Question

What is the answer to question 23.1?

23.1 Active low-pass filter You can make a low-pass filter by putting a capacitor Cr and resistor Rf in parallel for Zj as shown in Figure 23.1. At low frequencies (well below the corner frequency), the feedback impedance is approximately Rf and the gain of a non-inverting amplifier is is 1 +R//R,. At high frequencies (well above the corner frequency),the impedance is approx- imately 1/(jwCs), and the gain of a non-inverting amplifier is 1 +1/(juCRi), which gets smaller as the frequency goes up The inverting amplifier configuration, same as Figure 23.1 but with the Vin and Vref port names swapped, is more popular, because the gain goes to zero as goes to 00, rather than bottoming out at 1 as the non-inverting amplifier oes One disadvantage of the inverting configuration is that the input impedance is only Ri rather than the effectively infinite input impedance of the non-inverting configuration, so whatever is providing Vin needs to have a fairly low impedance. If the input to the active filter is being driven by an amplifier, then the inverting configuration is usually the better choice, but if the input is coming directly from a high-impedance sensor or a high-impedance passive filter, then the non-inverting configuration may be the only feasible one, despite the limited filtering at high frequencies. Exercise 23.1 Plot the gain of the amplifier in Figure 23.1 vs. frequency on a log-log plot from 0.1 Hz to 100 kHz, using the following parameter values: R2-1 kQ, Rf = 100 kΩ and C 22 nF