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S tep 2. A dd all t he a symptotes, as depicted in Fig. 7.8a.
S tep 3 . A pply t he following corrections (see Fig. 7.5a):
(i) T he c orrection a t w = 1 because of t he c orner frequency a t w = 2 is  1 dB. T he
c orrection a t w = 1 b ecause of t he c orner frequencies a t w = 10 a nd w = 100 a re quite
small (see Fig. 7 .5a) a nd may b e ignored. Hence, t he n et correction a t w = 1 is  1 dB.
(ii) T he c orrection a t w = 2 because of t he c orner frequency a t w = 2 is  3 dB,
a nd t he c orrection because of t he c orner frequency a t w = 10 is  0.17 dB. T he c orrection
because of t he c orner frequency w = 100 c an be safely ignored. Hence t he n et c orrection
a t w = 2 is  3.17 dB.
(iii) T he c orrection a t w = 10 b ecause of t he c orner frequency a t w = 10 is  3 dB,
a nd t he c orrection because of t he c orner frequency at w = 2 is  0.17 d B. T he c orrection
because of w = 1 00 is 0.04 dB a nd may be ignored. Hence the n et c orrection a t w = 10 is
 3.17 dB.
(iv) T he c orrection a t w = 100 b ecause of t he corner frequency a t w = 100 is 3 d B,
a nd t he c orrections because of t he o ther c orner frequencies may be ignored.
(v) T he c orrections a t w = 4 a nd w = 5 (because of corner frequencies a t w = 2 a nd
10) a re found t o b e a bout  1. 75 dB each.
W ith t hese corrections, t he r esulting amplitude plot is i llustrated in Fig. 7.8a. , ,t (7.25) I II i i\J ')..'+~9'"'tH"'M'1
'~It'i++ Lf,   1 111 \ \
1 ,''\ I l: \ I \ \' I , \~ \ I! " , ' \'1
' \, 90 'f"
"
:! b I) ".".
"
~ 45 ..c
Q" 0 F ig. 7 .8 A mplitude a nd p hase response of t he secondorder system in Exampie 7.3. (i) T he zero a t t he origin causes a 90° p hase shift.
(ii) T he pole a t s =  2 gives rise to a 45° / decade a symptote s tarting a t w = 0.2,
which goes up t o w = 20. For w < 0.2, t he a symptote is 0°, a nd, for w > 20, t he a symptotic
value is  90°.
(iii) T he pole a t s =  10 h as a n a symptote w ith a zero value for  00 < w < 1 a nd a
slope of  45° / decade b eginning a t w = 1 a nd going up to w = 100. T he a symptotic value
for w > 100 is  90°.
(iv) T he zero a t s =  100 gives rise t o a n a symptote w ith a 45° / decade slope,
beginning a t w = 10 a nd going up to w = 1000. For w < 10, t he a symptotic value is 0°,
a nd, for w > 1000, t he a symptotic value is 90°. All t he a symptotes are added, as shown
in Fig. 7.8b. T he a ppropriate corrections are applied from Fig. 7.5b, a nd t he e xact phase
•
plot is d epicted in Fig. 7.8b.  J:::;;:":>~.,, • 7.2 Bode P lots 7 Frequency Response and Analog Filters 488 E xample 7 .4
S ketch t he a mplitude a nd p hase response (Bode plots) for t he t ransfer function H (s) = I~O)
10(s + 100) = 1 0'"=S2 + 2s + 100 1 + to + :;0
( 1+ Here, t he c onstant t erm is 10; t hat is, 20 dB (20 log 10 = 20). T o a dd t his term, we
s imply label t he h orizontal axis (from where t he a symptotes...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.
 Spring '13
 Bayliss
 Signal Processing, The Land

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