Page 279 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

For o s 10,

On a log frequency scale, 2010glo(w/10) is a straight line with a slope of 20 dB/decade
(a decade is a 10-to-1 change in frequency). This straight line intersects the 0-dB axis at
o = 10 [Fig. 5-28(a)]. (This value of o is called the comer frequency.) At the corner
frequency w = 10
~(10)1,, = 2010glo11 + jll = 2010glofi -- 3 dB

The plot of (H(w)ldB is sketched in Fig. 5-28(a). Next,

Then
W
0
O,(o) = tan-' - --, aso-0
10

At w = 10, OH(lO) = tan-' 1 = ~/4 radian (rad). The plot of BH(o) is sketched in
Fig. 5-28(b). Note that the dotted lines represent the straight-line approximation of the
Bode plots.

For o 100,

For w >> 100,

On a log frequency scale -2010glo(w/100) is a straight line with a slope of
-20 dB/decade. This straight line intersects the 0-dB axis at the corner frequency
o = 100 [Fig. 5-29(a)]. At the corner frequency o = 100
H(100)1,, = -2010glofi = -3 dB

The plot of IH(w)ldB is sketched in Fig. 5-29(a). Next

Then

At o = 100, 8,(100) = -tanp' 1 = -~/4 rad. The plot of OH(w) is sketched in
Fig. 6).