Digital-to-analog conversion by pulse-count modulation methods

Three low-cost digital-to-analog converters (DACs) are described and compared. These designs can easily be implemented in an integrated circuit: the conventional pulse-width modulation (PWM) DAC, the new pulse-count modulation (PCM) DAC and the first-order noise shaping (FONS) DAC. All three methods control the ratio of the sum of all pulse durations to the constant total period. As the pulse durations are integral multiples of a unit pulse, all three can be classified as pulse-count modulation methods. Block diagrams of all three DACs consisting of a simple digital circuit and a low-pass filter are presented. For a constant digital input value the worst case ripple of the filter output is used to calculate the cutoff frequency of the low-pass filter. Approximations for the 3 dB cutoff frequency of first-order, second-order and fourth-order Butterworth low-pass filters are given. The dynamic properties are analyzed in the time domain (settling time) and in the frequency domain (unfiltered output spectrum of a full-scale sine wave input). The main influences on the static accuracy are analyzed. A case study demonstrates the abilities of PCM and FONS.