The circuit shown in Fig. 15.13 is a notch filter. At its resonant frequency, the L-C series circuit has zero effective impedance and, as a result, any signal at that frequency is short-circuited. For this reason, the filter is often referred to as a trap.

Question

The circuit shown in Fig. 15.13 is a notch filter. At its resonant frequency, the L-C series circuit has zero effective impedance and, as a result, any signal at that frequency is short-circuited. For this reason, the filter is often referred to as a trap.
Consider the following scenario. A system operating at 1 kHz has picked up noise at a fundamental frequency of 10 kHz, as well as some second- and third-harmonic junk. Given this information, we wish to design a filter that will eliminate both the noise and its attendant harmonics.

Accepted Answer

The key to the trap is setting the resonant frequency of the L-C series branch to the frequency we wish to eliminate. Since we have three frequency components to remove, 10 kHz, 20 kHz, and 30 kHz, we will simply use three different L-C branches as shown in Fig. 15.14 and set [latex]L_{1} C_{1} [/latex] to trap at 10 kHz, [latex]L_{2} C_{2} [/latex] at 20 kHz, and[latex]L_{3} C_{3} [/latex] at 30 kHz. If we arbitrarily set the value of all inductors to 10 μH and calculate the value of each capacitor, we obtain
[latex]C_{1}=\frac{1}{(2 \pi)^{2} f^{2} L}=\frac{1}{(2 \pi)^{2}\left(10^{8} ight)\left(10^{-5} ight)}=25.3 \mu F[/latex]
[latex]C_{2}=\frac{1}{(2 \pi)^{2}\left(4 imes 10^{8} ight)\left(10^{-5} ight)}=6.34 \mu F[/latex]
[latex]C_{3}=\frac{1}{(2 \pi)^{2}\left(9 imes 10^{8} ight)\left(10^{-5} ight)}=2.81 \mu F[/latex]
The three traps shown in Fig. 15.14 should eliminate the noise and its harmonics.

Question 15.8: The circuit shown in Fig. 15.13 is a notch filter. At its re...

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