Modelica.Electrical.Analog.Semiconductors

Semiconductor devices such as diode, MOS and bipolar transistor

Information

This package contains semiconductor devices:

diode
MOS transistors
bipolar transistors
thyristor
triac

Most of the semiconductor devices contain a conditional heat port, which is not active by default. If it is active the loss power is calculated to be used in a thermal net. The heating variants of the semiconductor devices are provided to use the thermal port temperature in the electric calculation. That means that for a true thermal electric interaction the heating device models have to be used.

Extends from Modelica.Icons.Package (Icon for standard packages).

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

SimpleTriac Simple triac, based on Semiconductors.Thyristor model

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
SimpleTriac	Simple triac, based on Semiconductors.Thyristor model

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.

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]

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

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

Zener diode with 3 working areas

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.

The thermal power is calculated by i*v.

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

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]

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

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);

  Real maxexp=exp(Maxexp);
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

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.

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  0.0085e-3  -0.15  0.41   0.839  -3.8e-6  -4.0e-6
  20.e-6  6.e-6  0.0105e-3  -1.0   0.41   0.839  -2.5e-6  -2.1e-6
  30.e-6  5.e-6  0.0059e-3  -0.3   0.98   1.01    0       -3.9e-6
  30.e-6  5.e-6  0.0152e-3  -0.69  0.104  1.1    -0.8e-6  -0.4e-6
  30.e-6  5.e-6  0.0163e-3  -0.69  0.104  1.1    -0.8e-6  -0.4e-6
  30.e-6  5.e-6  0.0182e-3  -0.69  0.086  1.06   -0.1e-6  -0.6e-6
  20.e-6  6.e-6  0.0074e-3  -1.    0.4    0.59    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]

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

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, "PMOS: Effective length must be positive");
  assert( W + dW > 0, "PMOS: 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

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.

  W       L      Beta         Vt      K2     K5       DW       DL
  m       m      A/V^2        V       -      -        m        m
  12.e-6  4.e-6  0.062e-3    -4.5     0.24   0.61    -1.2e-6  -0.9e-6      depletion
  60.e-6  3.e-6  0.048e-3     0.1     0.08   0.68    -1.2e-6  -0.9e-6      enhancement
  12.e-6  4.e-6  0.0625e-3   -0.8     0.21   0.78    -1.2e-6  -0.9e-6      zero
  50.e-6  8.e-6  0.0299e-3    0.24    1.144  0.7311  -5.4e-6  -4.e-6
  20.e-6  6.e-6  0.041e-3     0.8     1.144  0.7311  -2.5e-6  -1.5e-6
  30.e-6  9.e-6  0.025e-3    -4.0     0.861  0.878   -3.4e-6  -1.74e-6
  30.e-6  5.e-6  0.031e-3     0.6     1.5    0.72     0       -3.9e-6
  50.e-6  6.e-6  0.0414e-3   -3.8     0.34   0.8     -1.6e-6  -2.e-6       depletion
  50.e-6  5.e-6  0.03e-3      0.37    0.23   0.86    -1.6e-6  -2.e-6       enhancement
  50.e-6  6.e-6  0.038e-3    -0.9     0.23   0.707   -1.6e-6  -2.e-6       zero
  20.e-6  4.e-6  0.06776e-3   0.5409  0.065  0.71    -0.8e-6  -0.2e-6
  20.e-6  4.e-6  0.06505e-3   0.6209  0.065  0.71    -0.8e-6  -0.2e-6
  20.e-6  4.e-6  0.05365e-3   0.6909  0.03   0.8     -0.3e-6  -0.2e-6
  20.e-6  4.e-6  0.05365e-3   0.4909  0.03   0.8     -0.3e-6  -0.2e-6
  12.e-6  4.e-6  0.023e-3    -4.5     0.29   0.6      0        0           depletion
  60.e-6  3.e-6  0.022e-3     0.1     0.11   0.65     0        0           enhancement
  12.e-6  4.e-6  0.038e-3    -0.8     0.33   0.6      0        0           zero
  20.e-6  6.e-6  0.022e-3     0.8     1      0.66     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]

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

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, "NMOS: Effective length must be positive");
  assert( W + dW > 0, "NMOS: 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

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.

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]

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

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

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.

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

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

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

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]

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

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

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  0.062e-3    -4.5     0.24   0.61    -1.2e-6  -0.9e-6      depletion
  60.e-6  3.e-6  0.048e-3     0.1     0.08   0.68    -1.2e-6  -0.9e-6      enhancement
  12.e-6  4.e-6  0.0625e-3   -0.8     0.21   0.78    -1.2e-6  -0.9e-6      zero
  50.e-6  8.e-6  0.0299e-3    0.24    1.144  0.7311  -5.4e-6  -4.e-6
  20.e-6  6.e-6  0.041e-3     0.8     1.144  0.7311  -2.5e-6  -1.5e-6
  30.e-6  9.e-6  0.025e-3    -4.0     0.861  0.878   -3.4e-6  -1.74e-6
  30.e-6  5.e-6  0.031e-3     0.6     1.5    0.72     0       -3.9e-6
  50.e-6  6.e-6  0.0414e-3   -3.8     0.34   0.8     -1.6e-6  -2.e-6       depletion
  50.e-6  5.e-6  0.03e-3      0.37    0.23   0.86    -1.6e-6  -2.e-6       enhancement
  50.e-6  6.e-6  0.038e-3    -0.9     0.23   0.707   -1.6e-6  -2.e-6       zero
  20.e-6  4.e-6  0.06776e-3   0.5409  0.065  0.71    -0.8e-6  -0.2e-6
  20.e-6  4.e-6  0.06505e-3   0.6209  0.065  0.71    -0.8e-6  -0.2e-6
  20.e-6  4.e-6  0.05365e-3   0.6909  0.03   0.8     -0.3e-6  -0.2e-6
  20.e-6  4.e-6  0.05365e-3   0.4909  0.03   0.8     -0.3e-6  -0.2e-6
  12.e-6  4.e-6  0.023e-3    -4.5     0.29   0.6      0        0           depletion
  60.e-6  3.e-6  0.022e-3     0.1     0.11   0.65     0        0           enhancement
  12.e-6  4.e-6  0.038e-3    -0.8     0.33   0.6      0        0           zero
  20.e-6  6.e-6  0.022e-3     0.8     1      0.66     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]

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

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, "Heating NMOS: Effective length must be positive");
  assert(W + dW > 0, "Heating NMOS: Effective width  must be positive");
  assert(T_heatPort > 0,"Heating NMOS: 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

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  0.0085e-3  -0.15  0.41   0.839  -3.8e-6  -4.0e-6
  20.e-6  6.e-6  0.0105e-3  -1.0   0.41   0.839  -2.5e-6  -2.1e-6
  30.e-6  5.e-6  0.0059e-3  -0.3   0.98   1.01    0       -3.9e-6
  30.e-6  5.e-6  0.0152e-3  -0.69  0.104  1.1    -0.8e-6  -0.4e-6
  30.e-6  5.e-6  0.0163e-3  -0.69  0.104  1.1    -0.8e-6  -0.4e-6
  30.e-6  5.e-6  0.0182e-3  -0.69  0.086  1.06   -0.1e-6  -0.6e-6
  20.e-6  6.e-6  0.0074e-3  -1.    0.4    0.59    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]

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

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, "HeatingPMOS: Effective length must be positive");
  assert(W + dW > 0, "HeatingPMOS: Effective width  must be positive");
  assert( T_heatPort > 0,"HeatingPMOS: 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

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.

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]

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

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

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.

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]

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

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

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

Inputs

Type Name Default Description

Real x

Real y

Type	Name	Default	Description
Real	x
Real	y

Outputs

Type Name Description

Real z

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

Exponential function linearly continued for x > Maxexp

Inputs

Type Name Default Description

Real x

Real Maxexp

Type	Name	Default	Description
Real	x
Real	Maxexp

Outputs

Type Name Description

Real z

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

Simple Thyristor Model

Modelica.Electrical.Analog.Semiconductors.Thyristor

Information

This is a simple thyristor model with three pins: Anode, Cathode and Gate. There are three operating modes:conducting, blocking and reverse breakthrough.
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

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

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;

Modelica.Electrical.Analog.Semiconductors.SimpleTriac

Simple triac, based on Semiconductors.Thyristor model

Modelica.Electrical.Analog.Semiconductors.SimpleTriac

Information

This is a simple TRIAC model based on the extended thyristor model Modelica.Electrical.Analog.Semiconductors.Thyristor.
Two thyristors are contrarily connected in parallel, whereas each transistor is connected with a diode.
Further information regarding the electrical component TRIAC can be detected in documentation of the ideal TRIAC model.
As an additional information: this model is based on the Modelica.Electrical.Analog.Semiconductors.Thyristor.

Attention: The model seems to be very sensitive with respect to the choice of some parameters (e.g., VDRM, VRRM). This is caused by the thyristor model. Further investigations are necessary.

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

NegativePin n Cathode

PositivePin p Anode

PositivePin g Gate

Type	Name	Description
NegativePin	n	Cathode
PositivePin	p	Anode
PositivePin	g	Gate

Modelica definition

model SimpleTriac 
  "Simple triac, based on Semiconductors.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";

  Modelica.Electrical.Analog.Interfaces.NegativePin n "Cathode";
  Modelica.Electrical.Analog.Interfaces.PositivePin p "Anode";
  Modelica.Electrical.Analog.Interfaces.PositivePin g "Gate";
  Modelica.Electrical.Analog.Semiconductors.Thyristor thyristor(VDRM=VDRM, VRRM=VRRM);
  Modelica.Electrical.Analog.Semiconductors.Thyristor thyristor1(VDRM=VDRM, VRRM=VRRM);

  Modelica.Electrical.Analog.Ideal.IdealDiode idealDiode(Vknee=0);
  Modelica.Electrical.Analog.Ideal.IdealDiode idealDiode1(Vknee=0);
equation 
  connect(thyristor.Anode, n);
  connect(thyristor1.Anode, p);
  connect(thyristor1.Anode, thyristor.Cathode);
  connect(thyristor1.Cathode, thyristor.Anode);
  connect(thyristor.Gate, idealDiode.n);
  connect(idealDiode.p, g);
  connect(idealDiode1.n, thyristor1.Gate);
  connect(idealDiode1.p, g);
end SimpleTriac;

Automatically generated Fri Nov 12 16:28:10 2010.