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ECE 3155
Experiment IV
ACTIVE NONLINEAR CIRCUITS
Rev. lpt oct 2011
Introduction
As we have already seen in this course, it is common for engineers to simplify their
problems by treating them as linear processes. This is largely due to a wish for a simple world that
can be easily expressed in mathematical terms. However, there are several areas where the
problems that we deal with are inherently nonlinear. Conceptually, these areas include situations
where something turns on and off. A digital circuit is just one example.
The purpose of this experiment is to help you explore several important nonlinear circuits
that form the basis of much of the electronic circuitry in use today. These circuits are the
comparator, the limiter, the bistable circuit, and the astable multivibrator. This experiment will also
introduce a measurement technique that is very useful in measuring transfer characteristics. This
technique makes use of the x-y capability of your oscilloscope.
Oscilloscope x-y Format
With the exception of Step 7, each of the measurements in this lab will utilize the x-y
format to generate a transfer function. To do this, press DISPLAY on the oscilloscope front panel.
One of the options you see along the right side of the screen will be labeled “Format” and there will
be two choices. One is YT, which is the usual voltage vs. time display of the scope. The other is the
XY format. In this format, the oscilloscope gives you a “plot” generated by using channel 1 as the
x-axis and channel 2 as the y-axis. The vertical sensitivity knobs allow you to adjust the voltages
corresponding to “full scale” horizontally (x-direction) or vertically (y-direction).
To get the transfer characteristics for your circuits, set the function generator for a triangular
wave output of zero mean value, that is, with no DC component. Use a peak-to-peak value of
20[V], and a pulse repetition rate of several hundred [Hz]. Apply the output of the function
generator to the x input (channel 1), and to the input of the circuit to be tested. Then apply the
output of the circuit to the y input (channel 2). If now the XY format is selected, the oscilloscope
will display the circuit transfer characteristic. Adjust the vertical sensitivity so that the vertical axis
ECE 3155 – Exp. IV Active Nonlinear Circuits
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will display the desired voltage range, which is –15[V] to +15[V] in this exercise. This axis will be
used to display the output voltage of the circuit, which will typically be limited to the saturation
voltages of the operational amplifiers (op amps) used in the experiment. The horizontal sensitivity
should be adjusted to display the desired range of the input voltage, which in this case will be –
20[V] to +20[V].
The repetition rate you use for your triangle wave can affect your results in some cases.
This is due to the non-ideal properties of the op amps. As you perform the experiment, vary the
repetition rate, and note the effects. In general you will find that the behavior is more ideal at lower
frequencies, but as the repetition rate gets very low the display will flicker. Pick a frequency that is
a reasonable compromise between these two considerations.
Components Required
1 1N5227 Zener diode
Assorted resistors and capacitors from the lab kit
1 741 op amp
Pre-Lab
1. Step 3: Design the circuit of Figure 3, choosing values for VDC, R1, R2, and Rf as instructed in
that step.
2. Step 5: Design the circuit of Figure 6; that is, choose a value for R1 to satisfy the specifications
in that step.
3. Step 6: Design the astable multivibrator of step 6 based on the specifications in that step.
Procedure
The Comparator and the Limiter
The comparator and the limiter perform slightly different tasks, but have the same general
transfer characteristic, which is shown in Figure 1. The comparator generates one output when the
input is lower than a certain input value, and another when it is higher than that value. The limiter
is a circuit with gain that limits the output to some maximum and minimum values. In Figure 1, Vr
is the voltage to be compared to the input of the comparator, and VSAT+ and VSAT- are the output
values. For the limiter, VSAT+ and VSAT- are the minimum and maximum values.
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vOUT
VSAT+
vIN
Vr
VSAT-
Figure 1. Transfer characteristics for the comparator and the limiter.
It is easy to control all the parameters of this transfer characteristic independently. That is, you may
set the positive and negative saturation voltages VSAT- and VSAT+, the slope of the linear transition
region, and the offset voltage Vr, assuming that they are within the capability of the active element.
The most basic circuit for accomplishing this is shown in Figure 2. This as an ordinary op ampbased amplifier. In this case, the active element is the op amp.
Rf
Ri
vI
vO
Figure 2. Circuit for the comparator and limiter.
When used as a comparator, the circuit is meant to function with a range of input voltages
such that the amplifier output exceeds the linear part of the transfer characteristic and becomes
“clamped” to either its maximum positive value or its maximum negative value. The maximum
values are the positive and negative saturation voltages of the op amp.
1.
Build the circuit of Figure 2. Apply power supply voltages of–15[V] and +15[V] to the op
amp. Use Ri = 1[k], and a feedback resistor Rf1 such that the slope of the linear part of the transfer
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characteristic is -10. Measure and plot the transfer characteristic of the circuit on a piece of graph
paper. Measure and mark the amplifier saturation voltages clearly and carefully. You will be
plotting a number of transfer characteristics on this graph. Plot them neatly, and label each one
carefully. Record your value of Rf1 below.
Rf1 =
2.
Choose a new feedback resistor Rf2 such that the slope of the linear part of the transfer
characteristic is -100. Measure and plot this function on your graph paper. Record your value of Rf2
below.
Rf2 =
3.
An offset voltage Vr may be applied to the circuit at either the inverting or noninverting
inputs. For our purposes this is most easily done at the noninverting input, because a voltage
divider may be used. Construct the circuit shown in Figure 3, designing the indicated offset voltage
Vr to be 4.7[V] using the voltage divider formed by R1, R2, and VDC. To choose appropriate
component values, think of the voltage divider in terms of its Thevenin equivalent. Set the slope to
-27, with Ri = 1[k]. Measure the transfer characteristic and plot it on your graph paper. Record
your value of Rf as Rf3 below.
Rf3=
Rf
Ri
vI
vO
R1
VDC
R2
Figure 3. Comparator circuit.
The circuit of Figure 2 compares the input voltage to zero volts. The circuit of Figure 3
compares the input voltage to +4.7[V], and specifies its relationship to that voltage, thus the name
comparator. Analyze the circuit to understand exactly how it functions.
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4.
The circuits used in Steps 1 through 3 use the saturation voltages of the op amp to limit the
output voltages. The output may be limited to voltages smaller than these saturation voltages by
introducing fixed voltage drop elements in the op amp feedback loop. For example, the circuit
shown in Figure 4 uses a zener diode in the feedback loop to limit the positive output excursion to
approximately +0.7 V, and the negative output voltage to -VZ, the Zener voltage.
Construct the circuit of Figure 4 with a 1N5227 Zener diode in the feedback loop. Measure
and plot the transfer characteristic on your graph paper. Reverse the direction of the Zener diode
and repeat this step. To understand the operation of the Zener diode, remember that the forward
biased model of the Zener diode is (approximately) a 0.7[V] source, and that of the reverse-biased
Zener with sufficient applied potential is a source of value -VZ.
Ri
vI
vO
Figure 4. Comparator with Zener diode in the feedback loop.
The Comparator with Hysteresis
5.
A comparator can be designed with a hysteresis loop in the transfer characteristic. A
comparator with such a loop is frequently called a Schmidt Trigger circuit in honor of Dr. Otto
Schmidt, its inventor. The transfer function of such a circuit is shown in Figure 5. The “loop”
aspect of this transfer characteristic, indicating a different path for up-going and down-going
signals, resembles the B-H hysteresis loop of ferromagnetic materials; hence its name.
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vOUT
vT1
vT2
vIN
Figure 5. Comparator transfer characteristics showing hysteresis loop.
The circuit that produces this transfer characteristic is shown in Figure 6. Functionally it is
almost identical to that of Figure 3, a comparator with offset. Here, the slope of the linear part of
the transfer characteristic is equal to the op amp gain, i.e., it is very high. This is done by setting
Rf =  and Ri = 0. The offset voltage is derived from the output saturation voltage, so that if the
output is at VSAT+, the offset is at VSAT+ {R2/(R1 + R2)}; if the output is at VSAT-, the offset is at
VSAT- {R2/(R1 + R2)}.
vI
R1
R2
vO
Figure 6. Circuit with transfer characteristics as shown in Figure 5.
Design a Schmidt Trigger so that the loop back points VT1 and VT2 are 2[V]. Note that the
saturation voltages of a 741 are approximately 1.5[V] away from the supply voltages. Use
R2 = 1[k]. Record your value of R1 below. Construct the circuit, measure its transfer characteristic
and plot it on a new piece of graph paper. Indicate with arrows the directions associated with the
hysteresis.
R1=
6
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The Astable Multivibrator
6.
The astable multivibrator is a form of a Schmidt Trigger that utilizes both positive and
negative feedback. Its circuit is shown in Figure 7. This circuit is a Schmidt Trigger, which derives
its input from the output, via the R3C single time constant network. Since the circuit derives its
input from its own output, it requires no external input to have an output. Notice that because of the
capacitor, this circuit does not have negative feedback. You will find when you build this circuit
that the voltages at the inverting input and the non-inverting input are not equal. One way of
looking at this is that because of the capacitor at the inverting input, there is not a signal path from
the output to the inverting input.
R3
C
R1
R2
vO
Figure 7. Astable multivibrator circuit.
Design an op amp-based astable multivibrator to have an oscillation period of 13.5[ms].
Your textbook discusses the astable multivibrator in detail, and you should consult it to understand
the working of the circuit and how to do this design. In addition, you should base your design on
the Schmidt Trigger of the previous section, maintaining the 2[V] hysteresis limits, and determine
the proper R3C time delay circuit. (Hint: The Sedra and Smith textbook switches the names of R1
and R2, and defines a variable called  in terms of their values. You need to be very careful about
your definitions and names if you use the formula in the textbook.)
R3 =
C=
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7.
Construct the circuit you designed in Step 6. Sketch its output waveform on a new piece of
graph paper. For this part of the experiment, do not use the x-y mode of the oscilloscope. Measure
the period, and calculate the error in that period compared to the period you designed. Explain any
error greater than 10%.
Measured Period =
Percent Error in Period =
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Questions
1.
In using the x-y capability of the oscilloscope to display the transfer characteristics of your
circuits, we applied a triangle wave to the input. Why was this waveform used? Would a sine wave
work as well? How about a square wave? You may wish to try this and see what your results would
look like.
2.
Describe the effects that you saw on the measured transfer characteristics when you used a
frequency that was too high. What do we call such effects? Can you imagine what might account
for this behavior?
3. Describe in your own words, using complete sentences, the sequence of events in the operation
of your astable multivibrator.
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