Page 162 - Op Amps Design, Applications, and Troubleshooting

Zero-Crossing Detector with Hysteresis 145

Since this corresponds to half of the period of the highest input frequency, we can
determine the upper frequency as shown:

In our case, we have

The above equation represents a worst-case situation. It should be noted,
however, that the output waveform under these extreme conditions will more
closely resemble a triangle waveform than a square wave. Whether or not this is
objectionable is totally dependent upon the application. In cases where output rise
and fall times must be short compared to the pulse width, the following equation
can be used to determine the highest operating frequency for a particular ratio (p)
of switching time (t s) to stable time (t p).

In the case of Figure 3.7, we have already computed t$ as 56 microseconds.
Now suppose we want the switching times (rise and fall) to be one-tenth (0.1) of
the stable time (t p). This establishes our ratio p as 0.1. The highest frequency is
then computed as

/(max) =

If the input waveform is such that the output will not be symmetrical, then t s
establishes the shortest (either positive or negative) alternation of the output
waveform. The highest frequency of operation, however, can be obtained when
the output waveform is symmetrical.

3.3.3 Practical Design Techniques
Let us now design a zero-crossing detector circuit similar to that shown in Figure
3.7. We will design to achieve the following:

1. Upper threshold +0.5 volts
2. Lower threshold -0.5 volts