Question

Find the transfer function H ) that corresponds to the following asymptotic Bode plots. The gains are in dB while the frequencies are in rad/s. Write the transfer functions in the form shown in Problem 1(a)-(h) 2GB +200B/dec/ -2021B/dec 201B/dec IB -201B/dec +10dB/dec/ -OIB/dee 10 104 104 104 10 104 104 104 +204B/dec A +20<B/dec -102B/dec -20B/dec - B OB 2013/dee 10 102 104 10 10 10 10 10 10

Answer 1

A rain H -20dBldecade 14dB -- ! -20dB/decode 102 lo 103 بیا 10 Note: presence of pole gives -zodo/decade Tlope, presence of zero gives to dis/decade slope. TEHS) EKS (sto) -> ks (1+0) Cute ) (1+x)(+600) 20 log (kw) = 14dB wroo 20 Log Ck 200)) = 14 log look = 0.7 look. 5.011 K-0.05]

1.F2 HG1= 0.05s (it (1+ ) (+) )(1+2.00) (6) Gain +20dB/ decade 2603 220dB) decade L 2-400310 -40d13 decade cade +40013) 10 100 1000 104 T: E = HOS). ) (*) (*150 () : H(S) - pole (-20dB/decude) KS2 (+ ) (IXCXOTIN 200g (Kw²) = 26 do| wloo Lo log (K 10%) = 2601 Tog (K104)- 13 k10l = 19.95 = K = 0.0019

:. HS: 0.0019 s (176)(1+ 2) ("* .*)(1+ L) (c) - - 20dB de aude - +2dBaccade LOL 10 102 104 T-F = 167= ks. (1+6). .(+ ) E ks (1+ o) (not in the w=104 20 Log(kw)=-40d31 20 Log (104 ) = -40 Log (104 k) = -2 109K = 0.01 [k = 100 -FH(S7= 16'S (1+2)(* )

Grain +200g/derade (a) Ls yodg|decude todo a trods/decade Odo 103 104 los 100 w TF=H(s)= (* ) => 16)= ks + x 1 Cor Citations) (1+2)(1+600) (14 km) 2010g (kw) = o waloy 20 lg (10 k) = 0 Log (lo4K) = 0 10 k=1 [K= 10 T.F-HG) = 10^s(1+x)(1+y)(1+5) Tlt City Count)

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