CHAPTER 6. OPERATIONAL AMPLIFIERS1296.4Problems1. Consider the circuit below. (You may assume that the op-amps are ideal.)VoutVinR2R1C2C1(a) Write an expression for the transfer function G(ω). Express your result in termsof the amplitude of the output and the phase relative to the input. Let R1 =1 kΩ,R2 = 100 Ω, C1 = 100 µF and C2 =1 µF. Do not simplify the algebra.(b) What are the (real) zeroes in the transfer function, if any?(c) What are the (real) poles in the transfer function if any?(d) Sketch the transfer function as a function of ω on a log-log plot. Your sketch shouldshow the slope of|G(ω)| in the large and small ω limits, the corner frequencies,and the value of|G(ω)| at the corner frequencies.(e) Describe the dependence of the output on frequency at small and large frequenciesin dB/octave.2.(a) Write the two rules for the analysis of circuits which utilize “ideal” op-amps.(b) Write an expression for the potential Vout for the following circuit.Z1Z2VinVoutZ2Z1(c) Let Z1 = 1 kΩ and Z2 = 10 kΩ. Sketch a log-log plot showing the function G(ω)for the above circuit assuming that a general purpose op-amp such as the 741 isused.(d) The 741 op-amp has a corner frequencies of 4 Hz, DC open-loop gain of 2× 105and a fall oﬀ at high frequency of 6 dB/octave. What is the frequency domainover which the ampliﬁer deﬁned in part (c) will have constant gain? What is thegain of the ampliﬁer in this frequency domain?