Question

Question 1: For the circuit below: R С MH + + Vin L Vout Given that: R= 151, ZŁ= 35 2 and Zc = Answer the following questions: a. Calculate the input Admittance Yin(s) =1/ Zin(s) b. Consider Yin(s) as the system's transfer function, calculate the following: 1. Wp: 2. Bw: 3. W1 and W2: 4. Hm: C. Draw the second order response on the graph below (show W1, W2, HM values): |(200) DRESSE

Answer 1

Given circuit C R WWE + Vin Vout Zin - R+ ²c +ZL 15+ 6 + 35 S 155+ 6 + 3S S Yin(s) = Zin (5) 357155 +6 b) Tomter function is legs s?+ 55+2 Yin (5)= HES) = general second order system characteristic equation is CE s+2&wp 5 + wp? BW= 2£wp W2-W - BW wp =w, wa

comparing we get wp² = 2 is Wp = up 2 1.414 radls. 2 BW = 2 Gwn Bw - 5 raals W₂-W, = 5 W, W2 = wp²=2 (Wi+w2)-(W-Cy)2 = 4w, wz (Wg+wy)2 = 4(2) + 5)2 8+25 - 33 (W2 +W) - a) B + => 9W, = 5+133 W = 5+133 2 W2=5.3723 rads. Wi- W2-5 5. 3723-5 WI = 0.3723 rad's

4) Hm is the maximum admittance this occurs at Xc = XL (w=up) Hm = R 부 Hm o.O6645 H Cjw) S. Hm Hm V2 BW 3 W w=WP