EE315A Spring 2009
B. Murmann
Page 1 of 4
Last modified 4/28/09 4:47 PM
HOMEWORK #4
(Due: Tuesday
, May 5, 2009, 1pm PT)
1.
Read the paper the paper referenced below and answer the following questions (concisely):
a)
The author explains that it makes sense to differentiate in nomenclature between a “G
m
”
element used in a G
m
C filter and an OTA. Explain the reason(s) behind this argument.
b)
At the bottom of page 170, under 4), it is claimed that a G
m
COpAmp integrator
achieves a small phase lead for relatively small op amp gain. Prove this by deriving a
transfer function for the circuit of Fig. 13, and subsequently compare the finite DC gain
and phase lead of your result with the expression for an RCOpAmp integrator derived in
class. Assume that the op amp has infinite bandwidth and finite DC gain a
0
. Assume that
the G
m
element contains a shunt resistance R
o
across its output, and assume R
0
is greater
than R. You may use a single ended half circuit model for your analysis.
c)
Equation (7) provides a bound on the minimum achievable power dissipation for the
realization of a pole pair. Find a continuous time filter paper published in the IEEE
Journal of SolidState Circuits between 2004 and today and estimate its “
η
” factor. Use
common sense to factor in the number of poles and/or power breakdown among multiple
poles in your calculations. Use reasonable estimates for the Q values in case they are not
specified in the paper you chose. The purpose of this analysis is to estimate the “order of
magnitude” for
η
in recent implementations.
Reference: Y.P. Tsividis, "Integrated continuoustime filter design  an overview,"
IEEE
Journal of
SolidState Circuits
, vol. 29, no. 3, pp.166176, March 1994.
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 Spring '09
 BorisMurmann
 Signal Processing, RC circuit, Lowpass filter, Butterworth Filter, Chebyshev filter

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