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Mschichmanhodgesmosfet.m

## Copyright (C) 2006,2007,2008  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
## OCS - A Circuit Simulator for Octave
##
## OCS is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program (see the file LICENSE); if not,
## see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>, culpo@math.uni-wuppertal.de

## -*- texinfo -*-
##
## @deftypefn{Function File} @
## {[@var{a},@var{b},@var{c}]=} Mschichmanhodgesmosfet@
## (@var{string}, @var{parameters}, @var{parameternames}, @
## @var{extvar},@var{intvar},@var{t})
##
## SBN file implementing Schichman-Hodges MOSFETs model.
##
## @var{string} is used to select among models. Possible models are:
##
## @enumerate
## @item @var{string} = "NMOS" (Schichman-Hodges n-MOSFET)
## @item @var{string} = "PMOS" (Schichman-Hodges p-MOSFET)
## @item @var{string} = "NMOStpar" (n-MOSFET with temperature treated as a parameter)
## @item @var{string} = "PMOStpar" (p-MOSFET with temperature treated as a parameter)
## @item @var{string} = "NMOSnoP"  (n-MOSFET without heat-flux)
## @item @var{string} = "PMOSnoP"  (p-MOSFET without heat-flux)
## @end enumerate
##
## Parameters for all the above models are:
## @itemize
## @item rd     -> parasitic resistance between drain and source
## @item W      -> MOSFET width
## @item L      -> channel length
## @item mu0    -> reference value for mobility
## @item Vth    -> threshold voltage
## @item Cox    -> oxide capacitance
## @item Cgs    -> gate-source capacitance
## @item Cgd    -> gate-drain capacitance
## @item Cgb    -> gate-bulk capacitance
## @item Csb    -> source-bulk capacitance
## @item Cdb    -> drain-bulk capacitance
## @item Tshift -> shift for reference temperature on MOSFETs (default 0)
## @end itemize
##
## @seealso{ PRSiffparse, ASMinitsystem, ASMbuildsystem, the IFF file
## format  specifications }
## @end deftypefn

function [a,b,c]= Mschichmanhodgesmosfet (string,parameters,parameternames,extvar,intvar,t)   
  switch string
    case "NMOS"
      
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = .5;
      Cox  = 1e-9;
      Cgb  = Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;
      Tshift = 0;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor

      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        nmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);
      
      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = max(extvar(5),0);
  
      if isempty(intvar)
      intvar = zeros(5,1);
      endif
  
      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);
      
      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];

      b11 = [0        0                0      0     0; \
           -gm      (gm+gd)         -gd     0 -didT; \
           gm      -(gm+gd)          gd     0  didT; \
           0        0                0      0     0; \
           dPdvgs  -(dPdvgs+dPdvds)  dPdvds 0  dPdT];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; P];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      

      break;

    case "PMOS"
      
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = -.5;
      Cox  = 1e-9;
      Cgb=Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;
      Tshift = 0;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor

      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        pmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);

      
      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = extvar(5);

      if isempty(intvar)
      intvar = zeros(5,1);
      endif

      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);
      
      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];
     
      b11 = [0        0                0      0     0; \
           -gm      (gm+gd)         -gd     0 -didT; \
           gm      -(gm+gd)          gd     0  didT; \
           0        0                0      0     0; \
           dPdvgs  -(dPdvgs+dPdvds)  dPdvds 0  dPdT];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
     
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; P];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      
      break;

    case "NMOStpar"
      ## Nmos model with temperature treated as a parameter
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = .5;
      Cox  = 1e-9;
      Cgb  = Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor

      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        nmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);
      
      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = extvar(5);

      if isempty(intvar)
      intvar = zeros(5,1);
      endif

      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);

      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];

      b11 = [0        0                0      0  0; \
           -gm      (gm+gd)         -gd     0  0; \
           gm      -(gm+gd)          gd     0  0; \
           0        0                0      0  0; \
           0        0                0      0  0];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; 0];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      
      break;

    case "PMOStpar"
      ##  Pmos model with temperature treated as a parameter
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = -.5;
      Cox  = 1e-9;
      Cgb  = Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor
      
      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        pmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);

      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = extvar(5);

      if isempty(intvar)
      intvar = zeros(5,1);
      endif

      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);
      
      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];
     
      b11 = [0        0                0      0     0; \
           -gm      (gm+gd)         -gd     0 -didT; \
           gm      -(gm+gd)          gd     0  didT; \
           0        0                0      0     0; \
           0        0                0      0     0];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
     
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; 0];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      
      break;

    case "NMOSnoP"
      
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = .5;
      Cox  = 1e-9;
      Cgb=Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor

      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        nmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);
      
      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = extvar(5);

      if isempty(intvar)
      intvar = zeros(5,1);
      endif

      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);

      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];

      b11 = [0        0                0      0     0; \
           -gm      (gm+gd)         -gd     0 -didT; \
           gm      -(gm+gd)          gd     0  didT; \
           0        0                0      0     0; \
           0        0                0      0     0];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; 0];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      

      break;

    case "PMOSnoP"
      
      rd   = 1e6;
      W    = 1;
      L    = 1;
      mu0  = 1e-5;
      Vth  = -.5;
      Cox  = 1e-9;
      Cgb=Cox;
      Cgs=Cgd=Csb=Cdb=.1*Cox;

      for ii=1:length(parameternames)
      eval([parameternames{ii} "=",...
            num2str(parameters(ii)) " ;"])      
      endfor

      [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = \
        pmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift);

      vg   = extvar(1);
      vs   = extvar(2);
      vd   = extvar(3);
      vb   = extvar(4);
      T    = extvar(5);

      if isempty(intvar)
      intvar = zeros(5,1);
      endif

      Qgb  = intvar(1);
      Qgs  = intvar(2);
      Qgd  = intvar(3);
      Qsb  = intvar(4);
      Qdb  = intvar(5);
      
      a11 = a21 = a22 = zeros(5,5);
      a12 = [ 1  1  1  0  0; \
            0 -1  0  1  0; \
            0  0 -1  0  1; \
           -1  0  0 -1 -1; \
            0  0  0  0  0];

      a   = [a11 a12; a21 a22];
     
      b11 = [0        0                0      0     0; \
           -gm      (gm+gd)         -gd     0 -didT; \
           gm      -(gm+gd)          gd     0  didT; \
           0        0                0      0     0; \
           0        0                0      0     0];

      b12 = zeros(5,5);

      b21 = [Cgb  0        0   -Cgb  0; \
           Cgs -Cgs      0    0    0; \
           Cgd  0       -Cgd  0    0; \
           0    Csb      0   -Csb  0; \
           0    0        Cdb -Cdb  0];
     
      b22 = -eye(5);

      b   = [b11 b12; b21 b22];
      
      
      c1 = [0; -ids; ids; 0; 0];

      c2 = [Cgb*(vg - vb) - Qgb;\
          Cgs*(vg - vs) - Qgs;\
          Cgd*(vg - vd) - Qgd;\
          Csb*(vs - vb) - Qsb;\
          Cdb*(vd - vb) - Qdb];
      
      c = [c1;c2];
      
      break;

    otherwise
      error(["unknown option:" string]);
  endswitch

endfunction

function [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = nmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift)
  ##Computes values for nmos case
  
  vg   = extvar(1);
  vs   = extvar(2);
  vd   = extvar(3);
  vb   = extvar(4);
  T    = max(extvar(5),0);

  k    = mu0*Cox*((T + Tshift)/300)^(-3/2)*W/L;
  dkdT = mu0*Cox*W*(-3/2)*((T + Tshift)/300)^(-5/2)*(1/300)/L;
  
  vgs  = vg-vs;
  vds  = vd-vs;
  
  if (vgs < Vth)
    
    gm  = 0;
    gd  = 1/rd;
    ids = vds*gd;
    didT= 0;
    
  elseif ((vgs-Vth)>=(vds))&(vds>=0)
    
    ids = k*((vgs-Vth)*vds-(vds^2)/2)+vds/rd;
    gm  = k*vds;
    gd  = k*(vgs-Vth-vds) + 1/rd;
    didT= dkdT*((vgs-Vth)*vds-(vds^2)/2);
    
  elseif ((vgs-Vth)>=(vds))&(vds<0)
    
    gm  = 0;
    gd  = 1/rd;
    ids = vds*gd;
    didT= 0;
    
  else # (i.e. if 0 <= vgs-vth <= vds)
    
    ids = (k/2)*(vgs-Vth)^2+vds/rd;
    gm  = k*(vgs-Vth);
    gd  = 1/rd;
    didT= (dkdT/(2))*(vgs-Vth)^2;
    
  endif
  
  P       = -ids * vds;
  dPdT    = -didT* vds;
  dPdvgs  = -(gm*vds);
  dPdvds  = -(gd*vds + ids);

endfunction

function [gm,gd,ids,didT,P,dPdT,dPdvgs,dPdvds] = pmos(extvar,mu0,Cox,W,L,Vth,rd,Tshift)
  ##Computes values for pmos case

  vg   = extvar(1);
  vs   = extvar(2);
  vd   = extvar(3);
  vb   = extvar(4);
  T    = extvar(5);

  k    = - mu0 * Cox * ((T + Tshift)/300)^(-3/2) *W/L;
  dkdT = - mu0 * Cox * W *(-3/2)*((T + Tshift)/300)^(-5/2)*(1/300)/L;
  
  vgs  = vg-vs;
  vds  = vd-vs;

  if (vgs > Vth)
    
    gm  = 0;
    gd  = 1/rd;
    ids = vds*gd;
    didT= 0;

  elseif ((vgs-Vth)<=(vds))&(vds<=0)
    
    ids = k*((vgs-Vth)*vds-(vds^2)/2)+vds/rd;
    gm  = k*vds;
    gd  = k*(vgs-Vth-vds)+1/rd;
    didT= dkdT*((vgs-Vth)*vds-(vds^2)/2);

  elseif ((vgs-Vth)<=(vds))&(vds>0)
    
    gm  = 0;
    gd  = 1/rd;
    ids = vds*gd;
    didT= 0;

  else 

    ids = (k/2)*(vgs-Vth)^2+vds/rd;
    gm  = k*(vgs-Vth);
    gd  = 1/rd;
    didT= (dkdT/(2))*(vgs-Vth)^2;

  endif
  
  P    = -ids * vds;
  dPdT = -didT* vds;
  dPdvgs  = -(gm*vds);
  dPdvds  = -(gd*vds + ids);
  
endfunction

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