Solution Found!
The circuit shown in Figure P 16.4-3 is a secondorder low-pass filter. This filter
Chapter 16, Problem P16.4-3(choose chapter or problem)
The circuit shown in Figure P 16.4-3 is a second order low-pass filter. This filter circuit is called a multiple-loop feedback filter (MFF). The output impedance of this filter is zero, so the MFF low-pass filter is suitable for use as a filter stage in a cascade filter. The transfer function of the low-pass MFF filter is
\(H_{\mathrm{L}}(s)=\frac{-\frac{1}{R_1 R_3 C_1 C_2}}{s^2+\left(\frac{1}{R_1 C_1}+\frac{1}{R_2 C_1}+\frac{1}{R_3 C_1}\right) s+\frac{1}{R_2 R_3 C_1 C_2}}\)
Design this filter to have \(\omega_0=2000 \mathrm{rad} / \mathrm{s}\) and Q = 8. What is the value of the dc gain?
Hint: Let \(R_2=R_3=R\) and \(C_1=C_2=C\). Pick a convenient value of C and calculate R to obtain \(\omega_0=2000 \mathrm{rad} / \mathrm{s}\). Calculate \(R_1\) to obtain Q = 8.
Questions & Answers
QUESTION:
The circuit shown in Figure P 16.4-3 is a second order low-pass filter. This filter circuit is called a multiple-loop feedback filter (MFF). The output impedance of this filter is zero, so the MFF low-pass filter is suitable for use as a filter stage in a cascade filter. The transfer function of the low-pass MFF filter is
\(H_{\mathrm{L}}(s)=\frac{-\frac{1}{R_1 R_3 C_1 C_2}}{s^2+\left(\frac{1}{R_1 C_1}+\frac{1}{R_2 C_1}+\frac{1}{R_3 C_1}\right) s+\frac{1}{R_2 R_3 C_1 C_2}}\)
Design this filter to have \(\omega_0=2000 \mathrm{rad} / \mathrm{s}\) and Q = 8. What is the value of the dc gain?
Hint: Let \(R_2=R_3=R\) and \(C_1=C_2=C\). Pick a convenient value of C and calculate R to obtain \(\omega_0=2000 \mathrm{rad} / \mathrm{s}\). Calculate \(R_1\) to obtain Q = 8.
ANSWER:
Step 1 of 4
We are told to set 
Transfer function will look like this:
