For the network in Fig. 22.45(b), determine Ls and Lp for a capacitance C of 510 pF if a frequency of 200 kHz is to be rejected and a frequency of 600 kHz accepted. Assume Rs and Rp are zero ohms.

Question

For the network in Fig. 22.45(b), determine [latex]L_s and L_p[/latex] for a capacitance C of 510 pF if a frequency of 200 kHz is to be rejected and a frequency of 600 kHz accepted. Assume [latex]R_s and R_p[/latex] are zero ohms.

Accepted Answer

For series resonance, we have

[latex]f_s=\frac{1}{2\pi\sqrt{LC} }\[0.5cm] and\[0.5cm] L_s=\frac{1}{4\pi^2f^2_sC}=\frac{1}{4\pi^2(600 kHz)^2(510 pF)}=137.9 \mu H, use \enspace 150 \mu H \[0.5cm] At\enspace 200 kHz,\[0.5cm] X_{L_s}=\omega L =2\pi f_sL_s=2\pi (200 kHz)(150 \mu H) = 188.5 Ω \[0.5cm] and\qquad X_C=\frac{1}{\omega C}=\frac{1}{2\pi (200 kHz)(510 pF)}=1560.3 Ω [/latex]

For the series elements,

[latex]j(X_{L_s}-X_C)=j(188.5 Ω - 1560.3 Ω)=-j 1371.8 Ω = -jX^{\prime}_C[/latex]

At parallel resonance [latex](Q_l ≥ 10 \enspace assumed),[/latex]

[latex]X_{L_p}=X^{\prime}_C\[0.5cm] and\qquad L_p=\frac{X_{L_p}}{\omega}=\frac{1371.8 Ω}{(2\pi)(200 kHz)}=1.09 mH, use \enspace 1.1 mH [/latex]

The frequency response for the preceding network appears as one of the examples of PSpice in the last section of the chapter.

Question 22.9: For the network in Fig. 22.45(b), determine Ls and Lp for a ...

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