Ac analysis of bjt and mosfet inverting amplifiers

AC BJT and MOSFET Inverting Amplifiers

1. AC Analysis of
BJT and MOSFET
Inverting Amplifiers
AssocProf Chang Chip Hong email: [email protected]
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:
i
c
g
mv
be
i
b
E
CB
v
ber
p r
ov
ce40
C
mC
T
I
gI
V

where25 mV@25C
T
kT
V
q
 
Input resistance:m
r
g
p


–
+
–
+A CE A
o
CC
VVV
r
II


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 g
mv
be
can be transformed into current-controlled
current source.
g
mv
be
i
b
E
CB
v
be
r
p r
o
i
c
 i
b
i
b
E
CB
v
ber
p r
o
i
c
Basic relationship i
c= i
b
is useful
for both dc and ac analysis when
BJT is in forward-active region.beb
mbe mb b
ce
c b b
o
vir
gvgiri
v
iii
r
p
p





–
+
–
+

5. EE2002 Analog Electronics
V
CC
E
Q
R
C
R
E
C
1
C
2
C
3
B
C
R
B
R
C
R
I
v
i
+
-
R
L
R
I
R
B2
R
B1
v
i
+
-
Q
C
B
E R
L
+
v
o
-12B B B
R 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, g
m, r
p
, and r
o
of BJT can
be calculated.
AC Analysis of BJT and MOSFET Inverting Amplifiers 5
Small Signal Analysis of C-E Amplifier
with Fully Bypass R
E

6. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 6
C-E Amplifier with Fully Bypass R
E:
Voltage Gainc o mbeL
vt mL
b be be
vvgvR
A gR
vvv
-
-
Terminal voltage gain between
base and collectoris:
Overall voltage gain from source v
i
to output voltage v
oacross R
L
is:o c b b
v vt
i b i i
vvvv
AA
vvvv

R
I
v
i
+
- R
B r
o R
L
+
v
o
-
B C
E
r
p
R
C
g
mv
be
+
v
be
-0L C L
R r R R B
v mL
IB
Rr
AgR
RRr
p
p

-


 B
Rr
p

7. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 7
C-E Amplifier with Fully Bypass R
E:
Input Resistance
C
1
V
CC12B BB
RRR
R
I
R
B2
v
i
Q
R
B1
R
C C
2
C
3
+
-
R
L
R
in
v
x
+
-
i
x
R
E 
x xB
x
in
x
B
viRr
v
R
i
Rr
p
p



R
B
r
p r
o R
L
+
v
o
-
B C
E
R
C
g
mv
be
+
v
be
-B
Rr
p

8. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 8
C-E Amplifier with Fully Bypass R
E:
Output Resistance
C
10
xx
x mbe
Co
xx
be x
Co
vv
i gv
Rr
vv
vi
Rr


V
CC
R
I
Q
R
B2
R
B1
C
2
C
3
R
L
R
our12B BB
RRR
v
x
+
-
R
B r
o
R
I
B C
E
r
p R
C
g
mv
be
+
v
be
-
i
x
R
E
R
C
v
i
+
-1
11
x
out Co
x C o
out C
v
R Rr
iRr
RR
-





if

9. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 9
C-E Amplifier with Fully Bypass R
E:
Example
Problem:Find voltage gain, input
and output resistances.
Given: = 65, V
A= 50 V
Find the Q-point from dc equivalent circuit: 
33
100100.7661610(5)0
BB
II- 3.71 μA
65241 μA
66245 μA
B
CB
EB
I
II
II


 510 k241 μ16 k245 μ50
CE
V-----
+5 V
10 k
v
o
R
out
R
C
C
3 
C
1 
R
in
v
i
+
–
220 k
R
B
100 k
R
E
16 k
330 
R
I
–5 V
R
L
C
2 
+5 V
10 k
I
C
V
CE
+
–
I
E
16 k
–5 V
100 k
V
BE
+
–
I
B3.67V
CE
V

10. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 10
AC Analysis of C-E Amplifier with
Fully Bypass R
E9.64(22310220) 6.23 k
84.0
3306.23 k
bein
v vt
I in be
vR
AA
RR v
- 
  -  
 
  40241 μ9.64 mS
m
g 65
6.64k
9.64 m
r
p
 503.67
223k
241 μ
o
r

 100 k6.64 k6.23k
in
R  223 k10 k9.57k
out
R 
330
v
i
+
-
100 k

r
o
220 k

+
v
o
-
B C
E
r
p
10 k

g
mv
be
+
v
be
-
R
in
100 k

223 k

220 k

B C
E
6.64 k

10 k

9.64
m v
be
9.64
m v
be
R
out
100 k

223 k

330

B C
E
6.64 k

10 k

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 nGS TN DS
GSQpt
K
ivVv
i
g KVVV
v


-
-

-
 n nOX
W
KC
L


 

where
+
g
mv
gs
i
g
S
DG
v
gs r
o
i
d
v
ds
–
+
–2
2
1
1
D
m nD
GS TN
DS
o
DD
I
g KI
VV
V
r
II



-


if1


12. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 12
Small Signal Analysis of C-S
Amplifier with Fully Bypass R
S
V
DD
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
R
D
R
S
C
1
C
2
C
3
G
D
R
G
R
D
R
I
v
i
+
-
R
L
R
I
R
G2
R
G1
v
i
+
-
D
M
G
S R
L
+
v
o
-12G GG
RRR
v
o
•The small signal parameters, g
m
andr
o
of
the MOSFET is calculated at the Q-point,
I
D
and V
DS
.

13. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 13
C-S Amplifier with Fully Bypass R
S:
Voltage Gain
Terminal voltage gain between
gate and drain is:
Overall voltage gain from source v
i
to output voltage v
o
across R
L
is:
R
I
v
i
+
-
R
G r
o R
L
+
v
o
-
G D
S
R
D
g
mv
gs
+
v
gs
-0L DL
RrRR mgsLd
vt mL
g gs
gvRv
A gR
vv
-
- ggoo
v vt
i g i i
G
mL
IG
vvvv
AA
vvvv
R
gR
RR


-




14. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 14
C-S Amplifier with Fully Bypass R
S:
Input Resistance
R
G2
M
R
G1
R
D
R
S
C
2
C
3
R
L
R
in
C
1
R
G r
o R
L
+
v
o
-
G D
S
R
D
g
mv
gs
+
v
gs
-12G G G
RRR
V
DD
R
I
v
i
+
-x xG
x
in
x
G
viR
v
R
i
R



v
x
+
-
i
x

15. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 15
C-S Amplifier with Fully Bypass R
S:
Output Resistance
v
i
+
-
V
DD
C
1
Sincev
gs= 0, g
mv
gs= 0.
R
I
R
G2
R
G1
C
2
R
our
R
S
R
D
R
L
M
g
mv
gs
v
x
+
-
R
G r
o
R
I
G D
S
R
D
+
v
gs
-
i
x
C
321GGG
R R R  
x xDo
x
out Do
x
out D
viRr
v
RRr
i
RR



if

16. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 16
C-S Amplifier with Fully Bypass R
S:
Example
Problem:Find voltage gain, input and
output resistances.
Given: K
n= 500 A/V
2
, V
TN= 1V,
 = 0.0167 V
–1
DC Analysis:61
1
6
510
210
0.4
S
GS
D
DS
I
IV
V
V



 5,2,250 μA
DS GS D
VVVVI  
2500 μ
1
2
GSD
VI-
(1) 
3
1
102010
DS D
IVI-
(2)
+10 V
20 k
C
3 
v
o
+
–
R
out
100 k
R
L
R
D
R
G3
1 M
R
G22 M
R
G12 M
C
2 
C
1 
10 k
R
I
R
in
v
i
+10 V
20 k
R
G3
1 M
R
G2
2 M
R
G1
2 M
v
DS
+
–
+
–
v
GS
I
1
I
D
I
G
R
D

17. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 17
C-S Amplifier with Fully Bypass R
S:
Example 0.5260 k1 M20 k100 k 1 M
7.93
10 k1 M
gsin
v vt
I in gs
mvR
AA
RR v
- 
  - 
 
 22 1
in
R MMM  2500 μ250 μ0.5 mS
m
g 1
5
0.0167
260 k
250 μ
o
r


10k 
v
i
+
-
2 M

r
o
100 k

+
v
o
-
G
D
S
1 M

g
mv
gs
+
v
gs
-
2 M

20 k

R
in
1 M

260 k

16.4 k

G D
S
0.5
m
v
gs
0.5
m
v
gs
S
R
out1 M

260 k

10 k

GD
1 M

20 k
26012018.2
out
R kMk k  
16.4 k
1 M
Small Signal Equivalent Circuit:

18. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 18
C-E Amplifier with UnbypassR
E:
Terminal Voltage Gain
V
CC
R
B2
R
B1
R
C
R
E2
C
3
R
I
v
i
+
-
R
L
C
2
C
1
v
o
R
E1
Q
v
i
+
- R
B
R
L
+
v
o
-
R
C
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
I
R
E1
i
cL C L
R R R 1 1 1
1
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
  - - -
   
  
i
e12B B B
R R R

19. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 19
C-E Amplifier with UnbypassR
E:
Input Resistance
v
i
+
-
R
I

1
1
1
1
bb bE
b
in E
b
viriR
v
RrR
i
p
p




R
in
v
b
+
-R
B
R
L
+
v
o
-
R
C
r
o
B C
E
r
p
i
b
+
v
be
-
R
E1
(+1)i
b
i
b
R
inin inB
RRR in
R
R
B
R
L
+
v
o
-
R
C
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
E112B B B
R R R

20. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 20
C-E Amplifier with UnbypassR
E:
Overall Voltage Gain
+
v
b
-
R
in
R
B= R
B1|| R
B2
R
L
+
v
o
-
R
C
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
E1
R
in
V
CC
R
B2
R
B1
R
C
R
E2
C
3
R
I
v
i
+
-
R
L
C
2
C
1
v
o
R
E1
Qo o b in
v vt
i b i I in
vvvR
AA
vvvRR


v
i
+
-
R
I
R
in
v
i
+
-
R
I
+
v
b
-
R
in

21. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 21
C-E Amplifier with UnbypassR
E:
Output Resistance
R
th
R
C
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
E1
v
x
+
-
i
x
R
out12th I B B
RRRR
i
x  
1
be e
th
x th E
th
r
vv
rR
r
irRR
rR
p
p
p
p
p

-




- 


   
1ex th E
virRR
p
  
x mbex o e
v gvrvi-
current through r
oout
R
R
L
+
v
o
-
R
I
R
B
R
C
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
E112B B B
R R R
R
out
v
i
+
-

22. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 22
C-E Amplifier with UnbypassR
E:
Output Resistance 
  
  
1
1

x x mbeo e
x m x th E o
th
x th E
vigvrv
r
igirRRr
rR
irRR
p
p
p
p
-
 
  



R
th
r
o
B C
E
r
p
g
mv
be
+
v
be
-
R
E1
v
x
+
-
i
x
i
xout outC
RRR R
C
R
out  
1
1
x
out m th E o
x th
vr
R g rRRr
i rR
p
p
p

 


 out
R

23. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 23
C-S Amplifier with UnbypassR
S:
Terminal Voltage Gain
V
DD
R
G2
R
G1
R
D
R
S2
C
3
R
I
v
i
+
-
R
L
C
2
C
1
v
o
R
S1
v
i
+
- R
G
R
L
+
v
o
-
R
D
R
I
R
S1
i
d g
mv
gsL DL
RRR 1 1 1
1
mgsLd dL mL
vt
g gsdS gs mgsS mS
gvRviR gR
A
vviRvgvRgR
---
 
 
i
d12G GG
RRR
r
o
G D
S
g
mv
gs
+
v
gs
-
M

24. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 24
C-S Amplifier with UnbypassR
S:
Input Resistance
R
G = R
G1|| R
G1
R
L
+
v
o
-
R
D
R
S1
R
inin G
RR r
o
G D
S
g
mv
gs
+
v
gs
-v
i
+
-
R
I
R
in
R
G
R
L
+
v
o
-
R
D
R
S112G GG
RRR
r
o
G D
g
mv
gs
+
v
gs
-

25. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 25
C-S Amplifier with UnbypassR
S:
Overall Voltage Gain
V
DD
R
G= R
G1|| R
G2
R
L
+
v
o
-
R
D
r
o
G D
S
g
mv
gs
+
v
gs
-
R
S1
R
in
R
G2
R
G1
R
D
R
S2
C
3
R
I
v
i
+
-
R
L
C
2
C
1
v
o
R
S1
v
i
+
-
R
Igo o in
v vt
i g i I in
vvv R
AA
vvvRR


R
in
v
i
+
-
R
I
+
v
g
-
R
in
M

26. EE2002 Analog Electronics AC Analysis of BJT and MOSFET Inverting Amplifiers 26
C-S Amplifier with UnbypassR
S:
Output Resistance
R
th
R
D
R
S1
v
x
+
-
i
x
R
out12th IGG
RRRR
i
x1
1
0,
s xS
g gs s xS
viR
vvviR

--
r
o
G D
S
g
mv
gs
+
v
gs
- 
11x x mxSoxS
vigiRriR  
1
1
x
out mSo
x
v
R gRr
i
 out outD
RRR  x mgsx o s
v gvrvi-
current through r
oout
R
R
L
+
v
o
-
R
I
R
G
R
D
R
S112G GG
RRR
r
o
G D
g
mv
gs
+
v
gs
-
R
out
v
i
+
-