Question

4. (40 pts total, 10 pts per part) Bode Plots! Consider the transfer function, H(ja) Vout(ja) Vinjo), plotted in the figure below. This is the transfer function of some linear circuit and tells us how the input and output are related, depending on the frequency. The time-domain input to the circuit is vin(t) = 10 mV cos (at). a. What is Vin(jo)? Express in polar notation (as a phasor) b. If o 10 rad/s, what are H(ja), Vout(ja), and Vout(t)? If o 5 rad/s, what are Hja), Vout(ja), and Vout(t)? C. d. What frequencies are amplified by this circuit? What frequencies are attenuated?
Show clear work, please and thank you! Will upvote.

Answer 1

Answer:

given the

The time domain input the circuit is V in (t) = 10 m v cos(wt)

Transfer function H (jw) - Vorut (sw) / von (jw) a) . Find vin (jw) we know that volt) = 10 my cos(wt) Vin isla -los - mv 0.01 S stwor Vin (w). - vin lju) = joolo 0.016 i 90% اما اونها w=102 vadls we know that : H (jw) = 1/2 =26= 4101901 ..H(jw) = 2 L 90 Vout (jw) - Hlow).uih (jw) en 1909. o. o. 1950 0.02 = wo²w2

- 0.02 stwo is vout (uw) = 0.02. Wenn Wo . Stwo we know that Sinewol. =- Stuor Vout (t) = 0.02 sin wat sino.cz i Vout (1) = 95.60026 wa sradls Now -H600) - test 1+10.12 (it jo 7 = i Hlw= 1 tulos www H(S)- 00 (Stor 0.5 HC) = b S+0,5 S(S+0.1) S Poul (3) 1(3)Vis (5) - 0-0) S+0. 8 1 SiS+0:1) 5725

Now applying Partial Practed Sto,S 05+0 t- S +0.1) ($25) . S+0.1 (8 +0.1) $725 NOW Stos. A (S+01) ($+28) +B(5+25) + (CSD) (Sto) By Separating the lemy 53 - Atc=0 0.19 +1-+0.26 +D=0 S-> 5- 25A +23-+0.01 +20=1 constants - RSA +25B 40.0ID=o.s - 3+0 =0.1A - 25A 1210.1A) - 0.01A = 1 25.19 A 0.04 Aco D Now Atc=0 : = A=-c now a = -004 3+0=0.004 → 25(0.04)+95(0-04-) +001005 0.4+01-350 +0.010-05 --03 25 > D -0.012

we know that BTD - 0.004 -0.004-(-0.012) 0.004 +0.012 0.016 B : Vout(8) = 0.04 Stool 0.016 : 40.045 (Stol) / 5725 0.012 $425 i Vout (1.) = a.oyee OLC +0.016 le 0.04 Cossl - 0.0024 Sin st bit. Hoe 16te -o.lt It locoss! - 24 sinst cenu) circuit amplifies ferih (sw) sode Diteanalers I u cjus codes folosite stad to.014--0-02=0 W=0.259 vad/sec Frequency > 0.259 Frequency 2.0.259 - - Amplified Allemaled