//HICUM Level_2 Version_2.24: A Verilog-A Description //dw 09/10: Modifications for ngspice and adms: // backup to ddx for capacitance calculation // all V(...) <+ 0.0; are replaced by I(...) < V(...)/`MIN_R; // using GMIN from ngspice: _circuit_gmin // switch of section for correlated noise (see below) // removed obsolete variables S_avl, f_p // don't like internal variable declaration //**************New Implementations***************** //****************************************************************************** //This code contains a Verilog-A implementation of Vertical Non-Quasi-Static(NQS) //Effects using adjunct gyrator networks. To turn on this effect please set FLNQS=1. //Although Vertical NQS effects have been taken into account in HICUM from the very //beginning (see original FTN code and built-in v2.1 HICUM model inside most of the //existing circuit simulators) their implementation has been based on Weil's approach. //However, using Verilog, it is presently not possible to implement Weil's approach, //since there does not exist access to previous time-steps of the simulatior. //The nearly available Verilog-A solution reproduces the results of previous //HICUM versions (cf. documentation). //****************************************************************************** //****************************************************************************** // Implementation of noise correlation // Please turn-off (by front slash “//”) the noise correlation code section for simulation with Spectre //****************************************************************************** // ***************Bug fix and optimization************* // 12/09: Elimination of 'ddx' operator for internal capacitance determination // Capacitances will be calculated by Analytical Equations // 10/09: Temperature coefficient (ZETAxyz) range modified to [-10:10] // 09/09: VPT ranges modified from [0:inf] to (0:inf] // 07/09: DT0H rabge modified from no range to (-inf:inf) // 03/09: Simplified input NQS adjacent circuit (RC network) // 04/08: New range has been defined for FDQR0. // 11/07: Bugs have been fixed in macro HICFCI and HICQFC // 10/06: in @(initial_model), external if-block for HICTUN_T removed // 11/06: within HICQFC, minor changes made for LATB<=0.01; // also HICFCI and HICFCT are changed accordingly // to ensure correct derivatives // Upper limit of FGEO parameter was changed to infinity. // 12/06: expressions for Cdei and Cdci are corrected not to include // Ccdei and Cbdci respectively (used in Crbi expression). // 01/06: FCdf1_dw assigned expression (missing in v2.21) // FCa and FCa1 are found to have same expression: FCa is omitted in those cases // FCa1 written instead of FCa in the expression for FCf_ci // Thermal node "tnode" set as external // zetasct = mg+1-2.5 changed to zetasct = mg-1.5; // Code optimization: Temperature dependent parts are moduled in two separate blocks: // within @(initial_model) when self-heating is OFF // outside @(initial_model) when self-heating is ON // 03/06 : Further fix // vlim_t,ibcis_t,ibcxs_t,itss_t,iscs_t considered in compatibility block // ddt() operators are separated in contribution expressions. // FLCOMP parameter is given different values // 05/06: // all if-else blocks marked with begin-end // unused variables deleted // all series resistors and RTH are allowed to have a minimum value MIN_R // only tunelling current source contribution within if-then-else // 06/06: HICRBI deleted and instead the code changed (hyperbolic smoothing in // conductivity modulation part) and put in relevant portion of the code. // 07/06: ddx() operator used to find out capacitances from charges: // QJMODF,QJMOD,HICJQ changed accordingly // Lateral NQS effect modified with ddx() operator. // HICFCT included for downward compatibility reason. // Few macros are taken inside the code: HICICK, HICAVL, HICTUN (more optimized), // internal base resistance (Qjci included under conductivity modulation, hyperbolic smoothing used) // Gmin added at (bi,ei) and (bi,ci) branches. // 08/06: Units added in the parameter descriptions. // ********************************************************************************* // 06/06: Comment on NODE COLLAPSING: // Presently this verilog code permits a minimum of 1 milli-Ohm resistance for any // series resistance as well as for thermal resistance RTH. If any of the resistance // values drops below this minimum value, the corresponding nodes are shorted with // zero voltage contribution. We want the model compilers/simulators deal this // situation in such a manner that the corresponding node is COLLAPSED. // We expect that the simulators should permit current contribution statement // for any branch with resistance value more than (or equal to) 1 milli-Ohm without // any convergence problem. In fact, we wish NOT to have to use a voltage contribution // statement in our Verilog code, except as an indication for the model compiler/simulator // to interprete a zero branch voltage as NODE-COLLAPSING action. // ********************************************************************************** //Default simulator: Spectre `ifdef insideADMS `define MODEL @(initial_model) `define NOISE @(noise) `define ATTR(txt) (*txt*) `else `define MODEL `define NOISE `define ATTR(txt) `endif `define VPT_thresh 1.0e2 `define Dexp_lim 80.0 `define Cexp_lim 80.0 `define DFa_fj 1.921812 `define RTOLC 1.0e-5 `define l_itmax 100 `define TMAX 326.85 `define TMIN -100.0 `define LN_EXP_LIMIT 11.0 `define MIN_R 0.001 //`define Gmin 1.0e-12 //`define Gmin $simparam("gmin",1e-12) //suggested by L.L //ADS //`include "constants.vams" //`include "disciplines.vams" //`include "compact.vams" //Spectre `include "constants.h" `include "discipline.h" //////////////Explicit Capacitance and Charge Expression/////////////// // DEPLETION CHARGE CALCULATION // Hyperbolic smoothing used; no punch-through // INPUT: // c_0 : zero-bias capacitance // u_d : built-in voltage // z : exponent coefficient // a_j : control parameter for C peak value at high forward bias // U_cap : voltage across junction // IMPLICIT INPUT: // VT : thermal voltage // OUTPUT: // Qz : depletion Charge // C : depletion capacitance `define QJMODF(c_0,u_d,z,a_j,U_cap,C,Qz)\ if(c_0 > 0.0) begin\ DFV_f = u_d*(1.0-exp(-ln(a_j)/z));\ DFv_e = (DFV_f-U_cap)/VT;\ DFs_q = sqrt(DFv_e*DFv_e+`DFa_fj);\ DFs_q2 = (DFv_e+DFs_q)*0.5;\ DFv_j = DFV_f-VT*DFs_q2;\ DFdvj_dv = DFs_q2/DFs_q;\ DFb = ln(1.0-DFv_j/u_d);\ DFC_j1 = c_0*exp(-z*DFb)*DFdvj_dv;\ C = DFC_j1+a_j*c_0*(1.0-DFdvj_dv);\ DFQ_j = c_0*u_d*(1.0-exp(DFb*(1.0-z)))/(1.0-z);\ Qz = DFQ_j+a_j*c_0*(U_cap-DFv_j);\ end else begin\ C = 0.0;\ Qz = 0.0;\ end //////////////////////////////////////////////////////////////// //////////////Explicit Capacitance and Charge Expression/////////////// // DEPLETION CHARGE CALCULATION CONSIDERING PUNCH THROUGH // smoothing of reverse bias region (punch-through) // and limiting to a_j=Cj,max/Cj0 for forward bias. // Important for base-collector and collector-substrate junction // INPUT: // c_0 : zero-bias capacitance // u_d : built-in voltage // z : exponent coefficient // a_j : control parameter for C peak value at high forward bias // v_pt : punch-through voltage (defined as qNw^2/2e) // U_cap : voltage across junction // IMPLICIT INPUT: // VT : thermal voltage // OUTPUT: // Qz : depletion charge // C : depletion capacitance `define QJMOD(c_0,u_d,z,a_j,v_pt,U_cap,C,Qz)\ if(c_0 > 0.0) begin\ Dz_r = z/4.0;\ Dv_p = v_pt-u_d;\ DV_f = u_d*(1.0-exp(-ln(a_j)/z));\ DC_max = a_j*c_0;\ DC_c = c_0*exp((Dz_r-z)*ln(v_pt/u_d));\ Dv_e = (DV_f-U_cap)/VT;\ if(Dv_e < `Cexp_lim) begin\ De = exp(Dv_e);\ De_1 = De/(1.0+De);\ Dv_j1 = DV_f-VT*ln(1.0+De);\ end else begin\ De_1 = 1.0;\ Dv_j1 = U_cap;\ end\ Da = 0.1*Dv_p+4.0*VT;\ Dv_r = (Dv_p+Dv_j1)/Da;\ if(Dv_r < `Cexp_lim) begin\ De = exp(Dv_r);\ De_2 = De/(1.0+De);\ Dv_j2 = -Dv_p+Da*ln(1.0+De);\ end else begin\ De_2 = 1.0;\ Dv_j2 = Dv_j1;\ end\ Dv_j4 = U_cap-Dv_j1;\ DCln1 = ln(1.0-Dv_j1/u_d);\ DCln2 = ln(1.0-Dv_j2/u_d);\ Dz1 = 1.0-z;\ Dzr1 = 1.0-Dz_r;\ DC_j1 = c_0*exp(DCln2*(-z))*De_1*De_2;\ DC_j2 = DC_c*exp(DCln1*(-Dz_r))*(1.0-De_2);\ DC_j3 = DC_max*(1.0-De_1);\ C = DC_j1+DC_j2+DC_j3;\ DQ_j1 = c_0*(1.0-exp(DCln2*Dz1))/Dz1;\ DQ_j2 = DC_c*(1.0-exp(DCln1*Dzr1))/Dzr1;\ DQ_j3 = DC_c*(1.0-exp(DCln2*Dzr1))/Dzr1;\ Qz = (DQ_j1+DQ_j2-DQ_j3)*u_d+DC_max*Dv_j4;\ end else begin\ C = 0.0;\ Qz = 0.0;\ end // DEPLETION CHARGE & CAPACITANCE CALCULATION SELECTOR // Dependent on junction punch-through voltage // Important for collector related junctions `define HICJQ(c_0,u_d,z,v_pt,U_cap,C,Qz)\ if(v_pt < `VPT_thresh) begin\ `QJMOD(c_0,u_d,z,2.4,v_pt,U_cap,C,Qz)\ end else begin\ `QJMODF(c_0,u_d,z,2.4,U_cap,C,Qz)\ end // A CALCULATION NEEDED FOR COLLECTOR MINORITY CHARGE FORMULATION // INPUT: // zb,zl : zeta_b and zeta_l (model parameters, TED 10/96) // w : normalized injection width // OUTPUT: // hicfcio : function of equation (2.1.17-10) `define HICFCI(zb,zl,w,hicfcio,dhicfcio_dw)\ z = zb*w;\ lnzb = ln(1+zb*w);\ if(z > 1.0e-6) begin\ x = 1.0+z;\ a = x*x;\ a2 = 0.250*(a*(2.0*lnzb-1.0)+1.0);\ a3 = (a*x*(3.0*lnzb-1.0)+1.0)/9.0;\ r = zl/zb;\ hicfcio = ((1.0-r)*a2+r*a3)/zb;\ dhicfcio_dw = ((1.0-r)*x+r*a)*lnzb;\ end else begin\ a = z*z;\ a2 = 3.0+z-0.25*a+0.10*z*a;\ a3 = 2.0*z+0.75*a-0.20*a*z;\ hicfcio = (zb*a2+zl*a3)*w*w/6.0;\ dhicfcio_dw = (1+zl*w)*(1+z)*lnzb;\ end // NEEDED TO CALCULATE WEIGHTED ICCR COLLECTOR MINORITY CHARGE // INPUT: // z : zeta_b or zeta_l // w : normalized injection width // OUTPUT: // hicfcto : output // dhicfcto_dw : derivative of output wrt w `define HICFCT(z,w,hicfcto,dhicfcto_dw)\ a = z*w;\ lnz = ln(1+z*w);\ if (a > 1.0e-6) begin\ hicfcto = (a - lnz)/z;\ dhicfcto_dw = a / (1.0 + a);\ end else begin\ hicfcto = 0.5 * a * w;\ dhicfcto_dw = a;\ end // COLLECTOR CURRENT SPREADING CALCULATION // collector minority charge incl. 2D/3D current spreading (TED 10/96) // INPUT: // Ix : forward transport current component (itf) // I_CK : critical current // FFT_pcS : dependent on fthc and thcs (parameters) // IMPLICIT INPUT: // ahc, latl, latb : model parameters // VT : thermal voltage // OUTPUT: // Q_fC, Q_CT: actual and ICCR (weighted) hole charge // T_fC, T_cT: actual and ICCR (weighted) transit time // Derivative dfCT_ditf not properly implemented yet `define HICQFC(Ix,I_CK,FFT_pcS,Q_fC,Q_CT,T_fC,T_cT)\ Q_fC = FFT_pcS*Ix;\ FCa = 1.0-I_CK/Ix;\ FCrt = sqrt(FCa*FCa+ahc);\ FCa_ck = 1.0-(FCa+FCrt)/(1.0+sqrt(1.0+ahc));\ FCdaick_ditf = (FCa_ck-1.0)*(1-FCa)/(FCrt*Ix);\ if(latb > latl) begin\ FCz = latb-latl;\ FCxl = 1.0+latl;\ FCxb = 1.0+latb;\ if(latb > 0.01) begin\ FCln = ln(FCxb/FCxl);\ FCa1 = exp((FCa_ck-1.0)*FCln);\ FCd_a = 1.0/(latl-FCa1*latb);\ FCw = (FCa1-1.0)*FCd_a;\ FCdw_daick = -FCz*FCa1*FCln*FCd_a*FCd_a;\ FCa1 = ln((1.0+latb*FCw)/(1.0+latl*FCw));\ FCda1_dw = latb/(1.0+latb*FCw) - latl/(1.0+latl*FCw);\ end else begin\ FCf1 = 1.0-FCa_ck;\ FCd_a = 1.0/(1.0+FCa_ck*latb);\ FCw = FCf1*FCd_a;\ FCdw_daick = -1.0*FCd_a*FCd_a*FCxb*FCd_a;\ FCa1 = FCz*FCw;\ FCda1_dw = FCz;\ end\ FCf_CT = 2.0/FCz;\ FCw2 = FCw*FCw;\ FCf1 = latb*latl*FCw*FCw2/3.0+(latb+latl)*FCw2/2.0+FCw;\ FCdf1_dw = latb*latl*FCw2 + (latb+latl)*FCw + 1.0;\ `HICFCI(latb,latl,FCw,FCf2,FCdf2_dw)\ `HICFCI(latl,latb,FCw,FCf3,FCdf3_dw)\ FCf_ci = FCf_CT*(FCa1*FCf1-FCf2+FCf3);\ FCdfc_dw = FCf_CT*(FCa1*FCdf1_dw+FCda1_dw*FCf1-FCdf2_dw+FCdf3_dw);\ FCdw_ditf = FCdw_daick*FCdaick_ditf;\ FCdfc_ditf = FCdfc_dw*FCdw_ditf;\ if(flcomp == 0.0 || flcomp == 2.1) begin\ `HICFCT(latb,FCw,FCf2,FCdf2_dw)\ `HICFCT(latl,FCw,FCf3,FCdf3_dw)\ FCf_CT = FCf_CT*(FCf2-FCf3);\ FCdfCT_dw = FCf_CT*(FCdf2_dw-FCdf3_dw);\ FCdfCT_ditf = FCdfCT_dw*FCdw_ditf;\ end else begin\ FCf_CT = FCf_ci;\ FCdfCT_ditf = FCdfc_ditf;\ end\ end else begin\ if(latb > 0.01) begin\ FCd_a = 1.0/(1.0+FCa_ck*latb);\ FCw = (1.0-FCa_ck)*FCd_a;\ FCdw_daick = -(1.0+latb)*FCd_a*FCd_a;\ end else begin\ FCw = 1.0-FCa_ck-FCa_ck*latb;\ FCdw_daick = -(1.0+latb);\ end\ FCw2 = FCw*FCw;\ FCz = latb*FCw;\ FCz_1 = 1.0+FCz;\ FCd_f = 1.0/(FCz_1);\ FCf_ci = FCw2*(1.0+FCz/3.0)*FCd_f;\ FCdfc_dw = 2.0*FCw*(FCz_1+FCz*FCz/3.0)*FCd_f*FCd_f;\ FCdw_ditf = FCdw_daick*FCdaick_ditf;\ FCdfc_ditf = FCdfc_dw*FCdw_ditf;\ if(flcomp == 0.0 || flcomp == 2.1) begin\ if (FCz > 0.001) begin\ FCf_CT = 2.0*(FCz_1*ln(FCz_1)-FCz)/(latb*latb*FCz_1);\ FCdfCT_dw = 2.0*FCw*FCd_f*FCd_f;\ end else begin\ FCf_CT = FCw2*(1.0-FCz/3.0)*FCd_f;\ FCdfCT_dw = 2.0*FCw*(1.0-FCz*FCz/3.0)*FCd_f*FCd_f;\ end\ FCdfCT_ditf = FCdfCT_dw*FCdw_ditf;\ end else begin\ FCf_CT = FCf_ci;\ FCdfCT_ditf = FCdfc_ditf;\ end\ end\ Q_CT = Q_fC*FCf_CT;\ Q_fC = Q_fC*FCf_ci;\ T_fC = FFT_pcS*(FCf_ci+Ix*FCdfc_ditf);\ T_cT = FFT_pcS*(FCf_CT+Ix*FCdfCT_ditf); // TRANSIT-TIME AND STORED MINORITY CHARGE // INPUT: // itf : forward transport current // I_CK : critical current // T_f : transit time \ // Q_f : minority charge / for low current // IMPLICIT INPUT: // tef0, gtfe, fthc, thcs, ahc, latl, latb : model parameters // OUTPUT: // T_f : transit time \ // Q_f : minority charge / transient analysis // T_fT : transit time \ // Q_fT : minority charge / ICCR (transfer current) // Q_bf : excess base charge `define HICQFF(itf,I_CK,T_f,Q_f,T_fT,Q_fT,Q_bf)\ if(itf < 1.0e-6*I_CK) begin\ Q_fT = Q_f;\ T_fT = T_f;\ end else begin\ FFa = I_CK/itf;\ FFd_TfE = tef0_t*exp(-gtfe*ln(FFa));\ FFd_QfE = FFd_TfE*itf/(gtfe+1.0);\ FFT_fbS = (1.0-fthc)*thcs_t;\ FFx = 1.0-FFa;\ FFs = sqrt(FFx*FFx+ahc);\ FFw = (FFx+FFs)/(1.0+sqrt(1.0+ahc));\ FFw_2 = FFw*FFw;\ FFd_QfB = FFT_fbS*itf*FFw_2;\ Q_bf = FFd_QfB;\ FFa_w = FFw_2*(1.0+2.0*FFa/FFs);\ FFd_TfB = FFT_fbS*FFa_w;\ FFT_pcS = fthc*thcs_t;\ if(latb <= 0.0 && latl <= 0.0) begin\ FFQ_fC = FFT_pcS*itf*FFw_2;\ FFT_fC = FFT_pcS*FFa_w;\ FFQ_cT = FFQ_fC;\ FFT_cT = FFT_fC;\ end else begin\ `HICQFC(itf,I_CK,FFT_pcS,FFQ_fC,FFQ_cT,FFT_fC,FFT_cT)\ end\ Q_f = Q_f+FFd_QfB;\ T_f = T_f+FFd_TfB;\ Q_fT = Q_f+hfe*FFd_QfE+hfc*FFQ_cT;\ T_fT = T_f+hfe*FFd_TfE+hfc*FFT_cT;\ Q_f = Q_f+FFd_QfE+FFQ_fC;\ T_f = T_f+FFd_TfE+FFT_fC;\ end // IDEAL DIODE (WITHOUT CAPACITANCE): // conductance calculation not required // INPUT: // IS, IST : saturation currents (model parameter related) // UM1 : ideality factor // U : branch voltage // IMPLICIT INPUT: // VT : thermal voltage // OUTPUT: // Iz : diode current `define HICDIO(IS,IST,UM1,U,Iz)\ DIOY = U/(UM1*VT);\ if (IS > 0.0) begin\ if (DIOY > `Dexp_lim) begin\ le = (1 + (DIOY - `Dexp_lim));\ DIOY = `Dexp_lim;\ end else begin\ le = 1;\ end\ le = le*limexp(DIOY);\ Iz = IST*(le-1.0);\ if(DIOY <= -14.0) begin\ Iz = -IST;\ end\ end else begin\ Iz = 0.0;\ end // TEMPERATURE UPDATE OF JUNCTION CAPACITANCE RELATED PARAMETERS // INPUT: // mostly model parameters // x : zero bias junction capacitance // y : junction built-in potencial // z : grading co-efficient // w : ratio of maximum to zero-bias value of capacitance or punch-through voltage // is_al : condition factor to check what "w" stands for // vgeff : band-gap voltage // IMPLICIT INPUT: // VT : thermal voltage // vt0,qtt0,ln_qtt0,mg : other model variables // OUTPUT: // c_j_t : temperature update of "c_j" // vd_t : temperature update of "vd0" // w_t : temperature update of "w" `define TMPHICJ(c_j,vd0,z,w,is_al,vgeff,c_j_t,vd_t,w_t)\ if (c_j > 0.0) begin\ vdj0 = 2*vt0*ln(exp(vd0*0.5/vt0)-exp(-0.5*vd0/vt0));\ vdjt = vdj0*qtt0+vgeff*(1-qtt0)-mg*VT*ln_qtt0;\ vdt = vdjt+2*VT*ln(0.5*(1+sqrt(1+4*exp(-vdjt/VT))));\ vd_t = vdt;\ c_j_t = c_j*exp(z*ln(vd0/vd_t));\ if (is_al == 1) begin\ w_t = w*vd_t/vd0;\ end else begin\ w_t = w;\ end\ end else begin\ c_j_t = c_j;\ vd_t = vd0;\ w_t = w;\ end module hic2_full (c,b,e,s,tnode); //Node definitions inout c,b,e,s,tnode; electrical c,b,e,s,ci,ei,bp,bi,si; electrical xf1,xf2; electrical xf; //RC nw electrical tnode; electrical n1,n2; //Branch definitions branch (b,bp) br_bbp_i; branch (b,bp) br_bbp_v; branch (ci,c) br_cic_i; branch (ci,c) br_cic_v; branch (ei,e) br_eie_i; branch (ei,e) br_eie_v; branch (bp,bi) br_bpbi_i; branch (bp,bi) br_bpbi_v; branch (si,s) br_sis_i; branch (si,s) br_sis_v; branch (bi,ei) br_biei; branch (bi,ci) br_bici; branch (ci,bi) br_cibi; branch (ci,ei) br_ciei; branch (ei,ci) br_eici; branch (bp,e) br_bpe; branch (b,e) br_be; branch (bp,ei) br_bpei; branch (bp,ci) br_bpci; branch (b,ci) br_bci; branch (si,ci) br_sici; branch (bp,si) br_bpsi; branch (tnode ) br_sht; //Phase network for ITF branch (xf1 ) br_bxf1; branch (xf1 ) br_cxf1; branch (xf2 ) br_bxf2; branch (xf2 ) br_cxf2; //Phase network for QF branch (xf ) br_bxf; //for RC nw branch (xf ) br_cxf; //for RC nw //Noise branch (n1 ) b_n1; branch (n2 ) b_n2; // -- ########################################################### // -- ########### Parameters initialization ################ // -- ########################################################### //Transfer current parameter real c10 = 2.0E-30 from [0:1] `ATTR(info="GICCR constant" unit="A^2s"); parameter real qp0 = 2.0E-14 from (0:1] `ATTR(info="Zero-bias hole charge" unit="Coul"); parameter real ich = 0.0 from [0:inf) `ATTR(info="High-current correction for 2D and 3D effects" unit="A"); //`0' signifies infinity parameter real hfe = 1.0 from [0:inf] `ATTR(info="Emitter minority charge weighting factor in HBTs"); parameter real hfc = 1.0 from [0:inf] `ATTR(info="Collector minority charge weighting factor in HBTs"); parameter real hjei = 1.0 from [0:100] `ATTR(info="B-E depletion charge weighting factor in HBTs"); parameter real hjci = 1.0 from [0:100] `ATTR(info="B-C depletion charge weighting factor in HBTs"); //Base-Emitter diode currents parameter real ibeis = 1.0E-18 from [0:1] `ATTR(info="Internal B-E saturation current" unit="A"); parameter real mbei = 1.0 from (0:10] `ATTR(info="Internal B-E current ideality factor"); parameter real ireis = 0.0 from [0:1] `ATTR(info="Internal B-E recombination saturation current" unit="A"); parameter real mrei = 2.0 from (0:10] `ATTR(info="Internal B-E recombination current ideality factor"); parameter real ibeps = 0.0 from [0:1] `ATTR(info="Peripheral B-E saturation current" unit="A"); parameter real mbep = 1.0 from (0:10] `ATTR(info="Peripheral B-E current ideality factor"); parameter real ireps = 0.0 from [0:1] `ATTR(info="Peripheral B-E recombination saturation current" unit="A"); parameter real mrep = 2.0 from (0:10] `ATTR(info="Peripheral B-E recombination current ideality factor"); parameter real mcf = 1.0 from (0:10] `ATTR(info="Non-ideality factor for III-V HBTs"); //Transit time for excess recombination current at b-c barrier parameter real tbhrec = 0.0 from [0:inf) `ATTR(info="Base current recombination time constant at B-C barrier for high forward injection" unit="s"); //Base-Collector diode currents parameter real ibcis = 1.0E-16 from [0:1.0] `ATTR(info="Internal B-C saturation current" unit="A"); parameter real mbci = 1.0 from (0:10] `ATTR(info="Internal B-C current ideality factor"); parameter real ibcxs = 0.0 from [0:1.0] `ATTR(info="External B-C saturation current" unit="A"); parameter real mbcx = 1.0 from (0:10] `ATTR(info="External B-C current ideality factor"); //Base-Emitter tunneling current parameter real ibets = 0.0 from [0:1] `ATTR(info="B-E tunneling saturation current" unit="A"); parameter real abet = 40 from [0:inf) `ATTR(info="Exponent factor for tunneling current"); parameter integer tunode= 1 from [0:1] `ATTR(info="Specifies the base node connection for the tunneling current"); // =1 signifies perimeter node //Base-Collector avalanche current parameter real favl = 0.0 from [0:inf) `ATTR(info="Avalanche current factor" unit="1/V"); parameter real qavl = 0.0 from [0:inf) `ATTR(info="Exponent factor for avalanche current" unit="Coul"); parameter real alfav = 0.0 `ATTR(info="Relative TC for FAVL" unit="1/K"); parameter real alqav = 0.0 `ATTR(info="Relative TC for QAVL" unit="1/K"); //Series resistances parameter real rbi0 = 0.0 from [0:inf) `ATTR(info="Zero bias internal base resistance" unit="Ohm"); parameter real rbx = 0.0 from [0:inf) `ATTR(info="External base series resistance" unit="Ohm"); parameter real fgeo = 0.6557 from [0:inf] `ATTR(info="Factor for geometry dependence of emitter current crowding"); parameter real fdqr0 = 0.0 from [-0.5:100] `ATTR(info="Correction factor for modulation by B-E and B-C space charge layer"); parameter real fcrbi = 0.0 from [0:1] `ATTR(info="Ratio of HF shunt to total internal capacitance (lateral NQS effect)"); parameter real fqi = 1.0 from [0:1] `ATTR(info="Ration of internal to total minority charge"); parameter real re = 0.0 from [0:inf) `ATTR(info="Emitter series resistance" unit="Ohm"); parameter real rcx = 0.0 from [0:inf) `ATTR(info="External collector series resistance" unit="Ohm"); //Substrate transistor parameter real itss = 0.0 from [0:1.0] `ATTR(info="Substrate transistor transfer saturation current" unit="A"); parameter real msf = 1.0 from (0:10] `ATTR(info="Forward ideality factor of substrate transfer current"); parameter real iscs = 0.0 from [0:1.0] `ATTR(info="C-S diode saturation current" unit="A"); parameter real msc = 1.0 from (0:10] `ATTR(info="Ideality factor of C-S diode current"); parameter real tsf = 0.0 from [0:inf) `ATTR(info="Transit time for forward operation of substrate transistor" unit="s"); //Intra-device substrate coupling parameter real rsu = 0.0 from [0:inf) `ATTR(info="Substrate series resistance" unit="Ohm"); parameter real csu = 0.0 from [0:inf) `ATTR(info="Substrate shunt capacitance" unit="F"); //Depletion Capacitances parameter real cjei0 = 1.0E-20 from [0:inf) `ATTR(info="Internal B-E zero-bias depletion capacitance" unit="F"); parameter real vdei = 0.9 from (0:10] `ATTR(info="Internal B-E built-in potential" unit="V"); parameter real zei = 0.5 from (0:1] `ATTR(info="Internal B-E grading coefficient"); parameter real ajei = 2.5 from [1:inf) `ATTR(info="Ratio of maximum to zero-bias value of internal B-E capacitance"); parameter real cjep0 = 1.0E-20 from [0:inf) `ATTR(info="Peripheral B-E zero-bias depletion capacitance" unit="F"); parameter real vdep = 0.9 from (0:10] `ATTR(info="Peripheral B-E built-in potential" unit="V"); parameter real zep = 0.5 from (0:1] `ATTR(info="Peripheral B-E grading coefficient"); parameter real ajep = 2.5 from [1:inf) `ATTR(info="Ratio of maximum to zero-bias value of peripheral B-E capacitance"); parameter real cjci0 = 1.0E-20 from [0:inf) `ATTR(info="Internal B-C zero-bias depletion capacitance" unit="F"); parameter real vdci = 0.7 from (0:10] `ATTR(info="Internal B-C built-in potential" unit="V"); parameter real zci = 0.4 from (0:1] `ATTR(info="Internal B-C grading coefficient"); parameter real vptci = 100 from (0:100] `ATTR(info="Internal B-C punch-through voltage" unit="V"); parameter real cjcx0 = 1.0E-20 from [0:inf) `ATTR(info="External B-C zero-bias depletion capacitance" unit="F"); parameter real vdcx = 0.7 from (0:10] `ATTR(info="External B-C built-in potential" unit="V"); parameter real zcx = 0.4 from (0:1] `ATTR(info="External B-C grading coefficient"); parameter real vptcx = 100 from (0:100] `ATTR(info="External B-C punch-through voltage" unit="V"); parameter real fbcpar = 0.0 from [0:1] `ATTR(info="Partitioning factor of parasitic B-C cap"); parameter real fbepar = 1.0 from [0:1] `ATTR(info="Partitioning factor of parasitic B-E cap"); parameter real cjs0 = 0.0 from [0:inf) `ATTR(info="C-S zero-bias depletion capacitance" unit="F"); parameter real vds = 0.6 from (0:10] `ATTR(info="C-S built-in potential" unit="V"); parameter real zs = 0.5 from (0:1] `ATTR(info="C-S grading coefficient"); parameter real vpts = 100 from (0:100] `ATTR(info="C-S punch-through voltage" unit="V"); //Diffusion Capacitances parameter real t0 = 0.0 from [0:inf) `ATTR(info="Low current forward transit time at VBC=0V" unit="s"); parameter real dt0h = 0.0 from (-inf:inf) `ATTR(info="Time constant for base and B-C space charge layer width modulation" unit="s"); parameter real tbvl = 0.0 from [0:inf) `ATTR(info="Time constant for modelling carrier jam at low VCE" unit="s"); parameter real tef0 = 0.0 from [0:inf) `ATTR(info="Neutral emitter storage time" unit="s"); parameter real gtfe = 1.0 from (0:10] `ATTR(info="Exponent factor for current dependence of neutral emitter storage time"); parameter real thcs = 0.0 from [0:inf) `ATTR(info="Saturation time constant at high current densities" unit="s"); parameter real ahc = 0.1 from (0:10] `ATTR(info="Smoothing factor for current dependence of base and collector transit time"); parameter real fthc = 0.0 from [0:1] `ATTR(info="Partitioning factor for base and collector portion"); parameter real rci0 = 150 from (0:inf) `ATTR(info="Internal collector resistance at low electric field" unit="Ohm"); parameter real vlim = 0.5 from (0:10] `ATTR(info="Voltage separating ohmic and saturation velocity regime" unit="V"); parameter real vces = 0.1 from [0:1] `ATTR(info="Internal C-E saturation voltage" unit="V"); parameter real vpt = 100.0 from (0:inf] `ATTR(info="Collector punch-through voltage" unit="V"); // `0' signifies infinity parameter real tr = 0.0 from [0:inf) `ATTR(info="Storage time for inverse operation" unit="s"); //Isolation Capacitances parameter real cbepar = 0.0 from [0:inf) `ATTR(info="Total parasitic B-E capacitance" unit="F"); parameter real cbcpar = 0.0 from [0:inf) `ATTR(info="Total parasitic B-C capacitance" unit="F"); //Non-quasi-static Effect parameter real alqf = 0.0 from [0:1] `ATTR(info="Factor for additional delay time of minority charge"); parameter real alit = 0.0 from [0:1] `ATTR(info="Factor for additional delay time of transfer current"); parameter integer flnqs = 0 from [0:1] `ATTR(info="Flag for turning on and off of vertical NQS effect"); //Noise parameter real kf = 0.0 from [0:inf) `ATTR(info="Flicker noise coefficient"); parameter real af = 2.0 from (0:10] `ATTR(info="Flicker noise exponent factor"); parameter integer cfbe = -1 from [-2:-1] `ATTR(info="Flag for determining where to tag the flicker noise source"); //Lateral Geometry Scaling (at high current densities) parameter real latb = 0.0 from [0:inf) `ATTR(info="Scaling factor for collector minority charge in direction of emitter width"); parameter real latl = 0.0 from [0:inf) `ATTR(info="Scaling factor for collector minority charge in direction of emitter length"); //Temperature dependence parameter real vgb = 1.17 from (0:10] `ATTR(info="Bandgap voltage extrapolated to 0 K" unit="V"); parameter real alt0 = 0.0 `ATTR(info="First order relative TC of parameter T0" unit="1/K"); parameter real kt0 = 0.0 `ATTR(info="Second order relative TC of parameter T0"); parameter real zetaci = 0.0 from [-10:10] `ATTR(info="Temperature exponent for RCI0"); parameter real alvs = 0.0 `ATTR(info="Relative TC of saturation drift velocity" unit="1/K"); parameter real alces = 0.0 `ATTR(info="Relative TC of VCES" unit="1/K"); parameter real zetarbi = 0.0 from [-10:10] `ATTR(info="Temperature exponent of internal base resistance"); parameter real zetarbx = 0.0 from [-10:10] `ATTR(info="Temperature exponent of external base resistance"); parameter real zetarcx = 0.0 from [-10:10] `ATTR(info="Temperature exponent of external collector resistance"); parameter real zetare = 0.0 from [-10:10] `ATTR(info="Temperature exponent of emitter resistance"); parameter real zetacx = 1.0 from [-10:10] `ATTR(info="Temperature exponent of mobility in substrate transistor transit time"); parameter real vge = 1.17 from (0:10] `ATTR(info="Effective emitter bandgap voltage" unit="V"); parameter real vgc = 1.17 from (0:10] `ATTR(info="Effective collector bandgap voltage" unit="V"); parameter real vgs = 1.17 from (0:10] `ATTR(info="Effective substrate bandgap voltage" unit="V"); parameter real f1vg =-1.02377e-4 `ATTR(info="Coefficient K1 in T-dependent band-gap equation"); parameter real f2vg = 4.3215e-4 `ATTR(info="Coefficient K2 in T-dependent band-gap equation"); parameter real zetact = 3.0 from [-10:10] `ATTR(info="Exponent coefficient in transfer current temperature dependence"); parameter real zetabet = 3.5 from [-10:10] `ATTR(info="Exponent coefficient in B-E junction current temperature dependence"); parameter real alb = 0.0 `ATTR(info="Relative TC of forward current gain for V2.1 model" unit="1/K"); //Self-Heating parameter integer flsh = 0 from [0:2] `ATTR(info="Flag for turning on and off self-heating effect"); parameter real rth = 0.0 from [0:inf) `ATTR(info="Thermal resistance" unit="K/W"); parameter real cth = 0.0 from [0:inf) `ATTR(info="Thermal capacitance" unit="J/W"); //Compatibility with V2.1 parameter real flcomp = 0.0 from [0:inf) `ATTR(info="Flag for compatibility with v2.1 model (0=v2.1)"); //Circuit simulator specific parameters parameter real tnom = 27.0 `ATTR(info="Temperature at which parameters are specified" unit="C"); parameter real dt = 0.0 `ATTR(info="Temperature change w.r.t. chip temperature for particular transistor" unit="K"); // //======================== Transistor model formulation =================== // //Declaration of variables real _circuit_gmin; //Temperature and drift real VT,Tdev,qtt0,ln_qtt0,r_VgVT,V_gT,dT,k; real ireis_t,ibeis_t,ibcxs_t,ibcis_t,iscs_t,cjci0_t; real cjs0_t,rci0_t,vlim_t,vces_t,thcs_t,tef0_t,rbi0_t; real rbx_t,rcx_t,re_t,t0_t,vdei_t,vdci_t,vpts_t,itss_t,tsf_t; real c10_t,cjei0_t,qp0_t,vdcx_t,vptcx_t,cjcx01_t,cjcx02_t; real qjcx0_t_i,qjcx0_t_ii,cratio_t,c_dummy; real ibeps_t,ireps_t,cjep0_t; real ajei_t,qavl_t,favl_t,ibets_t,abet_t,vptci_t,vdep_t,ajep_t,zetatef; real k1,k2,dvg0,vge_t,vgb_t,vgbe_t,vds_t,vt0,Tnom,Tamb,a,avs; real zetabci,zetabcxt,zetasct,vgbe0,mg,vgb_t0,vge_t0,vgbe_t0,vgbc0,vgsc0; real cbcpar1,cbcpar2,cbepar2,cbepar1,Oich,Ovpt,Otbhrec; //Charges, capacitances and currents real Qjci,Qjei,Qjep; real it,ibei,irei,ibci,ibep,irep,ibh_rec; real Qdei,Qdci,qrbi; real ibet,iavl; real ijbcx,ijsc,Qjs,HSUM,HSI_Tsu,Qdsu; //Base resistance and self-heating power real rbi,pterm; //Variables for macro TMPHICJ real vdj0,vdjt,vdt; //Model initialization real k10,k20,C_1; //Model evaluation real Cjci,Cjcit,cc,Cjei,Cjep; real itf,itr,Tf,Tr,VT_f,i_0f,i_0r,a_bpt,Q_0,Q_p,Q_bpt; real Orci0_t,b_q,Q_fC,T_fC,T_cT,I_Tf1,T_f0,Q_fT,T_fT,Q_bf; real ICKa,d1; real A,a_h,Q_pT,d_Q,d_Q0; real Qf,Cdei,Qr,Cdci,Crbi; real ick,vc,vceff,cjcx01,cjcx02,HSa,HSb; integer l_it; //Variables for macros real DIOY,le;//HICDIO real FFT_fbS,FFa,FFx,FFs,FFw,FFw_2,FFd_QfB,FFd_TfB,FFT_pcS,FFQ_fC,FFT_fC,FFQ_cT,FFT_cT,FFd_TfE,FFd_QfE,FFa_w;//HICQFF real FCz,FCw2,FCf1,FCf2,FCf3,FCf_ci,FCz_1,FCa1,FCa_ck,FCxl,FCxb;//HICQFC real FCd_a,FCdaick_ditf,FCa,FCw,FCdw_daick,FCdfc_dw,FCdw_ditf,FCdfc_ditf,FCf_CT,FCdfCT_ditf,FCrt,FCln,lnz,FCda1_dw,FCdf1_dw,FCdf2_dw,FCdf3_dw,FCd_f,FCdfCT_dw;//HICQFC real Dz_r,Dv_p,DV_f,DC_max,DC_c,Da,Dv_e,De,De_1,Dv_j1,Dv_r,De_2,Dv_j2,Dv_j4,DQ_j1,DQ_j2,DQ_j3,DCln1,DCln2,Dz1,Dzr1,DC_j1,DC_j2,DC_j3;//QJMOD real DFV_f,DFv_e,DFv_j,DFb,DFQ_j,DFs_q,DFs_q2,DFdvj_dv,DFC_j1;//QJMODF real z,a2,a3,r,x;//HICFCI real zb,zl,lnzb,w,hicfcio,dhicfcio_dw; //HICFCT //Noise real fourkt,twoq,flicker_Pwr; real thermal_Rbx,thermal_Rbi,thermal_Rcx,thermal_Re,betad,betan,betadin,betadc,icn,icn1,icn2; //NQS real Ixf1,Ixf2,Qxf1,Qxf2,Vxf1,Vxf2,Itxf,TD1,Qdeix; real T, Vxf, Ixf, Qxf,fact; real pocce,czz; real Qz_nom,f_QR,ETA,Qz0,fQz; real v_bord,v_q,U0,av,avl; real cV_f,cv_e,cs_q,cs_q2,cv_j,cdvj_dv; real a_eg,ab,aa; //end of variables analog begin `MODEL begin : Model_initialization Tnom = tnom+`P_CELSIUS0; Tamb = $temperature; vt0 = `P_K*Tnom /`P_Q; k10 = f1vg*Tnom*ln(Tnom); k20 = f2vg*Tnom; avs = alvs*Tnom; vgb_t0 = vgb+k10+k20; vge_t0 = vge+k10+k20; vgbe_t0 = (vgb_t0+vge_t0)/2; vgbe0 = (vgb+vge)/2; vgbc0 = (vgb+vgc)/2; vgsc0 = (vgs+vgc)/2; mg = 3-`P_Q*f1vg/`P_K; zetabci = mg+1-zetaci; zetabcxt= mg+1-zetacx; zetasct = mg-1.5; //Depletion capacitance splitting at b-c junction //Capacitances at peripheral and external base node C_1 = (1.0-fbcpar)*(cjcx0+cbcpar); if (C_1 >= cbcpar) begin cbcpar1 = cbcpar; cbcpar2 = 0.0; cjcx01 = C_1-cbcpar; cjcx02 = cjcx0-cjcx01; end else begin cbcpar1 = C_1; cbcpar2 = cbcpar-cbcpar1; cjcx01 = 0.0; cjcx02 = cjcx0; end //Parasitic b-e capacitance partitioning: No temperature dependence cbepar2 = fbepar*cbepar; cbepar1 = cbepar-cbepar2; //Avoid devide-by-zero and define infinity other way //High current correction for 2D and 3D effects if (ich != 0.0) begin Oich = 1.0/ich; end else begin Oich = 0.0; end //Base current recombination time constant at b-c barrier if (tbhrec != 0.0) begin Otbhrec = 1.0/tbhrec; end else begin Otbhrec = 0.0; end // Temperature and resulting parameter drift if (flsh==0 || rth < `MIN_R) begin : Thermal_updat_without_self_heating Tdev = Tamb+dt; if(Tdev < `TMIN + 273.15) begin Tdev = `TMIN + 273.15; end else begin if (Tdev > `TMAX + 273.15) begin Tdev = `TMAX + 273.15; end end VT = `P_K*Tdev /`P_Q; dT = Tdev-Tnom; qtt0 = Tdev/Tnom; ln_qtt0 = ln(qtt0); k1 = f1vg*Tdev*ln(Tdev); k2 = f2vg*Tdev; vgb_t = vgb+k1+k2; vge_t = vge+k1+k2; vgbe_t = (vgb_t+vge_t)/2; //Internal b-e junction capacitance `TMPHICJ(cjei0,vdei,zei,ajei,1,vgbe0,cjei0_t,vdei_t,ajei_t) if (flcomp == 0.0 || flcomp == 2.1) begin V_gT = 3.0*VT*ln_qtt0 + vgb*(qtt0-1.0); r_VgVT = V_gT/VT; //Internal b-e diode saturation currents a = mcf*r_VgVT/mbei - alb*dT; ibeis_t = ibeis*exp(a); a = mcf*r_VgVT/mrei - alb*dT; ireis_t = ireis*exp(a); a = mcf*r_VgVT/mbep - alb*dT; //Peripheral b-e diode saturation currents ibeps_t = ibeps*exp(a); a = mcf*r_VgVT/mrep - alb*dT; ireps_t = ireps*exp(a); //Internal b-c diode saturation current a = r_VgVT/mbci; ibcis_t = ibcis*exp(a); //External b-c diode saturation currents a = r_VgVT/mbcx; ibcxs_t = ibcxs*exp(a); //Saturation transfer current for substrate transistor a = r_VgVT/msf; itss_t = itss*exp(a); //Saturation current for c-s diode a = r_VgVT/msc; iscs_t = iscs*exp(a); //Zero bias hole charge a = vdei_t/vdei; qp0_t = qp0*(1.0+0.5*zei*(1.0-a)); //Voltage separating ohmic and saturation velocity regime a = vlim*(1.0-alvs*dT)*exp(zetaci*ln_qtt0); k = (a-VT)/VT; if (k < `LN_EXP_LIMIT) begin vlim_t = VT + VT*ln(1.0+exp(k)); end else begin vlim_t = a; end //Neutral emitter storage time a = 1.0+alb*dT; k = 0.5*(a+sqrt(a*a+0.01)); tef0_t = tef0*qtt0/k; end else begin //Internal b-e diode saturation currents ibeis_t = ibeis*exp(zetabet*ln_qtt0+vge/VT*(qtt0-1)); ireis_t = ireis*exp(0.5*mg*ln_qtt0+0.5*vgbe0/VT*(qtt0-1)); //Peripheral b-e diode saturation currents ibeps_t = ibeps*exp(zetabet*ln_qtt0+vge/VT*(qtt0-1)); ireps_t = ireps*exp(0.5*mg*ln_qtt0+0.5*vgbe0/VT*(qtt0-1)); //Internal b-c diode saturation currents ibcis_t = ibcis*exp(zetabci*ln_qtt0+vgc/VT*(qtt0-1)); //External b-c diode saturation currents ibcxs_t = ibcxs*exp(zetabcxt*ln_qtt0+vgc/VT*(qtt0-1)); //Saturation transfer current for substrate transistor itss_t = itss*exp(zetasct*ln_qtt0+vgc/VT*(qtt0-1)); //Saturation current for c-s diode iscs_t = iscs*exp(zetasct*ln_qtt0+vgs/VT*(qtt0-1)); //Zero bias hole charge a = exp(zei*ln(vdei_t/vdei)); qp0_t = qp0*(2.0-a); //Voltage separating ohmic and saturation velocity regime vlim_t = vlim*exp((zetaci-avs)*ln_qtt0); //Neutral emitter storage time zetatef = zetabet-zetact-0.5; dvg0 = vgb-vge; tef0_t = tef0*exp(zetatef*ln_qtt0-dvg0/VT*(qtt0-1)); end //GICCR prefactor c10_t = c10*exp(zetact*ln_qtt0+vgb/VT*(qtt0-1)); // Low-field internal collector resistance rci0_t = rci0*exp(zetaci*ln_qtt0); //Voltage separating ohmic and saturation velocity regime //vlim_t = vlim*exp((zetaci-avs)*ln_qtt0); //Internal c-e saturation voltage vces_t = vces*(1+alces*dT); //Internal b-c diode saturation current //ibcis_t = ibcis*exp(zetabci*ln_qtt0+vgc/VT*(qtt0-1)); //Internal b-c junction capacitance `TMPHICJ(cjci0,vdci,zci,vptci,0,vgbc0,cjci0_t,vdci_t,vptci_t) //Low-current forward transit time t0_t = t0*(1+alt0*dT+kt0*dT*dT); //Saturation time constant at high current densities thcs_t = thcs*exp((zetaci-1)*ln_qtt0); //Avalanche caurrent factors favl_t = favl*exp(alfav*dT); qavl_t = qavl*exp(alqav*dT); //Zero bias internal base resistance rbi0_t = rbi0*exp(zetarbi*ln_qtt0); //Peripheral b-e junction capacitance `TMPHICJ(cjep0,vdep,zep,ajep,1,vgbe0,cjep0_t,vdep_t,ajep_t) //Tunneling current factors begin : HICTUN_T // real a_eg,ab,aa; ab = 1.0; aa = 1.0; a_eg=vgbe_t0/vgbe_t; if(tunode==1 && cjep0 > 0.0 && vdep >0.0) begin ab = (cjep0_t/cjep0)*sqrt(a_eg)*vdep_t*vdep_t/(vdep*vdep); aa = (vdep/vdep_t)*(cjep0/cjep0_t)*pow(a_eg,-1.5); end else if (tunode==0 && cjei0 > 0.0 && vdei >0.0) begin ab = (cjei0_t/cjei0)*sqrt(a_eg)*vdei_t*vdei_t/(vdei*vdei); aa = (vdei/vdei_t)*(cjei0/cjei0_t)*pow(a_eg,-1.5); end ibets_t = ibets*ab; abet_t = abet*aa; end //Temperature mapping for tunneling current is done inside HICTUN `TMPHICJ(1.0,vdcx,zcx,vptcx,0,vgbc0,cratio_t,vdcx_t,vptcx_t) cjcx01_t=cratio_t*cjcx01; cjcx02_t=cratio_t*cjcx02; //External b-c diode saturation currents //ibcxs_t = ibcxs*exp(zetabcxt*ln_qtt0+vgc/VT*(qtt0-1)); //Constant external series resistances rcx_t = rcx*exp(zetarcx*ln_qtt0); rbx_t = rbx*exp(zetarbx*ln_qtt0); re_t = re*exp(zetare*ln_qtt0); //Forward transit time in substrate transistor tsf_t = tsf*exp((zetacx-1.0)*ln_qtt0); //Capacitance for c-s junction `TMPHICJ(cjs0,vds,zs,vpts,0,vgsc0,cjs0_t,vds_t,vpts_t) end // of Thermal_update_without_self_heating end //of Model_initialization if (flsh!=0 && rth >= `MIN_R) begin : Thermal_update_with_self_heating Tdev = Tamb+dt+V(br_sht); // Limit temperature to avoid FPEs in equations if(Tdev < `TMIN + 273.15) begin Tdev = `TMIN + 273.15; end else begin if (Tdev > `TMAX + 273.15) begin Tdev = `TMAX + 273.15; end end VT = `P_K*Tdev /`P_Q; dT = Tdev-Tnom; qtt0 = Tdev/Tnom; ln_qtt0 = ln(qtt0); k1 = f1vg*Tdev*ln(Tdev); k2 = f2vg*Tdev; vgb_t = vgb+k1+k2; vge_t = vge+k1+k2; vgbe_t = (vgb_t+vge_t)/2; //Internal b-e junction capacitance `TMPHICJ(cjei0,vdei,zei,ajei,1,vgbe0,cjei0_t,vdei_t,ajei_t) if (flcomp == 0.0 || flcomp == 2.1) begin V_gT = 3.0*VT*ln_qtt0 + vgb*(qtt0-1.0); r_VgVT = V_gT/VT; //Internal b-e diode saturation currents a = mcf*r_VgVT/mbei - alb*dT; ibeis_t = ibeis*exp(a); a = mcf*r_VgVT/mrei - alb*dT; ireis_t = ireis*exp(a); a = mcf*r_VgVT/mbep - alb*dT; //Peripheral b-e diode saturation currents ibeps_t = ibeps*exp(a); a = mcf*r_VgVT/mrep - alb*dT; ireps_t = ireps*exp(a); //Internal b-c diode saturation current a = r_VgVT/mbci; ibcis_t = ibcis*exp(a); //External b-c diode saturation currents a = r_VgVT/mbcx; ibcxs_t = ibcxs*exp(a); //Saturation transfer current for substrate transistor a = r_VgVT/msf; itss_t = itss*exp(a); //Saturation current for c-s diode a = r_VgVT/msc; iscs_t = iscs*exp(a); //Zero bias hole charge a = vdei_t/vdei; qp0_t = qp0*(1.0+0.5*zei*(1.0-a)); //Voltage separating ohmic and saturation velocity regime a = vlim*(1.0-alvs*dT)*exp(zetaci*ln_qtt0); k = (a-VT)/VT; if (k < `LN_EXP_LIMIT) begin vlim_t = VT + VT*ln(1.0+exp(k)); end else begin vlim_t = a; end //Neutral emitter storage time a = 1.0+alb*dT; k = 0.5*(a+sqrt(a*a+0.01)); tef0_t = tef0*qtt0/k; end else begin //Internal b-e diode saturation currents ibeis_t = ibeis*exp(zetabet*ln_qtt0+vge/VT*(qtt0-1)); ireis_t = ireis*exp(0.5*mg*ln_qtt0+0.5*vgbe0/VT*(qtt0-1)); //Peripheral b-e diode saturation currents ibeps_t = ibeps*exp(zetabet*ln_qtt0+vge/VT*(qtt0-1)); ireps_t = ireps*exp(0.5*mg*ln_qtt0+0.5*vgbe0/VT*(qtt0-1)); //Internal b-c diode saturation currents ibcis_t = ibcis*exp(zetabci*ln_qtt0+vgc/VT*(qtt0-1)); //External b-c diode saturation currents ibcxs_t = ibcxs*exp(zetabcxt*ln_qtt0+vgc/VT*(qtt0-1)); //Saturation transfer current for substrate transistor itss_t = itss*exp(zetasct*ln_qtt0+vgc/VT*(qtt0-1)); //Saturation current for c-s diode iscs_t = iscs*exp(zetasct*ln_qtt0+vgs/VT*(qtt0-1)); //Zero bias hole charge a = exp(zei*ln(vdei_t/vdei)); qp0_t = qp0*(2.0-a); //Voltage separating ohmic and saturation velocity regime vlim_t = vlim*exp((zetaci-avs)*ln_qtt0); //Neutral emitter storage time zetatef = zetabet-zetact-0.5; dvg0 = vgb-vge; tef0_t = tef0*exp(zetatef*ln_qtt0-dvg0/VT*(qtt0-1)); end //GICCR prefactor c10_t = c10*exp(zetact*ln_qtt0+vgb/VT*(qtt0-1)); // Low-field internal collector resistance rci0_t = rci0*exp(zetaci*ln_qtt0); //Voltage separating ohmic and saturation velocity regime //vlim_t = vlim*exp((zetaci-avs)*ln_qtt0); //Internal c-e saturation voltage vces_t = vces*(1+alces*dT); //Internal b-c diode saturation current //ibcis_t = ibcis*exp(zetabci*ln_qtt0+vgc/VT*(qtt0-1)); //Internal b-c junction capacitance `TMPHICJ(cjci0,vdci,zci,vptci,0,vgbc0,cjci0_t,vdci_t,vptci_t) //Low-current forward transit time t0_t = t0*(1+alt0*dT+kt0*dT*dT); //Saturation time constant at high current densities thcs_t = thcs*exp((zetaci-1)*ln_qtt0); //Avalanche caurrent factors favl_t = favl*exp(alfav*dT); qavl_t = qavl*exp(alqav*dT); //Zero bias internal base resistance rbi0_t = rbi0*exp(zetarbi*ln_qtt0); //Peripheral b-e junction capacitance `TMPHICJ(cjep0,vdep,zep,ajep,1,vgbe0,cjep0_t,vdep_t,ajep_t) //Tunneling current factors if (V(br_bpei) < 0.0 || V(br_biei) < 0.0) begin : HICTUN_T // real a_eg,ab,aa; ab = 1.0; aa = 1.0; a_eg=vgbe_t0/vgbe_t; if(tunode==1 && cjep0 > 0.0 && vdep >0.0) begin ab = (cjep0_t/cjep0)*sqrt(a_eg)*vdep_t*vdep_t/(vdep*vdep); aa = (vdep/vdep_t)*(cjep0/cjep0_t)*pow(a_eg,-1.5); end else if (tunode==0 && cjei0 > 0.0 && vdei >0.0) begin ab = (cjei0_t/cjei0)*sqrt(a_eg)*vdei_t*vdei_t/(vdei*vdei); aa = (vdei/vdei_t)*(cjei0/cjei0_t)*pow(a_eg,-1.5); end ibets_t = ibets*ab; abet_t = abet*aa; end //Temperature mapping for tunneling current is done inside HICTUN `TMPHICJ(1.0,vdcx,zcx,vptcx,0,vgbc0,cratio_t,vdcx_t,vptcx_t) cjcx01_t=cratio_t*cjcx01; cjcx02_t=cratio_t*cjcx02; //External b-c diode saturation currents //ibcxs_t = ibcxs*exp(zetabcxt*ln_qtt0+vgc/VT*(qtt0-1)); //Constant external series resistances rcx_t = rcx*exp(zetarcx*ln_qtt0); rbx_t = rbx*exp(zetarbx*ln_qtt0); re_t = re*exp(zetare*ln_qtt0); //Forward transit time in substrate transistor tsf_t = tsf*exp((zetacx-1.0)*ln_qtt0); //Capacitance for c-s junction `TMPHICJ(cjs0,vds,zs,vpts,0,vgsc0,cjs0_t,vds_t,vpts_t) end //of Thermal_update_with_self_heating begin : Model_evaluation //Intrinsic transistor //Internal base currents across b-e junction `HICDIO(ibeis,ibeis_t,mbei,V(br_biei),ibei) `HICDIO(ireis,ireis_t,mrei,V(br_biei),irei) //HICCR: begin //Inverse of low-field internal collector resistance: needed in HICICK Orci0_t = 1.0/rci0_t; //Initialization //Transfer current, minority charges and transit times Tr = tr; VT_f = mcf*VT; i_0f = c10_t * limexp(V(br_biei)/VT_f); i_0r = c10_t * limexp(V(br_bici)/VT); //Internal b-e and b-c junction capacitances and charges //`QJMODF(cjei0_t,vdei_t,zei,ajei_t,V(br_biei),Qjei) //Cjei = ddx(Qjei,V(bi)); `QJMODF(cjei0_t,vdei_t,zei,ajei_t,V(br_biei),Cjei,Qjei) //`HICJQ(cjci0_t,vdci_t,zci,vptci_t,V(br_bici),Qjci) //Cjci = ddx(Qjci,V(bi)); `HICJQ(cjci0_t,vdci_t,zci,vptci_t,V(br_bici),Cjci,Qjci) //Hole charge at low bias a_bpt = 0.05; Q_0 = qp0_t + hjei*Qjei + hjci*Qjci; Q_bpt = a_bpt*qp0_t; b_q = Q_0/Q_bpt-1; Q_0 = Q_bpt*(1+(b_q +sqrt(b_q*b_q+1.921812))/2); //Transit time calculation at low current density if(cjci0_t > 0.0) begin : CJMODF // real cV_f,cv_e,cs_q,cs_q2,cv_j,cdvj_dv; cV_f = vdci_t*(1.0-exp(-ln(2.4)/zci)); cv_e = (cV_f-V(br_bici))/VT; cs_q = sqrt(cv_e*cv_e+1.921812); cs_q2 = (cv_e+cs_q)*0.5; cv_j = cV_f-VT*cs_q2; cdvj_dv = cs_q2/cs_q; Cjcit = cjci0_t*exp(-zci*ln(1.0-cv_j/vdci_t))*cdvj_dv+2.4*cjci0_t*(1.0-cdvj_dv); end else begin Cjcit = 0.0; end if(Cjcit > 0.0) begin cc = cjci0_t/Cjcit; end else begin cc = 1.0; end T_f0 = t0_t+dt0h*(cc-1.0)+tbvl*(1/cc-1.0); //Effective collector voltage vc = V(br_ciei)-vces_t; //Critical current for onset of high-current effects begin : HICICK Ovpt = 1.0/vpt; a = vc/VT; d1 = a-1; vceff = (1.0+((d1+sqrt(d1*d1+1.921812))/2))*VT; a = vceff/vlim_t; ick = vceff*Orci0_t/sqrt(1.0+a*a); ICKa = (vceff-vlim_t)*Ovpt; ick = ick*(1.0+0.5*(ICKa+sqrt(ICKa*ICKa+1.0e-3))); end //Initial formulation of forward and reverse component of transfer current Q_p = Q_0; if (T_f0 > 0.0 || Tr > 0.0) begin A = 0.5*Q_0; Q_p = A+sqrt(A*A+T_f0*i_0f+Tr*i_0r); end I_Tf1 =i_0f/Q_p; a_h = Oich*I_Tf1; itf = I_Tf1*(1.0+a_h); itr = i_0r/Q_p; //Initial formulation of forward transit time, diffusion, GICCR and excess b-c charge Q_bf = 0.0; Tf = T_f0; Qf = T_f0*itf; `HICQFF(itf,ick,Tf,Qf,T_fT,Q_fT,Q_bf) //Initial formulation of reverse diffusion charge Qr = Tr*itr; //Preparation for iteration to get total hole charge and related variables l_it = 0; if(Qf > `RTOLC*Q_p || a_h > `RTOLC) begin //Iteration for Q_pT is required for improved initial solution Qf = sqrt(T_f0*itf*Q_fT); Q_pT = Q_0+Qf+Qr; d_Q = Q_pT; while (abs(d_Q) >= `RTOLC*abs(Q_pT) && l_it <= `l_itmax) begin d_Q0 = d_Q; I_Tf1 = i_0f/Q_pT; a_h = Oich*I_Tf1; itf = I_Tf1*(1.0+a_h); itr = i_0r/Q_pT; Tf = T_f0; Qf = T_f0*itf; `HICQFF(itf,ick,Tf,Qf,T_fT,Q_fT,Q_bf) Qr = Tr*itr; if(Oich == 0.0) begin a = 1.0+(T_fT*itf+Qr)/Q_pT; end else begin a = 1.0+(T_fT*I_Tf1*(1.0+2.0*a_h)+Qr)/Q_pT; end d_Q = -(Q_pT-(Q_0+Q_fT+Qr))/a; //Limit maximum change of Q_pT a = abs(0.3*Q_pT); if(abs(d_Q) > a) begin if (d_Q>=0) begin d_Q = a; end else begin d_Q = -a; end end Q_pT = Q_pT+d_Q; l_it = l_it+1; end //while I_Tf1 = i_0f/Q_pT; a_h = Oich*I_Tf1; itf = I_Tf1*(1.0+a_h); itr = i_0r/Q_pT; //Final transit times, charges and transport current components Tf = T_f0; Qf = T_f0*itf; `HICQFF(itf,ick,Tf,Qf,T_fT,Q_fT,Q_bf) Qr = Tr*itr; end //if //NQS effect implemented with LCR networks //Once the delay in ITF is considered, IT_NQS is calculated afterwards it = itf-itr; //Diffusion charges for further use Qdei = Qf; Qdci = Qr; //High-frequency emitter current crowding (lateral NQS) Cdei = -1*ddx(Qdei,V(ei)); Cdci = -1*ddx(Qdci,V(ci)); Crbi = fcrbi*(Cjei+Cjci+Cdei+Cdci); qrbi = Crbi*V(br_bpbi_v); // qrbi = fcrbi*(Qjei+Qjci+Qdei+Qdci); //HICCR: end //Internal base current across b-c junction `HICDIO(ibcis,ibcis_t,mbci,V(br_bici),ibci) //Avalanche current if((V(br_bici) < 0.0) && (favl_t > 0.0) && (cjci0_t > 0.0)) begin : HICAVL // real v_bord,v_q,U0,av,avl; v_bord = vdci_t-V(br_bici); v_q = qavl_t/Cjci; U0 = qavl_t/cjci0_t; if(v_bord > U0) begin av = favl_t*exp(-v_q/U0); avl = av*(U0+(1.0+v_q/U0)*(v_bord-U0)); end else begin avl = favl_t*v_bord*exp(-v_q/v_bord); end iavl = itf*avl; end else begin iavl = 0.0; end //Excess base current from recombination at the b-c barrier ibh_rec = Q_bf*Otbhrec; //Internal base resistance if(rbi0_t > 0.0) begin : HICRBI // real Qz_nom,f_QR,ETA,Qz0,fQz; // Consideration of conductivity modulation // To avoid convergence problem hyperbolic smoothing used f_QR = (1+fdqr0)*qp0_t; Qz0 = Qjei+Qjci+Qf; Qz_nom = 1+Qz0/f_QR; fQz = 0.5*(Qz_nom+sqrt(Qz_nom*Qz_nom+0.01)); rbi = rbi0_t/fQz; // Consideration of emitter current crowding if( ibei > 0.0) begin ETA = rbi*ibei*fgeo/VT; if(ETA < 1.0e-6) begin rbi = rbi*(1.0-0.5*ETA); end else begin rbi = rbi*ln(1.0+ETA)/ETA; end end // Consideration of peripheral charge if(Qf > 0.0) begin rbi = rbi*(Qjei+Qf*fqi)/(Qjei+Qf); end end else begin rbi = 0.0; end //Base currents across peripheral b-e junction `HICDIO(ibeps,ibeps_t,mbep,V(br_bpei),ibep) `HICDIO(ireps,ireps_t,mrep,V(br_bpei),irep) //Peripheral b-e junction capacitance and charge `QJMODF(cjep0_t,vdep_t,zep,ajep_t,V(br_bpei),Cjep,Qjep) //Tunelling current if (V(br_bpei) <0.0 || V(br_biei) < 0.0) begin : HICTUN // real pocce,czz; if(tunode==1 && cjep0_t > 0.0 && vdep_t >0.0) begin pocce = exp((1-1/zep)*ln(Cjep/cjep0_t)); czz = -(V(br_bpei)/vdep_t)*ibets_t*pocce; ibet = czz*exp(-abet_t/pocce); end else if (tunode==0 && cjei0_t > 0.0 && vdei_t >0.0) begin pocce = exp((1-1/zei)*ln(Cjei/cjei0_t)); czz = -(V(br_biei)/vdei_t)*ibets_t*pocce; ibet = czz*exp(-abet_t/pocce); end else begin ibet = 0.0; end end else begin ibet = 0.0; end //Depletion capacitance and charge at peripheral b-c junction (bp,ci) `HICJQ(cjcx02_t,vdcx_t,zcx,vptcx_t,V(br_bpci),c_dummy,qjcx0_t_ii) //Base currents across peripheral b-c junction (bp,ci) `HICDIO(ibcxs,ibcxs_t,mbcx,V(br_bpci),ijbcx) //Depletion capacitance and charge at external b-c junction (b,ci) `HICJQ(cjcx01_t,vdcx_t,zcx,vptcx_t,V(br_bci),c_dummy,qjcx0_t_i) //Depletion substrate capacitance and charge at s-c junction (si,ci) `HICJQ(cjs0_t,vds_t,zs,vpts_t,V(br_sici),c_dummy,Qjs) //Parasitic substrate transistor transfer current and diffusion charge if(itss > 0.0) begin : Sub_Transfer HSUM = msf*VT; HSa = limexp(V(br_bpci)/HSUM); HSb = limexp(V(br_sici)/HSUM); HSI_Tsu = itss_t*(HSa-HSb); if(tsf > 0.0) begin Qdsu = tsf_t*itss_t*HSa; end else begin Qdsu = 0.0; end end else begin HSI_Tsu = 0.0; Qdsu = 0.0; end // Current gain computation for correlated noise implementation betad=ibei; if (betad > 0.0) begin betadin=betad; betan=it; betadc=betan/betad; end else begin betadc=0.0; end //Diode current for s-c junction (si,ci) `HICDIO(iscs,iscs_t,msc,V(br_sici),ijsc) //Self-heating calculation if (flsh == 1 && rth >= `MIN_R) begin pterm = V(br_ciei)*it + (vdci_t-V(br_bici))*iavl; end else if (flsh == 2 && rth >= `MIN_R) begin pterm = V(br_ciei)*it + (vdci_t-V(br_bici))*iavl + ibei*V(br_biei) + ibci*V(br_bici) + ibep*V(br_bpei) + ijbcx*V(br_bpci) + ijsc*V(br_sici); if (rbi >= `MIN_R) begin pterm = pterm + V(br_bpbi_i)*V(br_bpbi_i)/rbi; end if (re_t >= `MIN_R) begin pterm = pterm + V(br_eie_i)*V(br_eie_i)/re_t; end if (rcx_t >= `MIN_R) begin pterm = pterm + V(br_cic_i)*V(br_cic_i)/rcx_t; end if (rbx_t >= `MIN_R) begin pterm = pterm + V(br_bbp_i)*V(br_bbp_i)/rbx_t; end end Itxf = itf; Qdeix = Qdei; // Excess Phase calculation if (flnqs != 0 && Tf != 0) begin Vxf1 = V(br_bxf1); Vxf2 = V(br_bxf2); Ixf1 = (Vxf2-itf)/Tf*t0; Ixf2 = (Vxf2-Vxf1)/Tf*t0; Qxf1 = alit*Vxf1*t0; Qxf2 = alit*Vxf2/3*t0; Itxf = Vxf2; Vxf = V(br_bxf); //for RC nw fact = t0/Tf; //for RC nw Ixf = (Vxf - Qdei)*fact; //for RC nw Qxf = alqf*Vxf*t0; //for RC nw Qdeix = Vxf; //for RC nw end else begin Ixf1 = V(br_bxf1); Ixf2 = V(br_bxf2); Qxf1 = 0; Qxf2 = 0; Ixf = V(br_bxf); Qxf = 0; end end //of Model_evaluation begin : Load_sources I(br_biei) <+ _circuit_gmin*V(br_biei); I(br_bici) <+ _circuit_gmin*V(br_bici); I(br_bci) <+ ddt(qjcx0_t_i); I(br_bci) <+ ddt(cbcpar1*V(br_bci)); I(br_bpci) <+ ddt(cbcpar2*V(br_bpci)); if (rbx >= `MIN_R) begin I(br_bbp_i) <+ V(br_bbp_i)/rbx_t; end else begin // V(br_bbp_v) <+ 0.0; I(br_bbp_i) <+ V(br_bbp_i)/`MIN_R; end if(rbi0 >= `MIN_R) begin I(br_bpbi_i) <+ V(br_bpbi_i)/rbi; I(br_bpbi_i) <+ ddt(qrbi); end else begin // V(br_bpbi_v) <+ 0.0; I(br_bpbi_i) <+ V(br_bpbi_i)/`MIN_R; end if (tunode==1.0) begin I(br_bpei) <+ -ibet; end else begin I(br_biei) <+ -ibet; end I(br_bpei) <+ ibep; I(br_bpei) <+ irep; I(br_bpei) <+ ddt(Qjep); I(br_biei) <+ ibei; I(br_biei) <+ irei; I(br_biei) <+ ibh_rec; I(br_biei) <+ ddt(Qdeix+Qjei); I(br_bpsi) <+ HSI_Tsu; I(br_bpci) <+ ijbcx; I(br_bpci) <+ ddt(qjcx0_t_ii+Qdsu); I(br_be) <+ ddt(cbepar1*V(br_be)); I(br_bpe) <+ ddt(cbepar2*V(br_bpe)); I(br_bici) <+ ibci-iavl; I(br_bici) <+ ddt(Qdci+Qjci); I(br_sici) <+ ijsc; I(br_sici) <+ ddt(Qjs); I(br_ciei) <+ Itxf; I(br_eici) <+ itr; if (rcx >= `MIN_R) begin I(br_cic_i) <+ V(br_cic_i)/rcx_t; end else begin // V(br_cic_v) <+ 0.0; I(br_cic_i) <+ V(br_cic_i)/`MIN_R; end if (re >= `MIN_R) begin I(br_eie_i) <+ V(br_eie_i)/re_t; end else begin // V(br_eie_v) <+ 0.0; I(br_eie_i) <+ V(br_eie_i)/`MIN_R; end if(rsu >= `MIN_R) begin I(br_sis_i) <+ V(br_sis_i)/rsu; I(br_sis_i) <+ ddt(csu*V(br_sis_i)); end else begin // V(br_sis_v) <+ 0.0; I(br_sis_i) <+ V(br_sis_i)/`MIN_R; end // Following code is an intermediate solution (if branch contribution is not supported): // ****************************************** if(flsh == 0 || rth < `MIN_R) begin I(br_sht) <+ V(br_sht)/`MIN_R; end else begin I(br_sht) <+ V(br_sht)/rth-pterm; I(br_sht) <+ ddt(cth*V(br_sht)); end // ****************************************** // For simulators having no problem with V(br_sht) <+ 0.0 // with external thermal node, follwing code may be used. // Note that external thermal node should remain accessible // even without self-heating. // ******************************************** //if(flsh == 0 || rth < `MIN_R) begin // V(br_sht) <+ 0.0; //end else begin // I(br_sht) <+ V(br_sht)/rth-pterm; // I(br_sht) <+ ddt(cth*V(br_sht)); //end // ******************************************** // NQS effect I(br_bxf1) <+ Ixf1; I(br_cxf1) <+ ddt(Qxf1); I(br_bxf2) <+ Ixf2; I(br_cxf2) <+ ddt(Qxf2); I(br_bxf) <+ Ixf; //for RC nw I(br_cxf) <+ ddt(Qxf); //for RC nw end //of Load_sources `NOISE begin : Noise_sources //Thermal noise fourkt = 4.0 * `P_K * Tdev; if(rbx >= `MIN_R) begin I(br_bbp_i) <+ white_noise(fourkt/rbx_t, "thermal"); end if(rbi0 >= `MIN_R) begin I(br_bpbi_i) <+ white_noise(fourkt/rbi, "thermal"); end if(rcx >= `MIN_R) begin I(br_cic_i) <+ white_noise(fourkt/rcx_t, "thermal"); end if(re >= `MIN_R) begin I(br_eie_i) <+ white_noise(fourkt/re_t, "thermal"); end if(rsu >= `MIN_R) begin I(br_sis_i) <+ white_noise(fourkt/rsu, "thermal"); end //Flicker noise : Fully correlated between the perimeter and internal base-node flicker_Pwr = kf*pow((ibei+ibep),af); if (cfbe == -1) begin I(br_biei) <+ flicker_noise(flicker_Pwr,1.0); end else begin I(br_bpei) <+ flicker_noise(flicker_Pwr,1.0); end //Shot noise twoq = 2.0 * `P_Q; // I(br_ciei) <+ white_noise(twoq*it, "shot"); I(br_cibi) <+ white_noise(twoq*iavl, "shot"); // I(br_biei) <+ white_noise(twoq*ibei, "shot"); I(br_bici) <+ white_noise(twoq*abs(ibci), "shot"); I(br_bpei) <+ white_noise(twoq*ibep, "shot"); I(br_bpci) <+ white_noise(twoq*abs(ijbcx), "shot"); I(br_sici) <+ white_noise(twoq*abs(ijsc), "shot"); // Code section for correlated noise // Please turn-off this code section by "//" in order to run the code with Spectre // I(b_n1) <+ white_noise(2 * `P_Q * ibei, "shot"); // I(b_n1) <+ V(b_n1); // I(b_n2) <+ white_noise(2 * `P_Q * it, "shot"); // I(b_n2) <+ V(b_n2); // // I(bi,ei) <+ V(b_n1); // I(ci,ei) <+ V(b_n2)+ddt((betadc/2)*alit*Tf*alit*Tf*ddt(V(b_n2))); // I(ci,ei) <+ betadc*ddt(-(Tf*alit)*V(b_n1)); end //of Noise_sources end //analog endmodule