# hw5 - EE315A Spring 2009 B Murmann Page 1 of 3...

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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 single-stage 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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hw5 - EE315A Spring 2009 B Murmann Page 1 of 3...

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