Filter Design
Suppose that we need a filter that passes components higher in frequency than 1 kHz and rejects components lower than 1 kHz. Select a suitable second-order circuit configuration, choose L = 50 mH, and specify the values required for the other components.

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Accepted Answer

We need to pass high-frequency components and reject low-frequency components. Therefore, we need a highpass filter. The circuit diagram for a second-order highpass filter is shown in Figure 6.35(a), and the corresponding transfer-function magnitude plots are shown in Figure 6.35(b). Usually, we want the transfer function to be approximately constant in the passband. Thus, we choose Q_s ≅ 1. We select f₀ ≅ 1 kHz, so the components above 1 kHz are passed, while lower-frequency components are (at least partly) rejected. Solving Equation 6.30 for the capacitance and substituting values, we have

[latex]f_0=\frac{1}{2\pi \sqrt{LC}}[/latex] (6.30)

[latex]C=\frac{1}{(2\pi )^2 f_0^2 L}=\frac{1}{(2\pi )^2 imes 10^6 imes 50 imes 10^{-3}}=0.507~\mu\mathrm{F}[/latex]

Solving Equation 6.31 for the resistance and substituting values, we get

[latex]Q_s=\frac{2\pi f_0 L}{R}[/latex] (6.31)

[latex]R=\frac{2\pi f_0 L}{Q_s}=\frac{2 \pi imes 1000 imes 50 imes 10^{-3}}{1}=341.1~\Omega[/latex]

The circuit and values are shown in Figure 6.38.

Question 6.7: Filter Design Suppose that we need a filter that passes comp...

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