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U
niversity of
S
outhern
C
alifornia
USC Viterbi School of Engineering
Ming Hsieh Department of Electrical Engineering
EE 541:
Solutions, Homework #01-#02
Fall, 2010
Due: 09/09/2010
Choma
Solutions
−
Problem #01:
The model shown within the symbolic network “box” in Fig-
ure (P1) is a linearized equivalent circuit of an emitter-degenerated, common emitter amplifier.
The amplifier is driven by a voltage source whose Thévenin resistance is
R
s
, and its load termi-
nation consists of a resistance,
R
l
in shunt with a capacitance,
C
l
.
In this problem,
R
s
= 50
Ω
, R
l
= 1.2 K
, R
e
= 120
, and
C
l
= 300 fF
.
The transistor model parameters are
r
b
= 90
, r
π
= 2.8
K
, r
o
= 25 K
, and
β
= 120 amps/amp
.
β
I
+
−
V
s
R
s
R
e
r
b
r
π
C
l
R
l
I
r
o
I
2
V
2
I
1
V
1
R
out
R
in
Figure (P1)
(a).
Derive analytical expressions for each of the four h-parameters of the degenerated common
emitter amplifier.
In the network box delineated in Figure (P1), the input port current,
I
1
, is identical to the branch
current,
I
, whence
I
≡
I
1
.
The hybrid h-parameters,
h
11
and
h
21
, are each evaluated under the
condition of a short circuited output port; that is, under the condition of
V
2
= 0
.
With
V
2
= 0
,
()
(
o2
1
e1 2
0r
I
)
β
IR
I
I
=−
++
,
(P1-1)
which leads immediately to
2
oe
2
21
1o
e
V=0
β
rR
I
h
119.42 amps/amp .
Ir
R
−
==
=
+
(P1-2)
Note that
h
21
is very close to parameter
because
r
o
>> R
e
.
Continuing with
V
2
= 0
,
() (
1b
π
1e
1
2
Vr
r
I
I
=+
+
+
)
,
(P1-3)
and using (P1-1) to eliminate current
I
2
in this KVL relationship,
2
1
11
b
π
1
V
hr
r
β
1 r
R
17.34 K
Ω
.
I
+
+
+
=
(P1-4)
The hybrid h-parameters,
h
12
and
h
22
, reflect the operating constraint,
I
1
= 0
, which means that
I
≡
I
1
= 0
.
Accordingly, the input port voltage,
V
1
, in Figure (P1) appears directly across resistance

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EE 541
University of Southern California Viterbi School of Engineering
Choma
Solutions, Homework #01-#02
8
Fall Semester, 2010
R
e
, while
β
I
is an open circuited branch.
It follows that
1
2
22
2o
e
I=0
I1
h
39.81
μ
,
Vr
R
===
+
(P1-5)
and
1
e
1
12
e
R
V
h
4.78 mV/V .
R
+
(P1-6)
Parameter
h
12
effectively defines the degree to which the amplifier input port is isolated from its
output port.
Normally, this isolation level is expressed in decibels.
Thus, the I/O reverse feedback
of
h
12
= 4.78 mV/V
is equivalent to an isolation level of
–46.41 dB (20log
10
|h
12
|)
.
(b).
Using the h-parameter expressions deduced in Part (a), derive analytical expressions for
the low frequency, open loop values of voltage gain,
V
2
/V
s
, input resistance,
R
in
, and output
resistance,
R
out
.
Using the pertinent results disclosed in
Course Notes 1
, the open loop voltage gain,
A
vo
, is
()
21
vo
11
s
22
l
h
A
hR
h1
R
=−
=
++
7
.
8
6
V
/
V
.
(P1-7)
The open loop input resistance,
R
ino
, is simply
ino
11
Rh
1
7
.
3
4
K
Ω
,
==
(P1-8)
while the open loop output resistance,
R
outo
, is
outo
22
1
R
25.12 K
Ω
.
h
(P1-9)
(c).
Using the h-parameter expressions deduced in Part (a), derive an analytical expression for
the low frequency loop gain of the amplifier.
Discuss the influence that the emitter degen-
eration resistance,
R
e
, has on this loop gain.

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