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hw13sol

# hw13sol - Rsfinal = Km*Rs = 708.5(ohm Cfinal = 0.5 uF...

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Unformatted text preview: Rsfinal = Km*Rs = 708.5 (ohm) Cfinal = 0.5 uF Lfinal = Km*L/Kf = 0.1255H %%ECE homework Problem 50 % Part a Amax = 0.8; wp = 2*pi*600; ws = 2*pi*2200; Amin1 = 20; Amin2 = 25; while (Amin2-Amin1>0.001) n1 = buttord(wp, ws, Amax, Amin1, 's'); n2 = buttord(wp, ws, Amax, Amin2, 's'); if (n1==3) && (n2==3) Amin3 = Amin2 + 0.5*(Amin2 - Amin1); n3 = buttord(wp, ws, Amax, Amin3, 's'); end if (n3 == 3) Amin1 = Amin2; Amin2 = Amin3; elseif (n3 > 3) Amin4 = 0.5 * (Amin3 + Amin2); n4 = buttord(wp, ws, Amax, Amin4, 's'); Amin3 = Amin4; while (n4 ~= 3) Amin4 = 0.5 * (Amin3 + Amin2); Amin3 = Amin4; n4 = buttord(wp, ws, Amax, Amin4, 's'); end if (n4 == 3) Amin1 = Amin2; Amin2 = Amin4; end end end %% Result Amin1 = Amin2 = 26.92; %% So the largest integer value of Amin is 26, so that the filter order is 3. % Part b Amin = 26 wcmin = wp/(10^(0.1*Amax)-1)^(1/6); wcmax = ws/(10^(0.1*Amin)-1)^(1/6); fcmin = wcmin/2/pi; fcmax = wcmax/2/pi; %% Result: Allowable Wc is from 4920.5 to 5098.6 rad/s; %% Result: Allowable fc is from 783.1254 to 811.4680 Hz; % Part c syms s; H(s) = 1/(s^3+2*s^2+2*s+1); n = 3; [z,p,k]=buttap(n); %% Result %%! p = %%! ! %%! ! %%! %% Result Ploes: -0.5000 + 0.8660i -0.5000 - 0.8660i -1.0000 No zeros; % To check all the poles are on the unit circle abs(p) %% Results: %%! ! ans = %%! ! 1.0000 %%! ! 1.0000 %%! ! 1.0000 %%So all the three results above is 1, which means all the poles %%are on the unit circle w = 0:0.01:7; num = [1]; den = [1 2 2 1]; h = freqs(num, den, w); plot(w,abs(h)); grid on; % Part d H(s) = 1/((s+1)*(s^2+s+1)) % Part e Alpha = [wp/wcmin, 1, ws/wcmin]; h1 = 1/((i*Alpha(1)+1)*((i*Alpha(1))^2+i*Alpha(1)+1)); h2 = 1/((i*Alpha(2)+1)*((i*Alpha(2))^2+i*Alpha(2)+1)); h3 = 1/((i*Alpha(3)+1)*((i*Alpha(3))^2+i*Alpha(3)+1)); A1 = -20*log10(abs(h1)); A2 = -20*log10(abs(h2)); A3 = -20*log10(abs(h3)); %% Result: A1=0.8; A2=3; A3=26.92; %% so the filter response meet the given brickwall specs at fp and fs. % Part f fcmin = wcmin/2/pi; f = 0:4400; num = [1]; den = [1 2 2 1]; hf = freqs(num, den, f/fcmin); Aw = -20*log10(abs(hf)); plot(f, Aw); grid on; % Part g; f = 0:4400; num = [1]; den = [1 2 2 1]; hf = freqs(num, den, f/fcmin); plot(f, abs(hf)); grid on; H1(s) = 1/(s+1) H2(s) = 1/(s^2 + s +1) R1final = R2final = 10,000 (ohm) C1final = C1/(Km*Kf) = 20 nF RLfinal = 200 (ohm) C2final = C2/(Km*Kf) = 100 nF Lfinal = Km*L/Kf = 0.04H We could use separate magnitude scaling, because the op amp circuit is decoupled from the passive part which does not load down the output. Rfinal = 1355 ohm C1final = C2final = 150 nF Lfinal = Km*L/Kf = 0.55 H ** Profile: "SCHEMATIC1-ece202" Date/Time run: 03/26/10 14:29:19 500mV [ N:\Desktop\ffff-PSpiceFiles\SCHEMATIC1\ece202.sim ] Temperature: 27.0 (A) ece202 (active) 400mV (783.333,354.229m) 300mV 200mV 100mV 0V 0Hz V(R2:2) 0.5KHz 1.0KHz 1.5KHz 2.0KHz Frequency Page 1 2.5KHz 3.0KHz 3.5KHz 4.0KHz Date: March 26, 2010 Time: 14:33:00 ...
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