ECE 315 Homework 10
1.
(Frequency response of amplifiers)
For an NMOSFET in an amplifier setup with
C
gs
=0.5pF,
C
gd
=0.1pF,
C
db
=0.1pF,
C
L
=1pF (including Cdb),
g
m
=5mA/V,
r
o
= 20k
Ω
, and
R
sig
=
R
L
= 20k
Ω
,
(a)
In the CS amplifier of Fig. 6.20, use the Miller theorem to find the midband gain
A
M
and the 3-
dB corner frequency
f
H
. (4 pts)
The Miller Theorem allows us to substitute the feedback capacitor, C
gd
, with two separate capacitors
from the gate and the drain, both going to ground. The Miller Theorem estimates the equivalent
capacitance on the gate as
C
in,miller
= C
gd
[1 + g
m
(r
o
|| R
L
)] = 5.1 pF
The equivalent capacitance at the output at the output is given by
C
out,miller
= C
gd
[1 + (g
m
(r
o
|| R
L
))
-1
] ≈ C
gd
Therefore, the total input capacitance is
C
in
= C
in,miller
+ C
gs
= 5.6 pF
And we obtain the 3-dB corner frequency:
f
H
=
in
sig
C
R
π
2
1
= 1.42 MHz
The flatband gain for this simple first-order (single pole) system is just
A
M
= -g
m
(r
o
|| R
L
)
A
M
= -50
(b) Repeat (a) with the open-circuit time constant method.
Is the answer different? Give the
percentage contribution to
τ
H
by each of the three capacitances (
C
gs
,
C
gd
and
C
L
).
Give also the
gain-bandwidth product. (6 pts)
The open-circuit time constant method of finding the 3-dB frequency can be done by:
1)
Find the equivalent resistance seen by each capacitor using Thevenin/Norton equivalent circuits
(note that all other capacitors become open circuits, which is the origin of the name; don’t
forget what you did when finding Thevenin/Norton equivalents either, namely shorting
independent voltage sources to ground and opening independent current sources)
2)
For each capacitor, find the product τ
i
= R
i
C
i
, where R
i
is the equivalent resistance seen by C
i
3)
Find the estimated 3-dB frequency by τ
H
=
∑
i
i
i
C
R
Using this method we find:
The equivalent resistance seen by C
gs
, R
gs
= R
sig
= 20 kΩ
The equivalent resistance seen by C
gd
, R
gd
= R
sig
(1 + g
m
(r
o
|| R
L
)) + (r
o
|| R
L
) = 1.03 MΩ
The equivalent resistance seen by C
L
, R
L,eq
= (r
o
|| R
L
) = 10 kΩ
1