Question

Reference: Posted Notes and textbook Chap1 For all circuits assume ideal opamp. Problem 1: Filter order a. Explain the effect of order on the filter characteristics (Draw transfer characteristics for two orders). b. How can you tell a filter order from T(s) function and from filter circuit? c. Explain how third and fourth order circuit can be implemented (show circuits)

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Answer 1

Effected order on filter characteristics (ex: - low pass filter (LPF)) gain vs frequency for cutoff frequency = 300 Hz As order increases the scope of cutoff decreases & becomes 0 for large order implies Brick wall kind of response. Let us first derive transfer functions of 1^st order LPF Using on op-amp. Here R_F & R_1 decide gain of filter in pass band Impedance of Capacitor x_C = 1/2 pi f_c By voltage dividing rule, v_A = -J_x_c/R - J_x_c v_in v_A = -J(1/ 2pi f_c)/R - j(1 /2 pi f_c) v_in = -j/2 pi f_c R - j v_in = v_in/1 - 2 pi f_rc/lJ - Jn = 1/J & - 1/ J = J Therefore V_A = v_in/1 + j 2 pi F R C As op Amp in non inverting configuration, v_D = (1 + R_F/ R_1)V_A = (1 + R_F/ R_1) v_in/1 + J 2 pi F RC v_o /v_in = A_F/1 + J(F/F_n) where A_f = 1 + R_F/F_1 implies gain of filter in pass band f_r = 1