of Microprocessors

382 MUSICAL ApPLICATIONS OF MICROPROCESSORS
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SIGNAL FREQUENCY AS A FRACTION OF THE SAMPLE RATE
Fig. 12-11. Effect of finite DAC pulse width on high-frequency amplitude
Figure 12-10 shows a simplified schematic of a two-switch track-andground
circuit integrated with a sign-bit switch for a sign-magnitude DAC.
The A and B switches select between straight DAC output and inverted DAC
output according to the desired polarity. However, both are open while the
DAC is settling at a new voltage level. Switch C grounds the filter input
during the turn-off transient of A or B, the DAC settling time, and the
turnon of A or B. Although the grounding is not perfect due to on resistance
of C, it substantially attenuates feedthrough of DAC glitches and transients
from A and B. The only transient seen by the filter is from switch C itself and
most of that is shunted to ground. Finally, since there are no amplifiers in
the switching signal path, there is nothing to slew.
There does appear to be a drawback with the circuit, however. Rather
than getting a stairstep approximation of the audio waveform, the filter gets
pulses of constant width and variable height. Actually, the mathematics of
sampled waveform reconstruction are derived on the assumption that the
samples entering the filter are of zero width and varying but infinite height.
Fortunately, the only effect of finite width pulses is a slight reduction in the
amplitude of high-frequericy reconstructed waves, or simply a loss of treble.
A pure stairstep approximation such as from an ideal DAC or SAH deglitcher
is actually a train of pulses with width equal to the sample period.
The graph in Fig. 12-11 shows that even this is a relatively minor
effect. The stairstep approximation is down nearly 4 dB at the Nyquist
frequency but only about 1. 32 dB down at 60% of the Nyquist frequency,
which represents a 15-kHz signal at a 50-ks/s sample rate. With pulses half