Microelectronics Cheat Sheet

General amplifier models Model

Gain Parameter

Voltage amp

Open-circuit voltage gain:

 Avo "

Current amp

vo vi

  (V/V) io

=

 Ri = !  Ro = 0

0

Short-circuit current gain:

 Ais "

Transconductance amp

Transresistance amp

Ais

" R % $ ' #  R & o i

 Avo

=

 Avo

=

Gm Ro  Rm  Ri

io ii

  (A/A) vo

=

0

io vi

=

0

 Ri = 0  Ro = 0

vo ii

 Ri = !  Ro = !

  (A/V) vo

Open-circuit transresistance:  Rm "

=

 Ri = 0  Ro = !

Short-circuit transconductance: Gm "

 Avo

Ideal Characteristics

  (V/A) io

=

0

Small-signal models MOSFET Hybrid-" model

gm

=

gm

=

ro

µ n C ox

 L

2µ n C ox

V  A =

W 

BJT Hybrid-" model

(V GS  " V t ) W   L

 I  D

=

2 I  D

V GS  " V t 

1 =

 I  D

"  I  D

gm

Same for PMOS except use and replace µ n with µ  p.

T-models

V GS  " V t 

=

re

V T 

, |V  A|, |! |, r" 

 I C 

=

V T   I  B

=

T-models

# VT    I C 

=

=

V T   I  E 

#  gm

=

VT  

"  =

"  =

 I C 

(#  + 1) re

gm ro

V  A =

 I C 

High-frequency models MOSFET (simplified)

gm

=

gm

=

ro

µ n C ox

W   L

2µ n C ox

BJT

gm

(V GS  " V t ) W   L

 I  D

=

2 I  D

V GS  " V t 

V  A

C gs

C gd 

 I  D 2 =

=

3

WLC ox

WLov C ox

+

WLov C ox

 I C  V T 

V  A

ro

=

 I C 

r" 

=

=

#  =

gm

C  = C de + C  je C de  "  F gm C  je " 2C  je 0 " 

=

C µ 

=

C µ 0 1+

V CB V 0c