The circuit in Figure P7.48 is a hybrid− π equivalent circuit including the resistance r b . (a) Derive the expression for the voltage gain transfer function A υ ( s ) = V o ( s ) / V i ( s ) . (b) If the transistor is biased at I C Q =1mA , and if R L = 4 kΩ and β o = 100 , determine the midband voltage gain for (i) r b = 100 Ω and (ii) r b = 500 Ω . (c) For C 1 = 2.2 pF , determine the −3dB frequency for (i) r b = 100 Ω and (ii) r b = 500 Ω . Figure P7.48
The circuit in Figure P7.48 is a hybrid− π equivalent circuit including the resistance r b . (a) Derive the expression for the voltage gain transfer function A υ ( s ) = V o ( s ) / V i ( s ) . (b) If the transistor is biased at I C Q =1mA , and if R L = 4 kΩ and β o = 100 , determine the midband voltage gain for (i) r b = 100 Ω and (ii) r b = 500 Ω . (c) For C 1 = 2.2 pF , determine the −3dB frequency for (i) r b = 100 Ω and (ii) r b = 500 Ω . Figure P7.48
Solution Summary: The author explains the expression for the voltage gain of the transfer function.
The circuit in Figure P7.48 is a hybrid−
π
equivalent circuit including the resistance
r
b
. (a) Derive the expression for the voltage gain transfer function
A
υ
(
s
)
=
V
o
(
s
)
/
V
i
(
s
)
. (b) If the transistor is biased at
I
C
Q
=1mA
, and if
R
L
=
4
kΩ
and
β
o
=
100
, determine the midband voltage gain for (i)
r
b
=
100
Ω
and (ii)
r
b
=
500
Ω
. (c) For
C
1
=
2.2
pF
, determine the −3dB frequency for (i)
r
b
=
100
Ω
and (ii)
r
b
=
500
Ω
.
7.26. The sampling theorem, as we have derived it, states that a signal x(1) must be sam-
pled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its
highest frequency). This implies that if x(1) has a spectrum as indicated in Figure
P7.26(a) then x(1) must be sampled at a rate greater than 2002. However, since the
signal has most of its energy concentrated in a narrow band, it would seem reason-
able to expect that a sampling rate lower than twice the highest frequency could be
used. A signal whose energy is concentrated in a frequency band is often referred to
as a bandpass signal. There are a variety of techniques for sampling such signals,
generally referred to as bandpass-sampling techniques.
x(t)
X(jw)
MA
@₁ W₂
(a)
-W₂ -W₁
p(t) = Σ 8(t-nT)
Io.
Xp (t)
H(jw)
1
-Wo
n
Wa
p(t)
H(jw)
A+
(b)
3°
W
wp w
x, (t)
Figure P7.26
In the self-bias circuit of Figure 7.80
a. Draw the transfer characteristic curve of the device.
b. Draw additional circuit equations on the same graph.
Find c.lDQ and VGSQ.
d. Calculate VDS , VD, VG, Vs.
...
Consider the common source amplifier shown in the figure below. Assume that the transistorhas been biased in the saturation region. It has an ID = 1 mA, additionally k = 617 × 10−6 A/V2and Cgs = 1 pF. You may ignore channel length modulation and all other parasitic capacitors.Sketch the Bode plots for this amplifier.
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