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152 VOLTAGE COMPARATORS
Substituting this value into the maximum frequency formula, Equation (3,10),
gives us
The above equation represents a worst-case situation for a symmetrical out-
put waveform. As noted in the zero-crossing circuit, the output waveform under
these extreme conditions will more closely resemble a triangle waveform than a
square wave. In cases where output rise and fall times must be short compared to
the pulse width, Equation (3.11) 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 3.11, we have already computed t s as 40 microseconds. Now sup-
pose we want the switching times (rise and fall) to be one-eighth (0.125) of the sta-
ble time (t p). This establishes our ratio p as 0.125. The highest frequency is then
computed with Equation (3.11) as
3.4.3 Practical Design Techniques
Now let us design a voltage comparator circuit with hysteresis and obtain the fol-
lowing performance:
1. Upper threshold -4.25 volts
2. Lower threshold -7.75 volts
3. Hysteresis 3.5 volts
4. Highest operating frequency 60 hertz
5. Maximum ratio (p) of switching time to stable time 0.1
6. Power supply voltages ±15 volts
Determine the Required Slew Rote. The slew rate must be high enough to
allow the output to switch between saturation levels within the allowed switching
time (t$). The switching time is computed with Equation (3.12) as follows:
