Question

VouT IN Resistor Value Reactives Value 50 mH 1.6 nF 0.75 k12 R Use polelzero approximations to find the following: (fı is the lower cut-off frequency, f2 is the upper cut-off frequency)

Answer 1

Z_1 = sl times 1/sc/sl + 1/sc = l/c times sc/s^2 l c + 1 = sl/s^2 l c + 1 z_2 = r where sl and 1/s c are impedance in s - domain for induction and capacitor. The transfer function of circuit is v_0 (s)/v_in (s) = z_2/z_1 + z_2 = r/r + s l/(s^2 l c + 1) = s^2 l c + 1/s^2 r l c + s l + r = 1/r (s^2 + 1/l c)/(s^2 = 1/r c s + 1/l c) substituting r = 0.75 k, l = 50 m h and c = 1.6 nf we get v_0 (s)/v_in (s) = s^2 = 1.25 times 10^10/s^2 = 8.33 times 10^5 = 1.25 times 10^10 v-0 (s)/v_in (s) = s62 + w_0^2/s^2 + w_c s + w_0^2 w_0^2 = 1.25 times 10^10 implies w_0 = 2 n f_ = 1.118 times 10^5 f_ 1.7803 times 10^4 hz v_0 (s)