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934 ⏐⏐⏐ RESONANCE
Z Tp
GLOSSARY
40 k�
R l
FIG. 20.66
Problem 27.
20 �
L 200 �H �
C 2 nF
Band (cutoff, half-power, corner) frequencies Frequencies
that define the points on the resonance curve that are 0.707
of the peak current or voltage value. In addition, they define
the frequencies at which the power transfer to the resonant
circuit will be half the maximum power level.
Bandwidth (BW) The range of frequencies between the
band, cutoff, or half-power frequencies.
Quality factor (Q) A ratio that provides an immediate indication
of the sharpness of the peak of a resonance curve.
The higher the Q, the sharper the peak and the more quickly
it drops off to the right and left of the resonant frequency.
*27. For the parallel resonant circuit of Fig. 20.66:
a. Determine the resonant frequency.
b. Find the total impedance at resonance.
c. Find Q p.
d. Calculate the BW.
e. Repeat parts (a) through (d) for L � 20 mH and C �
20 nF.
f. Repeat parts (a) through (d) for L � 0.4 mH and C �
1 nF.
g. For the network of Fig. 20.66 and the parameters of
parts (e) and (f), determine the ratio L/C.
h. Do your results confirm the conclusions of Fig. 20.28
for changes in the L /C ratio?
SECTION 20.14 Computer Analysis
PSpice or Electronics Workbench
28. Verify the results of Example 20.8. That is, show that the
resonant frequency is in fact 40 kHz, the cutoff frequencies
are as calculated, and the bandwidth is 1.85 kHz.
29. Find fp and fm for the parallel resonant network of Fig.
20.58, and comment on the resulting bandwidth as it
relates to the quality factor of the network.
Programming Language (C��, QBASIC, Pascal, etc.)
30. Write a program to tabulate the impedance and current of
the network of Fig. 20.2 versus frequency for a frequency
range extending from 0.1fs to 2fs in increments of 0.1fs. For the first run, use the parameters defined by Example
20.1.
31. Write a program to provide a general solution for the network
of Fig. 20.36; that is, determine the parameters
requested in parts (a) through (e) of Example 20.9.
Resonance A condition established by the application of a
particular frequency (the resonant frequency) to a series or
parallel R-L-C network. The transfer of power to the system
is a maximum, and, for frequencies above and below, the
power transfer drops off to significantly lower levels.
Selectivity A characteristic of resonant networks directly
related to the bandwidth of the resonant system. High selectivity
is associated with small bandwidth (high Q’s), and
low selectivity with larger bandwidths (low Q’s).
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