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. 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

External links

• Bell System Technical Journal, v49: i5 May-June 1970 on archive.org
• Designers-Guide.org comparison paper Xiaochong Cao, J. McMacken, K. Stiles, P. Layman, Juin J. Liou, Adelmo Ortiz-Conde, and S. Moinian, "Comparison of the New VBIC and Conventional Gummel–Poon Bipolar Transistor Models," IEEE Trans-ED 47 #2, Feb. 2000.