Question 12.40: A fast-growing field within electrical engineering is mixed-...

A fast-growing field within electrical engineering is mixed-mode circuitry, which combines digital and analog networks to create a larger system. A key component in these systems is the analog-to-digital converter, or ADC. It “measures” an analog voltage and converts it to a digital representation. If these conversions are done quickly enough, the result is a sequence of data points, as shown in Fig. 12.84a. Connecting the dots reveals the original analog signal, v_{A}(t). Unfortunately, as seen in Fig. 12.84b, undesired signals such as v_{B}(t) at higher frequencies can also have the same set of data points. This phenomenon is called aliasing and can be avoided by employing a low-pass filter, called an anti-aliasing filter, before the ADC as shown in Fig. 12.84c. In general, the half-power frequency of the filter should be greater than the frequency of the signals you wish to convert but less than those you want to reject.
We wish to design an anti-aliasing filter, with a half-power frequency at 100 Hz, that will permit us to acquire a 60-Hz signal. In this design we will assume the ADC has infinite input resistance.