modelCjS
Spice-style junction capacitor model for bipolar transistors
Extends from BondLib.Interfaces.TwoPort (Partial model invoking two bondgraphic connectors).
Information
The Spice-style junction capacitance computes both the depletion capacitance value and the diffusion capacitance value of a junction used in a bipolar transistor. Different Spice dialects vary in the formulae they use for this purpose. Many Spice dialects actually don't use a formula for the junction capacitance at all, but rather compute the electric charge stored in the junction directly, which is conceptually cleaner. However, that approach is computationally cumbersome, as it leads to an awkward algebraic loop [1]. Thus, we chose to compute the junction capacitance, and use a (physically incorrect) approximate non-linear capacitor model (just as in the case of the simpler Ebers-Moll model). The numerical error should remain small, as the time constants associated with temperature change are much larger than those associated with electrical phenomena.This particular model uses the space charge formula advocated in [2]. Since:
f = der(q)
the space charge, q, was symbolically differentiated. In the differentiation, only electrical signals, i.e., the voltage, e, were considered time-varying. The temperature gradients were assumed to be negligible. This produced an equation of the form:
f = C(e)*der(e)
which is the formula that was used to compute the non-linear capacitance C(e) in the model.
Parameters: 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) VJ: Built-in potential at reference temperature (default value = 0.75 Volt) CJ: Zero-bias depletion capacitance at reference temperature (default value = 0.5e-12 F) XCJ: Fraction of base-collector depletion capacitance connected to internal base node (default value = 1) MJ: Junction grading coefficient (default value = 0.333) Tau: Ideal transit time (default value = 1e-9 sec) GminDC: Leakage conductance (default value = 1e-15 Mho) Area: Relative area occupied by the diode (default value = 1) Level: Transistor modeling level (Ebers-Moll = 1; Gummel-Poon = 2) (default value = 2) BE: True if base-emitter junction (default value = true)
References:
- Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York, pp. 224-225.
- Massobrio, G. and P. Antognetti (1993), Semiconductor Device Modeling with Spice, 2nd edition, McGraw Hill, New York, p.69.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.SIunits.Temperature | Tnom | 300.15 | Reference temperature |
| Modelica.SIunits.Current | IS | 1e-16 | Saturation current at reference temperature |
| Modelica.SIunits.Conductance | GminDC | 1e-15 | Leakage conductance |
| Real | N | 1 | Current emission coefficient |
| Modelica.SIunits.Capacitance | CJ | 0.5e-12 | Zero-bias depletion capacitance at reference temperature |
| Real | MJ | 0.333 | Junction grading coefficient |
| Modelica.SIunits.Voltage | VJ | 0.8 | Built-in potential at reference temperature |
| Real | XCJ | 1 | Fraction of depletion capacitance connected to internal base node |
| Real | FC | 0.5 | Factor for linearization of depletion capacitance formula |
| Modelica.SIunits.Time | Tau | 1e-9 | Ideal transit time |
| Real | XTI | 3 | Saturation current temperature exponent |
| Real | XTB | 0 | Forward and reverse beta temperature coefficient |
| Modelica.SIunits.Voltage | EG | 1.11 | Energy gap for temperature effect on saturation current |
| Real | Area | 1 | Relative area occupied by device |
| Integer | Level | 2 | Transistor modeling level (Ebers-Moll = 1; Gummel-Poon = 2) |
| Boolean | BE | true | True if base-emitter junction |
| 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 | |
| Modelica.Blocks.Interfaces.RealInput | qb | Base charge | |
| Modelica.Blocks.Interfaces.RealInput | C0 | Base capacitance | |
| Modelica.Blocks.Interfaces.RealOutput | ix | External base-collector capacitance current | |
| Modelica.Blocks.Interfaces.RealOutput | id | Diode current |
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 | |
| Junctions.J0p3 | J0p3_1 | ||
| Bonds.fBond | B1 | ||
| Sensors.De | vbi | ||
| Bonds.eBond | B2 | ||
| Sources.mSe | Vbi | ||
| Bonds.fBond | B3 | ||
| Junctions.J1p3 | J1p3_1 | ||
| Bonds.eBond | B4 | ||
| Sensors.Df | id1 | ||
| Bonds.fBond | B5 | ||
| Junctions.J0p3 | J0p3_2 | ||
| Bonds.fBond | B6 | ||
| Bonds.fBond | B7 | ||
| nlC | nlC1 | ||
| Bonds.fBond | B8 | ||
| Sensors.De | Tdev | ||
| DjS | DjS1 | ||
| mC3 | Cj1 | ||
| Junctions.J0p3 | J0p3_3 | ||
| Gj | Gj1 | ||
| Bonds.eBond | B9 |