Question

Learning Goal: To analyze and design a passive, first-order low- pass filter using a series RL circuit. The analysis and design will be repeated for a series RC circuit. An electrocardiogram needs to detect periodic signals of approximately 1 Hz (since the resting heart rate of a healthy adult is between 55 and 70 beats per minute). The instrument operates in an electrical environment that is very noisy with a frequency of 60 Hz. It is desirable to have a low- pass filter that will block any noise above 18 Hz. A low-pass RL filter can be built using available 130 Hinductors; a low-pass RC filter can be built using available 3.2 uF capacitors, resistors of any necessary value are also available

Answer 1

All the pats has been solved and solution has been attached.

pars filter L momont / Ti R こ SLIR STRIL - MIS Qi PART (B) soni series R-2 Low ekt-diagram Given L=1304 vi vo Cross -frequeney (in-s-domain) Vors) RIL fe = 18 hz KCS) = vics (Transfer-function) general form of LPf. sth me t = 4 fc = (e=time constant) शा८ Cutoff-frequency (rad/sec) = We = € and, we=aufe fez I fe 2T ( 4 > R=(25L) fc. z 2x3.14 x 1304 x 18 R=14695.22=19.695 kr Resistance, fence, - R 2 = 17 so, The cutols frequency ane R 25L PART ② Som as The Tater Function . Hes) = Vols) (R122 Vico (ste SLAR R Z H18 = 10 (1) vics Vorsz vico. R (SLR) in w-donan, s=gw, vo(jw)= vicow). R. Forte R Hence, magnitude of ole= (vo (JW)/= Given, Nopol (=lv for f= 11h2, xpo W (WL)R? W z 2 of zat rad (see

Hence, rocool (= 14.695x103 x 1 2 "24TX 130)2+ $4, 695*103)2 | Vo (142) 14.6958103 6166x105+ 2,155*108 14.6958103 46.53x10x102 - 0.998 v Any at f=18 hz, w = auf = 367 radisec . Mence, No (18 Hz)/= こ 14.645X103 x1 - 14.6958103 JC 3677X120)2 + (14.645x103)2 [2.159x10+2.1598100 Ans No (1842) = 7.347010 0.784 W at f= 60 Hz, W= auf? 201 14.6958103 14.6958103 (121X130)2+ (09.695 x103) 52.394 xwe. Ivo (Gonz}} = 0,287 v Any rad/sec x! Hense, No (60112) (= . +2.159608 لیان2 pass - filterin PART @ Soini series RC Transfer Function + vics) с Vout (S) H(5)= Voco) 1 (८ vils) HSLR R&te L fe cutoff-frequency=18 he, (= 3:2.5 = 3:24156 F The General LPF tafts. Transfer-Function = hes) z (1+50) De=8R (time const) wc (argules cutoff-frequency we=2afo » fez I بے لب = ㅗ २८ 25 2 TT CR > R= 1 aterte 2x3114 x 3.2x156x18 R = 2.764kn Any

The rifer nest ㅗ Itser wie - 1 port ( swini -V015) Function vies) » Vo(s)= vics) . (A+SCRI henre, imagnitude. (Vols) 1= vies) STT w2rer? or, in w-dornant, No (w) I=/ricost / It w²c²R2 view) = 1v at f 1 Hz w=25 rad(see. txt Nora hz) 1 = = 0.996 VAS Tit(0.055)2 WcR = 21 x 3. 2x156 x 2.7 64 X103 = 0.055 at f = 18 Hz, w= 36T rad/sec. Ixl No (18hula J1+(368* 3.2 X156x 21764x103)2 No (18 hz) 1 = 01 707 v f= Gotz, Isot rad/sec story علي at wera Golx 3.2x10t x2.7648103=1.666 hence, No/60 Hz) 1 = Ixl 0,514 v - Ang I+(1.66622