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c
c
Copyright 2010. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical
and Computer Engineering.
Frequency Response of the CE Ampli±er
Midband Voltage Gain
The Fgure shows the signal circuit of the commonemitter ampliFer. There are three capacitors in the
circuit. At the mid frequency band, these are considered to be short circuits. When
r
0
is neglected except
in calculating the collector output impedance
r
ic
, the midband voltage gain from
v
s
to
v
o
can be written
A
v
=
R
1
b
R
2
R
s
+
R
1
b
R
2
×
1
r
ie
+
R
te
×
α
×
(

r
ic
b
R
C
b
R
L
)
R
tb
=
R
S
b
R
1
b
R
2
R
te
=
R
E
b
R
3
r
ie
=
R
tb
+
r
x
+
r
π
1 +
β
r
ic
=
r
0
p
1 +
βR
te
R
tb
+
r
x
+
r
π
+
R
te
P
+
R
te
This solution corresponds to the third solution found in the class notes on the commonemitter ampliFer.
E²ect of
C
1
At low frequencies,
C
1
is an open circuit and the gain is zero. Thus
C
1
has a high pass e±ect on the gain, i.e.
it a±ects the lower cuto± frequency of the ampliFer. To account for
C
1
,
A
v
is multiplied by the highpass
transfer function
T
1
(
s
) =
τ
1
s
1 +
τ
1
s
where
τ
1
is the time constant for
C
1
. The worst case time constant for the calculation of the lower cuto±
frequency is the smallest value, i.e. the value which predicts the highest pole frequency. ²or this to be the
case, the base input resistance
r
ib
must be calculated with
C
3
a short circuit. This makes
r
ib
its smallest
possible value. Imagine
C
1
being replaced with an ohmmeter with the source zeroed. The time constant is
given by the resistance measured by the ohmmeter multiplied by
C
1
.
τ
1
= (
R
S
+
R
1
b
R
2
b
r
ib
)
C
1
r
ib
=
r
x
+
r
π
+ (1 +
β
)
R
te
The pole frequency is given by
f
1
=
1
2
πτ
1
1
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View Full Document Efect oF
C
2
Capacitor
C
2
also has a high pass efect on the gain. To account For
C
2
,
A
v
is multiplied by the highpass
transFer Function
T
2
(
s
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This note was uploaded on 05/26/2011 for the course ECE 3050 taught by Professor Hollis during the Summer '08 term at Georgia Institute of Technology.
 Summer '08
 HOLLIS
 Frequency, Volt

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