Appendix F.Transistor and amplifier formulas

Radio Frequency Circuit Design. W. Alan Davis, Krishna Agarwal

Copyright 2001 John Wiley & Sons, Inc.

Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

APPENDIX F

Transistor and Amplifier

Formulas

The following formulas are meant as a reminder of the fundamentals given in most standard electronics textbooks. Notation for the formulas have the traditional meanings. Depletion capacitances are all given with a negative sign in the denominator as in C D C0/ 1 V/ . Consequently, when the junction is reverse biased, the minus sign turns into a positive sign. Figure F.1 presents the basic FET features and symbols.

Bipolar Transistor Parameters (BJT)

DESCRIPTION

FORMULA

qVBE

Collector current

IC D IS exp

kT

Transconductance

gm D

qIC

kT

Input resistance

r D

ˇ0

gm

Output resistance

ro D

VA

IC

Base charging capacitance

CD D Fgm

1/3

qεN

Emitter base junction

Cje D AE

B

Vj

Input capacitance

C D CD C Cje

Collector base

C D

C o

[1 VBC/ oc ]1/3

300

TRANSISTOR AND AMPLIFIER FORMULAS

301

Collector substrate	Ccs D					Ccso
				[1 Vsc/ os ]1/2
Transition frequency	fT D	1				gm
		2 C C C
Thermal voltage	VT D		kT			D 0.259 V
			q

FET Symbols

					ID
			NMOS Depletion.				NMOS Enhance.
				NJFET
								VGS
PMOS Enhance.					PMOS Depletion.
					PJFET
n-Channel JFET					p-Channel JFET

n-Channel MOSFET —

p-Channel MOSFET —

Enhancement

Enhancement

n-Channel MOSFET —

p-Channel MOSFET —

Depletion

Depletion

FIGURE F.1 FET symbols.

302 TRANSISTOR AND AMPLIFIER FORMULAS

Junction Field Effect Transistor Parameters (JFET)

DESCRIPTION

FORMULA

VGS

2

VDS

Saturated drain current

ID D IDSS 1

1

VP

VA

VDS ½ VGS VP

VGS VDS 3/2

0

3

0

VGS

C

3/2

Ohmic region drain current

ID D Go VDS C

C VP 1/2

2

0

C

VDS < VGS VP

G0 D

2aW

c

L

Transconductance

ID ³ K 2 VGS VP VDS VDS2

gm D

VP

1 VP

2IDSS

VGS

Output resistance

ro D

VA

ID

Gate source capacitance

Cgs D

Cgs0

[1 VGS/ 0 ]1/3

Gate drain capacitance

Cgd D

Cgd0

VGD

1/3

1

0

Gate substrate capacitance

Cgss D

Cgss0

[1 VGSS/

0 ]1/2

N Channel JFET

VP < 0

P Channel JFET

VP > 0

Metal Oxide Semiconductor Field Effect Transistor Parameters (MOSFET)

DESCRIPTION

FORMULA

CoxW

VDS

Saturation region drain

ID D

VGS Vt 2

1

2L

VA

current

VDS ½ VGS Vt

CoxW

Ohmic region drain current

ID D

2 VGS Vt VDS VDS2

2L

ð 1 VA

VDS

VDS < VGS Vt

TRANSISTOR AND AMPLIFIER FORMULAS 303

Oxide capacitance

Cox D

εox

tox

Transconductance

W

gm D Cox

VGS Vt

L

Output resistance

r

jVAj

o D ID0

Input capacitance

Cin D CGS C CGD D CoxLW

Transition frequency

f

gm

s VGS Vt

c D 2 Cin D

2 L2

Surface mobility holes

s D 200

cm2/V-s

Surface mobility electrons

s D 450

cm2/V-s

N CHANNEL JFET

P CHANNEL JFET

IDSS > 0

IDSS < 0

VP < 0

VP > 0

g

2IDSS

g

2IDSS

mo

VP

mo D

VP

IDSS

IDSS

K D

> 0

K D

< 0

VP2

VP2

VP < VGS for jIDSj > 0

VGS < VP for jIDSj > 0

NMOS ENHANCEMENT

PMOS ENHANCEMENT

Vt > 0

Vt < 0

VGS > Vt

VGS < Vt

nCoxW

> 0

pCoxW

< 0

K D

K D

2L

2L

NMOS DEPLETION

PMOS DEPLETION

Vt < 0

Vt > 0

VGS > Vt < 0 for jIDSj > 0

VGS < Vt < 0 for jIDSj

nCoxW

> 0

pCoxW

< 0

K D

K D

2L

2L

304 TRANSISTOR AND AMPLIFIER FORMULAS

Small Signal Single-Transistor Amplifier Configurations

MOSFET

BJT

Common source

Common emitter

Rin D RG D R1jjR2

Rin D r C rb jjRB ³ r

Rout D RDjjr0

Rout D Rcjjr0

p

AV D gm Rcjjr0jjRL

AV D gm r0jjRDjjRL / 1/ ID

Source degeneration

Emitter degeneration

Rin D RG D R1jjR2

Rin D r C RE ˇ C 1

³ r 1 C gmRE

Rout D r0[1 C gm C gmb RS]

Rout D REjjr C r0

1 C gm r jjRE

CRS

³ r0 1 C gmRE

Gm D

gm

Gm D

gm

1 C gm C gmb RS

1 C gmRE

Commmon gate

Common base

Rin D

RD

Rin D re D

˛0

rb

˛0

C

³

1 C RD gm C gmb

gm

ˇ C 1

gm

1

³

gm C gmb

Rout D r0 1 C ˇ jjRc

Rout D RD

³ gm

Gm D gm C gmb

Gm D gm 1 C rb/r

1

AV D gm RcjjRL

AI D

gmRc

RE

³ gmre D ˛0

Rc C RL

1 C gmRE

Common drain (source follower)

Commmon collector (emitter follower)

Rin D R1jjR2

Rin D r C rb C ˇ C 1 r0jjRE

R

r0

R

r C RBB C rb

1

RBB C rb

out D

1 C r0 gm C gmb

out D

1 C ˇ

³

gm

C

1 C ˇ

1

³

gm C gmb

A

gm RSjjr0

A

1

1

V D 1 C RSjjr0 gm C gmb

V D 1 C [ RBB

C rb C r / ³

1

REjjr0 ˇ C 1 ]

³

³ 1

1 C gmb/gm