Comparator, Schmitt Trigger, and More
Comparator
A useful electrical function is an arithmetic comparison of two voltages; the outcome of the
comparison in general is an indication of whether one voltage is less than or greater than the other. In
general the comparator operation is provided by a high gain amplifier whose design emphasizes speed of
switching between saturation limits. The device characteristic
is suggested by the figure to the left. A problem which can
arise with the
comparator occurs when
noisy signals are
involved. This is
illustrated in the figure
to the right. The signal
fluctuates so that the
switching threshold is
crossed extraneously
several times, causing a
number of pulses.
A special form of
comparator, the Schmitt
‘Trigger’ is useful in
such circumstances. This circuit, which has a number of
variations introduces a memory capability which provides different switching thresholds for positiveand negative going signals.
Non-Inverting Schmitt Trigger
A simplified Schmitt Trigger circuit (different from that described
elsewhere for the project) is drawn to the right. Note the use of
regenerative (positive) feedback to obtain a rapid switching from one
saturated state to the other. Because of the feedback the reference
voltage is proportional to the amplifier output, and so will be different
depending on which saturated state the amplifier is placed in.
Suppose Vin is sufficiently small to assure the amplifier is in positive
saturation +Vsat. Then Vref = +Vsat (R1/(R1+R2) and the condition
for consistency is that Vin ≤ Vsat (R1/(R1+R2). Suppose Vin is
increased until it crosses this switching threshold, causing a regenerative switch to the -Vsat state. The
reference voltage now becomes Vref = -Vsat (R1/(R1+R2) < +Vsat (R1/(R1+R2), i.e., the reference
voltage for switching back to the –Vsat state is lowered requiring more than a small fluctuation for the
switching to occur. Similarly in switching from the –Vsat state the threshold for switching is increased.
This ‘hysteresis’, i.e., change of switching threshold is illustrated by a PSpice computation for a
representative circuit using a LM111 comparator (See Appendix 1 for the pin out). The circuit diagram
(Schematics) is drawn below. Vin is a triangular waveform as shown in the Probe plots following.
Rather than use the amplifier saturation voltages directly for the feedback the amplifier output voltage is
used to operate back-to-back Zener diodes (Zener voltage = 4.7v) through a 1kΩ current-limiting
resistance.
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Note the parallel feedback branches. The parametric resistance RVAL is assigned values of 100 MEGΩ
(effectively an open-circuit) and 390kΩ.
Consider the case where
RVAL = 100MEGΩ,i.e., is
electrically inactive (and the
diode plays no role). The
‘output voltage consists of
the voltage drop across one
Zener diode in breakdown,
4.7v, and one forward-biased
diode with a junction voltage
approximated as 0.7v.
The trip voltages then are
estimated to be
±(100/390)(4.7+0.7) = ±1.38v. These estimates can be compared to the trip voltages calculated by
PSpice and plotted in the figure to the left. Note also the ‘output’ voltage levels.
The hysteresis curve corresponding to
the circuit is drawn to the right. The
symmetry of the trip voltages is more or
less evident.
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Setting Different Threshold (‘trip’) Voltages
The linear resistive feedback network used in the preceding illustration leads to symmetrical threshold
voltages. Asymmetrical threshold voltages may be implemented using circuit elements that are not
bilateral, e.g., a junction diode. For this purposes RVAL is assigned (more or less arbitrarily) the value
of 390k, comparable to the resistance in the branch shunted. Because of the diode the added branch is
active only for negative voltages; the trip voltage for the negative output voltage is –(5.4)(100/(390/2) =
–2.76v (assuming an idealized diode model for simplicity; for a 0.7v ‘knee’ voltage approximation this
becomes 2.59v.) The switching characteristic is plotted below, followed by the hysteresis characteristic.
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Inverting Schmitt Trigger
A Schmitt Trigger circuit configuration using an LM111 inverting amplifier orientation is drawn below.
Note the regenerative feedback used to provide a ‘reference’ voltage that is a function of the current
saturated amplifier state.
The saturation output
voltages are ±10v
(approx.), and the
trigger voltages are ±2v
respectively. The
PSpice computation of
the hysteresis
characteristic is drawn
below, with the trigger
voltage points
determined with the
cursor capability noted.
The input/output voltage
relationships are plotted in the
next figures.
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Special Case
The circuit shown provides a positive trip voltage estimated as 4.55v (assuming an idealized diode
model for simplicity), and a lower trip voltage of approximately zero.. Note the change (more or less
arbitrary) in supply voltage, and the removal of the Zener diode arrangement.
The PSpice computed results are plotted below; interpretation is left as an exercise.
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Appendix 1: LM 111 Pin out
The LM111, unlike the ubiquitous 741, is an amplifier
specifically designed for fast switching between
saturation limits. The pin out diagram for the LM111
is drawn to the right. The device includes an internal
transistor to provider some user control over the output. For the illustrative purpose in this note a
collector resistor of 1kΩ is connected to pin 8 (V+) and the output ‘ground’ is connected to pin 4 (V-).
Appendix 2 Plotting the hysteresis characteristic.
To plot the hysteresis characteristic first plot Vout vs. Time. Then open the PLOT menu, select ‘x
variable’, and when the dialog box appears select ‘x-axis variable’. This opens the list of variables;
select Vin, and click OK.
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