# hw4 - EE315A Spring 2009 B. Murmann Page 1 of 4 HOMEWORK #4...

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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 -C-OpAmp 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 RC-OpAmp 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 Solid-State 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 continuous-time filter design - an overview," IEEE Journal of Solid-State Circuits , vol. 29, no. 3, pp.166-176, March 1994. Note: You can establish off-campus access to databases such as IEEEXplore using Stanford's

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## This note was uploaded on 08/23/2009 for the course EE 315A taught by Professor Borismurmann during the Spring '09 term at Stanford.

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hw4 - EE315A Spring 2009 B. Murmann Page 1 of 4 HOMEWORK #4...

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