Question 15.1: Objective: Design a two-pole low-pass Butterworth filter for...
Objective: Design a two-pole low-pass Butterworth filter for an audio amplifier application.
Specifications: The circuit with the configuration shown in Figure 15.7(a) is to be designed such that the bandwidth is 20 kHz.
Choices: An ideal op-amp is available and standard-valued resistors and capacitors must be used.
From Equation (15.19), we have
ω_{3 dB} = \frac{1}{RC} (15.19)
f_{3 dB} = \frac{1}{2π RC}
or
RC = \frac{1}{2π f_{3 dB}} = \frac{1}{2π(20 × 10^{3})} = 7.96 × 10^{−6}
If we let R = 100 kΩ, then C = 79.6 pF, which means that C_{3} = 1.414C = 113 pF and C_{4} = 0.707 C = 56.3 pF.
Trade-offs: Standard-valued 100 kΩ resistors can be used. Standard-valued C_{3} = 120 pF and C_{4} = 56 pF capacitors can be used. For these elements, a bandwidth of 20.1 kHz is obtained.
Comment: These resistance and capacitance values are generally too large to be fabricated conveniently on an IC. Instead, discrete resistors and capacitors, in conjunction with the IC op-amp, would need to be used.