Question

Given the circuit below: R3 C1 Vout C2 R1 R3 Vin R2 ts 1 a) derive the transfer function between the input and the output in terms of R1,C1,R2,C2 b) For this and all other parts below, assume Izl<Ipl, i..e that D(s) is a lead-type compensator. The transfer function is written in the following format ts 1 Express quantities K, z, p using R1,C1,R2,C2 Also, express Κα, α, τ using K,z, p c) Observe the values of s-jw on the imaginary axis, and derive the expressions for magnitude and phase of D(jco), i.e. find expressions for ID(jco) and 4D(ja) using the parameters Κα, α, τ d) Show that the frequency w for which the phase 4D (jw) is maximum is given by: e) Derive the expression for MAx in terms of z and p tS+1 CTs+1 MAX f) Show that the maximum phase that corresponds to MAx is such that sin(pMAX)-(1-a)/(1 + α)

Answer 1

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