4/22/2011
Midband Gain
1/4
Mid-band Gain
15 V
15 V
Q: So, to find the mid-band
gain of this amplifier:
1K
3.7 K
vO (t )
COUS
β = 100
vi (t )
+
-
2.3K
1K
COUS
we must find the analyze this small signal circuit:
1
1
B
jωCi
C
jωC μ
Vo (ω )
+
+
-
3.7 K
Vi (ω )
v be (ω )
2.3 K
1
jωCπ
0 .5 K
1K
200 v be (ω )
−
E
1K
Jim Stiles
The Univ. of Kansas
1
jωCE
Dept. of EECS
4/22/2011
Midband Gain
2/4
to determine:
Vo (ω )
(
)
Avo ω =
Vi (ω )
and then plotting the magnitude:
Avo ( ω )
AM
ωL
ω
ωH
we determine mid-band gain AM , right?
A: You could do all that, but there is an easier way.
Recall the midband gain is the value af Avo ( ω ) for
frequencies within the amplifier bandwidth. For those
frequencies, the AC coupling capacitors (i.e., COUS) are
approximate AC short-circuits (i.e., very low impedance) .
Jim Stiles
The Univ. of Kansas
Dept. of EECS
4/22/2011
Midband Gain
3/4
Likewise, for the signal frequencies within the amplifier
bandwidth, the parasitic BJT capacitances are approximate
AC open-circuits (i.e., very high impedance).
Thus, we can apply these approximations to the capacitors in
our small-signal circuit:
B
Vo (ω )
C
+
+
-
2.3 K
3.7 K
v be (ω )
Vi (ω )
0 .5 K
1K
200 v be (ω )
−
E
1K
Now simplifying this circuit (look, no capacitors!):
Vo (ω )
+
Vi (ω )
+
-
vbe
-
Jim Stiles
0.37 K
RC =1 K
200 v be
The Univ. of Kansas
Dept. of EECS
4/22/2011
Midband Gain
4/4
Q: Hey wait! Isn’t this the same small-signal circuit that we
analyzed earlier, where we found that:
vo (t ) = −200 vi (t ) ??
A: It is exactly!
All of the small-signal analysis that we performed previously
(i.e., the circuits with no capacitors!) actually provided us with
the mid-band amplifier gain.
Taking the Fourier transform of the equation above:
Vo ( ω ) = −200 Vi ( ω )
= e jπ 200 Vi ( ω )
Thus, the midband gain of this amplifier is:
AM = −200 = e jπ 200
Jim Stiles
The Univ. of Kansas
Dept. of EECS