Comparator
Hystereses Design Equations
A comparator is an electronics
circuit which compares the voltage of a signal to a voltage
reference. If the signal's voltage is greater than the reference,
the the output of the comparator swings to the top rail, and likewise if
it is less than, it swings to the bottom rail. Comparators are
useful in converting analog signals into square digital
signals.
Hystereses
is often employed in comparators, and is useful in eliminated noise and
glitches. With hystereses a comparator has two voltage
thresholds: a high threshold when the output is low, and a low threshold
when the output is high. If the output is currently low, then the
input voltage must swing above the high threshold, which is higher than
the reference voltage, to make the output swing high. Likewise, when
the output is high, the input voltage must swing below the low threshold,
to make the output swing to the low rail.
A
popular comparator is the LM339 which contains 4 comparators in a 14 pin
package. The LM393 contains 2 comparators. The TL331 contains a
single comparator.
Hystereses
can be designed into a comparator circuit, by inserting a resistor from
the output to the positive terminal of the comparator.
Computing
the resistor values for a given high and low threshold voltage is a common
engineering task when dealing with comparators.
The
general expression for the reference voltage VR in terms of the
output voltage, input voltage and resistors is as follows:
We
can rearrange for the input voltage:
We want to determine the input voltage such
that the positive terminal of the comparator is equal to the reference
voltage for both cases when the output voltage has swung to the positive
rail and alternatively to the lower power supply rail. These two voltages
are the high and low threshold voltages of the hystereses curve. 
Given
the above two equations, we can express either threshold voltage in terms
of the other threshold voltage: 
Thus,
the resistor ratio can be expressed as: 
and
the reference voltage can be expressed as: 
The
design steps are as follows:
- Determine appropriate high and low
thresholds of the hystereses curve.
- Solve for the resistor ratio, and select
R1 and R2.
- Solve for the reference voltage.
Normally a resistor divider is used to set this voltage, but other
methods can be used.
We've created a simple hystereses
calculator which computes the resistor values and reference voltage. Daycounter
is a contract electrical engineering company, specializing in electronics
and software design. Please contact
us to find out how we can help you with your electronics design.
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