WAVEFORM GENERATORS
I OBJECTIVES
Overall, the goal of this experiment is to familiarize you with some quite general ideas concerning the
generation of waveforms using a combination of fast-acting positive feedback and delayed negative feedback, ideas
which are captured in the generic term, multivibrators. For reasons both of convenience and importance in practice,
we will explore circuits, which employ op amps. While the op amp with its differential inputs makes some of these
implementations very straightforward, the topological (and connectedness) ideas are far more universal, being
directly applicable to both discrete-component implementations, and logic-gate formulations, as well.
II PREPARATION
As is the recurring pattern in this Manual, Preparation will be keyed to the Explorations to follow, by the use
of the same titling and section numbering employed there, but with a P prefix.
P1.0 The Schmitt Trigger, a Bistable Multivibrator
Pl.l Non-Inverting Operation
(a)
For the circuit of Fig. 2 adjusted for ±10V output and with node A grounded, sketch and label the transfer
characteristic which applies from node D to node C.
(b) Modify your sketch to account for a second 100 kΩ resistor in series with an ideal diode whose cathode is at
node B, all shunting R2.
P1.2 Inverting Operation
(a)
For the circuit of Fig.2, adjusted for ±10V output and with node D grounded, sketch and label the transfer
characteristic which applies from node A to node C.
P2.0 Generating a Square-Wave
P2.1 A Square Wave Oscillator
(a)
For the circuit of Fig. 3 operating with output levels of ±10V, a design providing a nearly ideal triangle wave at
node D is required. For what value of/ R1, all other components remaining at their present values, are the peaks
of the waveform at D delayed by 1% from the value they would have if the initial charging slope had been
maintained?
* P2.2 Other Pulse Waveforms
(a) The circuit of Fig. 3, in which the output voltage is ±10V, has an external voltage VA applied to the leftmost end
of R1. What value of VA results in the output being positive 40% of the time?
P3.0 A Monostable Topology
P3.1 Low-Frequency Operation
(a) For the circuit shown in Fig. 4, estimate the voltage at node E in the stable state, assuming both diode drops to be
0.7V and output levels to be ±10V. By what amount must the input at F fall to trigger the monostable?
(b) For the circuit of Fig. 4, what is the effect of removing R1 ?
* P3.2 Higher-Frequency Operation
(a) For the circuit of Fig. 4, for which vc = ± 10V, sketch waveforms at nodes B and D under the conditions that a
narrow 1-volt negative-going trigger pulse is introduced at node B, from node F. As the input frequency is
increased from relatively low values, at what frequency does the pulse width begin to decrease? What is the
slightly higher frequency at which a second trigger pulse is just missed?
F4.0 A Multiple-Waveform Generator
P4.1 The Basic Square/Triangle-Waveform Generator
(a) What are the nominal limiting levels at node C, of the circuit of Fig.5. What input thresholds at node A result?
(b) What frequency of oscillation do you expect? What simple change would double the frequency while
maintaining in the amplitude at node H? What simple change would double the frequency and halve the
amplitude at node H?
** P4.2 The Sine-Wave Shaper
(a) Prepare a table of sine-wave slopes as indicated in the preamble to E4.2.
(b) For vH in Fig. 5, being an 8.2V peak triangle wave, with 0.7V diodes, what is the appropriate setting of P1 for a
sine-wave output at node J?
(c) For what setting of P2 do diodes Ds and D-j barely conduct at the triangle peaks? For what setting does each
conduct for 20°?
III EXPLORATIONS
E1.0 The Schmitt Trigger, a Bistable Multivibrator
Figure 2 shows a basic element, which recurs in the circuits to follow. It
is the positive-feedback Schmitt-Trigger Bistable (Multivibrator). It is operated
typically with either of nodes A or D as input, while the other is connected to a
reference voltage, often ground. Because of positive feedback, the output
voltage (C) is stable at one of two limiting values (a high one, L+, and a low
one, L-) which values depend on the choice of power-supplies V+ and V-, and
amplifier saturation characteristics. Toward the latter part of this exploration
we will consider one particular approach to making the output independent of
supply-voltage and op-amp variabilities.
Figure 2 A Versatile Schmitt-Trigger Topology
E1.1 Non-Inverting Operation
Assemble the circuit of Fig. 2, with node D grounded and A connected to a waveform generator. Adjust the
power supplies to about ±12 V. Externally trigger your oscilloscope from the generator's trigger-source.
• Now, with the generator providing a 5 Vpp triangle wave at 1 kHz to node A, display the waveforms at nodes A
and C, noting the limiting voltage levels at node C.
• Now, adjust the supply voltages so that the limiting voltages at node C are closely ±10 V.
Note that while the previous step is not essential, it makes subsequent measurement and interpretation very
convenient. However, be quite aware that this is a measurement artifice only; Thus, in normal designs, the cost of
special supply voltages makes the idea impractical, and, as we shall see, other means would be used to establish
convenient symmetric output-voltage values.
• Now, displaying A and C, then A and B, note carefully the voltage values at which interesting waveform
changes occur. Estimate the rise and fall times of the signals at C and B.
• * Now, to improve your sense of the (complementary) roles of each of the resistors R1, R2, shunt each in turn by
ones of equal value, observing the changes in thresholds at node A which result.
Consider the operation of this circuit by sketching its transfer characteristic (vC versus vA). Note the hysteresis
region, its width, and the simple relationship it bears to the limiting voltages (L+, L-) and the resistors (R1, R2).
E1.2 Inverting Operation
Assemble the circuit of Fig. 2 with node A grounded and D connected to a waveform generator. Adjust the
supplies initially to ±12 V.
• Now, with the generator providing a 3 Vpp triangle wave at 1 kHz to node D, and observing node C, adjust the
supply voltages so that the limiting voltages at node C are closely ±10 V.
• Now, with your scope triggered directly from a fixed-voltage generator output, and displaying both nodes D and
C, adjust the amplitude of the triangle wave input, so as to identify the input triggering levels, the relative timing
of the output, and the minimum input signal for which node C reverses state.
• Now, shunt R1 by an additional 10 kΩ resistor, first measuring nodes D and C and then D and B, to identify
input triggering levels and the input signal amplitude below which operation ceases.
Consider the operation of the circuit in relationship to the version explored earlier in Exp. 1.1, noting the relative
differences in polarity, input resistance, and the simplicity with which thresholds can be calculated. As we shall see,
next, the signal-inverting property can be of special importance.
E2.0 Generating a Square Wave
In general, one approach to creating an oscillator is to use a positivefeedback-based bistable element with delayed negative feedback. From a linearcircuits point of view, the idea is that of a negative feedback loop which is
unstable because of the infinite loop gain, which the positive-feedback element
can provide. From a more digital point of view, the idea is to derive a signal
from the output of the bistable which, fed back to the input, reverses the original
state.
A simple implementation of this idea is shown in Fig. 3
Figure 3 A Square-Wave Oscillator, or Astable Multivibrator
Here, the connections of the amplifier with R1, R2 form an noninverting bistable whose output and input signals are
of reversed polarity with input going high (or low) (beyond the corresponding threshold) causing tile output to go
low (or high), respectively. Components R3and C1 form a simple non-inverting delay\, whose output D follows its
input C after a delay related to the time constant R 3 C1. The combination is a circuit which reverses its state
periodically, forming a square-wave oscillator.
E2.1 A Square-Wave Oscillator
Assemble the circuit shown in Fig.3. To make the interpretation of your measurements somewhat easier, you may
find it useful to adjust the supply voltages so that the signal levels at node C are ±10 V.
• Connect your scope probes to nodes C and D, noting the relative voltage levels, time intervals and frequency.
• Now, observe nodes D and B in order to verify that the output state reverses when the capacitor voltage reaches
one of the bistable thresholds.
• Now, while observing nodes C and D, shunt C1 with a capacitor of equal value, noting the changes in time
intervals and frequency, but not of waveform.
• Now, with the additional capacitor removed, shunt R1 by a 10 kΩ resistor, noting changes in waveshape at node
D and the corresponding frequency.
Consider the ease with which a square wave can be generated using this idea. Note that when the bistable
switching threshold is made quite small, a reasonable triangle wave is also available at node D. A low-impedance
triangle wave of amplitude equal to that of the square wave can be created using a second op-amp connected as an
amplifying buffer with virtually the same values of R \ and R 2 as employed in the oscillator.
* E2.2 Other Pulse Waveforms
Return to the basic circuit shown in Fig. 3.
• Now, shunt node B with a diode to ground, noting the waveforms at nodes C and D.
• Now, reverse the diode connection and note the changes. Remove the diode.
• * Now, remove the connection of R1 (at node A) from ground, and join it to the top of a 10 kΩ potentiometer Rp
whose ends are connected to the ± supplies. Note the effect of varying the pot on the waveforms at C and D.
• ** Now, with a DVM to measure the dc voltage V node A, and an oscilloscope at node C to measure the widths
(at the zero-volt level) of the positive and negative output signals (T+ and T- respectively), take enough
measurements to characterize the relationships between voltage and pulse widths, duty cycle and frequency.
Consider the various flexibilities in pulse-width control which the circuit presents. What do you think will
happen if a series combination of a diode and a 1 kΩ resistor is used to shunt the resistor R3 ?
E4.0 A Multiple-Waveform Generator
The circuit shown in Fig.5 is a simplified version of a general-purpose laboratory instrument called a Function
Generator, or Waveform Generator. It follows the basic principle enunciated earlier in conjunction with Fig. 3: that of
a bistable connected in a negative-feedback loop with a delay element.
Figure 5 A Function Generator
Here A1 with R1,R2, R3, D1, D2, D3, D4 and Z, constitute a non-inverting bistable (Schmitt Trigger) circuit
having a shunt regulator at its output to ensure power-supply-voltage independence. The diode bridge (D1-D4) allows
a single zener diode, Z, to function as a shunt regulator for both positive and negative output voltages at node C.
Resistor R3 limits the zener-diode and amplifier-output currents. Amplifier A2 with R4 and C1, comprise an inverting
integrator which provides a delay in the signal fed back to the bistable input. The circuit consisting of R5, P1, P2 and
with diodes D5-D8 is a very basic 5-segment wave shaper with an approximate sine-wave output at node J.
E4.1 The Basic Square/Triangle-Wave Generator
Assemble (at least) the part of Fig. 5 that includes A1, A2 and the connection from node H to node A. Here Z is
a 6.8 V zener diode. Use ±15 V supplies.
• Now, display the signals at nodes C and H. Note the two waveforms, their peak values, and frequency f2
• Now, in turn, shunt R1, R4, C1 by components of equal value, and note the effects on signal amplitudes and
frequencies f3, f4, f5.
•
•
•
* With the circuit in its original form, display the waveform at node C with those at nodes G, H, B, D, E, F, in
turn, as the basis of a structured timing sketch.
* While displaying the waveforms at nodes C and H, short out zener Z intermittently, noting the changes in
amplitude and frequency.
** Now, while displaying nodes C and H, remove zener Z, observing the overall effect. Note that operation
depends on the relative saturation voltages of A1 and A2. Operation is guaranteed for R1 less than R2 by some
(small) amount. (Why?)
Consider the variety of waveforms available, and the means for their control.
IV REPORTING
.
R1.0 The Schmitt Trigger, a Bistable Multivibrator
R1.1 Non-Inverting Operation
• Table of R1, R2, vA, vB, vC, v+, v-, tr, tf, for R1 = 10 kΩ, R2= 100 kΩ initially, then individually halved, all for vA
= 3 Vpeak where v+, v-, are the thresholds at A.
• Sketches of waveforms and transfer characteristics for values of R1, R2.
R1.2 Inverting Operation
• Table of R1, vD, vC, vD+, vD-,
• Commentary.
R2.0 Generating a Square-Wave
R2.1 A Square-Wave Oscillator
• Table of R1, C1, vD, vB, vC, f, T+, T-, for C1, R1 each of 2 values.
• Waveform sketches, vD, vB.
R2.2 Other Pulse Waveforms
• Waveform sketches for diode connections, and VA = ±1V (say).
• Table of values of VA , T+, T-, T, T+/T, f where T=T++T- and f=l/T.
• Graph of T+, T-, f all versus VA.
• Conjecture.
R4.0 A Multiple-Waveform Generator
R4.1 The Basic Square/Triangle-Wave Generator
•
•
R1, R 4, C1, vC form C , vH , form H, f, for R1, R4, C1 of normal, and shunted values.
Table of Z , vC , vG , v H , v B , v D , v E , v F , f
•
Timing diagram.
Table of