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ƒ r
Z p
0
L/C fixed
R l3 > R l2 > R l1
R l1
to their effect on the series resonance curve. Whether or not R l is zero,
the parallel resonant circuit will frequently appear in a network
schematic as shown in Fig. 20.28.
At resonance, an increase in R l or a decrease in the ratio L/C will
result in a decrease in the resonant impedance, with a corresponding
increase in the current. The bandwidth of the resonance curves is given
by Eq. (20.38). For increasing R l or decreasing L (or L/C for constant
C), the bandwidth will increase as shown in Fig. 20.28.
At low frequencies, the capacitive reactance is quite high, and the
inductive reactance is low. Since the elements are in parallel, the total
impedance at low frequencies will therefore be inductive. At high frequencies,
the reverse is true, and the network is capacitive. At resonance
( f p), the network appears resistive. These facts lead to the phase
plot of Fig. 20.29. Note that it is the inverse of that appearing for the
series resonant circuit because at low frequencies the series resonant
circuit was capacitive and at high frequencies it was inductive.
90°
45°
0°
–45°
–90°
θ (V p leads I)
Circuit inductive
Lagging F p
20.10 EFFECT OF Q l ≥ 10
f p
f r
R l2
R l3
f
Z p
R l
0
L3 L2 C3 C2 Rl fixed
> >
L 1
C 1
FIG. 20.28
Effect of R l, L, and C on the parallel resonance curve.
Resonance (resistive)
Circuit capacitive
Leading F p
FIG. 20.29
Phase plot for the parallel resonant circuit.
The content of the previous section may suggest that the analysis of
parallel resonant circuits is significantly more complex than encountered
for series resonant circuits. Fortunately, however, this is not the
case since, for the majority of parallel resonant circuits, the quality factor
of the coil Q l is sufficiently large to permit a number of approximations
that simplify the required analysis.
f
f r
EFFECT OF Q l ≥ 10 ⏐⏐⏐ 907
L 2 /C 2
L 3 /C 3
L 1 /C 1
f