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Anholt HBT Model: HBTRA



The Anholt HBT model is a modification of the well known Gummel-Poon model. Although it uses a similar topology, its expressions for temperature effects and transit time are very different. The model includes self-heating and accounts for nonreciprocal behavior.

Equivalent Circuit


Name Description Unit Type Default
ID Device ID Text HA1
*ISF Forward saturation current Current 1e-13
*ISR Reverse saturation current Current 1e-13
*BF Forward current gain   100.0
*NF Forward ideality factor   1.0
*VAF Forward early voltage Voltage 1.0x109
*IKF Forward current knee Current 1e12
*ISE BE leakage current param Current 0.0
*NE BE leakage ideality factor   1.5
*BR Reverse current gain   1.0
*NR Reverse ideality factor   1.0
*VAR Reverse early voltage Voltage 1.0x109
*IKR Reverse current knee Current 10e12
*ISC BC leakage current param Current 0.0
*NC BC leakage ideality factor   2.0
*CJE CJ0 for BE junction Capacitance 0.0
*VJE BE built-in voltage Voltage 0.75
*MJE BE capacitance exponent   0.50
*TB0 Constant part of the base transit time Time 0.0
*TB1 Variable part of the base transit time Time 0.0
*NTB Exponent for the base transit time   5.0
*TC0 Collector transit time Time 0.0
*BVS Saturation velocity parameter for TC   1.0x109
*ITF High-current parameter for the transit time   0.0
*PTF Excess phase param; must be in degrees Degrees 0.0
*CJC CJ0 for BC junction Capacitance 0.0
*VJC BC built-in voltage Voltage 0.75
*MJC BC capacitance exponent   0.50
XCJC Fraction of Cbc connected to the internal node   1.0
TR Reverse transit time Time 0.0
*CJS CJ0 for substrate capacitance Capacitance 0.0
*VJS Built-in voltage of the substrate capacitance Voltage 0.75
*MJS Substrate capacitance exponent   0.50
*RB Base resistance Resistance 0.01
*RB2 Extrinsic base resistance Resistance 0.01
*RE1 Emitter resistance Resistance 0.01
*RC2 Collector resistance Resistance 0.01
*CBE Extrinsic BE capacitance Capacitance 0.0
*CBC Extrinsic BC capacitance Capacitance 0.0
*CCE Extrinsic CE capacitance Capacitance 0.0
*LB Base inductance (not scaled) Inductance 0.0
*LE Emitter inductance (not scaled) Inductance 0.0
*LC Collector inductance (not scaled) Inductance 0.0
*FC Linearization term for forward-bias depletion capacitance   0.5
*ISS Collector-substrate current param Current 0.0
*NS Collector-substrate ideality factor   1.0
*TS Collector-substrate diode storage time Time 0.0
*TNOM Temperature at which parameters were extracted Temperature 26.85
*TBP Baseplate temperature Temperature 26.85
*XTI Temperature exponent for diode currents   0.0
*ABF BF temperature coefficient   0.0
*ABR BR temperature coefficient   0.0
*ANF NF temperature coefficient   0.0
*ANR NR temperature coefficient   0.0
*ANE NE temperature coefficient   0.0
*ANC NC temperature coefficient   0.0
*ANS NS temperature coefficient   0.0
*VSF Barrier height for ISF thermal modeling Voltage 0.0
*VSR Barrier height for ISR thermal modeling Voltage 0.0
*VSE Barrier height for ISE thermal modeling Voltage 0.0
*VSC Barrier height for ISC thermal modeling Voltage 0.0
*VSS Barrier height for ISS thermal modeling Voltage 0.0
*ARB RB temperature coefficient   0.0
*ARB2 RB2 temperature coefficient   0.0
*ARE RE temperature coefficient   0.0
*ARE1 RE1 temperature coefficient   0.0
*ARC2 RC2 temperature coefficient   0.0
*ACJE CJE temperature coefficient   0.0
*ACJC CJC temperature coefficient   0.0
*AVJE VJE temperature coefficient   0.0
*AVJC VJC temperature coefficient   0.0
*ATB0 TB0 temperature coefficient   0.0
*ATB1 TB1 temperature coefficient   0.0
*ATC0 TB1 temperature coefficient   0.0
*AITF ITF temperature coefficient   0.0
*RTH Thermal resistance Capacitance 0.001
*CTH Thermal capacitance Capacitance 1.0
*AFAC Area scale factor   1.0

* indicates a secondary parameter

Parameter Details

  1. Certain parameters (especially IKF, IKR, VAF, and VAR) are seldom needed in HBTs. These are included to allow the model to be used for conventional BJTs as well as HBTs. It is essential to note that including such parameters does not necessarily make the model equivalent to the SPICE Gummel-Poon model.

  2. Default parameter values for this model may not be the same as those of the SPICE Gummel-Poon model (GBJT). Be sure to be aware of differences when porting existing Gummel-Poon model parameters to this model.

  3. Be careful specifying temperature coefficients. It is possible to create nonphysical parameters if they are too great. This is especially true of the NF, NE, NR, and NC parameters.

Implementation Details


Resistances, capacitances, and currents are scaled in the usual manner: all resistors are scaled as 1/AFAC; junction currents and all capacitors are scaled in proportion to AFAC. Inductances LB, LE, and LC are not scaled.


The model is fundamentally the same as the Gummel-Poon model used in SPICE, with the addition of allowance for nonreciprocal behavior, self-heating, and a new expression for transit time as a function of collector voltage and current. The model also includes common extensions over the expressions in the references.


The collector current expression in the Gummel-Poon model has been modified to allow for nonreciprocal behavior of HBT devices. The SPICE parameter IS has been replaced by two parameters, ISF and ISR, that describe forward and reverse conduction, respectively. The current expression is

Qb is the normalized base charge, as used in the Gummel-Poon model; q is electron charge, K is Boltzmann's constant, and T is temperature in Kelvin degrees. Note that T varies with power dissipation in the device. ISF and ISR are also functions of temperature (see below).


The expression for transit time is

(When Vbc > VJC, the square-root term in is corrected in the same manner as similar terms in depletion capacitances; the method is identical to the one used in SPICE.) The base-to-emitter diffusion charge is

Reverse diffusion charge is included in the model; it is part of the "inner" base-to-collector capacitance. In reverse operation, the transit time is simply TR.


The PTF parameter is an awkward way of specifying a simple time delay in the base-to-emitter voltage. PTF is defined as in the SPICE Gummel-Poon model. It must be given in degrees; then, the delay represented by this quantity is


Saturation currents (ISF, ISR, ISE, ISC, ISS) are scaled as follows:

where ISX is one of the parameters above, and VSX is the corresponding voltage parameter.

Other parameters are scaled as

where P is any of the thermally scaled parameters and AP is the corresponding temperature coefficient. (Be careful using this capability; see Note 3, above.) T is the instantaneous temperature, which includes effects of self-heating.


The model uses a conventional electrothermal self-heating model. RTH is the thermal resistance in degrees C per watt of power dissipation. CTH is the thermal capacitance, defined as

where tTH is the thermal time constant of the device. CTH should never be set to zero; otherwise, the device temperature T cycles at the RF frequency. When the time constant is long compared to a period of the excitation waveform, the device temperature T is

The power dissipation, Pdiss, includes all power dissipated in the device: DC sources at both the base and collector, as well as RF dissipation.


To prevent numerical difficulties, the device temperature, T, is limited to values greater than 100 K. An abrupt limit at 100 K would introduce convergence difficulties; therefore, the limiting function smooths the temperature in the vicinity of 100 K. This smoothing function introduces a small error throughout the entire temperature range; the maximum error, which occurs at 100 K, is approximately 7 K. Above 200K, the error is less than 0.5 K.


The expression for tf is somewhat different from those in the references. This modified expression, which is common in industry, provides better accuracy and convergence in harmonic-balance simulators.


This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.


[1] R. Anholt et al., "HBT Model Parameter Extractor for SPICE and Harmonic Balance Simulators," IEEE MTT-S International Microwave Symposium Digest, 1994, p. 1257.

[2] R. Anholt, Electrical and Thermal Characterization of MESFETs, HEMTs, and HBTs, Artech House, Norwood, MA, 1995.

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