# Gummel–Poon model

The Gummel–Poon model is a model of the bipolar junction transistor. It was first described in an article published by Hermann Gummel and H. C. Poon at Bell Labs in 1970.[1]

The Gummel–Poon model and modern variants of it are widely used in popular circuit simulators such as SPICE. A significant effect that the Gummel–Poon model accounts for is the variation of the transistor ${\displaystyle \beta _{\text{F}}}$ and ${\displaystyle \beta _{\text{R}}}$ values with the direct current level. When certain parameters are omitted, the Gummel–Poon model reduces to the simpler Ebers–Moll model.[1]

## Model parameters

Spice Gummel–Poon model parameters[2]

# Name Property
modeled
Parameter Units Default
value
1 IS current transport saturation current A 1×10−16
2 BF current ideal max. forward beta 100
3 NF current forward-current emission coefficient 1
4 VAF current forward early voltage V
5 IKF current corner for forward-beta high-current roll-off A
6 ISE current B–E leakage saturation current A 0
7 NE current B–E leakage emission coefficient 1.5
8 BR current ideal max. reverse beta 1
9 NR current reverse-current emission coefficient 1
10 VAR current reverse early voltage V
11 IKR current corner for reverse-beta high-current roll-off A
12 ISC current B–C leakage saturation current A 0
13 NC current B–C leakage emission coefficient 2
14 RB resistance zero-bias base resistance Ω 0
15 IRB resistance current where base resistance falls half-way to its minimum A
16 RBM resistance minimum base resistance at high currents Ω RB
17 RE resistance emitter resistance Ω 0
18 RC resistance collector resistance Ω 0
19 CJE capacitance B–E zero-bias depletion capacitance F 0
20 VJE capacitance B–E built-in potential V 0.75
21 MJE capacitance B–E junction exponential factor 0.33
22 TF capacitance ideal forward transit time s 0
23 XTF capacitance coefficient for bias dependence of TF 0
24 VTF capacitance voltage describing VBC dependence of TF V
25 ITF capacitance high-current parameter for effect on TF A 0
26 PTF excess phase at frequency = 1/(2π TF) ° 0
27 CJC capacitance B–C zero-bias depletion capacitance F 0
28 VJC capacitance B–C built-in potential V 0.75
29 MJC capacitance B–C junction exponential factor 0.33
30 XCJC capacitance fraction of B–C depletion capacitance connected to internal base node 1
31 TR capacitance ideal reverse transit time s 0
32 CJS capacitance zero-bias collector–substrate capacitance F 0
33 VJS capacitance substrate–junction built-in potential V 0.75
34 MJS capacitance substrate–junction exponential factor 0
35 XTB forward- and reverse-beta temperature exponent 0
36 EG energy gap for temperature effect of IS eV 1.1
37 XTI temperature exponent for effect of IS 3
38 KF flicker-noise coefficient 0
39 AF flicker-noise exponent 1
40 FC coefficient for forward-bias depletion capacitance formula 0.5
41 TNOM parameter measurement temperature °C 27