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ee541F10HWSolutions06

# ee541F10HWSolutions06 - U niversity of S outhern C...

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U U U niversity of S S S outhern C C C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Solutions, Homework #06 Fall, 2010 Due: 11/02/2010 Choma Solutions Problem #26: Five operational transconductors (OTAs) and several capacitors are interconnected as shown in the schematic diagram of Figure (P26). The filter realizes a voltage transfer func- tion, H(s) = V o /V i , that assumes the biquadratic form, ( ) 2 o o 2 i n n H 1 as bs V H(s) . V s s 1 Q ω ω + + = = + + + + G 1 G 4 + G 2 2C x 2C x + G 3 2C y 2C y + V o + G 5 V c1 V c4 V C2 V c3 V c5 2C z 2C z V i + Figure (P26) (a). Using the modeling guidelines documented on Page #134 of Lecture Aid #3 , derive the ex- pression for the network transfer function. Specifically, derive relationships, in terms of network parameters, for the zero frequency gain, H o , quality factor Q , self-resonant fre- quency ω n , and parameters a and b . Figure (26.1) displays a roadmap of node voltages and branch currents that are used to compile the relevant KVL and KCL equations of equilibrium for the subject biquadratic filter. For the current, I y , conducted by the capacitances, (2C y ) , in the filter diagram,

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