EECE 290 Homework, Spring 2008

13.39 In the circuit in Fig. P13.39, switch 1 closes at t = 0, p and the make-before-break switch moves instanta- neously from position a to position b. a) Construct the s-domain equivalent circuit fort > 0. b) Find k. c) Use the initial- and final-value theorems to check the initial and final values of i,. d) Find i, fort > 0°. we Te Ly r=0 (O)av 3H P 13.39 [a] s-domain equivalent circuit is ANy owe + an 63) 1209 as 18s 36V § Sei ——, ao ¢ -3sb2 \ 244 S600 A } gsa0¢ aan Oe Ss \ re Tt Ge OV 20 Note: i,(0t) = -— = -2 ote i2(07) 10 [b] — — = (1204 38), + 3slo +6 0=-64 38h, + (3604 15s)In + 36 In standard form, (6 +40), + slo = (8/8) — 2 sl, + (5s + 120)I5 = —10 5 +40 Ss A= = d(s + 20)(s + 60) s 58+ 120 N= (8/s)-2 8 —200(s — 4.8) 1= = —10 5s+120 7 I Ny, —50(s — 4.8) A ~ s(s + 20)(s + 60) —50(s — 4.8 [e) sl, = 50(s — 4.8) (s + 20)(s + 60) Jim sh = i,(07) =0A (—50)(—4.8) limsh =i = ~ =0.2A ing sh = (00) = —T99y@O) fd] hh _ Ky Ko ; K3 8 s+20 s+60 . 240 —50(—2 Qe Ky = 0.2 Ky = O20) +240 as 12000" ° (—20)(40) _ =50(-60) +240 A ep rr l. : 8 = ~(—60)(—40) 3 i(t) = [0.2 — 1.55e77" + 1.356 u(t) A 13.44 Find v,(t) in the circuit shown in Fig. P13.44 if the P ideal op amp operates within its linear range and i Ve = 4.8u(t) V. Figure P1344 080 IP Vv 6 v0) v v QO P 13.44 1.250 V¥, — 4.8/s aM Man Me 08 ‘I/s* I/s | 0-Va O-% _, 1/s 1.25 Y= Vo 1.258 ——‘* "i, + < o —_ —7.5 —6 ° "1.2582 +2641.25 s24+1.6s4+1 _ Ky ; Ay s+0.8—-j0.6 9 s+0.8+ j0.6 ke —6 | 5 90° a OO =, ts +08 + 0.6 |.=-0.8+j0.6 vo(t) = 10e~°*' cos(0.6¢ + 90°)u(t) V = —10e~° sin(0.6¢)u(t) V 13.62 The operational amplifier in the circuit in Fig. P13.52 is ideal. a) Findthe numerical expression for the trans- fer function H(s) = V,/Vg. b) Give the numerical value of each zero and pole of H(s). Figure Pi3.82 1kQ 200 nF e—w—} Dg y y v 6 1000(s +5 P 13.52 [a] Z,= 1000 4 10 _ 1000(s + 5000) Ss Ss 40 x 10° 40 x 10° Z,= 40.000 = 2 1Y f 5 '40,000 s+ 1000 H(s) = _ 2; — —40 x 108/(s + 1000) —40,000s Z; 1000(s + 5000)/s (s + 1000)(s + 5000) [b] Zero at s = 0; Poles at —p; = —1000 rad/s and —p = —5000 rad/s 13.54 In the circuit of Fig. P13.54 v, is the output signal * and vg is the input signal. Find the poles and zeros of the transfer function. Figure P13.54 y e@ SH S 10k -————» ]10H ° + + aL Ug C) 25H Vo =~ 62.5 nF