Typically, when a digital transducer is employed to generate the feedback signal for an analog controller, a digital-to-analog converter (DAC) would be needed to convert the digital output from the transducer into a continuous (analog) signal. Similarly, when a digital controller is used to drive an analog process, a DAC has to be used to convert the digital output from the controller into the analog drive signal. There are ways, however, to eliminate the need for a DAC in these types of situations.

(a) Show how a shaft encoder and a frequency-to-voltage converter can replace an analog tachometer in an analog speed-control loop.

(b) Show how a digital controller with PWM can be employed to drive a dc motor without the use of a DAC.