapsc2 = 0.5*czcs*xms*sarg/(arg*ps); lcapsc3 = czcs*xms*(xms+1)*sarg/(arg*arg*ps*ps*6); } else { lcapsc1 = czcs*(1+xms*vsc/ps); lcapsc2 = czcs*0.5*xms/ps; lcapsc3 = 0; } /* * store small-signal parameters */ here->ic_x = d_ic.d1_p; here->ic_y = d_ic.d1_q; here->ic_xd = d_ic.d1_r; here->ic_x2 = 0.5*model->BJTtype*d_ic.d2_p2; here->ic_y2 = 0.5*model->BJTtype*d_ic.d2_q2; here->ic_w2 = 0.5*model->BJTtype*d_ic.d2_r2; here->ic_xy = model->BJTtype*d_ic.d2_pq; here->ic_yw = model->BJTtype*d_ic.d2_qr; here->ic_xw = model->BJTtype*d_ic.d2_pr; here->ic_x3 = d_ic.d3_p3/6.; here->ic_y3 = d_ic.d3_q3/6.; here->ic_w3 = d_ic.d3_r3/6.; here->ic_x2w = 0.5*d_ic.d3_p2r; here->ic_x2y = 0.5*d_ic.d3_p2q; here->ic_y2w = 0.5*d_ic.d3_q2r; here->ic_xy2 = 0.5*d_ic.d3_pq2; here->ic_xw2 = 0.5*d_ic.d3_pr2; here->ic_yw2 = 0.5*d_ic.d3_qr2; here->ic_xyw = d_ic.d3_pqr; here->ib_x = d_ib.d1_p; here->ib_y = d_ib.d1_q; here->ib_x2 = 0.5*model->BJTtype*d_ib.d2_p2; here->ib_y2 = 0.5*model->BJTtype*d_ib.d2_q2; here->ib_xy = model->BJTtype*d_ib.d2_pq; here->ib_x3 = d_ib.d3_p3/6.; here->ib_y3 = d_ib.d3_q3/6.; here->ib_x2y = 0.5*d_ib.d3_p2q; here->ib_xy2 = 0.5*d_ib.d3_pq2; here->ibb_x = d_ibb.d1_p; here->ibb_y = d_ibb.d1_q; here->ibb_z = d_ibb.d1_r; here->ibb_x2 = 0.5*model->BJTtype*d_ibb.d2_p2; here->ibb_y2 = 0.5*model->BJTtype*d_ibb.d2_q2; here->ibb_z2 = 0.5*model->BJTtype*d_ibb.d2_r2; here->ibb_xy = model->BJTtype*d_ibb.d2_pq; here->ibb_yz = model->BJTtype*d_ibb.d2_qr; here->ibb_xz = model->BJTtype*d_ibb.d2_pr; here->ibb_x3 = d_ibb.d3_p3/6.; here->ibb_y3 = d_ibb.d3_q3/6.; here->ibb_z3 = d_ibb.d3_r3/6.; here->ibb_x2z = 0.5*d_ibb.d3_p2r; here->ibb_x2y = 0.5*d_ibb.d3_p2q; here->ibb_y2z = 0.5*d_ibb.d3_q2r; here->ibb_xy2 = 0.5*d_ibb.d3_pq2; here->ibb_xz2 = 0.5*d_ibb.d3_pr2; here->ibb_yz2 = 0.5*d_ibb.d3_qr2; here->ibb_xyz = d_ibb.d3_pqr; here->qbe_x = d_qbe.d1_p; here->qbe_y = d_qbe.d1_q; here->qbe_x2 = 0.5*model->BJTtype*d_qbe.d2_p2; here->qbe_y2 = 0.5*model->BJTtype*d_qbe.d2_q2; here->qbe_xy = model->BJTtype*d_qbe.d2_pq; here->qbe_x3 = d_qbe.d3_p3/6.; here->qbe_y3 = d_qbe.d3_q3/6.; here->qbe_x2y = 0.5*d_qbe.d3_p2q; here->qbe_xy2 = 0.5*d_qbe.d3_pq2; here->capbc1 = lcapbc1; here->capbc2 = lcapbc2; here->capbc3 = lcapbc3; here->capbx1 = lcapbx1; here->capbx2 = lcapbx2; here->capbx3 = lcapbx3; here->capsc1 = lcapsc1; here->capsc2 = lcapsc2; here->capsc3 = lcapsc3; } } return(OK); }