0195136047.pdf

162 TIME-DEPENDENT CIRCUIT ANALYSIS

0.707

1.0

−1.5 − 1 −0.5 0 0.5

Y

Y 0

Z

orZ 0 Bandwidth

For

series

()RLC

For

parallel

()GLC

Half-power points

1 1.5 δQ

ω 1 ω 0 ω 2 ω

Figure 3.4.9Universal resonance curve.

EXAMPLE 3.4.2

Consider the circuit shown in Figure E3.4.2 withR<<ωL. Find (a) the resonant angular

frequencyω 0 , (b) the quality factorQ, and (c) the maximum impedanceZm. Comment on the

applicability of the universal resonance curve.

R

L

C

Figure E3.4.2Circuit.

Solution

Z ̄(jω)=^1

jωC+ 1 /(R+jωL)

=

R+jωL

1 +jωRC−ω^2 LC

ForR<<ωL,

Z ̄(jω)= jωL

1 +jωRC−ω^2 LC

=

1

(RC/L)+j(ωC− 1 /ωL)