790 Chapter 23
(23-25)(23-26)where,
fc is the cutoff frequency,
Z 0 is the line impedance.
23.2.3.3 Parallel Resonant Elements
A parallel resonant circuit element has impedance that
is at a maximum at the resonant frequency (Fig. 23-9).
The impedance of the element is given by
(23-27)where,
Z is the impedance,
XL is the reactance of the inductor,
XC is the reactance of the capacitor.
At very low frequencies, the reactance of the
inductor approaches a short circuit, reducing the overall
impedance. At high frequencies, the reactance of the
capacitor approaches a short circuit, reducing the
overall impedance.23.2.3.4 Series Resonant ElementsA series resonant circuit element has impedance that is
at a minimum at the resonant frequency. The impedance
of the element is given by(23-28)where,
Z is the impedance,
XL is the reactance of the inductor,
XC is the reactance of the capacitor.At very low frequencies, the reactance of the capac-
itor approaches an open circuit, increasing the overall
impedance. At high frequencies, the reactance of the
inductor approaches an open circuit, increasing the
overall impedance.Figure 23-7. Configuration and characteristics of low-pass
filters.
Figure 23-9. Parallel resonant circuit.
Z increasesConfiguration Attenuation ImpedanceL = Half sectionT = Full section"Pi" or P sectionL 1 L 1ZTC 2ZT ZTZTZT ZPZP ZPZPZP
C 2 C 22 C 2fcfcfcZ 0Z 0Z 0fcfcfcwhere Z 0 = line
impedanceC 2 = 2 P^1 f
cZ 0L = 2 ZP^0 f
cIc = cutoff frequencyL 1L 1Attenuation–dBAttenuation–dBAttenuation–dB± ±±±±±C 1 1
2 SfcZ 0-----------------=L 2Z 0
2 Sfc=----------ZXLuXC
XL+XC=-------------------CLFigure 23-8. Configuration and characteristics of high-pass
filters.Figure 23-10. Series-resonant circuit.Configuration Attenuation ImpedanceL = Half sectionT = Full section"Pi" or P sectionC 1 C 1ZTC 1ZT ZTZT ZPZP ZPZPZP
L 2 L 22 L 2fcfcfcZ 0Z 0Z 0fcfcfcwhere Z 0 = line
impedanceC 1 = 2 P^1 f
cZ 0L 2 =Z 0
2 PfcL 2p pppppdBdBdB2 C 1ZTZXL+= XCL C