1. For the following filters, assume the op-amps are ideal. i. Derive the transfer functions, T(s) ii. If R₁ = 10km2, R₂ = 100k, C₁= 1 μF, C₂ = 0.1 μF, L₁ = 1nH, and L₂= 1µH, plot the magnitude and phase responses of each filter.

3. Active Analog Filter Topologies You already know from our class discussions that Circuit 1 is an active analog Low-Pass Filter For each of the remaining three circuits, state whether the circuit will function as a low-pass or high-pass filter. Each of your answers must be accompanied by a brief explanation and justification incorporating the frequency dependent characteristics of the reactive circuit elements. That is you should look at the asymptotic impedance of the L and C if the input signal the frequency is very low or very high. Sketch the expected Bode plot for 20 log(Vo/Vs) as a function of log (f) labeling the corner frequencies. No equations are required! R2 R2 R2 R2 R1 R1 R1 Vs Vs o W- Vs Vs Vo Vo Vo Vo Circuit 1 Citcuit 2 Circuit 3 Circuit 4

3. In this problem, use the two closed loop systems given in the figure to answer the questions below. 4 R(s) K₁ 0.0099 In thin K₂ Y(s) R(s) K₁ 4 S(s) = 0.09 K₂ 0.09 (a) Show that these two systems have the same transfer function for K₁ = K₂ = 100 (b) Using the definition of sensitivity, S(s), for each system calculate the sensitivity to the parameter K₁ with K₁ and K₂ as variables. Recall: Y(s) OG G OG Gal (c) Substitute K₁ = K₂ = 100 into each S(s) and compare the sensitivities to parameter K₁.

Assume the op-amps are ideal for the filters that follow.Now; Determine the transfer functions, T(s). ii. Plot the magnitude and phase responses of each filter if R1 = 10kΩ, R2 = 100kΩ, C1 = 1μF, C2 = 0.1μF, L1 = 1nH, and L 2 = 1μH.