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]

Schematic of Spice Gummel–Poon model NPN

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

See also

• Gummel plot