Modelica.Electrical.Analog.Semiconductors

Modelica.Electrical.Analog.Semiconductors.Diode Modelica.Electrical.Analog.Semiconductors.PMOS Modelica.Electrical.Analog.Semiconductors.NMOS Modelica.Electrical.Analog.Semiconductors.NPN Modelica.Electrical.Analog.Semiconductors.PNP Modelica.Electrical.Analog.Semiconductors.HeatingDiode Modelica.Electrical.Analog.Semiconductors.HeatingNMOS Modelica.Electrical.Analog.Semiconductors.HeatingPMOS Modelica.Electrical.Analog.Semiconductors.HeatingNPN Modelica.Electrical.Analog.Semiconductors.HeatingPNP

Information




This package contains semiconductor devices:










NameDescription


Diode
Simple diode


PMOS
Simple MOS Transistor


NMOS
Simple MOS Transistor


NPN
Simple BJT according to Ebers-Moll


PNP
Simple BJT according to Ebers-Moll


HeatingDiode
Simple diode with heating port


HeatingNMOS
Simple MOS Transistor with heating port


HeatingPMOS
Simple PMOS Transistor with heating port


HeatingNPN
Simple NPN BJT according to Ebers-Moll with heating port


HeatingPNP
Simple PNP BJT according to Ebers-Moll with heating port


pow
Just a helper function for x^y in order that a symbolic engine can apply some transformations more easily


exlin
Exponential function linearly continued for x > Maxexp








Modelica.Electrical.Analog.Semiconductors.HeatingPMOS
Modelica.Electrical.Analog.Semiconductors.HeatingPMOS

Simple PMOS Transistor with heating port

Modelica.Electrical.Analog.Semiconductors.HeatingPMOS

Information





The PMOS model is a simple model of a p-channel metal-oxide semiconductor
FET. It differs slightly from the device used in the SPICE simulator.
For more details please care for H. Spiro.




A heating port is added for thermal electric simulation. The heating port
is defined in the Modelica.Thermal library.




The model does not consider capacitances. A high drain-source resistance RDS
is included to avoid numerical difficulties.





References:

Spiro, H.: Simulation integrierter Schaltungen. R. Oldenbourg Verlag 
  Muenchen Wien 1990.   




Some typical parameter sets are:



  W       L      Beta        Vt       K2       K5       DW         DL    
  m       m      A/V^2       V        -        -        m          m    
  50.e-6  8.e-6  .0085e-3   -.15     .41      .839    -3.8e-6    -4.0e-6           
  20.e-6  6.e-6  .0105e-3  -1.0      .41      .839    -2.5e-6    -2.1e-6 
  30.e-6  5.e-6  .0059e-3   -.3      .98     1.01      0         -3.9e-6   
  30.e-6  5.e-6  .0152e-3   -.69     .104    1.1       -.8e-6     -.4e-6         
  30.e-6  5.e-6  .0163e-3   -.69     .104    1.1       -.8e-6     -.4e-6         
  30.e-6  5.e-6  .0182e-3   -.69     .086    1.06      -.1e-6     -.6e-6         
  20.e-6  6.e-6  .0074e-3  -1.       .4       .59      0          0           








Parameters




NameDefaultDescription


W20.0e-6Width [m]


L6.0e-6Length [m]


Beta0.0105e-3Transconductance parameter [A/(V*V)]


Vt-1.0Zero bias threshold voltage [V]


K20.41Bulk threshold parameter


K50.839Reduction of pinch-off region


dW-2.5e-6Narrowing of channel [m]


dL-2.1e-6Shortening of channel [m]


RDS1.e+7Drain-Source-Resistance [Ohm]


Tnom300.15Parameter measurement temperature [K]


kvt-2.9e-3fitting parameter for Vt


kk26.2e-4fitting parameter for Kk2




Modelica definition


model HeatingPMOS "Simple PMOS Transistor with heating port" 
  // 6.12.2001 parameter RDS added, Clauss    
  
  
  Modelica.Electrical.Analog.Interfaces.Pin D "Drain";
  Modelica.Electrical.Analog.Interfaces.Pin G "Gate";
  Modelica.Electrical.Analog.Interfaces.Pin S "Source";
  Modelica.Electrical.Analog.Interfaces.Pin B "Bulk";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort(
                                                               T(start=
          300.15));
  parameter Modelica.SIunits.Length W =      20.0e-6 "Width";
  parameter Modelica.SIunits.Length L =      6.0e-6 "Length";
  parameter Modelica.SIunits.Transconductance Beta =      0.0105e-3 
    "Transconductance parameter";
  parameter Modelica.SIunits.Voltage Vt =      -1.0 "Zero bias threshold voltage";
  parameter Real K2=0.41 "Bulk threshold parameter";
  parameter Real K5=0.839 "Reduction of pinch-off region";
  parameter Modelica.SIunits.Length dW =      -2.5e-6 "Narrowing of channel";
  parameter Modelica.SIunits.Length dL =      -2.1e-6 "Shortening of channel";
  parameter Modelica.SIunits.Resistance RDS =      1.e+7 "Drain-Source-Resistance";
  parameter Modelica.SIunits.Temperature Tnom =      300.15 
    "Parameter measurement temperature";
  parameter Real kvt=-2.9e-3 "fitting parameter for Vt";
  parameter Real kk2=6.2e-4 "fitting parameter for Kk2";
protected 
  Real v;
  Real uds;
  Real ubs;
  Real ugst;
  Real ud;
  Real us;
  Real id;
  Real gds;
  Real beta_t;
  Real vt_t;
  Real k2_t;
equation 
  assert(L + dL > 0, "Effective length must be positive");
  assert(W + dW > 0, "Effective width  must be positive");
  assert( heatPort.T > 0,"temperature must be positive");
  gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS;
  v = beta_t*(W + dW)/(L + dL);
  ud = if (D.v > S.v) then S.v else D.v;
  us = if (D.v > S.v) then D.v else S.v;
  uds = ud - us;
  ubs = if (B.v < us) then 0 else B.v - us;
  ugst = (G.v - us - vt_t + k2_t*ubs)*K5;
  id = if (ugst >= 0) then v*uds*gds else if (ugst < uds) then -v*uds*(
    ugst - uds/2 - gds) else -v*(ugst*ugst/2 - uds*gds);
  
  beta_t = Beta*pow((heatPort.T/Tnom), -1.5);
  vt_t = Vt*(1 + (heatPort.T - Tnom)*kvt);
  k2_t = K2*(1 + (heatPort.T - Tnom)*kk2);
  
  G.i = 0;
  D.i = if (D.v > S.v) then -id else id;
  S.i = if (D.v > S.v) then id else -id;
  B.i = 0;
  heatPort.Q_dot = -D.i*(D.v - S.v);
end HeatingPMOS;







Modelica.Electrical.Analog.Semiconductors.HeatingNMOS
Modelica.Electrical.Analog.Semiconductors.HeatingNMOS

Simple MOS Transistor with heating port

Modelica.Electrical.Analog.Semiconductors.HeatingNMOS

Information





The NMos model is a simple model of a n-channel metal-oxide semiconductor
FET. It differs slightly from the device used in the SPICE simulator.
For more details please care for H. Spiro.




A heating port is added for thermal electric simulation. The heating port
is defined in the Modelica.Thermal library.




The model does not consider capacitances. A high drain-source resistance RDS
is included to avoid numerical difficulties.





  W       L      Beta        Vt       K2      K5       DW         DL    
  m       m      A/V^2       V        -       -        m          m    
  12.e-6  4.e-6  .062e-3   -4.5      .24     .61     -1.2e-6     -.9e-6      depletion
  60.e-6  3.e-6  .048e-3     .1      .08     .68     -1.2e-6     -.9e-6      enhancement
  12.e-6  4.e-6  .0625e-3   -.8      .21     .78     -1.2e-6     -.9e-6      zero
  50.e-6  8.e-6  .0299e-3    .24    1.144    .7311   -5.4e-6    -4.e-6          
  20.e-6  6.e-6  .041e-3     .8     1.144    .7311   -2.5e-6    -1.5e-6         
  30.e-6  9.e-6  .025e-3   -4.       .861    .878    -3.4e-6    -1.74e-6        
  30.e-6  5.e-6  .031e-3     .6     1.5      .72      0         -3.9e-6         
  50.e-6  6.e-6  .0414e-3  -3.8      .34     .8      -1.6e-6    -2.e-6       depletion
  50.e-6  5.e-6  .03e-3      .37     .23     .86     -1.6e-6    -2.e-6       enhancement
  50.e-6  6.e-6  .038e-3    -.9      .23     .707    -1.6e-6    -2.e-6       zero
  20.e-6  4.e-6  .06776e-3   .5409   .065    .71      -.8e-6     -.2e-6      
  20.e-6  4.e-6  .06505e-3   .6209   .065    .71      -.8e-6     -.2e-6         
  20.e-6  4.e-6  .05365e-3   .6909   .03     .8       -.3e-6     -.2e-6        
  20.e-6  4.e-6  .05365e-3   .4909   .03     .8       -.3e-6     -.2e-6        
  12.e-6  4.e-6  .023e-3   -4.5      .29     .6       0          0           depletion
  60.e-6  3.e-6  .022e-3     .1      .11     .65      0          0           enhancement
  12.e-6  4.e-6  .038e-3    -.8      .33     .6       0          0           zero
  20.e-6  6.e-6  .022e-3     .8     1        .66      0          0            







References:

Spiro, H.: Simulation integrierter Schaltungen. R. Oldenbourg Verlag 
Muenchen Wien 1990.  








Parameters




NameDefaultDescription


W20.e-6Width [m]


L6.e-6Length [m]


Beta0.041e-3Transconductance parameter [A/(V*V)]


Vt0.8Zero bias threshold voltage [V]


K21.144Bulk threshold parameter


K50.7311Reduction of pinch-off region


dW-2.5e-6narrowing of channel [m]


dL-1.5e-6shortening of channel [m]


RDS1.e+7Drain-Source-Resistance [Ohm]


Tnom300.15Parameter measurement temperature [K]


kvt-6.96e-3fitting parameter for Vt


kk26.0e-4fitting parameter for K22




Modelica definition


model HeatingNMOS "Simple MOS Transistor with heating port" 
  
  Modelica.Electrical.Analog.Interfaces.Pin D "Drain";
  Modelica.Electrical.Analog.Interfaces.Pin G "Gate";
  Modelica.Electrical.Analog.Interfaces.Pin S "Source";
  Modelica.Electrical.Analog.Interfaces.Pin B "Bulk";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort(
                                                               T(start=
          300.15));
  parameter Modelica.SIunits.Length W =      20.e-6 "Width";
  parameter Modelica.SIunits.Length L =      6.e-6 "Length";
  parameter Modelica.SIunits.Transconductance Beta =      0.041e-3 
    "Transconductance parameter";
  parameter Modelica.SIunits.Voltage Vt =      0.8 "Zero bias threshold voltage";
  parameter Real K2=1.144 "Bulk threshold parameter";
  parameter Real K5=0.7311 "Reduction of pinch-off region";
  parameter Modelica.SIunits.Length dW =      -2.5e-6 "narrowing of channel";
  parameter Modelica.SIunits.Length dL =      -1.5e-6 "shortening of channel";
  parameter Modelica.SIunits.Resistance RDS =      1.e+7 "Drain-Source-Resistance";
  parameter Modelica.SIunits.Temperature Tnom =      300.15 
    "Parameter measurement temperature";
  parameter Real kvt=-6.96e-3 "fitting parameter for Vt";
  parameter Real kk2=6.0e-4 "fitting parameter for K22";
protected 
  Real v;
  Real uds;
  Real ubs;
  Real ugst;
  Real ud;
  Real us;
  Real id;
  Real gds;
  Real beta_t;
  Real vt_t;
  Real k2_t;
equation 
  assert(L + dL > 0, "Effective length must be positive");
  assert(W + dW > 0, "Effective width  must be positive");
  assert( heatPort.T > 0,"temperature must be positive");
  gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS;
  v = beta_t*(W + dW)/(L + dL);
  ud = if (D.v < S.v) then S.v else D.v;
  us = if (D.v < S.v) then D.v else S.v;
  uds = ud - us;
  ubs = if (B.v > us) then 0 else B.v - us;
  ugst = (G.v - us - vt_t + k2_t*ubs)*K5;
  id = if (ugst <= 0) then v*uds*gds else if (ugst > uds) then v*uds*(
    ugst - uds/2 + gds) else v*(ugst*ugst/2 + uds*gds);
  
  beta_t = Beta*pow((heatPort.T/Tnom), -1.5);
  vt_t = Vt*(1 + (heatPort.T - Tnom)*kvt);
  k2_t = K2*(1 + (heatPort.T - Tnom)*kk2);
  
  G.i = 0;
  D.i = if (D.v < S.v) then -id else id;
  S.i = if (D.v < S.v) then id else -id;
  B.i = 0;
  heatPort.Q_dot = -D.i*(D.v - S.v);
end HeatingNMOS;







Modelica.Electrical.Analog.Semiconductors.HeatingNPN
Modelica.Electrical.Analog.Semiconductors.HeatingNPN

Simple NPN BJT according to Ebers-Moll with heating port

Modelica.Electrical.Analog.Semiconductors.HeatingNPN

Information





This model is a simple model of a bipolar npn junction transistor according
to Ebers-Moll.




A heating port is added for thermal electric simulation. The heating port
is defined in the Modelica.Thermal library.




A typical parameter set is (the parameter Vt is no longer used):



  Bf  Br  Is     Vak  Tauf    Taur  Ccs   Cje     Cjc     Phie  Me   PHic   Mc     Gbc    Gbe      
  -   -   A      V    s       s     F     F       F       V     -    V      -      mS     mS     
  50  0.1 1e-16  0.02 0.12e-9 5e-9  1e-12 0.4e-12 0.5e-12 0.8   0.4  0.8    0.333  1e-15  1e-15 







References:

Vlach, J.; Singal, K.: Computer methods for circuit analysis and design.
Van Nostrand Reinhold, New York 1983
on page 317 ff.








Parameters




NameDefaultDescription


Bf50Forward beta


Br0.1Reverse beta


Is1.e-16Transport saturation current [A]


Vak0.02Early voltage (inverse), 1/Volt [1/V]


Tauf0.12e-9Ideal forward transit time [s]


Taur5e-9Ideal reverse transit time [s]


Ccs1e-12Collector-substrat(ground) cap. [F]


Cje0.4e-12Base-emitter zero bias depletion cap. [F]


Cjc0.5e-12Base-coll. zero bias depletion cap. [F]


Phie0.8Base-emitter diffusion voltage [V]


Me0.4Base-emitter gradation exponent


Phic0.8Base-collector diffusion voltage [V]


Mc0.333Base-collector gradation exponent


Gbc1e-15Base-collector conductance [S]


Gbe1e-15Base-emitter conductance [S]


EMin-100if x < EMin, the exp(x) function is linearized


EMax40if x > EMax, the exp(x) function is linearized


Tnom300.15Parameter measurement temperature [K]


XTI3Temperature exponent for effect on Is


XTB0Forward and reverse beta temperature exponent


EG1.11Energy gap for temperature effect on Is


NF1.0Forward current emission coefficient


NR1.0Reverse current emission coefficient


K1.3806226e-23Boltzmann's constant


q1.6021918e-19Elementary electronic charge




Modelica definition


model HeatingNPN 
  "Simple NPN BJT according to Ebers-Moll with heating port" 
  parameter Real Bf=50 "Forward beta";
  parameter Real Br=0.1 "Reverse beta";
  parameter Modelica.SIunits.Current Is =      1.e-16 "Transport saturation current";
  parameter Modelica.SIunits.InversePotential Vak =      0.02 
    "Early voltage (inverse), 1/Volt";
  parameter Modelica.SIunits.Time Tauf =      0.12e-9 "Ideal forward transit time";
  parameter Modelica.SIunits.Time Taur =      5e-9 "Ideal reverse transit time";
  parameter Modelica.SIunits.Capacitance Ccs =      1e-12 
    "Collector-substrat(ground) cap.";
  parameter Modelica.SIunits.Capacitance Cje =      0.4e-12 
    "Base-emitter zero bias depletion cap.";
  parameter Modelica.SIunits.Capacitance Cjc =      0.5e-12 
    "Base-coll. zero bias depletion cap.";
  parameter Modelica.SIunits.Voltage Phie =      0.8 "Base-emitter diffusion voltage";
  parameter Real Me=0.4 "Base-emitter gradation exponent";
  parameter Modelica.SIunits.Voltage Phic =      0.8 
    "Base-collector diffusion voltage";
  parameter Real Mc=0.333 "Base-collector gradation exponent";
  parameter Modelica.SIunits.Conductance Gbc =      1e-15 "Base-collector conductance";
  parameter Modelica.SIunits.Conductance Gbe =      1e-15 "Base-emitter conductance";
  parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized";
  parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized";
  parameter Modelica.SIunits.Temperature Tnom =      300.15 
    "Parameter measurement temperature";
  parameter Real XTI=3 "Temperature exponent for effect on Is";
  parameter Real XTB=0 "Forward and reverse beta temperature exponent";
  parameter Real EG=1.11 "Energy gap for temperature effect on Is";
  parameter Real NF=1.0 "Forward current emission coefficient";
  parameter Real NR=1.0 "Reverse current emission coefficient";
  parameter Real K=1.3806226e-23 "Boltzmann's constant";
  parameter Real q=1.6021918e-19 "Elementary electronic charge";
  /*protected*/
  Real vbc;
  Real vbe;
  Real qbk;
  Real ibc;
  Real ibe;
  Real cbc;
  Real cbe;
  Real ExMin;
  Real ExMax;
  Real Capcje;
  Real Capcjc;
  Real is_t;
  Real br_t;
  Real bf_t;
  Real vt_t;
  Real hexp;
  Real htempexp;
  
public 
  Modelica.Electrical.Analog.Interfaces.Pin C "Collector";
  Modelica.Electrical.Analog.Interfaces.Pin B "Base";
  Modelica.Electrical.Analog.Interfaces.Pin E "Emitter";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort(
                                                               T(start=
          300.15));
equation 
  assert( heatPort.T > 0,"temperature must be positive");
  ExMin = exp(EMin);
  ExMax = exp(EMax);
  vbc = B.v - C.v;
  vbe = B.v - E.v;
  qbk = 1 - vbc*Vak;
  
  hexp = (heatPort.T/Tnom - 1)*EG/vt_t;
  htempexp = if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if (
    hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp);
  
  is_t = Is*pow((heatPort.T/Tnom), XTI)*htempexp;
  br_t = Br*pow((heatPort.T/Tnom), XTB);
  bf_t = Bf*pow((heatPort.T/Tnom), XTB);
  vt_t = (K/q)*heatPort.T;
  
  ibc = if (vbc/(NR*vt_t) < EMin) then is_t*(ExMin*(vbc/(NR*vt_t) -
    EMin + 1) - 1) + vbc*Gbc else if (vbc/(NR*vt_t) > EMax) then is_t*(
    ExMax*(vbc/(NR*vt_t) - EMax + 1) - 1) + vbc*Gbc else is_t*(exp(vbc/
    (NR*vt_t)) - 1) + vbc*Gbc;
  ibe = if (vbe/(NF*vt_t) < EMin) then is_t*(ExMin*(vbe/(NF*vt_t) -
    EMin + 1) - 1) + vbe*Gbe else if (vbe/(NF*vt_t) > EMax) then is_t*(
    ExMax*(vbe/(NF*vt_t) - EMax + 1) - 1) + vbe*Gbe else is_t*(exp(vbe/
    (NF*vt_t)) - 1) + vbe*Gbe;
  Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1
     - vbc/Phic, -Mc);
  Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1
     - vbe/Phie, -Me);
  cbc = if (vbc/(NR*vt_t) < EMin) then Taur*is_t/(NR*vt_t)*ExMin*(vbc/(
    NR*vt_t) - EMin + 1) + Capcjc else if (vbc/(NR*vt_t) > EMax) then 
    Taur*is_t/(NR*vt_t)*ExMax*(vbc/(NR*vt_t) - EMax + 1) + Capcjc else 
    Taur*is_t/(NR*vt_t)*exp(vbc/(NR*vt_t)) + Capcjc;
  cbe = if (vbe/(NF*vt_t) < EMin) then Tauf*is_t/(NF*vt_t)*ExMin*(vbe/(
    NF*vt_t) - EMin + 1) + Capcje else if (vbe/(NF*vt_t) > EMax) then 
    Tauf*is_t/(NF*vt_t)*ExMax*(vbe/(NF*vt_t) - EMax + 1) + Capcje else 
    Tauf*is_t/(NF*vt_t)*exp(vbe/(NF*vt_t)) + Capcje;
  C.i = (ibe - ibc)*qbk - ibc/br_t - cbc*der(vbc) + Ccs*der(C.v);
  B.i = ibe/bf_t + ibc/br_t + cbc*der(vbc) + cbe*der(vbe);
  E.i = -B.i - C.i + Ccs*der(C.v);
  
  heatPort.Q_dot = -(vbc*ibc/br_t + vbe*ibe/bf_t + (ibe - ibc)*qbk*(C.v
     - E.v));
end HeatingNPN;







Modelica.Electrical.Analog.Semiconductors.HeatingDiode
Modelica.Electrical.Analog.Semiconductors.HeatingDiode

Simple diode with heating port

Modelica.Electrical.Analog.Semiconductors.HeatingDiode

Information





The simple diode is an electrical one port, where a heat port is added, which is 
defined in the Modelica.Thermal library. It consists of the diode itself and an parallel ohmic
resistance R. The diode formula is:



 
                v/vt_t
  i  =  ids ( e        - 1).


where vt_t depends on the temperature of the heat port: 

 
  vt_t = k*temp/q




If the exponent v/vt_t reaches the limit maxex, the diode characterisic is linearly
continued to avoid overflow.

The thermal power is calculated by i*v.






Parameters




NameDefaultDescription


Ids1.e-6Saturation current [A]


Maxexp15Max. exponent for linear continuation


R1.e8Parallel ohmic resistance [Ohm]


EG1.11activation energy


N1Emission coefficient


TNOM300.15Parameter measurement temperature [K]


XTI3Temperature exponent of saturation current




Modelica definition


model HeatingDiode "Simple diode with heating port" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort(
                                                               T(start=
          300.15));
  parameter Modelica.SIunits.Current Ids =      1.e-6 "Saturation current";
  
    /* parameter Modelica.SIunits.Voltage Vt=0.04 "Voltage equivalent of temperature (kT/qn)"; */
  parameter Real Maxexp(final min=Modelica.Constants.SMALL) = 15 
    "Max. exponent for linear continuation";
  parameter Modelica.SIunits.Resistance R =      1.e8 "Parallel ohmic resistance";
  parameter Real EG=1.11 "activation energy";
  parameter Real N=1 "Emission coefficient";
  parameter Modelica.SIunits.Temperature TNOM =      300.15 
    "Parameter measurement temperature";
  parameter Real XTI=3 "Temperature exponent of saturation current";
  Modelica.SIunits.Temperature vt_t "Temperature voltage";
  Modelica.SIunits.Current id "diode current";
protected 
  Real k=1.380662e-23 "Boltzmann's constant, J/K";
  Real q=1.6021892e-19 "Electron charge, As";
  Modelica.SIunits.Temperature htemp "auxiliary temperature";
  Real aux;
  Real auxp;
  Real maxexp=exp(Maxexp);
equation 
  assert( heatPort.T > 0,"temperature must be positive");
  htemp = heatPort.T;
  vt_t = k*htemp/q;
  
  id = exlin((v/(N*vt_t)), Maxexp) - 1;
  
  aux = (htemp/TNOM - 1)*EG/(N*vt_t);
  auxp = exp(aux);
  
  i = Ids*id*pow(htemp/TNOM, XTI/N)*auxp + v/R;
  
  heatPort.Q_dot = -i*v;
end HeatingDiode;







Modelica.Electrical.Analog.Semiconductors.Diode
Modelica.Electrical.Analog.Semiconductors.Diode

Simple diode

Modelica.Electrical.Analog.Semiconductors.Diode

Information





The simple diode is a one port. It consists of the diode itself and an parallel ohmic
resistance R. The diode formula is:



 
                v/vt
  i  =  ids ( e      - 1).




If the exponent v/vt reaches the limit maxex, the diode characterisic is linearly
continued to avoid overflow.





Parameters




NameDefaultDescription


Ids1.e-6Saturation current [A]


Vt0.04Voltage equivalent of temperature (kT/qn) [V]


Maxexp15Max. exponent for linear continuation


R1.e8Parallel ohmic resistance [Ohm]




Modelica definition


model Diode "Simple diode" 
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  parameter SIunits.Current Ids =      1.e-6 "Saturation current";
  parameter SIunits.Voltage Vt =      0.04 "Voltage equivalent of temperature (kT/qn)";
  parameter Real Maxexp(final min=Modelica.Constants.SMALL) = 15 
    "Max. exponent for linear continuation";
  parameter SIunits.Resistance R =      1.e8 "Parallel ohmic resistance";
equation 
  i = if (v/Vt > Maxexp) then Ids*(exp(Maxexp)*(1 + v/Vt - Maxexp) - 1) +
    v/R else Ids*(exp(v/Vt) - 1) + v/R;
end Diode;







Modelica.Electrical.Analog.Semiconductors.PMOS
Modelica.Electrical.Analog.Semiconductors.PMOS

Simple MOS Transistor

Modelica.Electrical.Analog.Semiconductors.PMOS

Information





The PMOS model is a simple model of a p-channel metal-oxide semiconductor
FET. It differs slightly from the device used in the SPICE simulator.
For more details please care for H. Spiro.




The model does not consider capacitances. A high drain-source resistance RDS
is included to avoid numerical difficulties.





References:

Spiro, H.: Simulation integrierter Schaltungen. R. Oldenbourg Verlag 
  Muenchen Wien 1990.   




Some typical parameter sets are:



  W       L      Beta        Vt       K2       K5       DW         DL    
  m       m      A/V^2       V        -        -        m          m    

  50.e-6  8.e-6  .0085e-3   -.15     .41      .839    -3.8e-6    -4.0e-6           
  20.e-6  6.e-6  .0105e-3  -1.0      .41      .839    -2.5e-6    -2.1e-6 
  30.e-6  5.e-6  .0059e-3   -.3      .98     1.01      0         -3.9e-6   
  30.e-6  5.e-6  .0152e-3   -.69     .104    1.1       -.8e-6     -.4e-6         
  30.e-6  5.e-6  .0163e-3   -.69     .104    1.1       -.8e-6     -.4e-6         
  30.e-6  5.e-6  .0182e-3   -.69     .086    1.06      -.1e-6     -.6e-6         
  20.e-6  6.e-6  .0074e-3  -1.       .4       .59      0          0           





Parameters




NameDefaultDescription


W20.0e-6Width [m]


L6.0e-6Length [m]


Beta0.0105e-3Transconductance parameter [A/(V*V)]


Vt-1.0Zero bias threshold voltage [V]


K20.41Bulk threshold parameter


K50.839Reduction of pinch-off region


dW-2.5e-6Narrowing of channel [m]


dL-2.1e-6Shortening of channel [m]


RDS1.e+7Drain-Source-Resistance [Ohm]




Modelica definition


model PMOS "Simple MOS Transistor" 
  // 6.12.2001 parameter RDS added, Clauss    
  
  
  Interfaces.Pin D "Drain";
  Interfaces.Pin G "Gate";
  Interfaces.Pin S "Source";
  Interfaces.Pin B "Bulk";
  
  parameter SIunits.Length W =      20.0e-6 "Width";
  parameter SIunits.Length L =      6.0e-6 "Length";
  parameter SIunits.Transconductance Beta =      0.0105e-3 
    "Transconductance parameter";
  parameter SIunits.Voltage Vt =      -1.0 "Zero bias threshold voltage";
  parameter Real K2=0.41 "Bulk threshold parameter";
  parameter Real K5=0.839 "Reduction of pinch-off region";
  parameter SIunits.Length dW =      -2.5e-6 "Narrowing of channel";
  parameter SIunits.Length dL =      -2.1e-6 "Shortening of channel";
  parameter SIunits.Resistance RDS =      1.e+7 "Drain-Source-Resistance";
protected 
  Real v;
  Real uds;
  Real ubs;
  Real ugst;
  Real ud;
  Real us;
  Real id;
  Real gds;
equation 
  //assert (L + dL > 0, "Effective length must be positive");
  //assert (W + dW > 0, "Effective width  must be positive");
  gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS;
  v = Beta*(W + dW)/(L + dL);
  ud = if (D.v > S.v) then S.v else D.v;
  us = if (D.v > S.v) then D.v else S.v;
  uds = ud - us;
  ubs = if (B.v < us) then 0 else B.v - us;
  ugst = (G.v - us - Vt + K2*ubs)*K5;
  id = if (ugst >= 0) then v*uds*gds else if (ugst < uds) then -v*uds*(
    ugst - uds/2 - gds) else -v*(ugst*ugst/2 - uds*gds);
  G.i = 0;
  D.i = if (D.v > S.v) then -id else id;
  S.i = if (D.v > S.v) then id else -id;
  B.i = 0;
end PMOS;







Modelica.Electrical.Analog.Semiconductors.NMOS
Modelica.Electrical.Analog.Semiconductors.NMOS

Simple MOS Transistor

Modelica.Electrical.Analog.Semiconductors.NMOS

Information





The NMos model is a simple model of a n-channel metal-oxide semiconductor
FET. It differs slightly from the device used in the SPICE simulator.
For more details please care for H. Spiro.




The model does not consider capacitances. A high drain-source resistance RDS
is included to avoid numerical difficulties.





  W       L      Beta        Vt       K2      K5       DW         DL    
  m       m      A/V^2       V        -       -        m          m    

  12.e-6  4.e-6  .062e-3   -4.5      .24     .61     -1.2e-6     -.9e-6      depletion
  60.e-6  3.e-6  .048e-3     .1      .08     .68     -1.2e-6     -.9e-6      enhancement
  12.e-6  4.e-6  .0625e-3   -.8      .21     .78     -1.2e-6     -.9e-6      zero
  50.e-6  8.e-6  .0299e-3    .24    1.144    .7311   -5.4e-6    -4.e-6          
  20.e-6  6.e-6  .041e-3     .8     1.144    .7311   -2.5e-6    -1.5e-6         
  30.e-6  9.e-6  .025e-3   -4.       .861    .878    -3.4e-6    -1.74e-6        
  30.e-6  5.e-6  .031e-3     .6     1.5      .72      0         -3.9e-6         
  50.e-6  6.e-6  .0414e-3  -3.8      .34     .8      -1.6e-6    -2.e-6       depletion
  50.e-6  5.e-6  .03e-3      .37     .23     .86     -1.6e-6    -2.e-6       enhancement
  50.e-6  6.e-6  .038e-3    -.9      .23     .707    -1.6e-6    -2.e-6       zero
  20.e-6  4.e-6  .06776e-3   .5409   .065    .71      -.8e-6     -.2e-6      
  20.e-6  4.e-6  .06505e-3   .6209   .065    .71      -.8e-6     -.2e-6         
  20.e-6  4.e-6  .05365e-3   .6909   .03     .8       -.3e-6     -.2e-6        
  20.e-6  4.e-6  .05365e-3   .4909   .03     .8       -.3e-6     -.2e-6        
  12.e-6  4.e-6  .023e-3   -4.5      .29     .6       0          0           depletion
  60.e-6  3.e-6  .022e-3     .1      .11     .65      0          0           enhancement
  12.e-6  4.e-6  .038e-3    -.8      .33     .6       0          0           zero
  20.e-6  6.e-6  .022e-3     .8     1        .66      0          0            







References:

Spiro, H.: Simulation integrierter Schaltungen. R. Oldenbourg Verlag 
Muenchen Wien 1990.  





Parameters




NameDefaultDescription


W20.e-6Width [m]


L6.e-6Length [m]


Beta0.041e-3Transconductance parameter [A/(V*V)]


Vt0.8Zero bias threshold voltage [V]


K21.144Bulk threshold parameter


K50.7311Reduction of pinch-off region


dW-2.5e-6narrowing of channel [m]


dL-1.5e-6shortening of channel [m]


RDS1.e+7Drain-Source-Resistance [Ohm]




Modelica definition


model NMOS "Simple MOS Transistor" 
  // 6.12.2001 parameter RDS added, Clauss    
  Interfaces.Pin D "Drain";
  Interfaces.Pin G "Gate";
  Interfaces.Pin S "Source";
  Interfaces.Pin B "Bulk";
  parameter SIunits.Length W =      20.e-6 "Width";
  parameter SIunits.Length L =      6.e-6 "Length";
  parameter SIunits.Transconductance Beta =      0.041e-3 "Transconductance parameter";
  parameter SIunits.Voltage Vt =      0.8 "Zero bias threshold voltage";
  parameter Real K2=1.144 "Bulk threshold parameter";
  parameter Real K5=0.7311 "Reduction of pinch-off region";
  parameter SIunits.Length dW =      -2.5e-6 "narrowing of channel";
  parameter SIunits.Length dL =      -1.5e-6 "shortening of channel";
  parameter SIunits.Resistance RDS =      1.e+7 "Drain-Source-Resistance";
protected 
  Real v;
  Real uds;
  Real ubs;
  Real ugst;
  Real ud;
  Real us;
  Real id;
  Real gds;
equation 
  //assert (L + dL > 0, "Effective length must be positive");
  //assert (W + dW > 0, "Effective width  must be positive");
  gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS;
  v = Beta*(W + dW)/(L + dL);
  ud = if (D.v < S.v) then S.v else D.v;
  us = if (D.v < S.v) then D.v else S.v;
  uds = ud - us;
  ubs = if (B.v > us) then 0 else B.v - us;
  ugst = (G.v - us - Vt + K2*ubs)*K5;
  id = if (ugst <= 0) then v*uds*gds else if (ugst > uds) then v*uds*(ugst
     - uds/2 + gds) else v*(ugst*ugst/2 + uds*gds);
  G.i = 0;
  D.i = if (D.v < S.v) then -id else id;
  S.i = if (D.v < S.v) then id else -id;
  B.i = 0;
end NMOS;







Modelica.Electrical.Analog.Semiconductors.NPN
Modelica.Electrical.Analog.Semiconductors.NPN

Simple BJT according to Ebers-Moll

Modelica.Electrical.Analog.Semiconductors.NPN

Information





This model is a simple model of a bipolar npn junction transistor according
to Ebers-Moll.




A typical parameter set is:



  Bf  Br  Is     Vak  Tauf    Taur  Ccs   Cje     Cjc     Phie  Me   PHic   Mc     Gbc    Gbe    Vt   
  -   -   A      V    s       s     F     F       F       V     -    V      -      mS     mS     V

  50  0.1 1e-16  0.02 0.12e-9 5e-9  1e-12 0.4e-12 0.5e-12 0.8   0.4  0.8    0.333  1e-15  1e-15  0.02585







References:

Vlach, J.; Singal, K.: Computer methods for circuit analysis and design.
Van Nostrand Reinhold, New York 1983
on page 317 ff.







Parameters




NameDefaultDescription


Bf50Forward beta


Br0.1Reverse beta


Is1.e-16Transport saturation current [A]


Vak0.02Early voltage (inverse), 1/Volt [1/V]


Tauf0.12e-9Ideal forward transit time [s]


Taur5e-9Ideal reverse transit time [s]


Ccs1e-12Collector-substrat(ground) cap. [F]


Cje0.4e-12Base-emitter zero bias depletion cap. [F]


Cjc0.5e-12Base-coll. zero bias depletion cap. [F]


Phie0.8Base-emitter diffusion voltage [V]


Me0.4Base-emitter gradation exponent


Phic0.8Base-collector diffusion voltage [V]


Mc0.333Base-collector gradation exponent


Gbc1e-15Base-collector conductance [S]


Gbe1e-15Base-emitter conductance [S]


Vt0.02585Voltage equivalent of temperature [V]


EMin-100if x < EMin, the exp(x) function is linearized


EMax40if x > EMax, the exp(x) function is linearized




Modelica definition


model NPN "Simple BJT according to Ebers-Moll" 
  parameter Real Bf=50 "Forward beta";
  parameter Real Br=0.1 "Reverse beta";
  parameter SIunits.Current Is =      1.e-16 "Transport saturation current";
  parameter SIunits.InversePotential Vak =      0.02 "Early voltage (inverse), 1/Volt";
  parameter SIunits.Time Tauf =      0.12e-9 "Ideal forward transit time";
  parameter SIunits.Time Taur =      5e-9 "Ideal reverse transit time";
  parameter SIunits.Capacitance Ccs =      1e-12 "Collector-substrat(ground) cap.";
  parameter SIunits.Capacitance Cje =      0.4e-12 
    "Base-emitter zero bias depletion cap.";
  parameter SIunits.Capacitance Cjc =      0.5e-12 
    "Base-coll. zero bias depletion cap.";
  parameter SIunits.Voltage Phie =      0.8 "Base-emitter diffusion voltage";
  parameter Real Me=0.4 "Base-emitter gradation exponent";
  parameter SIunits.Voltage Phic =      0.8 "Base-collector diffusion voltage";
  parameter Real Mc=0.333 "Base-collector gradation exponent";
  parameter SIunits.Conductance Gbc =      1e-15 "Base-collector conductance";
  parameter SIunits.Conductance Gbe =      1e-15 "Base-emitter conductance";
  parameter SIunits.Voltage Vt =      0.02585 "Voltage equivalent of temperature";
  parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized";
  parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized";
protected 
  Real vbc;
  Real vbe;
  Real qbk;
  Real ibc;
  Real ibe;
  Real cbc;
  Real cbe;
  Real ExMin;
  Real ExMax;
  Real Capcje;
  Real Capcjc;
  function pow "Just a helper function for x^y" 
    input Real x;
    input Real y;
    output Real z;
  algorithm 
    z:=x^y;
  end pow;
public 
  Modelica.Electrical.Analog.Interfaces.Pin C "Collector";
  Modelica.Electrical.Analog.Interfaces.Pin B "Base";
  Modelica.Electrical.Analog.Interfaces.Pin E "Emitter";
equation 
  ExMin = exp(EMin);
  ExMax = exp(EMax);
  vbc = B.v - C.v;
  vbe = B.v - E.v;
  qbk = 1 - vbc*Vak;
  
  ibc = if (vbc/Vt < EMin) then Is*(ExMin*(vbc/Vt - EMin + 1) - 1) + vbc*Gbc else 
          if (vbc/Vt > EMax) then Is*(ExMax*(vbc/Vt - EMax + 1) - 1) + vbc*
    Gbc else Is*(exp(vbc/Vt) - 1) + vbc*Gbc;
  ibe = if (vbe/Vt < EMin) then Is*(ExMin*(vbe/Vt - EMin + 1) - 1) + vbe*Gbe else 
          if (vbe/Vt > EMax) then Is*(ExMax*(vbe/Vt - EMax + 1) - 1) + vbe*
    Gbe else Is*(exp(vbe/Vt) - 1) + vbe*Gbe;
  Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc
    /Phic, -Mc);
  Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe
    /Phie, -Me);
  cbc = if (vbc/Vt < EMin) then Taur*Is/Vt*ExMin*(vbc/Vt - EMin + 1) +
    Capcjc else if (vbc/Vt > EMax) then Taur*Is/Vt*ExMax*(vbc/Vt - EMax + 1)
     + Capcjc else Taur*Is/Vt*exp(vbc/Vt) + Capcjc;
  cbe = if (vbe/Vt < EMin) then Tauf*Is/Vt*ExMin*(vbe/Vt - EMin + 1) +
    Capcje else if (vbe/Vt > EMax) then Tauf*Is/Vt*ExMax*(vbe/Vt - EMax + 1)
     + Capcje else Tauf*Is/Vt*exp(vbe/Vt) + Capcje;
  C.i = (ibe - ibc)*qbk - ibc/Br - cbc*der(vbc) + Ccs*der(C.v);
  B.i = ibe/Bf + ibc/Br + cbc*der(vbc) + cbe*der(vbe);
  E.i = -B.i - C.i + Ccs*der(C.v);
end NPN;







Modelica.Electrical.Analog.Semiconductors.PNP
Modelica.Electrical.Analog.Semiconductors.PNP

Simple BJT according to Ebers-Moll

Modelica.Electrical.Analog.Semiconductors.PNP

Information





This model is a simple model of a bipolar pnp junction transistor according
to Ebers-Moll.


A typical parameter set is:



  Bf  Br  Is     Vak  Tauf    Taur  Ccs   Cje     Cjc     Phie  Me   PHic   Mc     Gbc    Gbe    Vt   
  -   -   A      V    s       s     F     F       F       V     -    V      -      mS     mS     V

  50  0.1 1e-16  0.02 0.12e-9 5e-9  1e-12 0.4e-12 0.5e-12 0.8   0.4  0.8    0.333  1e-15  1e-15  0.02585







References:

Vlach, J.; Singal, K.: Computer methods for circuit analysis and design.
Van Nostrand Reinhold, New York 1983
on page 317 ff.







Parameters




NameDefaultDescription


Bf50Forward beta


Br0.1Reverse beta


Is1.e-16Transport saturation current [A]


Vak0.02Early voltage (inverse), 1/Volt [1/V]


Tauf0.12e-9Ideal forward transit time [s]


Taur5e-9Ideal reverse transit time [s]


Ccs1e-12Collector-substrat(ground) cap. [F]


Cje0.4e-12Base-emitter zero bias depletion cap. [F]


Cjc0.5e-12Base-coll. zero bias depletion cap. [F]


Phie0.8Base-emitter diffusion voltage [V]


Me0.4Base-emitter gradation exponent


Phic0.8Base-collector diffusion voltage [V]


Mc0.333Base-collector gradation exponent


Gbc1e-15Base-collector conductance [S]


Gbe1e-15Base-emitter conductance [S]


Vt0.02585Voltage equivalent of temperature [V]


EMin-100if x < EMin, the exp(x) function is linearized


EMax40if x > EMax, the exp(x) function is linearized




Modelica definition


model PNP "Simple BJT according to Ebers-Moll" 
  parameter Real Bf=50 "Forward beta";
  parameter Real Br=0.1 "Reverse beta";
  parameter SIunits.Current Is =      1.e-16 "Transport saturation current";
  parameter SIunits.InversePotential Vak =      0.02 "Early voltage (inverse), 1/Volt";
  parameter SIunits.Time Tauf =      0.12e-9 "Ideal forward transit time";
  parameter SIunits.Time Taur =      5e-9 "Ideal reverse transit time";
  parameter SIunits.Capacitance Ccs =      1e-12 "Collector-substrat(ground) cap.";
  parameter SIunits.Capacitance Cje =      0.4e-12 
    "Base-emitter zero bias depletion cap.";
  parameter SIunits.Capacitance Cjc =      0.5e-12 
    "Base-coll. zero bias depletion cap.";
  parameter SIunits.Voltage Phie =      0.8 "Base-emitter diffusion voltage";
  parameter Real Me=0.4 "Base-emitter gradation exponent";
  parameter SIunits.Voltage Phic =      0.8 "Base-collector diffusion voltage";
  parameter Real Mc=0.333 "Base-collector gradation exponent";
  parameter SIunits.Conductance Gbc =      1e-15 "Base-collector conductance";
  parameter SIunits.Conductance Gbe =      1e-15 "Base-emitter conductance";
  parameter SIunits.Voltage Vt =      0.02585 "Voltage equivalent of temperature";
  parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized";
  parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized";
protected 
  Real vbc;
  Real vbe;
  Real qbk;
  Real ibc;
  Real ibe;
  Real cbc;
  Real cbe;
  Real ExMin;
  Real ExMax;
  Real Capcje;
  Real Capcjc;
  function pow "Just a helper function for x^y" 
    input Real x;
    input Real y;
    output Real z;
  algorithm 
    z:=x^y;
  end pow;
public 
  Modelica.Electrical.Analog.Interfaces.Pin C "Collector";
  Modelica.Electrical.Analog.Interfaces.Pin B "Base";
  Modelica.Electrical.Analog.Interfaces.Pin E "Emitter";
equation 
  ExMin = exp(EMin);
  ExMax = exp(EMax);
  vbc = C.v - B.v;
  vbe = E.v - B.v;
  qbk = 1 - vbc*Vak;
  
  ibc = if (vbc/Vt < EMin) then Is*(ExMin*(vbc/Vt - EMin + 1) - 1) + vbc*Gbc else 
          if (vbc/Vt > EMax) then Is*(ExMax*(vbc/Vt - EMax + 1) - 1) + vbc*
    Gbc else Is*(exp(vbc/Vt) - 1) + vbc*Gbc;
  
  ibe = if (vbe/Vt < EMin) then Is*(ExMin*(vbe/Vt - EMin + 1) - 1) + vbe*Gbe else 
          if (vbe/Vt > EMax) then Is*(ExMax*(vbe/Vt - EMax + 1) - 1) + vbe*
    Gbe else Is*(exp(vbe/Vt) - 1) + vbe*Gbe;
  
  Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc
    /Phic, -Mc);
  Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe
    /Phie, -Me);
  cbc = if (vbc/Vt < EMin) then Taur*Is/Vt*ExMin*(vbc/Vt - EMin + 1) +
    Capcjc else if (vbc/Vt > EMax) then Taur*Is/Vt*ExMax*(vbc/Vt - EMax + 1)
     + Capcjc else Taur*Is/Vt*exp(vbc/Vt) + Capcjc;
  cbe = if (vbe/Vt < EMin) then Tauf*Is/Vt*ExMin*(vbe/Vt - EMin + 1) +
    Capcje else if (vbe/Vt > EMax) then Tauf*Is/Vt*ExMax*(vbe/Vt - EMax + 1)
     + Capcje else Tauf*Is/Vt*exp(vbe/Vt) + Capcje;
  C.i = -((ibe - ibc)*qbk - ibc/Br - cbc*der(vbc) - Ccs*der(C.v));
  B.i = -(ibe/Bf + ibc/Br + cbe*der(vbe) + cbc*der(vbc));
  E.i = -B.i - C.i + Ccs*der(C.v);
end PNP;







Modelica.Electrical.Analog.Semiconductors.HeatingPNP
Modelica.Electrical.Analog.Semiconductors.HeatingPNP

Simple PNP BJT according to Ebers-Moll with heating port

Modelica.Electrical.Analog.Semiconductors.HeatingPNP

Information





This model is a simple model of a bipolar pnp junction transistor according
to Ebers-Moll.


A heating port is added for thermal electric simulation. The heating port
is defined in the Modelica.Thermal library.




A typical parameter set is  (the parameter Vt is no longer used):



  Bf  Br  Is     Vak  Tauf    Taur  Ccs   Cje     Cjc     Phie  Me   PHic   Mc     Gbc    Gbe  
  -   -   A      V    s       s     F     F       F       V     -    V      -      mS     mS     
  50  0.1 1e-16  0.02 0.12e-9 5e-9  1e-12 0.4e-12 0.5e-12 0.8   0.4  0.8    0.333  1e-15  1e-15 







References:

Vlach, J.; Singal, K.: Computer methods for circuit analysis and design.
Van Nostrand Reinhold, New York 1983
on page 317 ff.






Parameters




NameDefaultDescription


Bf50Forward beta


Br0.1Reverse beta


Is1.e-16Transport saturation current [A]


Vak0.02Early voltage (inverse), 1/Volt [1/V]


Tauf0.12e-9Ideal forward transit time [s]


Taur5e-9Ideal reverse transit time [s]


Ccs1e-12Collector-substrat(ground) cap. [F]


Cje0.4e-12Base-emitter zero bias depletion cap. [F]


Cjc0.5e-12Base-coll. zero bias depletion cap. [F]


Phie0.8Base-emitter diffusion voltage [V]


Me0.4Base-emitter gradation exponent


Phic0.8Base-collector diffusion voltage [V]


Mc0.333Base-collector gradation exponent


Gbc1e-15Base-collector conductance [S]


Gbe1e-15Base-emitter conductance [S]


EMin-100if x < EMin, the exp(x) function is linearized


EMax40if x > EMax, the exp(x) function is linearized


Tnom300.15Parameter measurement temperature [K]


XTI3Temperature exponent for effect on Is


XTB0Forward and reverse beta temperature exponent


EG1.11Energy gap for temperature effect on Is


NF1.0Forward current emission coefficient


NR1.0Reverse current emission coefficient


K1.3806226e-23Boltzmann's constant


q1.6021918e-19Elementary electronic charge




Modelica definition


model HeatingPNP 
  "Simple PNP BJT according to Ebers-Moll with heating port" 
  
  parameter Real Bf=50 "Forward beta";
  parameter Real Br=0.1 "Reverse beta";
  parameter Modelica.SIunits.Current Is =      1.e-16 "Transport saturation current";
  parameter Modelica.SIunits.InversePotential Vak =      0.02 
    "Early voltage (inverse), 1/Volt";
  parameter Modelica.SIunits.Time Tauf =      0.12e-9 "Ideal forward transit time";
  parameter Modelica.SIunits.Time Taur =      5e-9 "Ideal reverse transit time";
  parameter Modelica.SIunits.Capacitance Ccs =      1e-12 
    "Collector-substrat(ground) cap.";
  parameter Modelica.SIunits.Capacitance Cje =      0.4e-12 
    "Base-emitter zero bias depletion cap.";
  parameter Modelica.SIunits.Capacitance Cjc =      0.5e-12 
    "Base-coll. zero bias depletion cap.";
  parameter Modelica.SIunits.Voltage Phie =      0.8 "Base-emitter diffusion voltage";
  parameter Real Me=0.4 "Base-emitter gradation exponent";
  parameter Modelica.SIunits.Voltage Phic =      0.8 
    "Base-collector diffusion voltage";
  parameter Real Mc=0.333 "Base-collector gradation exponent";
  parameter Modelica.SIunits.Conductance Gbc =      1e-15 "Base-collector conductance";
  parameter Modelica.SIunits.Conductance Gbe =      1e-15 "Base-emitter conductance";
  parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized";
  parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized";
  parameter Modelica.SIunits.Temperature Tnom =      300.15 
    "Parameter measurement temperature";
  parameter Real XTI=3 "Temperature exponent for effect on Is";
  parameter Real XTB=0 "Forward and reverse beta temperature exponent";
  parameter Real EG=1.11 "Energy gap for temperature effect on Is";
  parameter Real NF=1.0 "Forward current emission coefficient";
  parameter Real NR=1.0 "Reverse current emission coefficient";
  parameter Real K=1.3806226e-23 "Boltzmann's constant";
  parameter Real q=1.6021918e-19 "Elementary electronic charge";
protected 
  Real vcb;
  Real veb;
  Real qbk;
  Real icb;
  Real ieb;
  Real ccb;
  Real ceb;
  Real ExMin;
  Real ExMax;
  Real Capcje;
  Real Capcjc;
  Real is_t;
  Real br_t;
  Real bf_t;
  Real vt_t;
  Real hexp;
  Real htempexp;
  
public 
  Modelica.Electrical.Analog.Interfaces.Pin C "Collector";
  Modelica.Electrical.Analog.Interfaces.Pin B "Base";
  Modelica.Electrical.Analog.Interfaces.Pin E "Emitter";
  Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort(
                                                               T(start=
          300.15));
equation 
  assert( heatPort.T > 0,"temperature must be positive");
  ExMin = exp(EMin);
  ExMax = exp(EMax);
  vcb = C.v - B.v;
  veb = E.v - B.v;
  qbk = 1 - vcb*Vak;
  
  hexp = (heatPort.T/Tnom - 1)*EG/vt_t;
  htempexp = if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if (
    hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp);
  
  is_t = Is*pow((heatPort.T/Tnom), XTI)*htempexp;
  br_t = Br*pow((heatPort.T/Tnom), XTB);
  bf_t = Bf*pow((heatPort.T/Tnom), XTB);
  vt_t = (K/q)*heatPort.T;
  
  icb = if (vcb/(NR*vt_t) < EMin) then is_t*(ExMin*(vcb/(NR*vt_t) -
    EMin + 1) - 1) + vcb*Gbc else if (vcb/(NR*vt_t) > EMax) then is_t*(
    ExMax*(vcb/(NR*vt_t) - EMax + 1) - 1) + vcb*Gbc else is_t*(exp(vcb/
    (NR*vt_t)) - 1) + vcb*Gbc;
  
  ieb = if (veb/(NF*vt_t) < EMin) then is_t*(ExMin*(veb/(NF*vt_t) -
    EMin + 1) - 1) + veb*Gbe else if (veb/(NF*vt_t) > EMax) then is_t*(
    ExMax*(veb/(NF*vt_t) - EMax + 1) - 1) + veb*Gbe else is_t*(exp(veb/
    (NF*vt_t)) - 1) + veb*Gbe;
  
  Capcjc = if (vcb/Phic > 0) then Cjc*(1 + Mc*vcb/Phic) else Cjc*pow(1
     - vcb/Phic, -Mc);
  Capcje = if (veb/Phie > 0) then Cje*(1 + Me*veb/Phie) else Cje*pow(1
     - veb/Phie, -Me);
  ccb = if (vcb/(NR*vt_t) < EMin) then Taur*is_t/(NR*vt_t)*ExMin*(vcb/(
    NR*vt_t) - EMin + 1) + Capcjc else if (vcb/(NR*vt_t) > EMax) then 
    Taur*is_t/(NR*vt_t)*ExMax*(vcb/(NR*vt_t) - EMax + 1) + Capcjc else 
    Taur*is_t/(NR*vt_t)*exp(vcb/(NR*vt_t)) + Capcjc;
  ceb = if (veb/(NF*vt_t) < EMin) then Tauf*is_t/(NF*vt_t)*ExMin*(veb/(
    NF*vt_t) - EMin + 1) + Capcje else if (veb/(NF*vt_t) > EMax) then 
    Tauf*is_t/(NF*vt_t)*ExMax*(veb/(NF*vt_t) - EMax + 1) + Capcje else 
    Tauf*is_t/(NF*vt_t)*exp(veb/(NF*vt_t)) + Capcje;
  C.i = icb/br_t + ccb*der(vcb) + Ccs*der(C.v) + (icb - ieb)*qbk;
  B.i = -ieb/bf_t - icb/br_t - ceb*der(veb) - ccb*der(vcb);
  E.i = -B.i - C.i + Ccs*der(C.v);
  
  heatPort.Q_dot = -(vcb*icb/br_t + veb*ieb/bf_t + (icb - ieb)*qbk*(E.v
     - C.v));
end HeatingPNP;







Modelica.Electrical.Analog.Semiconductors.pow

Just a helper function for x^y in order that a symbolic engine can apply some transformations more easily


Modelica definition


function pow 
  "Just a helper function for x^y in order that a symbolic engine can apply some transformations more easily" 
  
  input Real x;
  input Real y;
  output Real z;
algorithm 
  z := x^y;
end pow;







Modelica.Electrical.Analog.Semiconductors.exlin

Exponential function linearly continued for x > Maxexp


Modelica definition


function exlin 
  "Exponential function linearly continued for x > Maxexp" 
  
  input Real x;
  input Real Maxexp;
  output Real z;
algorithm 
  z := if x > Maxexp then exp(Maxexp)*(1 + x - Maxexp) else exp(x);
end exlin;





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