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2 P57-58 clear; clc; format long; Amax = 1.4; Amin = 33; wp = 3400; ws = 16500; % Compute filter order n = ellipord(wp,ws,amax,amin, 's') % Compute the zeros, poles, and gain constant of HNLP(s) [z,p,k] = ellipap(,amax,amin); % Compute the numerator and denominator polynomial coefficients of HNLP(s) coefnum = k*poly(z) coefden = poly(p) syms s HNLP = (polysym(coefnum, s))/(polysym(coefden, s)); fprintf('%s\n','the HNLP(s) is:'); pretty(vpa((hnlp), 6)) OUTPUT: n = coefnum = coefden = The HNLP(s) is: s s s %Part (a) w = 0:0.001:10; HNLP = freqs(coefnum, coefden, w); %(i) subplot(,,1); plot(w,abs(hnlp)); grid on; xlabel('normalized frequency (rad/s)'); ylabel(' HNLP(jw) '); %(ii) subplot(,,); semilogx(w,abs(hnlp)); grid on; xlabel('normalized frequency (rad/s)'); ylabel(' HNLP(jw) '); %(iii)

3 subplot(,,3); plot(w,-0*log10(abs(hnlp))); grid on; xlabel('normalized frequency (rad/s)'); ylabel('loss (db)'); %(iv) subplot(,,4); semilogx(w,-0*log10(abs(hnlp))); grid on; xlabel('normalized frequency (rad/s)'); ylabel('loss (db)'); %(v) dcgain = coefnum(3)/coefden(3); fprintf('the approx dc gain is %f.\n', dcgain); [val idx] = max(abs(hnlp)); fprintf('the max val of abs(hnlp) is %f, which occurs at %f rad/sec\n', val, w(idx)); %(vi) [val idx] = min(abs(hnlp)); fprintf('\nthe abs(hnlp) becomes almost zero at %f rad/sec\n', w(idx));

4 OUTPUT: The approx dc gain is The max val of abs(hnlp) is 1.00, which occurs at 0.71 rad/sec The abs(hnlp) becomes almost zero at 6.06 rad/sec (iv) The loss in db at w = 1 rad/s is 1.4 db which is Amax as per the given specs, and the graph shows NLP characterstics. %Part (b) a = coefden(); b = coefden(3); e = coefnum(1); f = coefnum(3); R = 1 R1 = 1/b R = 1/a R3 = 1/e R4 = 1/(f - e*b) R5 = 1/(e*a) C = 1 OUTPUT: R = 1 R1 = R = R3 = R4 = R5 = C = 1

7 %Part (c) kf = wp; km = round(1/(kf*9.4e-9)); Rn = R*km; R1n = R1*km; Rn = R*km; R3n = R3*km; R4n = R4*km; R5n = R5*km; Cn = C/(kf*km); fprintf('\nkf = %f\n', kf); fprintf('km = %f\n', km); fprintf('\ng = %f changes to Rn = %f\n', 1/R, Rn); fprintf('g1 = %f changes to R1n = %f\n', 1/R1, R1n); fprintf('g = %f changes to Rn = %f\n', 1/R, Rn); fprintf('g3 = %f changes to R3n = %f\n', 1/R3, R3n); fprintf('g4 = %f changes to R4n = %f\n', 1/R4, R4n); fprintf('g5 = %f changes to R5n = %f\n', 1/R5, R5n); fprintf('c = %f changes to Cn = %i\n', C, Cn); figure() semilogx(w*kf/(*pi),abs(hnlp)); grid on; xlabel('frequency (Hz)'); ylabel(' HNLP(jw) '); OUTPUT: kf = km = G = changes to Rn = G1 = changes to R1n = G = changes to Rn = G3 = changes to R3n = G4 = changes to R4n = G5 = changes to R5n = C = changes to Cn = e-08 Freq (Hz) Matlab Spice

9 D C DC = 0 AC = 1 TRAN = Vin V1 0 R8 10k R9 10k R10 11k - + U1 0 -Vout_hat C1 9.4n OPAMP OUT -D(Vout_hat) R5 10k U3 + OUT R7 10k R6 10k - + U 0 C 9.4n OPAMP OUT Vout_hat R 447k R3 476k R4 13k - + U4 0 R1 10k OPAMP OUT Vout V D C OPAMP - 0 B B A A Title <Title> Size Document Number Rev A <Doc> <RevCod Date: Monday, March 6, 018 Sheet 1 of 1 1

10 ** Profile: "SCHEMATIC1-dcAnal" [ \\myhome.itap.purdue.edu\myhome\farooqs\ecn.data\desktop\spice\3\p57_5... Date/Time run: 03/6/18 16:50:40 Temperature: 7.0 (A) dcanal.dat (active) V 0.6V 0.4V 0.V 1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz V(R1:) Frequency Date: March 6, 018 Page 1 Time: 16:51:9

11 P59-60 clear; clc; format long; Amax = 1.45; Amin = 30; fs = 3000; fp = 1000; n = ellipord(1,fp/fs,amax,amin,'s') [z,p,k] = ellipap(,amax,amin); % Compute the numerator and denominator polynomial coefficients of equivalent HNLP(s) % associated with the given HP filter specs. coefnum = k*poly(z) coefden = poly(p) syms s fprintf('%s\n','the HNLP(s) is:'); pretty(vpa((polysym(coefnum,s)/polysym(coefden,s)), 6)) OUTPUT: n = coefnum = coefden = The HNLP(s) is: s s s The HNHP(s) is: s s s %Part (a) HNLP = (polysym(coefnum, s))/(polysym(coefden, s)); HNHP = collect(subs(hnlp, s, 1/s)); [n d] = numden(hnhp); % cleaning HNHP for print. numnhp = sympoly(n); dennhp = sympoly(d); numnhp = numnhp/dennhp(1);

12 dennhp = dennhp/dennhp(1); fprintf('%s\n','the HNHP(s) is:'); pretty(vpa((polysym(numnhp,s)/polysym(dennhp,s)), 6)) OUTPUT: The HNHP(s) is: s s s %Part (b) w = 0:0.005:10; h = freqs(numnhp,dennhp,w); subplot(,,1); plot(w,abs(h)); grid; xlabel('normalized frequency (rad/s)'); ylabel('magnitude NHP'); subplot(,,); semilogx(w,abs(h)); grid; xlabel('normalized frequency (rad/s)'); ylabel('magnitude NHP'); subplot(,,3); plot(w,-0*log10(abs(h))); grid; xlabel('normalized frequency (rad/s)'); ylabel('loss in db'); subplot(,,4); semilogx(w,-0*log10(abs(h))); grid; xlabel('normalized frequency (rad/s)'); ylabel('loss in db');

13 %Part(c) a = numnhp(1); b = numnhp(3); e = dennhp(); f = dennhp(3); G = 1 G1 = f*a - b G = f G3 = e G4 = e*a G5 = a C = 1 OUTPUT: G = 1 G1 = G =

14 G3 = G4 = G5 = C = 1

17 %Part (d) kf = fp/(*pi); km = 1/(11.905e-9*kf); km = round(km); OUTPUT: kf = km = %Part (e) R = km/g; R1 = km/g1; R = km/g; R3 = km/g3; R4 = km/g4; R5 = km/g5; Cn = C/(kf*km); fprintf('kf = %f\n', kf); fprintf('km = %f\n', km); fprintf('\ng = %f changes to Rn = %f\n', G, R); fprintf('g1 = %f changes to R1n = %f\n', G1, R1); fprintf('g = %f changes to Rn = %f\n', G, R); fprintf('g3 = %f changes to R3n = %f\n', G3, R3); fprintf('g4 = %f changes to R4n = %f\n', G4, R4); fprintf('g5 = %f changes to R5n = %f\n', G5, R5); fprintf('c = %f changes to Cn = %i\n', C, Cn); figure() semilogx(w*kf/(*pi),abs(h)); grid on; xlabel('frequency (Hz)'); ylabel(' HNLP(jw) '); OUTPUT: G = changes to Rn = G1 = changes to R1n = G = changes to Rn = G3 = changes to R3n = G4 = changes to R4n = G5 = changes to R5n = C = changes to Cn = e-08

18 Freq (Hz) Matlab Spice 1k k k k k

19 D D x1 R C DC = 0 AC = 1 TRAN = 0 V1 0 Vin x1 R R 1066 C1 R6 C R9 R n Vin n Vin1316 R3 R5 R8 OPAMP OPAMP OPAMP OUT x OUT -x OUT x U1 U U3 U R OPAMP OUT Vout V C B B A A Title <Title> Size Document Number Rev A <Doc> <RevCod Date: Thursday, March 9, 018 Sheet 1 of 1 1

20 ** Profile: "SCHEMATIC1-p59-60" [ \\myhome.itap.purdue.edu\myhome\farooqs\ecn.data\desktop\spice\p Date/Time run: 03/9/18 :6:51 Temperature: 7.0 (A) p59-60.dat (active) 1.V V 0.6V 0.4V 0.V 1.0Hz 10Hz 100Hz 1.0KHz 10KHz 100KHz V(R10:) Frequency Date: March 9, 018 Page 1 Time: :7:18

Lecture 16 FREQUENCY RESPONSE OF SIMPLE CIRCUITS

Lecture 16 FREQUENCY RESPONSE OF SIMPLE CIRCUITS Lecture 6 FREQUENCY RESPONSE OF SIMPLE CIRCUITS Ray DeCarlo School of ECE Purdue University West Lafayette, IN 47907-285 decarlo@ecn.purdue.edu EE-202, Frequency Response p 2 R. A. DeCarlo I. WHAT IS FREQUENCY