Modelica.Electrical.Analog.Semiconductors

Information

This package contains semiconductor devices:

• diode
• MOS transistors
• bipolar transistors

Extends from Modelica.Icons.Library (Icon for library).

Package Content

Name	Description
Diode	Simple diode
ZDiode	Zener Diode with 3 working areas
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
Thyristor	Simple Thyristor Model

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.

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

Extends from Modelica.Electrical.Analog.Interfaces.OnePort (Component with two electrical pins p and n and current i from p to n), Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Current	Ids	1.e-6	Saturation current [A]
Voltage	Vt	0.04	Voltage equivalent of temperature (kT/qn) [V]
Real	Maxexp	15	Max. exponent for linear continuation
Resistance	R	1.e8	Parallel ohmic resistance [Ohm]
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
PositivePin	p	Positive pin (potential p.v > n.v for positive voltage drop v)
NegativePin	n	Negative pin
HeatPort_a	heatPort

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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
equation 
  i = smooth(1,(if (v/Vt > Maxexp) then Ids*(exp(Maxexp)*(1 + v/Vt - Maxexp) - 1) +
    v/R else Ids*(exp(v/Vt) - 1) + v/R));
  LossPower = v*i;
end Diode;

Modelica.Electrical.Analog.Semiconductors.ZDiode

Information

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

                v/Vt                -(v+Bv)/(Nbv*Vt)
  i  =  Ids ( e      - 1) - Ibv ( e                  ).

If the exponent in one of the two branches reaches the limit Maxexp, the diode characterisic is linearly continued to avoid overflow.

The zener diode model permits (in contrast to the simple diode model) current in reverse direction if the breakdown voltage Bv (also known zener knee voltage) is exceeded.

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

Extends from Modelica.Electrical.Analog.Interfaces.OnePort (Component with two electrical pins p and n and current i from p to n), Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Current	Ids	1.e-6	Saturation current [A]
Voltage	Vt	0.04	Voltage equivalent of temperature (kT/qn) [V]
Real	Maxexp	30	Max. exponent for linear continuation
Resistance	R	1.e8	Parallel ohmic resistance [Ohm]
Voltage	Bv	5.1	Breakthrough voltage = Zener- or Z-voltage [V]
Current	Ibv	0.7	Breakthrough knee current [A]
Real	Nbv	0.74	Breakthrough emission coefficient
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
PositivePin	p	Positive pin (potential p.v > n.v for positive voltage drop v)
NegativePin	n	Negative pin
HeatPort_a	heatPort

Modelica definition

model ZDiode "Zener Diode with 3 working areas"
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  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) = 30 
    "Max. exponent for linear continuation";
  parameter Modelica.SIunits.Resistance R=1.e8 "Parallel ohmic resistance";
  parameter Modelica.SIunits.Voltage Bv=5.1 
    "Breakthrough voltage = Zener- or Z-voltage";
  parameter Modelica.SIunits.Current Ibv=0.7 "Breakthrough knee current";
  parameter Real Nbv=0.74 "Breakthrough emission coefficient";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
equation 
  i = smooth(1, if (v>Maxexp*Vt) then 
            Ids*( exp(Maxexp)*(1 + v/Vt - Maxexp)-1) + v/R else 
         if ( (v+Bv)<-Maxexp*(Nbv*Vt)) then 
            -Ids -Ibv* exp(Maxexp)*(1 - (v+Bv)/(Nbv*Vt) - Maxexp) +v/R else 
            Ids*(exp(v/Vt)-1) - Ibv*exp(-(v+Bv)/(Nbv*Vt)) + v/R);
  LossPower = v*i;
end ZDiode;

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.

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

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

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Length	W	20.0e-6	Width [m]
Length	L	6.0e-6	Length [m]
Transconductance	Beta	0.0105e-3	Transconductance parameter [A/V2]
Voltage	Vt	-1.0	Zero bias threshold voltage [V]
Real	K2	0.41	Bulk threshold parameter
Real	K5	0.839	Reduction of pinch-off region
Length	dW	-2.5e-6	Narrowing of channel [m]
Length	dL	-2.1e-6	Shortening of channel [m]
Resistance	RDS	1.e+7	Drain-Source-Resistance [Ohm]
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
Pin	D	Drain
Pin	G	Gate
Pin	S	Source
Pin	B	Bulk
HeatPort_a	heatPort

Modelica definition

model PMOS "Simple MOS Transistor"

  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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
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 = smooth(0,if (D.v > S.v) then S.v else D.v);
  us = smooth(0,if (D.v > S.v) then D.v else S.v);
  uds = ud - us;
  ubs = smooth(0,if (B.v < us) then 0 else B.v - us);
  ugst = (G.v - us - Vt + K2*ubs)*K5;
  id = smooth(0,if (ugst >= 0) then uds*gds else if (ugst < uds) then -v*uds*(
    ugst - uds/2) + uds*gds else -v*ugst*ugst/2 + uds*gds);
  G.i = 0;
  D.i = smooth(0,if (D.v > S.v) then -id else id);
  S.i = smooth(0,if (D.v > S.v) then id else -id);
  B.i = 0;
  LossPower = D.i * (D.v - S.v);
end PMOS;

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.

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

  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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Length	W	20.e-6	Width [m]
Length	L	6.e-6	Length [m]
Transconductance	Beta	0.041e-3	Transconductance parameter [A/V2]
Voltage	Vt	0.8	Zero bias threshold voltage [V]
Real	K2	1.144	Bulk threshold parameter
Real	K5	0.7311	Reduction of pinch-off region
Length	dW	-2.5e-6	narrowing of channel [m]
Length	dL	-1.5e-6	shortening of channel [m]
Resistance	RDS	1.e+7	Drain-Source-Resistance [Ohm]
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
Pin	D	Drain
Pin	G	Gate
Pin	S	Source
Pin	B	Bulk
HeatPort_a	heatPort

Modelica definition

model NMOS "Simple MOS Transistor"

  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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
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 = smooth(0,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 = smooth(0,if (B.v > us) then 0 else B.v - us);
  ugst = (G.v - us - Vt + K2*ubs)*K5;
  id = smooth(0,if (ugst <= 0) then uds*gds else if (ugst > uds) then v*uds*(ugst
     - uds/2) + uds*gds else v*ugst*ugst/2 + uds*gds);
  G.i = 0;
  D.i = smooth(0,if (D.v < S.v) then -id else id);
  S.i = smooth(0,if (D.v < S.v) then id else -id);
  B.i = 0;
  LossPower = D.i * (D.v - S.v);
end NMOS;

Modelica.Electrical.Analog.Semiconductors.NPN

Information

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

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Real	Bf	50	Forward beta
Real	Br	0.1	Reverse beta
Current	Is	1.e-16	Transport saturation current [A]
InversePotential	Vak	0.02	Early voltage (inverse), 1/Volt [1/V]
Time	Tauf	0.12e-9	Ideal forward transit time [s]
Time	Taur	5e-9	Ideal reverse transit time [s]
Capacitance	Ccs	1e-12	Collector-substrat(ground) cap. [F]
Capacitance	Cje	0.4e-12	Base-emitter zero bias depletion cap. [F]
Capacitance	Cjc	0.5e-12	Base-coll. zero bias depletion cap. [F]
Voltage	Phie	0.8	Base-emitter diffusion voltage [V]
Real	Me	0.4	Base-emitter gradation exponent
Voltage	Phic	0.8	Base-collector diffusion voltage [V]
Real	Mc	0.333	Base-collector gradation exponent
Conductance	Gbc	1e-15	Base-collector conductance [S]
Conductance	Gbe	1e-15	Base-emitter conductance [S]
Voltage	Vt	0.02585	Voltage equivalent of temperature [V]
Real	EMin	-100	if x < EMin, the exp(x) function is linearized
Real	EMax	40	if x > EMax, the exp(x) function is linearized
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
HeatPort_a	heatPort
Pin	C	Collector
Pin	B	Base
Pin	E	Emitter

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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
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 = smooth(1,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 = smooth(1,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 = smooth(1,(if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc
    /Phic, -Mc)));
  Capcje = smooth(1,(if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe
    /Phie, -Me)));
  cbc = smooth(1,(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 = smooth(1,(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);

  LossPower = (C.v-E.v)*(ibe-ibc)*qbk + vbc*ibc/Br + vbe*ibe/Bf;
end NPN;

Modelica.Electrical.Analog.Semiconductors.PNP

Information

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

Please note: In case of useHeatPort=true the temperature dependence of the electrical behavior is not modelled yet. The parameters are not temperature dependent.

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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Real	Bf	50	Forward beta
Real	Br	0.1	Reverse beta
Current	Is	1.e-16	Transport saturation current [A]
InversePotential	Vak	0.02	Early voltage (inverse), 1/Volt [1/V]
Time	Tauf	0.12e-9	Ideal forward transit time [s]
Time	Taur	5e-9	Ideal reverse transit time [s]
Capacitance	Ccs	1e-12	Collector-substrat(ground) cap. [F]
Capacitance	Cje	0.4e-12	Base-emitter zero bias depletion cap. [F]
Capacitance	Cjc	0.5e-12	Base-coll. zero bias depletion cap. [F]
Voltage	Phie	0.8	Base-emitter diffusion voltage [V]
Real	Me	0.4	Base-emitter gradation exponent
Voltage	Phic	0.8	Base-collector diffusion voltage [V]
Real	Mc	0.333	Base-collector gradation exponent
Conductance	Gbc	1e-15	Base-collector conductance [S]
Conductance	Gbe	1e-15	Base-emitter conductance [S]
Voltage	Vt	0.02585	Voltage equivalent of temperature [V]
Real	EMin	-100	if x < EMin, the exp(x) function is linearized
Real	EMax	40	if x > EMax, the exp(x) function is linearized
Boolean	useHeatPort	false	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
HeatPort_a	heatPort
Pin	C	Collector
Pin	B	Base
Pin	E	Emitter

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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(T=293.15);
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 = smooth(1,(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 = smooth(1,(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 = smooth(1,(if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc
    /Phic, -Mc)));
  Capcje = smooth(1,if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe
    /Phie, -Me));
  cbc = smooth(1,(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 = smooth(1,(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);

  LossPower = (E.v-C.v)*(ibe-ibc)*qbk + vbc*ibc/Br + vbe*ibe/Bf;
end PNP;

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).

  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.

Extends from Modelica.Electrical.Analog.Interfaces.OnePort (Component with two electrical pins p and n and current i from p to n), Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Current	Ids	1.e-6	Saturation current [A]
Real	Maxexp	15	Max. exponent for linear continuation
Resistance	R	1.e8	Parallel ohmic resistance [Ohm]
Real	EG	1.11	activation energy
Real	N	1	Emission coefficient
Temperature	TNOM	300.15	Parameter measurement temperature [K]
Real	XTI	3	Temperature exponent of saturation current
Boolean	useHeatPort	true	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
PositivePin	p	Positive pin (potential p.v > n.v for positive voltage drop v)
NegativePin	n	Negative pin
HeatPort_a	heatPort

Modelica definition

model HeatingDiode "Simple diode with heating port"
  extends Modelica.Electrical.Analog.Interfaces.OnePort;
  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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(useHeatPort=true);

  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( T_heatPort > 0,"temperature must be positive");
  htemp = T_heatPort;
  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;

  LossPower = i*v;
end HeatingDiode;

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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Length	W	20.e-6	Width [m]
Length	L	6.e-6	Length [m]
Transconductance	Beta	0.041e-3	Transconductance parameter [A/V2]
Voltage	Vt	0.8	Zero bias threshold voltage [V]
Real	K2	1.144	Bulk threshold parameter
Real	K5	0.7311	Reduction of pinch-off region
Length	dW	-2.5e-6	narrowing of channel [m]
Length	dL	-1.5e-6	shortening of channel [m]
Resistance	RDS	1.e+7	Drain-Source-Resistance [Ohm]
Temperature	Tnom	300.15	Parameter measurement temperature [K]
Real	kvt	-6.96e-3	fitting parameter for Vt
Real	kk2	6.0e-4	fitting parameter for K22
Boolean	useHeatPort	true	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
Pin	D	Drain
Pin	G	Gate
Pin	S	Source
Pin	B	Bulk
HeatPort_a	heatPort

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";
  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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(useHeatPort=true);
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( T_heatPort > 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 = smooth(0,if (D.v < S.v) then S.v else D.v);
  us = smooth(0,if (D.v < S.v) then D.v else S.v);
  uds = ud - us;
  ubs = smooth(0,if (B.v > us) then 0 else B.v - us);
  ugst = (G.v - us - vt_t + k2_t*ubs)*K5;
  id = smooth(0,if (ugst <= 0) then uds*gds else if (ugst > uds) then v*uds*(
    ugst - uds/2) + uds*gds else v*ugst*ugst/2 + uds*gds);

  beta_t = Beta*pow((T_heatPort/Tnom), -1.5);
  vt_t = Vt*(1 + (T_heatPort - Tnom)*kvt);
  k2_t = K2*(1 + (T_heatPort - Tnom)*kk2);

  G.i = 0;
  D.i = smooth(0,if (D.v < S.v) then -id else id);
  S.i = smooth(0,if (D.v < S.v) then id else -id);
  B.i = 0;
  LossPower = D.i*(D.v - S.v);
end HeatingNMOS;

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

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Length	W	20.0e-6	Width [m]
Length	L	6.0e-6	Length [m]
Transconductance	Beta	0.0105e-3	Transconductance parameter [A/V2]
Voltage	Vt	-1.0	Zero bias threshold voltage [V]
Real	K2	0.41	Bulk threshold parameter
Real	K5	0.839	Reduction of pinch-off region
Length	dW	-2.5e-6	Narrowing of channel [m]
Length	dL	-2.1e-6	Shortening of channel [m]
Resistance	RDS	1.e+7	Drain-Source-Resistance [Ohm]
Temperature	Tnom	300.15	Parameter measurement temperature [K]
Real	kvt	-2.9e-3	fitting parameter for Vt
Real	kk2	6.2e-4	fitting parameter for Kk2
Boolean	useHeatPort	true	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
Pin	D	Drain
Pin	G	Gate
Pin	S	Source
Pin	B	Bulk
HeatPort_a	heatPort

Modelica definition

model HeatingPMOS "Simple PMOS 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";
  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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(useHeatPort=true);
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( T_heatPort > 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 = smooth(0,if (D.v > S.v) then S.v else D.v);
  us = smooth(0,if (D.v > S.v) then D.v else S.v);
  uds = ud - us;
  ubs = smooth(0,if (B.v < us) then 0 else B.v - us);
  ugst = (G.v - us - vt_t + k2_t*ubs)*K5;
  id = smooth(0,if (ugst >= 0) then uds*gds else if (ugst < uds) then -v*uds*(
    ugst - uds/2) + uds*gds else -v*ugst*ugst/2 + uds*gds);

  beta_t = Beta*pow((T_heatPort/Tnom), -1.5);
  vt_t = Vt*(1 + (T_heatPort - Tnom)*kvt);
  k2_t = K2*(1 + (T_heatPort - Tnom)*kk2);

  G.i = 0;
  D.i = smooth(0,if (D.v > S.v) then -id else id);
  S.i = smooth(0,if (D.v > S.v) then id else -id);
  B.i = 0;
  LossPower = D.i*(D.v - S.v);
end HeatingPMOS;

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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Real	Bf	50	Forward beta
Real	Br	0.1	Reverse beta
Current	Is	1.e-16	Transport saturation current [A]
InversePotential	Vak	0.02	Early voltage (inverse), 1/Volt [1/V]
Time	Tauf	0.12e-9	Ideal forward transit time [s]
Time	Taur	5e-9	Ideal reverse transit time [s]
Capacitance	Ccs	1e-12	Collector-substrat(ground) cap. [F]
Capacitance	Cje	0.4e-12	Base-emitter zero bias depletion cap. [F]
Capacitance	Cjc	0.5e-12	Base-coll. zero bias depletion cap. [F]
Voltage	Phie	0.8	Base-emitter diffusion voltage [V]
Real	Me	0.4	Base-emitter gradation exponent
Voltage	Phic	0.8	Base-collector diffusion voltage [V]
Real	Mc	0.333	Base-collector gradation exponent
Conductance	Gbc	1e-15	Base-collector conductance [S]
Conductance	Gbe	1e-15	Base-emitter conductance [S]
Real	EMin	-100	if x < EMin, the exp(x) function is linearized
Real	EMax	40	if x > EMax, the exp(x) function is linearized
Temperature	Tnom	300.15	Parameter measurement temperature [K]
Real	XTI	3	Temperature exponent for effect on Is
Real	XTB	0	Forward and reverse beta temperature exponent
Real	EG	1.11	Energy gap for temperature effect on Is
Real	NF	1.0	Forward current emission coefficient
Real	NR	1.0	Reverse current emission coefficient
Real	K	1.3806226e-23	Boltzmann's constant
Real	q	1.6021918e-19	Elementary electronic charge
Boolean	useHeatPort	true	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
HeatPort_a	heatPort
Pin	C	Collector
Pin	B	Base
Pin	E	Emitter

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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(useHeatPort=true);
  /*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";
equation 
  assert( T_heatPort > 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 = (T_heatPort/Tnom - 1)*EG/vt_t;
  htempexp = smooth(1,if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if (
    hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp));

  is_t = Is*pow((T_heatPort/Tnom), XTI)*htempexp;
  br_t = Br*pow((T_heatPort/Tnom), XTB);
  bf_t = Bf*pow((T_heatPort/Tnom), XTB);
  vt_t = (K/q)*T_heatPort;

  ibc = smooth(1,(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 = smooth(1,(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 = smooth(1,(if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1
     - vbc/Phic, -Mc)));
  Capcje = smooth(1,(if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1
     - vbe/Phie, -Me)));
  cbc = smooth(1,(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 = smooth(1,(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);

  LossPower = (vbc*ibc/br_t + vbe*ibe/bf_t + (ibe - ibc)*qbk*(C.v - E.v));
end HeatingNPN;

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.

Extends from Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort (Partial model to include a conditional HeatPort in order to describe the power loss via a thermal network).

Parameters

Type	Name	Default	Description
Real	Bf	50	Forward beta
Real	Br	0.1	Reverse beta
Current	Is	1.e-16	Transport saturation current [A]
InversePotential	Vak	0.02	Early voltage (inverse), 1/Volt [1/V]
Time	Tauf	0.12e-9	Ideal forward transit time [s]
Time	Taur	5e-9	Ideal reverse transit time [s]
Capacitance	Ccs	1e-12	Collector-substrat(ground) cap. [F]
Capacitance	Cje	0.4e-12	Base-emitter zero bias depletion cap. [F]
Capacitance	Cjc	0.5e-12	Base-coll. zero bias depletion cap. [F]
Voltage	Phie	0.8	Base-emitter diffusion voltage [V]
Real	Me	0.4	Base-emitter gradation exponent
Voltage	Phic	0.8	Base-collector diffusion voltage [V]
Real	Mc	0.333	Base-collector gradation exponent
Conductance	Gbc	1e-15	Base-collector conductance [S]
Conductance	Gbe	1e-15	Base-emitter conductance [S]
Real	EMin	-100	if x < EMin, the exp(x) function is linearized
Real	EMax	40	if x > EMax, the exp(x) function is linearized
Temperature	Tnom	300.15	Parameter measurement temperature [K]
Real	XTI	3	Temperature exponent for effect on Is
Real	XTB	0	Forward and reverse beta temperature exponent
Real	EG	1.11	Energy gap for temperature effect on Is
Real	NF	1.0	Forward current emission coefficient
Real	NR	1.0	Reverse current emission coefficient
Real	K	1.3806226e-23	Boltzmann's constant
Real	q	1.6021918e-19	Elementary electronic charge
Boolean	useHeatPort	true	=true, if HeatPort is enabled
Temperature	T	293.15	Fixed device temperature if useHeatPort = false [K]

Connectors

Type	Name	Description
HeatPort_a	heatPort
Pin	C	Collector
Pin	B	Base
Pin	E	Emitter

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";
  extends Modelica.Electrical.Analog.Interfaces.ConditionalHeatPort(useHeatPort=true);
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";
equation 
  assert( T_heatPort > 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 = (T_heatPort/Tnom - 1)*EG/vt_t;
  htempexp = smooth(1,if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if (
    hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp));

  is_t = Is*pow((T_heatPort/Tnom), XTI)*htempexp;
  br_t = Br*pow((T_heatPort/Tnom), XTB);
  bf_t = Bf*pow((T_heatPort/Tnom), XTB);
  vt_t = (K/q)*T_heatPort;

  icb = smooth(1,(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 = smooth(1,(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 = smooth(1,(if (vcb/Phic > 0) then Cjc*(1 + Mc*vcb/Phic) else Cjc*pow(1
     - vcb/Phic, -Mc)));
  Capcje = smooth(1,(if (veb/Phie > 0) then Cje*(1 + Me*veb/Phie) else Cje*pow(1
     - veb/Phie, -Me)));
  ccb = smooth(1,(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 = smooth(1,(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);

  LossPower = (vcb*icb/br_t + veb*ieb/bf_t + (icb - ieb)*qbk*(C.v- E.v));
end HeatingPNP;

Modelica.Electrical.Analog.Semiconductors.pow

Inputs

Type	Name	Default	Description
Real	x
Real	y

Outputs

Type	Name	Description
Real	z

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

Inputs

Type	Name	Default	Description
Real	x
Real	Maxexp

Outputs

Type	Name	Description
Real	z

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;

Modelica.Electrical.Analog.Semiconductors.Thyristor

Information

As long as the thyristor is in blocking mode it behaves like a linear resistance Roff=VDRM^2/(VTM*IH).
But if the voltage between anode and cathode exceeds VDRM or a positive gate current flows for a sufficient time the mode changes to conducting mode.
The model stays in conducting mode until the anode current falls below the holding current IH. There is no way to switch off the thyristor via the gate.
If the voltage between anode and cathode is negative, the model represents a diode (parameters Vt, Nbv) with reverse breakthrough voltage VRRM.

The dV/dt switch on is not taken into account in this model. The gate circuit is not influenced by the main circuit.

Parameters

Type	Name	Default	Description
Voltage	VDRM	100	Forward breakthrough voltage [V]
Voltage	VRRM	100	Reverse breakthrough voltage [V]
Current	IDRM	0.1	Saturation current [A]
Voltage	VTM	1.7	Conducting voltage [V]
Current	IH	6e-3	Holding current [A]
Current	ITM	25	Conducting current [A]
Voltage	VGT	0.7	Gate trigger voltage [V]
Current	IGT	5e-3	Gate trigger current [A]
Time	TON	1e-6	Switch on time [s]
Time	TOFF	15e-6	Switch off time [s]
Voltage	Vt	0.04	Voltage equivalent of temperature (kT/qn) [V]
Real	Nbv	0.74	Reverse Breakthrough emission coefficient

Connectors

Type	Name	Description
PositivePin	Anode
NegativePin	Cathode
PositivePin	Gate

Modelica definition

model Thyristor "Simple Thyristor Model"
  parameter Modelica.SIunits.Voltage VDRM(final min=0) = 100 
    "Forward breakthrough voltage";
  parameter Modelica.SIunits.Voltage VRRM(final min=0) = 100 
    "Reverse breakthrough voltage";
  parameter Modelica.SIunits.Current IDRM=0.1 "Saturation current";
  parameter Modelica.SIunits.Voltage VTM= 1.7 "Conducting voltage";
  parameter Modelica.SIunits.Current IH=6e-3 "Holding current";
  parameter Modelica.SIunits.Current ITM= 25 "Conducting current";

  parameter Modelica.SIunits.Voltage VGT= 0.7 "Gate trigger voltage";
  parameter Modelica.SIunits.Current IGT= 5e-3 "Gate trigger current";

  parameter Modelica.SIunits.Time TON = 1e-6 "Switch on time";
  parameter Modelica.SIunits.Time TOFF = 15e-6 "Switch off time";
  parameter Modelica.SIunits.Voltage Vt=0.04 
    "Voltage equivalent of temperature (kT/qn)";
  parameter Real Nbv=0.74 "Reverse Breakthrough emission coefficient";

  Real iGK "gate current";
  Real vGK "voltage between gate and cathode";
  Real vAK "voltage between anode and cathode";
  Real vControl(start=0);
  Real vContot;
  Real vConmain;

public 
  Modelica.Electrical.Analog.Interfaces.PositivePin Anode;
  Modelica.Electrical.Analog.Interfaces.NegativePin Cathode;
  Modelica.Electrical.Analog.Interfaces.PositivePin Gate;

protected 
  parameter Modelica.SIunits.Voltage Von=5;
  parameter Modelica.SIunits.Voltage Voff= 1.5;
  parameter Modelica.SIunits.Resistance Ron=(VTM-0.7)/ITM 
    "Forward conducting mode resistance";
  parameter Modelica.SIunits.Resistance Roff=(VDRM^2)/VTM/IH 
    "Blocking mode resistance";

equation 
  //Kirchhoff's equations
  Anode.i+Gate.i+Cathode.i=0;
  vGK=Gate.v-Cathode.v;
  vAK=Anode.v-Cathode.v;

  // Gate and Control voltage
  iGK = Gate.i;
  vGK = smooth(0,(if vGK < 0.65 then VGT/IGT*iGK else 
        0.65^2/VGT+iGK*(VGT-0.65)/IGT));
  vContot = vConmain + smooth(0, if iGK < 0.95 * IGT then 0 else if iGK < 0.95*IGT + 1e-3 then 10000*(iGK-0.95*IGT)*vAK else 10* vAK);
  der(vControl)= (vContot - vControl) / (if (vContot - vControl) > 0 then 1.87*TON else 0.638*TOFF);

  // Anode-Cathode characteristics
  Anode.i= smooth(1, if vAK < -VRRM then -VRRM/Roff*exp(-(vAK+VRRM)/(Nbv*Vt)) else 
         if vControl<Voff then vAK/Roff else 
         if vControl<Von then vAK/(sqrt(Ron*Roff)*(Ron/Roff)^((3*((2*vControl-Von-Voff)/(2*(Von-Voff)))-4*((2*vControl-Von-Voff)/(2*(Von-Voff)))^3)/2)) else 
          vAK/Ron);

  // holding effect and forward breakthrough
  vConmain = (if Anode.i>IH or vAK>VDRM then Von else 0);

end Thyristor;