Question

Please solve all these questions and give a detailed explanation for your answer. When drawing the bode plots, please make sure that they are hand drawn. Please show in detail how you got them and hopefully all your answers are correct. When drawing the bode plots for the magnitude, the y-axis should be 20log(abs(H(jw))). When drawing the bode plots for the phase, the y-axis should be in degrees. The x-axis for both plots should be "w". Thank you very much for all your help in advanced.

2. Draw (by hand) the Bode plots (magnitude and phase) for each of the following transfer functions. s+10 (a) H(s) = 554192 10082 (s+10) (s+100) (s+1002 (s+1)(s+104) 0.1(82 +58+100) (d) H(s) = *-* *52(8+1)

Answer 1

H(SI = S410 101 to sto) S(SH 5 (5412 Mljw) - j wtlo jw (j wt THLUNDI w2110 w (w²11) <H (JW) = tant" (W/10) -9° -grant (w) plot deldec) corner frequency slope effective slepe (dBle) -20 Bldec) - 20 Bode term - 60 stuja -40 : 10 20 -40 (6 +10) starting frequency w=0:1 at w-ol, golog | Hewll - 2010g 10 - 40 (AB) 0.1 to I one dec, so HIJ who I - 40- 20 (1) - 20 dB)

Hy wil do 40 7 -20 drlded! 109 -40d 1 -4old & dec) to to tradisec) - no ot deseades = 109 10 1091 How I w-10 = 20- 60L) - 40(do) 10 to 100 fadisec) non ut decades = log10² 10g10 1H (jw) | w-100 = - 40 - (11 (646) 280(de)

<H(SW)= tant (600) aortan (~) w < HIGW) - 100.80 -174.29° 10 - 2/3.580 100 - 184.6° <Hljw) -aot -1204 -158 -1807 2100 - igu 240 HLS) = TOUS 2 (Y60) (0) (foot!) (8+10) (54100) - w/10 HLGW) = (deldee) slope term Corner teruency (radwee) effective slope deldec) 40 40 ale -20 20 tule 100

starting toeruency wool M(WW) I w=01 - 2010go 2010g10 - --- 60dB) 1 Hjul de yo 20 de deo) s logo 100 103 40 (ABldec) Onl to 10 Crad (see) , slope = 40 (deldee) TH(jw) I w=10 = -60 + 40x no of decades no. of decades log 10 - logist = 1152 THC Gol = = – 60+4082 20 (dB) 108100 Crad (see) , slopez 20 (dB / dec) no.of decades. 10groo- 10g 10 TH(ja) | w-100 = 20+2011) = 40(dB)

ZH LJU) = 1800 tant/w/10) - tam (w/100) <Hlja) 179 170 129° 100 103 <Hlju), 180+ 13507 90+ ugot --- "T so we H(S)= 1988 (1 oo + 132 (6+1) (2 164 +1) X109 ( + 1)2 (W+r) (suo ant) H(jw) = pecjuslinisco H (ju)luso term corner (oad sec) corner Grad fresmene slope (d& effect effective clope Blder) -20 – 20 40 Go to 100 20 100 - 20 ( + )

Starting Starting w=0.1 rad(ec) Hl5W) I w=0.1 = sologell) - old B) Hull do oldigt 20 (1B (dec) 40 (013) logio 1 10 102 ios 1 4 1 to 102 (rad bee), slope=– 20 A Blde() no.ot decades= 10g 10²-1091 = 2 H(ju) Iw=10² = o-20x2=-40 102 to 104 Cradlee), slope 22 20 (ABlace) no.ut decacles = log10h-log? MIGN) | w=104 = – 40+2x20 = 0 (dB) Phase vs to LH (SW) = gtant (o) - tan (w) - tan (20/10) <Hliw) 0.) - u 3.86 10 - 730 103 104 43.90 5.60 101

KHLGW) 0 30 +++htts E Oo 30° + -60+ -98 1 10 102 103 104 105 Hera al (2 + 56+1) X 100 x² (5+1) He Lu) a 10 (220 + 5+1) s2 (5+1) Hlows a 10 1-0 5W+1) - w² (; with) THL "w) vs w term corner (oad Lee) trequeny slope dsdec) etective clope (dB (ded) -40 Leon - - 40 140 -40 2 - 20 -60 St 40 -20 t 100 starting frequency w=o. I 1 H (gu) (w = 0.1 = 20 109 10.12 - Gode

preciul do 60 * culdaldee) logio - 10 -60 AB dee) 407 - 60 (dol -old Bf dee) ool to loadsec), slope = -40 dB (dee & no ot decades. loge-loglot TH(SW) I wil = 60-40 41) = 20 dB) I to 10 fad kec), clope = -60 dB/dee) no-ot. decades = log 1_1091 Ir Law) (w= 10 = 20-60(1) =-40 (dB) 10 to 102 Cradlsee) , slope z - 20 dB(dec) no ot- decades a Log 102-cogl Hlju), w = 182. – 40-2011) =- 60dB)

5 w (100-w? tem 1 <H184) = tant Low ) - 1800 _ tans (w), wat <H (SW) 2 460- tan w o) 180 - tan (60) = - tant (su oro ) - tan (w) wsco 311 <Hliw) -1850 - 222° - 10 -1940 102 - 92,0 A x H Ciw) -2400 / - 2100 180° 7 -1500- 1200 90 / logo 2