EE315A Spring 2009
B. Murmann
Page 1 of 3
Last modified 5/5/2009 10:27:00 AM
HOMEWORK #5
(Due: Tuesday, May 12, 2009, 1pm PT)
1.
Consider the idealized singlestage OTA feedback circuit shown below.
The OTA is
described by the “OTA1” behavioral model discussed in class and has the following
parameters: f
T
=5GHz, a
0
→∞
,
γ
=1, C
L
=5pF, C
f
=300fF and C
s
=4C
f
.
a)
Consider f
T
to be fixed and let C
in
vary (C
in
refers to the input capacitance of the OTA).
Derive the C
in
(C
in_opt
) in terms of C
s
and C
f
that maximizes the ratio f
c
/N
tot
.
Here f
c
is the
unity gain frequency of the loop gain T(s) and N
tot
is the total integrated noise power at
the output of the circuit.
b)
Assuming C
in
=C
in_opt
and using the parameters above, calculate the feedback factor
(
β),
the required
G
m
of the OTA, and the total load capacitance (C
Ltot
) at the output of the
OTA (C
Ltot
is C
L
plus loading from the feedback network).
c)
From the values found in part b), calculate f
c
and N
tot
.
Also calculate the square root of
the total integrated noise power at the output in
μ
V
rms
.
Assume the circuit is operating at
a temperature of 25
°
C.
d)
Simulate the circuit in Cadence, using a
0
=10
12
.
You can use the “OTA1” model in the
ee315a library.
In order to establish a proper operating point, add a 1 T
Ω
resistor in
parallel with C
s
.
For all simulations, assume C
in
=C
in_opt
and use the corresponding G
m
value.
i.
Set up a “stb” analysis to measure the loop gain, T(s).
For this purpose, insert an
“iprobe” element such that it breaks the loop either at the input or output of the
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 Spring '09
 BorisMurmann
 loop gain, unity gain frequency

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