Question

please answer thoroughly ahow each step.. please provide detail bode plots.. please answer complelty

Consider the following transfer function: G(8) = Tstl 1. Write the polar form of hand 1+jWT 2. Write the magnitude and phase of G(jw). 3. Write the magnitude in dB of G(jw). 4. What is the approximate magnitude of Gw) in dBs for the low and high frequencies w, respectively? 5. What is the approximate phase of G(w) for the low and high frequencies w, respec- tively? 6. Draw the approximate Bode plot of G(jw). Show clearly the slope of the approximate asymptotes, if different from zero.

Answer 1

D = dat het ons tv 490°. Polar form = MCO M-magnitude 0-phase polar form of the = 490°. (kw] ܗܘܝܢ - ܘܝܙ 2 Lton (WT) > polar form of 1 tot 1+42-т? - (2) Given G(S) = TSH G(jw)= T(jw)+ = 1+jWT Magnitude = M = IGCW)) = 1 itw2t2 phase = $= [orcjw)= tavl(wt) (3) Magnitude in dB = 20 log.ml = 20 logideciw) = 20 log (1 tw272)

W 1GCjw) in dB = 20 le = 20xlog. (1+w?72) = lo logo(1+w272) wno > GCjw) in dB > to log. (1+0°+2) = lo logo = odb w 700 ) Gcwl in dB > lolog,. (1+(59)2 +2) = (5) phase = YGcW) = tant(WT) W90 => Locjw) = tan (ot)=o? W → ZGcjw) = tan(at) = 900 (6) G(jw)= 1+jWT = GCS) = 1+5T = T (1+9) Ek (1+) constant term => 1 GCjw) = 20 log, k = k' (say). → Slope = od Bldec. Zero tem → YG Splitimo Slope = +20dBdec from corner frequency of 'T.

Gw) indB y+20dBldec Tio TO 100 100o kogu