HW3_sol

# Collects all the ss vin laplace10exp t zin collectr

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Unformatted text preview: cl)/Zin)*Vin); pretty(Vc) vc = ilaplace(Vc); pretty(vc) s2 + s + 2 Zin = ---------- Ω s2 + 2 10 s Vc = ------------------ V s3 + 2 s2 + 3 s + 2 Vc = / / 71/2 t \ 1/2 | 3 (7 ) sin| ----- | | / 71/2 t \ \ 2 / 5 |cos| ----- | + ------------------\ \ 2 / 7 () ( ( √ ) √ ( √ )) %Problem 11c syms Yin Zin Vin Iin Iin = s*Vin + 2*Vin + (Vin - (-0.5*Vin))/s; Yin = Iin/Vin; Yin = collect(Yin); pretty(Yin) Zin = 1/Yin; pretty(Zin) 2 s2 + 4 s + 3 Yin = -------------- mhos 2s 2s Zin = -------------- Ω 2 s2 + 4 s + 3 \ | | | e(-0.5 / () t) u(t) - 5 e(-t) u(t) V () ECE 202, Spring 2013, HW#3 (Problems 9-12) %Problem 12a syms Vout vout Iin s t Y1 Y2 Z2 Z1 Zin Yin R1 = 15; R2 = 15; L = 2; C = 0.01; Z1 = R1+L*s; Z2 = collect(R2 + 1/(C*s); Y1 = 1/Z1; Y2 = 1/Z2; Yin = collect(Y1 + Y2); pretty(Yin) Zin = 1/Yin; pretty(Zin) 2 s2 + 30 s + 100 Yin = -------------------- mhos 30 s2 + 425 s + 1500 30 s2 + 425 s + 1500 Zin = -------------------- Ω 2 s2 + 30 s + 100 N = roots([30 425 1500]) D = roots([2 30 100]) N= -7.5 -6.6667 D= -10 -5 Therefore Zin (s ) = 15 s 2 + 14.1667 s + 50 s + 15 s + 10 2 = 15 (s + 7.5 )(s + 6.6667 ) Ω (s + 10 )(s + 5) %Problem 12b and c (code), continues from 12a and 12b Iin = 10*(s+10)/((s+5)*(s+7.5)); Vout = collect(Zin*Iin); pretty(Vout) % Vout(s) = Zin(s)*Iin(s) is solution to 12b vout = ilaplace(Vout); pretty(vout) 150 s + 1000 Vout = -------------- V s2 + 10 s + 25 Hence Vout (s ) = 15 (s + 7.5 )( s + 6.6667 ) s + 10 s + 6.6667 V ´ 10 = 150 ( s + 10 )(s + 5) (s + 5)(s + 7.5 ) (s + 5)2 vout = (150 + 250 t) e(-5t) u(t) V ECE 202, Spring 2013, HW#3 (Problems 9-12) %Problem 12d, continues from 12c Iout = collect(Iin*Y1/Yin); pretty(Iout) iout = ilaplace(Iout); pretty(iout) 150 s + 1000 Iout = ------------------------- A 2 s3 + 35 s2 + 200 s + 375 iout = (10 + 50 t) e(-5t) u(t) - 10 e(-7.5t) u(t) A ) () 4Ω 0.25F ) 0.5Ω ECE 202, Spring 2013, HW#3 (Problems 9-12) 0.25H 0.125H 0.25Ω 0.25Ω 1Ω ) () 0.5F 0.5H 0.5F 0.5H ECE 202, Spring 2013, HW#3 (Problems 9-12) ) () 0.0625F 0.5F 4H 2H ECE 202, Spring 2013, HW#3 (Problems 9-12) %Plots for 10c, 10d, and 11a t = 0:0.01:2; subplot(1,2,1); plot(t,(-2/7)*exp(-0.5*t)-(12/7)*exp(-4*t)) title('V_{out}(t) for 10c'); subplot(1,2,2); plot(t,(10/3)*exp(-0.5*t)-(4/3)*exp(-2*t)) title('V_{out}(t) for 10d'); figure; t1 = 0:0.01:2; t2 = 2:0.01:5; plot(t1,8*t1+(16/5)*(exp(-2.5*t1)-1)); hold on %plot 0<t<2 plot(t2,8*t2+(16/5)*(exp(-2.5*t2)-1)-(8*(t2-2)+(16/5)*(exp(-2.5*(t2-2))-1))); %plot 2<t<5 title('V_{out}(t) for 11a'); Vout(t) for 10c Vout(t) for 10d 0 2.2 -0.2 2.1 -0.4 2 -0.6 1.9 -0.8 1.8 -1 1.7 -1.2 1.6 -1.4 1.5 -1.6 1.4 -1.8 1.3 -2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 ECE 202, Spring 2013, HW#3 (Problems 9-12) Vout(t) for 11a 16 14 12 10 8 6 4 2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5...
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