This package contains semiconductor devices:
Name | Description |
---|---|
Diode | Simple diode |
PMOS | Simple MOS Transistor |
NMOS | Simple MOS Transistor |
NPN | Simple BJT according to Ebers-Moll |
PNP | Simple BJT according to Ebers-Moll |
HeatingDiode | Simple diode with heating port |
HeatingNMOS | Simple MOS Transistor with heating port |
HeatingPMOS | Simple PMOS Transistor with heating port |
HeatingNPN | Simple NPN BJT according to Ebers-Moll with heating port |
HeatingPNP | Simple PNP BJT according to Ebers-Moll with heating port |
pow | Just a helper function for x^y in order that a symbolic engine can apply some transformations more easily |
exlin | Exponential function linearly continued for x > Maxexp |
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.
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
Name | Default | Description |
---|---|---|
W | 20.0e-6 | Width [m] |
L | 6.0e-6 | Length [m] |
Beta | 0.0105e-3 | Transconductance parameter [A/(V*V)] |
Vt | -1.0 | Zero bias threshold voltage [V] |
K2 | 0.41 | Bulk threshold parameter |
K5 | 0.839 | Reduction of pinch-off region |
dW | -2.5e-6 | Narrowing of channel [m] |
dL | -2.1e-6 | Shortening of channel [m] |
RDS | 1.e+7 | Drain-Source-Resistance [Ohm] |
Tnom | 300.15 | Parameter measurement temperature [K] |
kvt | -2.9e-3 | fitting parameter for Vt |
kk2 | 6.2e-4 | fitting parameter for Kk2 |
model HeatingPMOS "Simple PMOS Transistor with heating port" // 6.12.2001 parameter RDS added, Clauss Modelica.Electrical.Analog.Interfaces.Pin D "Drain"; Modelica.Electrical.Analog.Interfaces.Pin G "Gate"; Modelica.Electrical.Analog.Interfaces.Pin S "Source"; Modelica.Electrical.Analog.Interfaces.Pin B "Bulk"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort( T(start= 300.15)); parameter Modelica.SIunits.Length W = 20.0e-6 "Width"; parameter Modelica.SIunits.Length L = 6.0e-6 "Length"; parameter Modelica.SIunits.Transconductance Beta = 0.0105e-3 "Transconductance parameter"; parameter Modelica.SIunits.Voltage Vt = -1.0 "Zero bias threshold voltage"; parameter Real K2=0.41 "Bulk threshold parameter"; parameter Real K5=0.839 "Reduction of pinch-off region"; parameter Modelica.SIunits.Length dW = -2.5e-6 "Narrowing of channel"; parameter Modelica.SIunits.Length dL = -2.1e-6 "Shortening of channel"; parameter Modelica.SIunits.Resistance RDS = 1.e+7 "Drain-Source-Resistance"; parameter Modelica.SIunits.Temperature Tnom = 300.15 "Parameter measurement temperature"; parameter Real kvt=-2.9e-3 "fitting parameter for Vt"; parameter Real kk2=6.2e-4 "fitting parameter for Kk2"; protected Real v; Real uds; Real ubs; Real ugst; Real ud; Real us; Real id; Real gds; Real beta_t; Real vt_t; Real k2_t; equation assert(L + dL > 0, "Effective length must be positive"); assert(W + dW > 0, "Effective width must be positive"); assert( heatPort.T > 0,"temperature must be positive"); gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS; v = beta_t*(W + dW)/(L + dL); ud = if (D.v > S.v) then S.v else D.v; us = if (D.v > S.v) then D.v else S.v; uds = ud - us; ubs = if (B.v < us) then 0 else B.v - us; ugst = (G.v - us - vt_t + k2_t*ubs)*K5; id = if (ugst >= 0) then v*uds*gds else if (ugst < uds) then -v*uds*( ugst - uds/2 - gds) else -v*(ugst*ugst/2 - uds*gds); beta_t = Beta*pow((heatPort.T/Tnom), -1.5); vt_t = Vt*(1 + (heatPort.T - Tnom)*kvt); k2_t = K2*(1 + (heatPort.T - Tnom)*kk2); G.i = 0; D.i = if (D.v > S.v) then -id else id; S.i = if (D.v > S.v) then id else -id; B.i = 0; heatPort.Q_dot = -D.i*(D.v - S.v); end HeatingPMOS;
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
Name | Default | Description |
---|---|---|
W | 20.e-6 | Width [m] |
L | 6.e-6 | Length [m] |
Beta | 0.041e-3 | Transconductance parameter [A/(V*V)] |
Vt | 0.8 | Zero bias threshold voltage [V] |
K2 | 1.144 | Bulk threshold parameter |
K5 | 0.7311 | Reduction of pinch-off region |
dW | -2.5e-6 | narrowing of channel [m] |
dL | -1.5e-6 | shortening of channel [m] |
RDS | 1.e+7 | Drain-Source-Resistance [Ohm] |
Tnom | 300.15 | Parameter measurement temperature [K] |
kvt | -6.96e-3 | fitting parameter for Vt |
kk2 | 6.0e-4 | fitting parameter for K22 |
model HeatingNMOS "Simple MOS Transistor with heating port" Modelica.Electrical.Analog.Interfaces.Pin D "Drain"; Modelica.Electrical.Analog.Interfaces.Pin G "Gate"; Modelica.Electrical.Analog.Interfaces.Pin S "Source"; Modelica.Electrical.Analog.Interfaces.Pin B "Bulk"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort( T(start= 300.15)); parameter Modelica.SIunits.Length W = 20.e-6 "Width"; parameter Modelica.SIunits.Length L = 6.e-6 "Length"; parameter Modelica.SIunits.Transconductance Beta = 0.041e-3 "Transconductance parameter"; parameter Modelica.SIunits.Voltage Vt = 0.8 "Zero bias threshold voltage"; parameter Real K2=1.144 "Bulk threshold parameter"; parameter Real K5=0.7311 "Reduction of pinch-off region"; parameter Modelica.SIunits.Length dW = -2.5e-6 "narrowing of channel"; parameter Modelica.SIunits.Length dL = -1.5e-6 "shortening of channel"; parameter Modelica.SIunits.Resistance RDS = 1.e+7 "Drain-Source-Resistance"; parameter Modelica.SIunits.Temperature Tnom = 300.15 "Parameter measurement temperature"; parameter Real kvt=-6.96e-3 "fitting parameter for Vt"; parameter Real kk2=6.0e-4 "fitting parameter for K22"; protected Real v; Real uds; Real ubs; Real ugst; Real ud; Real us; Real id; Real gds; Real beta_t; Real vt_t; Real k2_t; equation assert(L + dL > 0, "Effective length must be positive"); assert(W + dW > 0, "Effective width must be positive"); assert( heatPort.T > 0,"temperature must be positive"); gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS; v = beta_t*(W + dW)/(L + dL); ud = if (D.v < S.v) then S.v else D.v; us = if (D.v < S.v) then D.v else S.v; uds = ud - us; ubs = if (B.v > us) then 0 else B.v - us; ugst = (G.v - us - vt_t + k2_t*ubs)*K5; id = if (ugst <= 0) then v*uds*gds else if (ugst > uds) then v*uds*( ugst - uds/2 + gds) else v*(ugst*ugst/2 + uds*gds); beta_t = Beta*pow((heatPort.T/Tnom), -1.5); vt_t = Vt*(1 + (heatPort.T - Tnom)*kvt); k2_t = K2*(1 + (heatPort.T - Tnom)*kk2); G.i = 0; D.i = if (D.v < S.v) then -id else id; S.i = if (D.v < S.v) then id else -id; B.i = 0; heatPort.Q_dot = -D.i*(D.v - S.v); end HeatingNMOS;
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
Name | Default | Description |
---|---|---|
Bf | 50 | Forward beta |
Br | 0.1 | Reverse beta |
Is | 1.e-16 | Transport saturation current [A] |
Vak | 0.02 | Early voltage (inverse), 1/Volt [1/V] |
Tauf | 0.12e-9 | Ideal forward transit time [s] |
Taur | 5e-9 | Ideal reverse transit time [s] |
Ccs | 1e-12 | Collector-substrat(ground) cap. [F] |
Cje | 0.4e-12 | Base-emitter zero bias depletion cap. [F] |
Cjc | 0.5e-12 | Base-coll. zero bias depletion cap. [F] |
Phie | 0.8 | Base-emitter diffusion voltage [V] |
Me | 0.4 | Base-emitter gradation exponent |
Phic | 0.8 | Base-collector diffusion voltage [V] |
Mc | 0.333 | Base-collector gradation exponent |
Gbc | 1e-15 | Base-collector conductance [S] |
Gbe | 1e-15 | Base-emitter conductance [S] |
EMin | -100 | if x < EMin, the exp(x) function is linearized |
EMax | 40 | if x > EMax, the exp(x) function is linearized |
Tnom | 300.15 | Parameter measurement temperature [K] |
XTI | 3 | Temperature exponent for effect on Is |
XTB | 0 | Forward and reverse beta temperature exponent |
EG | 1.11 | Energy gap for temperature effect on Is |
NF | 1.0 | Forward current emission coefficient |
NR | 1.0 | Reverse current emission coefficient |
K | 1.3806226e-23 | Boltzmann's constant |
q | 1.6021918e-19 | Elementary electronic charge |
model HeatingNPN "Simple NPN BJT according to Ebers-Moll with heating port" parameter Real Bf=50 "Forward beta"; parameter Real Br=0.1 "Reverse beta"; parameter Modelica.SIunits.Current Is = 1.e-16 "Transport saturation current"; parameter Modelica.SIunits.InversePotential Vak = 0.02 "Early voltage (inverse), 1/Volt"; parameter Modelica.SIunits.Time Tauf = 0.12e-9 "Ideal forward transit time"; parameter Modelica.SIunits.Time Taur = 5e-9 "Ideal reverse transit time"; parameter Modelica.SIunits.Capacitance Ccs = 1e-12 "Collector-substrat(ground) cap."; parameter Modelica.SIunits.Capacitance Cje = 0.4e-12 "Base-emitter zero bias depletion cap."; parameter Modelica.SIunits.Capacitance Cjc = 0.5e-12 "Base-coll. zero bias depletion cap."; parameter Modelica.SIunits.Voltage Phie = 0.8 "Base-emitter diffusion voltage"; parameter Real Me=0.4 "Base-emitter gradation exponent"; parameter Modelica.SIunits.Voltage Phic = 0.8 "Base-collector diffusion voltage"; parameter Real Mc=0.333 "Base-collector gradation exponent"; parameter Modelica.SIunits.Conductance Gbc = 1e-15 "Base-collector conductance"; parameter Modelica.SIunits.Conductance Gbe = 1e-15 "Base-emitter conductance"; parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized"; parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized"; parameter Modelica.SIunits.Temperature Tnom = 300.15 "Parameter measurement temperature"; parameter Real XTI=3 "Temperature exponent for effect on Is"; parameter Real XTB=0 "Forward and reverse beta temperature exponent"; parameter Real EG=1.11 "Energy gap for temperature effect on Is"; parameter Real NF=1.0 "Forward current emission coefficient"; parameter Real NR=1.0 "Reverse current emission coefficient"; parameter Real K=1.3806226e-23 "Boltzmann's constant"; parameter Real q=1.6021918e-19 "Elementary electronic charge"; /*protected*/ Real vbc; Real vbe; Real qbk; Real ibc; Real ibe; Real cbc; Real cbe; Real ExMin; Real ExMax; Real Capcje; Real Capcjc; Real is_t; Real br_t; Real bf_t; Real vt_t; Real hexp; Real htempexp; public Modelica.Electrical.Analog.Interfaces.Pin C "Collector"; Modelica.Electrical.Analog.Interfaces.Pin B "Base"; Modelica.Electrical.Analog.Interfaces.Pin E "Emitter"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort( T(start= 300.15)); equation assert( heatPort.T > 0,"temperature must be positive"); ExMin = exp(EMin); ExMax = exp(EMax); vbc = B.v - C.v; vbe = B.v - E.v; qbk = 1 - vbc*Vak; hexp = (heatPort.T/Tnom - 1)*EG/vt_t; htempexp = if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if ( hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp); is_t = Is*pow((heatPort.T/Tnom), XTI)*htempexp; br_t = Br*pow((heatPort.T/Tnom), XTB); bf_t = Bf*pow((heatPort.T/Tnom), XTB); vt_t = (K/q)*heatPort.T; ibc = if (vbc/(NR*vt_t) < EMin) then is_t*(ExMin*(vbc/(NR*vt_t) - EMin + 1) - 1) + vbc*Gbc else if (vbc/(NR*vt_t) > EMax) then is_t*( ExMax*(vbc/(NR*vt_t) - EMax + 1) - 1) + vbc*Gbc else is_t*(exp(vbc/ (NR*vt_t)) - 1) + vbc*Gbc; ibe = if (vbe/(NF*vt_t) < EMin) then is_t*(ExMin*(vbe/(NF*vt_t) - EMin + 1) - 1) + vbe*Gbe else if (vbe/(NF*vt_t) > EMax) then is_t*( ExMax*(vbe/(NF*vt_t) - EMax + 1) - 1) + vbe*Gbe else is_t*(exp(vbe/ (NF*vt_t)) - 1) + vbe*Gbe; Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc/Phic, -Mc); Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe/Phie, -Me); cbc = if (vbc/(NR*vt_t) < EMin) then Taur*is_t/(NR*vt_t)*ExMin*(vbc/( NR*vt_t) - EMin + 1) + Capcjc else if (vbc/(NR*vt_t) > EMax) then Taur*is_t/(NR*vt_t)*ExMax*(vbc/(NR*vt_t) - EMax + 1) + Capcjc else Taur*is_t/(NR*vt_t)*exp(vbc/(NR*vt_t)) + Capcjc; cbe = if (vbe/(NF*vt_t) < EMin) then Tauf*is_t/(NF*vt_t)*ExMin*(vbe/( NF*vt_t) - EMin + 1) + Capcje else if (vbe/(NF*vt_t) > EMax) then Tauf*is_t/(NF*vt_t)*ExMax*(vbe/(NF*vt_t) - EMax + 1) + Capcje else Tauf*is_t/(NF*vt_t)*exp(vbe/(NF*vt_t)) + Capcje; C.i = (ibe - ibc)*qbk - ibc/br_t - cbc*der(vbc) + Ccs*der(C.v); B.i = ibe/bf_t + ibc/br_t + cbc*der(vbc) + cbe*der(vbe); E.i = -B.i - C.i + Ccs*der(C.v); heatPort.Q_dot = -(vbc*ibc/br_t + vbe*ibe/bf_t + (ibe - ibc)*qbk*(C.v - E.v)); end HeatingNPN;
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.
Name | Default | Description |
---|---|---|
Ids | 1.e-6 | Saturation current [A] |
Maxexp | 15 | Max. exponent for linear continuation |
R | 1.e8 | Parallel ohmic resistance [Ohm] |
EG | 1.11 | activation energy |
N | 1 | Emission coefficient |
TNOM | 300.15 | Parameter measurement temperature [K] |
XTI | 3 | Temperature exponent of saturation current |
model HeatingDiode "Simple diode with heating port" extends Modelica.Electrical.Analog.Interfaces.OnePort; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort( T(start= 300.15)); parameter Modelica.SIunits.Current Ids = 1.e-6 "Saturation current"; /* parameter Modelica.SIunits.Voltage Vt=0.04 "Voltage equivalent of temperature (kT/qn)"; */ parameter Real Maxexp(final min=Modelica.Constants.SMALL) = 15 "Max. exponent for linear continuation"; parameter Modelica.SIunits.Resistance R = 1.e8 "Parallel ohmic resistance"; parameter Real EG=1.11 "activation energy"; parameter Real N=1 "Emission coefficient"; parameter Modelica.SIunits.Temperature TNOM = 300.15 "Parameter measurement temperature"; parameter Real XTI=3 "Temperature exponent of saturation current"; Modelica.SIunits.Temperature vt_t "Temperature voltage"; Modelica.SIunits.Current id "diode current"; protected Real k=1.380662e-23 "Boltzmann's constant, J/K"; Real q=1.6021892e-19 "Electron charge, As"; Modelica.SIunits.Temperature htemp "auxiliary temperature"; Real aux; Real auxp; Real maxexp=exp(Maxexp); equation assert( heatPort.T > 0,"temperature must be positive"); htemp = heatPort.T; vt_t = k*htemp/q; id = exlin((v/(N*vt_t)), Maxexp) - 1; aux = (htemp/TNOM - 1)*EG/(N*vt_t); auxp = exp(aux); i = Ids*id*pow(htemp/TNOM, XTI/N)*auxp + v/R; heatPort.Q_dot = -i*v; end HeatingDiode;
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.
Name | Default | Description |
---|---|---|
Ids | 1.e-6 | Saturation current [A] |
Vt | 0.04 | Voltage equivalent of temperature (kT/qn) [V] |
Maxexp | 15 | Max. exponent for linear continuation |
R | 1.e8 | Parallel ohmic resistance [Ohm] |
model Diode "Simple diode" extends Modelica.Electrical.Analog.Interfaces.OnePort; parameter SIunits.Current Ids = 1.e-6 "Saturation current"; parameter SIunits.Voltage Vt = 0.04 "Voltage equivalent of temperature (kT/qn)"; parameter Real Maxexp(final min=Modelica.Constants.SMALL) = 15 "Max. exponent for linear continuation"; parameter SIunits.Resistance R = 1.e8 "Parallel ohmic resistance"; equation i = if (v/Vt > Maxexp) then Ids*(exp(Maxexp)*(1 + v/Vt - Maxexp) - 1) + v/R else Ids*(exp(v/Vt) - 1) + v/R; end Diode;
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.
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
Name | Default | Description |
---|---|---|
W | 20.0e-6 | Width [m] |
L | 6.0e-6 | Length [m] |
Beta | 0.0105e-3 | Transconductance parameter [A/(V*V)] |
Vt | -1.0 | Zero bias threshold voltage [V] |
K2 | 0.41 | Bulk threshold parameter |
K5 | 0.839 | Reduction of pinch-off region |
dW | -2.5e-6 | Narrowing of channel [m] |
dL | -2.1e-6 | Shortening of channel [m] |
RDS | 1.e+7 | Drain-Source-Resistance [Ohm] |
model PMOS "Simple MOS Transistor" // 6.12.2001 parameter RDS added, Clauss Interfaces.Pin D "Drain"; Interfaces.Pin G "Gate"; Interfaces.Pin S "Source"; Interfaces.Pin B "Bulk"; parameter SIunits.Length W = 20.0e-6 "Width"; parameter SIunits.Length L = 6.0e-6 "Length"; parameter SIunits.Transconductance Beta = 0.0105e-3 "Transconductance parameter"; parameter SIunits.Voltage Vt = -1.0 "Zero bias threshold voltage"; parameter Real K2=0.41 "Bulk threshold parameter"; parameter Real K5=0.839 "Reduction of pinch-off region"; parameter SIunits.Length dW = -2.5e-6 "Narrowing of channel"; parameter SIunits.Length dL = -2.1e-6 "Shortening of channel"; parameter SIunits.Resistance RDS = 1.e+7 "Drain-Source-Resistance"; protected Real v; Real uds; Real ubs; Real ugst; Real ud; Real us; Real id; Real gds; equation //assert (L + dL > 0, "Effective length must be positive"); //assert (W + dW > 0, "Effective width must be positive"); gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS; v = Beta*(W + dW)/(L + dL); ud = if (D.v > S.v) then S.v else D.v; us = if (D.v > S.v) then D.v else S.v; uds = ud - us; ubs = if (B.v < us) then 0 else B.v - us; ugst = (G.v - us - Vt + K2*ubs)*K5; id = if (ugst >= 0) then v*uds*gds else if (ugst < uds) then -v*uds*( ugst - uds/2 - gds) else -v*(ugst*ugst/2 - uds*gds); G.i = 0; D.i = if (D.v > S.v) then -id else id; S.i = if (D.v > S.v) then id else -id; B.i = 0; end PMOS;
The NMos model is a simple model of a n-channel metal-oxide semiconductor FET. It differs slightly from the device used in the SPICE simulator. For more details please care for H. Spiro.
The model does not consider capacitances. A high drain-source resistance RDS is included to avoid numerical difficulties.
W L Beta Vt K2 K5 DW DL m m A/V^2 V - - m m 12.e-6 4.e-6 .062e-3 -4.5 .24 .61 -1.2e-6 -.9e-6 depletion 60.e-6 3.e-6 .048e-3 .1 .08 .68 -1.2e-6 -.9e-6 enhancement 12.e-6 4.e-6 .0625e-3 -.8 .21 .78 -1.2e-6 -.9e-6 zero 50.e-6 8.e-6 .0299e-3 .24 1.144 .7311 -5.4e-6 -4.e-6 20.e-6 6.e-6 .041e-3 .8 1.144 .7311 -2.5e-6 -1.5e-6 30.e-6 9.e-6 .025e-3 -4. .861 .878 -3.4e-6 -1.74e-6 30.e-6 5.e-6 .031e-3 .6 1.5 .72 0 -3.9e-6 50.e-6 6.e-6 .0414e-3 -3.8 .34 .8 -1.6e-6 -2.e-6 depletion 50.e-6 5.e-6 .03e-3 .37 .23 .86 -1.6e-6 -2.e-6 enhancement 50.e-6 6.e-6 .038e-3 -.9 .23 .707 -1.6e-6 -2.e-6 zero 20.e-6 4.e-6 .06776e-3 .5409 .065 .71 -.8e-6 -.2e-6 20.e-6 4.e-6 .06505e-3 .6209 .065 .71 -.8e-6 -.2e-6 20.e-6 4.e-6 .05365e-3 .6909 .03 .8 -.3e-6 -.2e-6 20.e-6 4.e-6 .05365e-3 .4909 .03 .8 -.3e-6 -.2e-6 12.e-6 4.e-6 .023e-3 -4.5 .29 .6 0 0 depletion 60.e-6 3.e-6 .022e-3 .1 .11 .65 0 0 enhancement 12.e-6 4.e-6 .038e-3 -.8 .33 .6 0 0 zero 20.e-6 6.e-6 .022e-3 .8 1 .66 0 0
Name | Default | Description |
---|---|---|
W | 20.e-6 | Width [m] |
L | 6.e-6 | Length [m] |
Beta | 0.041e-3 | Transconductance parameter [A/(V*V)] |
Vt | 0.8 | Zero bias threshold voltage [V] |
K2 | 1.144 | Bulk threshold parameter |
K5 | 0.7311 | Reduction of pinch-off region |
dW | -2.5e-6 | narrowing of channel [m] |
dL | -1.5e-6 | shortening of channel [m] |
RDS | 1.e+7 | Drain-Source-Resistance [Ohm] |
model NMOS "Simple MOS Transistor" // 6.12.2001 parameter RDS added, Clauss Interfaces.Pin D "Drain"; Interfaces.Pin G "Gate"; Interfaces.Pin S "Source"; Interfaces.Pin B "Bulk"; parameter SIunits.Length W = 20.e-6 "Width"; parameter SIunits.Length L = 6.e-6 "Length"; parameter SIunits.Transconductance Beta = 0.041e-3 "Transconductance parameter"; parameter SIunits.Voltage Vt = 0.8 "Zero bias threshold voltage"; parameter Real K2=1.144 "Bulk threshold parameter"; parameter Real K5=0.7311 "Reduction of pinch-off region"; parameter SIunits.Length dW = -2.5e-6 "narrowing of channel"; parameter SIunits.Length dL = -1.5e-6 "shortening of channel"; parameter SIunits.Resistance RDS = 1.e+7 "Drain-Source-Resistance"; protected Real v; Real uds; Real ubs; Real ugst; Real ud; Real us; Real id; Real gds; equation //assert (L + dL > 0, "Effective length must be positive"); //assert (W + dW > 0, "Effective width must be positive"); gds = if (RDS < 1.e-20 and RDS > -1.e-20) then 1.e20 else 1/RDS; v = Beta*(W + dW)/(L + dL); ud = if (D.v < S.v) then S.v else D.v; us = if (D.v < S.v) then D.v else S.v; uds = ud - us; ubs = if (B.v > us) then 0 else B.v - us; ugst = (G.v - us - Vt + K2*ubs)*K5; id = if (ugst <= 0) then v*uds*gds else if (ugst > uds) then v*uds*(ugst - uds/2 + gds) else v*(ugst*ugst/2 + uds*gds); G.i = 0; D.i = if (D.v < S.v) then -id else id; S.i = if (D.v < S.v) then id else -id; B.i = 0; end NMOS;
This model is a simple model of a bipolar npn junction transistor according to Ebers-Moll.
A typical parameter set is:
Bf Br Is Vak Tauf Taur Ccs Cje Cjc Phie Me PHic Mc Gbc Gbe Vt - - A V s s F F F V - V - mS mS V 50 0.1 1e-16 0.02 0.12e-9 5e-9 1e-12 0.4e-12 0.5e-12 0.8 0.4 0.8 0.333 1e-15 1e-15 0.02585
Name | Default | Description |
---|---|---|
Bf | 50 | Forward beta |
Br | 0.1 | Reverse beta |
Is | 1.e-16 | Transport saturation current [A] |
Vak | 0.02 | Early voltage (inverse), 1/Volt [1/V] |
Tauf | 0.12e-9 | Ideal forward transit time [s] |
Taur | 5e-9 | Ideal reverse transit time [s] |
Ccs | 1e-12 | Collector-substrat(ground) cap. [F] |
Cje | 0.4e-12 | Base-emitter zero bias depletion cap. [F] |
Cjc | 0.5e-12 | Base-coll. zero bias depletion cap. [F] |
Phie | 0.8 | Base-emitter diffusion voltage [V] |
Me | 0.4 | Base-emitter gradation exponent |
Phic | 0.8 | Base-collector diffusion voltage [V] |
Mc | 0.333 | Base-collector gradation exponent |
Gbc | 1e-15 | Base-collector conductance [S] |
Gbe | 1e-15 | Base-emitter conductance [S] |
Vt | 0.02585 | Voltage equivalent of temperature [V] |
EMin | -100 | if x < EMin, the exp(x) function is linearized |
EMax | 40 | if x > EMax, the exp(x) function is linearized |
model NPN "Simple BJT according to Ebers-Moll" parameter Real Bf=50 "Forward beta"; parameter Real Br=0.1 "Reverse beta"; parameter SIunits.Current Is = 1.e-16 "Transport saturation current"; parameter SIunits.InversePotential Vak = 0.02 "Early voltage (inverse), 1/Volt"; parameter SIunits.Time Tauf = 0.12e-9 "Ideal forward transit time"; parameter SIunits.Time Taur = 5e-9 "Ideal reverse transit time"; parameter SIunits.Capacitance Ccs = 1e-12 "Collector-substrat(ground) cap."; parameter SIunits.Capacitance Cje = 0.4e-12 "Base-emitter zero bias depletion cap."; parameter SIunits.Capacitance Cjc = 0.5e-12 "Base-coll. zero bias depletion cap."; parameter SIunits.Voltage Phie = 0.8 "Base-emitter diffusion voltage"; parameter Real Me=0.4 "Base-emitter gradation exponent"; parameter SIunits.Voltage Phic = 0.8 "Base-collector diffusion voltage"; parameter Real Mc=0.333 "Base-collector gradation exponent"; parameter SIunits.Conductance Gbc = 1e-15 "Base-collector conductance"; parameter SIunits.Conductance Gbe = 1e-15 "Base-emitter conductance"; parameter SIunits.Voltage Vt = 0.02585 "Voltage equivalent of temperature"; parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized"; parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized"; protected Real vbc; Real vbe; Real qbk; Real ibc; Real ibe; Real cbc; Real cbe; Real ExMin; Real ExMax; Real Capcje; Real Capcjc; function pow "Just a helper function for x^y" input Real x; input Real y; output Real z; algorithm z:=x^y; end pow; public Modelica.Electrical.Analog.Interfaces.Pin C "Collector"; Modelica.Electrical.Analog.Interfaces.Pin B "Base"; Modelica.Electrical.Analog.Interfaces.Pin E "Emitter"; equation ExMin = exp(EMin); ExMax = exp(EMax); vbc = B.v - C.v; vbe = B.v - E.v; qbk = 1 - vbc*Vak; ibc = if (vbc/Vt < EMin) then Is*(ExMin*(vbc/Vt - EMin + 1) - 1) + vbc*Gbc else if (vbc/Vt > EMax) then Is*(ExMax*(vbc/Vt - EMax + 1) - 1) + vbc* Gbc else Is*(exp(vbc/Vt) - 1) + vbc*Gbc; ibe = if (vbe/Vt < EMin) then Is*(ExMin*(vbe/Vt - EMin + 1) - 1) + vbe*Gbe else if (vbe/Vt > EMax) then Is*(ExMax*(vbe/Vt - EMax + 1) - 1) + vbe* Gbe else Is*(exp(vbe/Vt) - 1) + vbe*Gbe; Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc /Phic, -Mc); Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe /Phie, -Me); cbc = if (vbc/Vt < EMin) then Taur*Is/Vt*ExMin*(vbc/Vt - EMin + 1) + Capcjc else if (vbc/Vt > EMax) then Taur*Is/Vt*ExMax*(vbc/Vt - EMax + 1) + Capcjc else Taur*Is/Vt*exp(vbc/Vt) + Capcjc; cbe = if (vbe/Vt < EMin) then Tauf*Is/Vt*ExMin*(vbe/Vt - EMin + 1) + Capcje else if (vbe/Vt > EMax) then Tauf*Is/Vt*ExMax*(vbe/Vt - EMax + 1) + Capcje else Tauf*Is/Vt*exp(vbe/Vt) + Capcje; C.i = (ibe - ibc)*qbk - ibc/Br - cbc*der(vbc) + Ccs*der(C.v); B.i = ibe/Bf + ibc/Br + cbc*der(vbc) + cbe*der(vbe); E.i = -B.i - C.i + Ccs*der(C.v); end NPN;
This model is a simple model of a bipolar pnp junction transistor according to Ebers-Moll.
A typical parameter set is:
Bf Br Is Vak Tauf Taur Ccs Cje Cjc Phie Me PHic Mc Gbc Gbe Vt - - A V s s F F F V - V - mS mS V 50 0.1 1e-16 0.02 0.12e-9 5e-9 1e-12 0.4e-12 0.5e-12 0.8 0.4 0.8 0.333 1e-15 1e-15 0.02585
Name | Default | Description |
---|---|---|
Bf | 50 | Forward beta |
Br | 0.1 | Reverse beta |
Is | 1.e-16 | Transport saturation current [A] |
Vak | 0.02 | Early voltage (inverse), 1/Volt [1/V] |
Tauf | 0.12e-9 | Ideal forward transit time [s] |
Taur | 5e-9 | Ideal reverse transit time [s] |
Ccs | 1e-12 | Collector-substrat(ground) cap. [F] |
Cje | 0.4e-12 | Base-emitter zero bias depletion cap. [F] |
Cjc | 0.5e-12 | Base-coll. zero bias depletion cap. [F] |
Phie | 0.8 | Base-emitter diffusion voltage [V] |
Me | 0.4 | Base-emitter gradation exponent |
Phic | 0.8 | Base-collector diffusion voltage [V] |
Mc | 0.333 | Base-collector gradation exponent |
Gbc | 1e-15 | Base-collector conductance [S] |
Gbe | 1e-15 | Base-emitter conductance [S] |
Vt | 0.02585 | Voltage equivalent of temperature [V] |
EMin | -100 | if x < EMin, the exp(x) function is linearized |
EMax | 40 | if x > EMax, the exp(x) function is linearized |
model PNP "Simple BJT according to Ebers-Moll" parameter Real Bf=50 "Forward beta"; parameter Real Br=0.1 "Reverse beta"; parameter SIunits.Current Is = 1.e-16 "Transport saturation current"; parameter SIunits.InversePotential Vak = 0.02 "Early voltage (inverse), 1/Volt"; parameter SIunits.Time Tauf = 0.12e-9 "Ideal forward transit time"; parameter SIunits.Time Taur = 5e-9 "Ideal reverse transit time"; parameter SIunits.Capacitance Ccs = 1e-12 "Collector-substrat(ground) cap."; parameter SIunits.Capacitance Cje = 0.4e-12 "Base-emitter zero bias depletion cap."; parameter SIunits.Capacitance Cjc = 0.5e-12 "Base-coll. zero bias depletion cap."; parameter SIunits.Voltage Phie = 0.8 "Base-emitter diffusion voltage"; parameter Real Me=0.4 "Base-emitter gradation exponent"; parameter SIunits.Voltage Phic = 0.8 "Base-collector diffusion voltage"; parameter Real Mc=0.333 "Base-collector gradation exponent"; parameter SIunits.Conductance Gbc = 1e-15 "Base-collector conductance"; parameter SIunits.Conductance Gbe = 1e-15 "Base-emitter conductance"; parameter SIunits.Voltage Vt = 0.02585 "Voltage equivalent of temperature"; parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized"; parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized"; protected Real vbc; Real vbe; Real qbk; Real ibc; Real ibe; Real cbc; Real cbe; Real ExMin; Real ExMax; Real Capcje; Real Capcjc; function pow "Just a helper function for x^y" input Real x; input Real y; output Real z; algorithm z:=x^y; end pow; public Modelica.Electrical.Analog.Interfaces.Pin C "Collector"; Modelica.Electrical.Analog.Interfaces.Pin B "Base"; Modelica.Electrical.Analog.Interfaces.Pin E "Emitter"; equation ExMin = exp(EMin); ExMax = exp(EMax); vbc = C.v - B.v; vbe = E.v - B.v; qbk = 1 - vbc*Vak; ibc = if (vbc/Vt < EMin) then Is*(ExMin*(vbc/Vt - EMin + 1) - 1) + vbc*Gbc else if (vbc/Vt > EMax) then Is*(ExMax*(vbc/Vt - EMax + 1) - 1) + vbc* Gbc else Is*(exp(vbc/Vt) - 1) + vbc*Gbc; ibe = if (vbe/Vt < EMin) then Is*(ExMin*(vbe/Vt - EMin + 1) - 1) + vbe*Gbe else if (vbe/Vt > EMax) then Is*(ExMax*(vbe/Vt - EMax + 1) - 1) + vbe* Gbe else Is*(exp(vbe/Vt) - 1) + vbe*Gbe; Capcjc = if (vbc/Phic > 0) then Cjc*(1 + Mc*vbc/Phic) else Cjc*pow(1 - vbc /Phic, -Mc); Capcje = if (vbe/Phie > 0) then Cje*(1 + Me*vbe/Phie) else Cje*pow(1 - vbe /Phie, -Me); cbc = if (vbc/Vt < EMin) then Taur*Is/Vt*ExMin*(vbc/Vt - EMin + 1) + Capcjc else if (vbc/Vt > EMax) then Taur*Is/Vt*ExMax*(vbc/Vt - EMax + 1) + Capcjc else Taur*Is/Vt*exp(vbc/Vt) + Capcjc; cbe = if (vbe/Vt < EMin) then Tauf*Is/Vt*ExMin*(vbe/Vt - EMin + 1) + Capcje else if (vbe/Vt > EMax) then Tauf*Is/Vt*ExMax*(vbe/Vt - EMax + 1) + Capcje else Tauf*Is/Vt*exp(vbe/Vt) + Capcje; C.i = -((ibe - ibc)*qbk - ibc/Br - cbc*der(vbc) - Ccs*der(C.v)); B.i = -(ibe/Bf + ibc/Br + cbe*der(vbe) + cbc*der(vbc)); E.i = -B.i - C.i + Ccs*der(C.v); end PNP;
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
Name | Default | Description |
---|---|---|
Bf | 50 | Forward beta |
Br | 0.1 | Reverse beta |
Is | 1.e-16 | Transport saturation current [A] |
Vak | 0.02 | Early voltage (inverse), 1/Volt [1/V] |
Tauf | 0.12e-9 | Ideal forward transit time [s] |
Taur | 5e-9 | Ideal reverse transit time [s] |
Ccs | 1e-12 | Collector-substrat(ground) cap. [F] |
Cje | 0.4e-12 | Base-emitter zero bias depletion cap. [F] |
Cjc | 0.5e-12 | Base-coll. zero bias depletion cap. [F] |
Phie | 0.8 | Base-emitter diffusion voltage [V] |
Me | 0.4 | Base-emitter gradation exponent |
Phic | 0.8 | Base-collector diffusion voltage [V] |
Mc | 0.333 | Base-collector gradation exponent |
Gbc | 1e-15 | Base-collector conductance [S] |
Gbe | 1e-15 | Base-emitter conductance [S] |
EMin | -100 | if x < EMin, the exp(x) function is linearized |
EMax | 40 | if x > EMax, the exp(x) function is linearized |
Tnom | 300.15 | Parameter measurement temperature [K] |
XTI | 3 | Temperature exponent for effect on Is |
XTB | 0 | Forward and reverse beta temperature exponent |
EG | 1.11 | Energy gap for temperature effect on Is |
NF | 1.0 | Forward current emission coefficient |
NR | 1.0 | Reverse current emission coefficient |
K | 1.3806226e-23 | Boltzmann's constant |
q | 1.6021918e-19 | Elementary electronic charge |
model HeatingPNP "Simple PNP BJT according to Ebers-Moll with heating port" parameter Real Bf=50 "Forward beta"; parameter Real Br=0.1 "Reverse beta"; parameter Modelica.SIunits.Current Is = 1.e-16 "Transport saturation current"; parameter Modelica.SIunits.InversePotential Vak = 0.02 "Early voltage (inverse), 1/Volt"; parameter Modelica.SIunits.Time Tauf = 0.12e-9 "Ideal forward transit time"; parameter Modelica.SIunits.Time Taur = 5e-9 "Ideal reverse transit time"; parameter Modelica.SIunits.Capacitance Ccs = 1e-12 "Collector-substrat(ground) cap."; parameter Modelica.SIunits.Capacitance Cje = 0.4e-12 "Base-emitter zero bias depletion cap."; parameter Modelica.SIunits.Capacitance Cjc = 0.5e-12 "Base-coll. zero bias depletion cap."; parameter Modelica.SIunits.Voltage Phie = 0.8 "Base-emitter diffusion voltage"; parameter Real Me=0.4 "Base-emitter gradation exponent"; parameter Modelica.SIunits.Voltage Phic = 0.8 "Base-collector diffusion voltage"; parameter Real Mc=0.333 "Base-collector gradation exponent"; parameter Modelica.SIunits.Conductance Gbc = 1e-15 "Base-collector conductance"; parameter Modelica.SIunits.Conductance Gbe = 1e-15 "Base-emitter conductance"; parameter Real EMin=-100 "if x < EMin, the exp(x) function is linearized"; parameter Real EMax=40 "if x > EMax, the exp(x) function is linearized"; parameter Modelica.SIunits.Temperature Tnom = 300.15 "Parameter measurement temperature"; parameter Real XTI=3 "Temperature exponent for effect on Is"; parameter Real XTB=0 "Forward and reverse beta temperature exponent"; parameter Real EG=1.11 "Energy gap for temperature effect on Is"; parameter Real NF=1.0 "Forward current emission coefficient"; parameter Real NR=1.0 "Reverse current emission coefficient"; parameter Real K=1.3806226e-23 "Boltzmann's constant"; parameter Real q=1.6021918e-19 "Elementary electronic charge"; protected Real vcb; Real veb; Real qbk; Real icb; Real ieb; Real ccb; Real ceb; Real ExMin; Real ExMax; Real Capcje; Real Capcjc; Real is_t; Real br_t; Real bf_t; Real vt_t; Real hexp; Real htempexp; public Modelica.Electrical.Analog.Interfaces.Pin C "Collector"; Modelica.Electrical.Analog.Interfaces.Pin B "Base"; Modelica.Electrical.Analog.Interfaces.Pin E "Emitter"; Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a heatPort( T(start= 300.15)); equation assert( heatPort.T > 0,"temperature must be positive"); ExMin = exp(EMin); ExMax = exp(EMax); vcb = C.v - B.v; veb = E.v - B.v; qbk = 1 - vcb*Vak; hexp = (heatPort.T/Tnom - 1)*EG/vt_t; htempexp = if (hexp < EMin) then ExMin*(hexp - EMin + 1) else if ( hexp > EMax) then ExMax*(hexp - EMax + 1) else exp(hexp); is_t = Is*pow((heatPort.T/Tnom), XTI)*htempexp; br_t = Br*pow((heatPort.T/Tnom), XTB); bf_t = Bf*pow((heatPort.T/Tnom), XTB); vt_t = (K/q)*heatPort.T; icb = if (vcb/(NR*vt_t) < EMin) then is_t*(ExMin*(vcb/(NR*vt_t) - EMin + 1) - 1) + vcb*Gbc else if (vcb/(NR*vt_t) > EMax) then is_t*( ExMax*(vcb/(NR*vt_t) - EMax + 1) - 1) + vcb*Gbc else is_t*(exp(vcb/ (NR*vt_t)) - 1) + vcb*Gbc; ieb = if (veb/(NF*vt_t) < EMin) then is_t*(ExMin*(veb/(NF*vt_t) - EMin + 1) - 1) + veb*Gbe else if (veb/(NF*vt_t) > EMax) then is_t*( ExMax*(veb/(NF*vt_t) - EMax + 1) - 1) + veb*Gbe else is_t*(exp(veb/ (NF*vt_t)) - 1) + veb*Gbe; Capcjc = if (vcb/Phic > 0) then Cjc*(1 + Mc*vcb/Phic) else Cjc*pow(1 - vcb/Phic, -Mc); Capcje = if (veb/Phie > 0) then Cje*(1 + Me*veb/Phie) else Cje*pow(1 - veb/Phie, -Me); ccb = if (vcb/(NR*vt_t) < EMin) then Taur*is_t/(NR*vt_t)*ExMin*(vcb/( NR*vt_t) - EMin + 1) + Capcjc else if (vcb/(NR*vt_t) > EMax) then Taur*is_t/(NR*vt_t)*ExMax*(vcb/(NR*vt_t) - EMax + 1) + Capcjc else Taur*is_t/(NR*vt_t)*exp(vcb/(NR*vt_t)) + Capcjc; ceb = if (veb/(NF*vt_t) < EMin) then Tauf*is_t/(NF*vt_t)*ExMin*(veb/( NF*vt_t) - EMin + 1) + Capcje else if (veb/(NF*vt_t) > EMax) then Tauf*is_t/(NF*vt_t)*ExMax*(veb/(NF*vt_t) - EMax + 1) + Capcje else Tauf*is_t/(NF*vt_t)*exp(veb/(NF*vt_t)) + Capcje; C.i = icb/br_t + ccb*der(vcb) + Ccs*der(C.v) + (icb - ieb)*qbk; B.i = -ieb/bf_t - icb/br_t - ceb*der(veb) - ccb*der(vcb); E.i = -B.i - C.i + Ccs*der(C.v); heatPort.Q_dot = -(vcb*icb/br_t + veb*ieb/bf_t + (icb - ieb)*qbk*(E.v - C.v)); end HeatingPNP;
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;
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;