modelDjS
Ebers-Moll junction diode model for bipolar transistors
Extends from Interfaces.TwoPort (Partial model invoking two bondgraphic connectors).
Information
The junction diodic source element is a directed TwoPort. It inherits the effort and flow variables from the directed TwoPort. Junction diodes are a special class of non-linear resistors.The junction diode model is a simple diode with an exponential characteristic. The diode formula essentially is:
f = Is*(exp(e/Vt) - 1)
However, if the exponent e/Vt reaches either an upper limit EMax or a lower limit Emin, the diode characterisic is linearly continued to avoid overflow or underflow, respectively.
The causality of the junction diode element is free.
Potential variables: e1: Bondgraphic effort variable of inflow f1: Bondgraphic flow variable of inflow, normalized positive for flows into the model e2: Bondgraphic effort variable of outflow f2: Bondgraphic flow variable of outflow, normalized positive for flows out of the model Parameters: Tnom: Reference temperature (default value = 300.15 K) Is: Transport saturation current (default value = 1e-16 Amp) EG: Energy gap for temperature effect on saturation current (default value = 1.11 Volt) N: Current emission coefficient (default value = 1) XTI: Saturation current temperature exponent (default value = 3) EMin: Minimum exponent (default value = -100) EMax: Maximum exponent (default value = 40)
Equations:
RTemp = e2/Tnom
ISval = IS*exp((RTemp - 1)*EG/Vt + XTI*ln(RTemp))
ExMin = exp(EMin)
ExMax = exp(EMax)
et = e1/(Vt*N)
f1 = ISval*(if et < EMin then ExMin*(et - EMin + 1) - 1 else
if et > EMax then ExMax*(et - EMax + 1) - 1 else exp(et) - 1)
f2 = 0
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Real | k | 1.3806226e-23 | Boltzmann's constant |
| Modelica.SIunits.ElectricCharge | q | 1.6021918e-19 | Electron charge |
| Modelica.SIunits.Temperature | Tnom | 300.15 | Reference temperature |
| Modelica.SIunits.Current | Is | 1e-16 | Saturation current at reference temperature |
| Modelica.SIunits.Voltage | EG | 1.11 | Energy gap for temperature effect on saturation current |
| Real | N | 1 | Current emission coefficient |
| Real | XTI | 3 | Saturation current temperature exponent |
| Real | EMin | -100 | if x < EMin, the exp(x) function is linearized |
| Real | EMax | 40 | if x > EMax, the exp(x) function is linearized |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| BondLib.Interfaces.BondCon | BondCon1 (from TwoPort) | Left bond graph connector | |
| BondLib.Interfaces.BondCon | BondCon2 (from TwoPort) | Right bond graph connector |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real | e1 (from TwoPort) | Bondgraphic primary effort | |
| Real | f1 (from TwoPort) | Bondgraphic primary flow | |
| Real | e2 (from TwoPort) | Bondgraphic secondary effort | |
| Real | f2 (from TwoPort) | Bondgraphic secondary flow | |
| Modelica.SIunits.Voltage | Vt | Thermal voltage | |
| Modelica.SIunits.Current | ISval | Saturation current at device temperature |