Question

The filter shown in Figure P15.36 is a Sallen and Key band-pass filter circuit, where $K$ is the DC gain of the filter. Derive the following expression for the filter's frequency response: $$ \begin{aligned} & H(j \omega)= \\ & (j \omega)^2+j \omega\left(\frac{1}{R_1 C_1}+\frac{1}{R_3 C_2}+\frac{1}{R_3 C_1}+\frac{1-K}{R_2 C_1}\right)+\frac{R_1+R_2}{R_1 R_2 R_3 C_1 C_2} \end{aligned} $$

   The filter shown in Figure P15.36 is a Sallen and Key band-pass filter circuit, where $K$ is the DC gain of the filter. Derive the following expression for the filter's frequency response:

$$
\begin{aligned}
& H(j \omega)= \\
& (j \omega)^2+j \omega\left(\frac{1}{R_1 C_1}+\frac{1}{R_3 C_2}+\frac{1}{R_3 C_1}+\frac{1-K}{R_2 C_1}\right)+\frac{R_1+R_2}{R_1 R_2 R_3 C_1 C_2}
\end{aligned}
$$

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Principles and Applications of Electrical Engineering

Principles and Applications of Electrical Engineering

Giorgio Rizzoni 4th Edition

Chapter 15, Problem 36

Instant Answer

Step 1

Although we don't have the figure P15.36, we can proceed with the analysis based on the standard Sallen and Key band-pass filter topology. The circuit typically consists of an op-amp with resistors R₁, R₂, R₃ and capacitors C₁, C₂. Show more…

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The filter shown in Figure P15.36 is a Sallen and Key band-pass filter circuit, where $K$ is the DC gain of the filter. Derive the following expression for the filter's frequency response: $$ \begin{aligned} & H(j \omega)= \\ & (j \omega)^2+j \omega\left(\frac{1}{R_1 C_1}+\frac{1}{R_3 C_2}+\frac{1}{R_3 C_1}+\frac{1-K}{R_2 C_1}\right)+\frac{R_1+R_2}{R_1 R_2 R_3 C_1 C_2} \end{aligned} $$

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