Question

С R w L 0000 + VW) C R Viw) } V.W) V.6) Haw) = jw/wc) 1 + j(w/w) H,(W) = -jQs(w/w) 1+jQs(w/w. - wo/w) (a) (b) с L 0000 R W He o + 10000 w (+) VW) R V.W) Viw) VW) 1 H_(w) = 1+jQf(w/wo – wo/w) Ha(w) = jQs(w/w. - w/w) 1+jQs(w/w. - w/w) (C) (d) Each of the ac circuits shown is a type of a frequency filter with the voltage transfer function defined as V.W) H(W) = Vi(w) The component values are the same in all the circuits: R = 50 N C = 10 nF L = 100 uH. Some of the circuits have the natural resonant frequencies and the quality factors defined as 1 wol wo Qs VLC R Calculate wc, wo and Qs and explain their meaning|

Answer 1

Given fou ас Circuits. Each of the Circupt shown type of a frequency filter with the voltage trausfee function defined as Volw) Hewl VLW) The component Values are the lame all the Ciruits R = 50u c = louf (2=100MH some of the circuits have the natural frequency and the quality factor is defined as WOL resonant Wo al VRC I Qs = R C given that HE + i Lw/wc) til w/wc) Jocuri Halw) = R Vo(w) VW Je The given frequency felter & as high pass filter, Caft off frequency Es given as و فرا 1 RC ( 50x10xio wc - 2010 9X106 M2

b. gquen that son + 1 Volw) - f Qs (wolw) Нь(0) - volw) (tjas (w/wo-wolw) given frequency filter Called Low pass falten. 1 The es Now wo ус 100 x 10 x 1080 1x 106 Hz Wo 6 Quality factor Qs = Woh R - 6 10° x 100 x 10 50 Ces c. ginen that С o HC (w) (tj Qs (w/wo-wo/w) R { The given frequency filter Vica) Vo(W) J + Called Raud Pass follten, Now wo a The

100x10 10x10 2 1x100 HZ Quality facto Qs - WOL 10% 100x10 50 Qs = 2 d. gruen that R qQs (w/wo wolw) voca) 1 Ha(w) - Volw) 14jQs (w/wowo (w) L The pe frequally filter ginen Called Baud elop faller. mane Now wo Quality | 100x10 como wo a 1x 100 M2 factor Qs - R Coocoono WOL 50