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# Gummel–Poon model

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 Title: Gummel–Poon model Author: World Heritage Encyclopedia Language: English Subject: Collection: Transistor Modeling Publisher: World Heritage Encyclopedia Publication Date:

### Gummel–Poon model

Schematic of Spice Gummel-Poon Model NPN

The Gummel–Poon model is a model of the bipolar junction transistor. It was first described in a paper 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 via incorporation in the popular circuit simulators such as SPICE. A significant effect that the Gummel–Poon model accounts for is the variation of the transistors' \beta_\mathrm{F} and \beta_\mathrm{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

# Name Property
Modeled
Parameter Units Default
Value
1 IS current transport saturation current A 1.00E-016
2 BF current ideal max forward beta - 100
3 NF current forward current emission coefficient - 1
4 VAF current forward Early voltage V inf
5 IKF current corner for forward beta high current roll-off A inf
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 inf
11 IKR current corner for reverse beta high current roll-off A inf
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 ohms 0
15 IRB resistance current where base resistance falls half-way to its minimum A inf
16 RBM resistance minimum base resistance at high currents ohms RB
17 RE resistance emitter resistance ohms 0
18 RC resistance collector resistance ohms 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 inf
25 ITF capacitance high-current parameter for effect on TF A 0
26 PTF excess phase at freq=1.0/(TF*2PI) Hz deg 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 deg.C 27
[2]

## References

1. ^ a b H. K. Gummel and H. C. Poon, "An integral charge control model of bipolar transistors", Bell Syst. Tech. J., vol. 49, pp. 827–852, May–June 1970
2. ^ http://virtual.cvut.cz/dynlabmodules/ihtml/dynlabmodules/semicond/node48.html Summary of model with schematics and equations