Question

Question 3 (2+2+2+2) For both CT and DT systems, give one differential/difference equation and the frequency response plot for a. Band stop filter b. Band pass filter

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Answer 1

Band pars felter m! SL ! SC R V. & I (S): Vi (s) Reslet sc and Vo - R. I (3) R Vili) se ŠLC + gReal SRC V. Vi rict g RCA we Vo(s) 3²LC + SV. (S) RC Vols) s Vels) RC Now taking inverse haplace Transform, get d²vo sto vo at² at Rc dvi at LC RC do + = kadlo Vo (n) - Von-1) Now for discrete tome, alv. olt and a²V. delete at د ہل (voim) - vo (n-1) - (vo (n-1) - 611-21) V. (n) - 2 V. (n-1) + V (1-2) to the CiT diffrential equation becomes. LC (voln) -2 V, (n-1) + V. in -2)) + RC (vo. (M)- v. n-1) V. - RC (V; (ni-V, 11-11) (LC + RC+1) Voln) - QLC + Rc) Voln-1) + LCV (0-2) & RC Vilnl - RC Vi(n-1)


Band stop filter SL Vi V. I(s). V: 1s) SLARI Sc and Vols). Ilsl. (sli ) Vils) so (SLIT) s²LC + SRCA Vils) lit s'LC) s²LCAIRCHI we Vo(s) s LC + 3 VoIR CANO(S) = Vi (S) + s² Vies) LC Taking inverse Laplace Tranform, eget Le d'vo + Rc do - Vo V. + dt? dt V. (n) - Voln-1) at again for discrete teme and d'vo dt² Von)-3 Voin-1) + Vo (n=2) LC (vo(m)- 2o In 1) + Voľn-2) + RC ( vorm) - Voln-1) + V, V;+ LC ( VP (n) - JV; (n-1)+ vi(n-21) (LC +RC+l)vo (n) = vo In-1) ( 24C +RC) + LC V, (n-2) Vi (HLC) - 2 viin-1 LC LCV; (n-3)