Question

1. The circuit below, which uses one inductor and two identical resistors, (30 pts] can be described as a filter. Using this circuit: a. Determine the transfer function, H(@) = Vout/Vin. b. Determine the magnitude and phase (in terms of R, L, and o) of the transfer function from part a. Now, assume R = 5022 and L = 2mH c. What is the value of the magnitude as 0 0 d. The value of the magnitude as → e. Is this circuit a high-pass, low-pass, band-pass, or band-reject filter? f. What is the cutoff frequency in Hertz)? g. Make a sketch of the magnitude versus frequency, labeling important values on both the vertical (M (dB)) and horizontal (o (rad/s)) axes. You must EXPLAIN how you arrived at your answer to receive credit - Show your work Vout

Answer 1

redrawn in s-domain. The cir a) The circuit can be R IS) Vin(s) ☺ R$ 32 SL Yout (5) I (s) = Minis) R & RIISL Vinls) R+ RsL - R+ SL Vines) (R 482) Vout(s) = - R² + 2R.SL RSL 43 RYS? = Vinis). SE R+25L را را نرم ا So, HL)= vout to be Nupo sto Tincs) R+ 2SL ? L1 SWLCL = selberoest A(W) = o pen yrit aj 2wL 1#(w)) = = 16) magnitude R² + 4W2L2 I Dehu - 2017 IRWL tar 13.do 18.0 - phas CR L=2mH = 2x1G 3 H 1 c) now. R=50 www 2x10-3 wo sos- So, I HIM))=- (50) ² + 16 x 10b w2 so, as ws 0, THW I = 0

d) Now, I How is recita 2 wite As wed, IH(w) - Žiež As wyd 1H(W) 2L e) The gain is zero for w eo and have a finite - value when wes sauti So, high pass forgreavey filter . +) L*(W)/ a JWT. s (4x10-5) jw J25177 - jw tle 12500 1251 (2) nov (ON (od 2 Centre frequency= 12500 rad) sec. = 1990 H2 g) So, the asymptotic plot for magnitude is frequency choll follow this, 4x05 - 2010g (ux 16+9).d6-87.95 dB () ja) – 20dB) decade (23. 2500 to WL 12500 -200B/ decade ,w12500 (3) Scanned with CamScanner

20 dB/decade H(jw)] (dB) -20 dB/decade -87.95 dB 10 10000 100 1000 100000 w (rad/sec) The asymptotic bode plot will be summation of these 3 plots.
Now, the actual plot will be at 3 dB lower at breakaway point/ center frequency.

Asymtotic plot Actual plot TUT TIL TIN III 10 100 1000 1000 10000 100000 Wc=12500