The document discusses the AC analysis of BJT and MOSFET inverting amplifiers. It begins by stating the lesson objectives which are to draw small signal models, calculate parameters, and analyze performance characteristics like voltage gain, input and output resistances. It then discusses the hybrid-pi model of BJTs and defines the transconductance, output resistance and input resistance. Equivalent circuit models are shown for common-emitter and common-source amplifiers using BJTs and MOSFETs. Calculations are presented for voltage gain, input and output resistances of these amplifiers both with and without bypassing the emitter or source resistances. Examples are also worked through.

1. AC Analysis of
BJT and MOSFET
Inverting Amplifiers
Assoc Prof Chang Chip Hong email: echchang@ntu.edu.sg
EE2002 Analog Electronics

2. EE2002 Analog Electronics
Lesson Objectives
AC Analysis of BJT and MOSFET Inverting Amplifiers 2
At the end of this lesson, you should be able to:
Draw small signal model for BJT and MOSFET
Calculate the small signal parameters of BJT and MOSFET
Construct AC equivalent circuit of BJT and MOSFET inverting amplifiers
Calculate the following performance characteristics of C-E and C-S amplifiers
Voltage gain
Input resistance
Output resistance

3. EE2002 Analog Electronics
Hybrid-Pi Model of BJT
AC Analysis of BJT and MOSFET Inverting Amplifiers 3
This hybrid-pi small-signal model is
the intrinsic low-frequency
representation of the BJT.
Small-signal parameters are
controlled by the Q-point and are
independent of geometry of BJT.
Transconductance:
Output resistance:
ic
gmvbe
ib
E
CB
vbe r r vce
40C
m C
T
I
g I
V
where 25 mV@25 CT
kT
V
q
Input resistance:
m
r
g
++
A CE A
o
C C
V V V
r
I I
if

4. EE2002 Analog Electronics
Equivalent Forms of Small-Signal
Model for BJT
AC Analysis of BJT and MOSFET Inverting Amplifiers 4
Voltage-controlled current source gmvbe can be transformed into current-controlled
current source.
gmvbe
ib
E
CB
vbe
r r
ic
ib
ib
E
CB
vbe r r
ic
Basic relationship ic= ib is useful
for both dc and ac analysis when
BJT is in forward-active region.
be b
m be m b b
ce
c b b
o
v i r
g v g i r i
v
i i i
r
+ +

5. EE2002 Analog Electronics
VCC
E
Q
RC
RE
C1
C2
C3
B
C
RB
RC
RI
vi
RL
RI
RB2
RB1
vi
Q
C
B
E RL
+
vo
1 2B B BR R R
The ac equivalent circuit is
constructed by assuming that all
capacitances have zero
impedance at signal frequency and
dc voltage source is ac ground.
Assume that Q-point has already
been calculated from DC analysis.
Hence, gm, r and ro of BJT can
be calculated.
AC Analysis of BJT and MOSFET Inverting Amplifiers 5
Small Signal Analysis of C-E Amplifier
with Fully Bypass RE

6. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 6
C-E Amplifier with Fully Bypass RE:
Voltage Gain
c o m be L
vt m L
b be be
v v g v R
A g R
v v v
Terminal voltage gain between
base and collector is:
Overall voltage gain from source vi
to output voltage vo across RL is:
o c b b
v vt
i b i i
v v v v
A A
v v v v
RI
vi RB ro RL
+
vo
B C
E
r
RC
gmvbe
+
vbe
0L C L
R r R R
B
v m L
I B
R r
A g R
R R r
B
R r

7. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 7
C-E Amplifier with Fully Bypass RE:
Input Resistance
C1
VCC
1 2B B BR R R
RI
RB2
vi
Q
RB1
RC C2
C3
RL
Rin
vx
ix
RE
x x B
x
in
x
B
v i R r
v
R
i
R r
RB r ro RL
+
vo
B C
E
RC
gmvbe
+
vbe
B
R r

8. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 8
C-E Amplifier with Fully Bypass RE:
Output Resistance
C1
0
x x
x m be
C o
x x
be x
C o
v v
i g v
R r
v v
v i
R r
VCC
RI
Q
RB2
RB1 C2
C3
RL
Rour
1 2B B BR R R
vxRB ro
RI
B C
E
r RC
gmvbe
+
vbe
ix
RE
RC
vi
1
1 1x
out C o
x C o
out C
v
R R r
i R r
R R if

9. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 9
C-E Amplifier with Fully Bypass RE:
Example
Problem: Find voltage gain, input
and output resistances.
Given: = 65, VA = 50 V
Find the Q-point from dc equivalent circuit:
3 3
100 10 0.7 66 16 10 ( 5) 0B BI I
3.71
65 241
66 245
B
C B
E B
I
I I
I I
5 10 k 241 CEV
+5 V
10 k
voRout
RC
C3
C1
Rin
vi
+
220 k
RB
100 k
RE
16 k
330
RI
5 V
RL
C2
+5 V
10 k
IC
VCE
+
IE
16 k
5 V
100 k VBE
+
IB
3.67 VCEV

10. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 10
AC Analysis of C-E Amplifier with
Fully Bypass RE
9.64 (223 10 220) 6.23 k
84.0
330 6.23 k
bein
v vt
I in be
vR
A A
R R v
40 241mg
65
6.64 k
9.64 m
r
50 3.67
223 k
241
or
100 k 6.64 k 6.23 kinR
223 k 10 k 9.57 koutR
330
vi
100k
ro
220k
+
vo
B C
E
r
10k
gmvbe
+
vbe
Rin
100k
223k
220k
B C
E
6.64k
10k
9.64mvbe9.64mvbe
Rout
100k
223k
330
B C
E
6.64k
10k
Small signal equivalent

11. EE2002 Analog Electronics
Small Signal Parameters of MOSFET
AC Analysis of BJT and MOSFET Inverting Amplifiers 11
Since gate is insulated from channel
by gate-oxide, input resistance = .
Small-signal parameters are
controlled by the Q-point.
MOSFET transconductance is
geometry dependent.
2
1
2
1
n
D GS TN DS
D
m n GS TN DS
GS Q pt
K
i v V v
i
g K V V V
v
n n OX
W
K C
L
where
+
gmvgs
ig
S
DG
vgs r
id
vds
+
2
2
1
1
D
m n D
GS TN
DS
o
D D
I
g K I
V V
V
r
I I
if
1

12. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 12
Small Signal Analysis of C-S
Amplifier with Fully Bypass RS
VDD
S
AC equivalent circuit is constructed by
assuming that all capacitances have zero
impedance at signal frequency and dc
voltage sources represent ac grounds. M
RD
RS
C1
C2
C3
G
D
RG
RD
RI
vi
RL
RI
RG2
RG1
vi
D
MG
S RL
+
vo
1 2G G GR R R
vo
The small signal parameters, gm and ro of
the MOSFET is calculated at the Q-point,
ID and VDS.

13. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 13
C-S Amplifier with Fully Bypass RS:
Voltage Gain
Terminal voltage gain between
gate and drain is:
Overall voltage gain from source vi
to output voltage vo across RL is:
RI
vi RG ro RL
+
vo
G D
S
RD
gmvgs
+
vgs
0L D LR r R R
m gs Ld
vt m L
g gs
g v Rv
A g R
v v
g go o
v vt
i g i i
G
m L
I G
v vv v
A A
v v v v
R
g R
R R

14. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 14
C-S Amplifier with Fully Bypass RS:
Input Resistance
RG2
M
RG1
RD
RS
C2
C3
RL
Rin
C1
RG ro RL
+
vo
G D
S
RD
gmvgs
+
vgs
1 2G G GR R R
VDD
RI
vi
x x G
x
in
x
G
v i R
v
R
i
R
vx
ix

15. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 15
C-S Amplifier with Fully Bypass RS:
Output Resistance
vi
VDD
C1
Since vgs = 0, gmvgs = 0.
RI
RG2
RG1 C2
Rour
RS
RD
RL
M
gmvgs
vxRG ro
RI
G D
S
RD
+
vgs
ix
C3
21 GG G
R R R
x x D o
x
out D o
x
out D
v i R r
v
R R r
i
R R if

16. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 16
C-S Amplifier with Fully Bypass RS:
Example
Problem: Find voltage gain, input and
output resistances.
Given: Kn = 500 A/V2, VTN = 1V,
= 0.0167 V 1
DC Analysis:
61
1
6
5 10
2 10
0.4
S
GS
D
DS
I
IV
V
V
5 , 2 , 250DS GS DV V V V I
2500
1
2
GSD VI (1)
3
110 20 10DS D IV I (2)
+10 V
20 k
C3
vo
+Rout
100 k
RL
RD
RG3
1 M
RG2 2 M
RG1 2 M
C2
C1
10 k
RI
Rin
vi
+10 V
20 k
RG3
1 M
RG2
2 M
RG1
2 M
vDS
+
+
vGS
I1
ID
IG
RD

17. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 17
C-S Amplifier with Fully Bypass RS:
Example
0.5 260 k 1 M 20 k 100 k 1 M
7.93
10 k 1 M
gsin
v vt
I in gs
m vR
A A
R R v
2 2 1inR M M M
2 500m
g
1
5
0.0167 260 k
250
or
10k
vi
2M
ro
100k
+
vo
G
D
S
1M
gmvgs
+
vgs
2M
20k
Rin
1M
260k
16.4k
G D
S
0.5mvgs
0.5mvgs
S
Rout
1M
260k
10k
G D
1M
20k
260 1 20 18.2outR k M k k
16.4 k1 M
Small Signal Equivalent Circuit:

18. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 18
C-E Amplifier with Unbypass RE:
Terminal Voltage Gain
VCC
RB2
RB1
RC
RE2 C3
RI
vi
RL
C2
C1
vo
RE1
Q
vi RB
RL
+
voRC
ro
B C
E
r
gmvbe
+
vbe
RI
RE1
ic
L C LR R R
1 1 11
c c L m be L m L
vt
b be e E be m be E m E
v i R g v R g R
A
v v i R v g v R g R
ie
1 2B B BR R R

19. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 19
C-E Amplifier with Unbypass RE:
Input Resistance
vi
RI
1
1
1
1
b b b E
b
in E
b
v i r i R
v
R r R
i
Rin
vb RB
RL
+
voRC
ro
B C
E
r
ib
+
vbe
RE1
( +1)ib
ib
Rin
in in BR R R
inR
RB
RL
+
voRC
ro
B C
E
r
gmvbe
+
vbe
RE1
1 2B B BR R R

20. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 20
C-E Amplifier with Unbypass RE:
Overall Voltage Gain
+
vbRin
RB = RB1 || RB2
RL
+
voRC
ro
B C
E
r
gmvbe
+
vbe
RE1
Rin
VCC
RB2
RB1
RC
RE2 C3
RI
vi
RL
C2
C1
vo
RE1
Q
o o b in
v vt
i b i I in
v v v R
A A
v v v R R
vi
RI
Rin
vi
RI
+
vbRin

21. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 21
C-E Amplifier with Unbypass RE:
Output Resistance
Rth
RC
ro
B C
E
r
gmvbe
+
vbe
RE1
vx
ix
Rout
1 2th I B BR R R R
ix
1
be e
th
x th E
th
r
v v
r R
r
i r R R
r R1e x th Ev i r R R
x m bex o ev g v r vi
current through ro
outR
RL
+
vo
RI
RB
RC
ro
B C
E
r
gmvbe
+
vbe
RE1
1 2B B BR R R
Rout
vi

22. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 22
C-E Amplifier with Unbypass RE:
Output Resistance
1
1
x x m be o e
x m x th E o
th
x th E
v i g v r v
r
i g i r R R r
r R
i r R RRth
ro
B C
E
r
gmvbe
+
vbe
RE1
vx
ix
ix
out out CR R R
RC
Rout
11x
out m th E o
x th
v r
R g r R R r
i r R
outR