ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
CHAPTER 6
Generators
INTRODUCTION
In this chapter we shall briefly discuss the application of op-amps to generate various kinds of simple
waveforms. However, it should be kept in mind that there now are several integrated circuits that will
perform the same function.
OBJECTIVES
At the completion of this chapter, you will be able to do the following:
•
Design and build op-amp circuits to generate:
o
o
o
o
sine and cosine waves
triangle waves
square waves
staircase waves
SINE WAVES
The sine-wave oscillator, shown in Fig. 6-1, is called a Wienbridge oscillator. The resistor-capacitor
combinations R1-C1 and R2-C2 provide a positive feedback path around the op-amp, while resistor R3 and
the lamp L1 provide negative feedback. It is the application of positive feedback that causes the circuit to
oscillate with a sine-wave output. The frequency of oscillation is given by:
Fo=
1
2πR1C1
(Eq. 6-1)
R1=R2
C1=C2
The lamp helps to regulate the amount of negative feedback, stabilizing the amplitude of the sinewave output. Resistors R3 and R4 are used to account for lamp tolerances, so that this series combination
approximately equals 750 Ohm. The value for R1 depends on the type of op-amp used, which is
summarized below in Table 6-1.
Where
Fig. 6-1. Wienbridge sine-wave oscillator.
Table 6-1. Value of R1 and Operating Frequency for Various Op-Amps
R1
OP-AMP
108,1556,8007
> 1 MOhm
118,107,741
< 1 MOhm
fo
OP-AMP
> 1KHZ
118,1556,8007
< 1KHZ
107,108,741,1556,8007
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ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
Another commonly used sine-wave oscillator is the twin-T, or double-integrator oscillator, shown in Fig. 62 The frequency of oscillation for this circuit is given by:
Fo=
1
2πRC
(Eq. 6-2)
and the variable resistor R/ 2 is adjusted so that the circuit oscillates. To assure that this circuit starts
immediately when the power is applied, R2 is twice R, and R1 is made approximately 10 times R2.
Fig. 6-2. Twin-T sine-wave oscillator.
Example
Design a 500-Hz sine-wave oscillator, using the circuit of Fig. 6-2. For example, letting
C = .047 uF, then from Equation 6-2,
Ro=
1
2πfC
= 6775 Ohms(use 6.8K)
Capacitor 2C is then two .047-uF capacitors connected in parallel. Since resistor R/2 is approximately 3.4kOhm, we can use a 5-kOhm potentiometer. To complete the design, resistor R2 is twice R, or 13.6 kOhm,
so that two 6.8-kOhm resistors connected in series are used. In addition, resistor R1 is made approximately
10 times R2, or 136 kOhm, for which a 130-kOhm resistor can be used. The completed design of the twin-T
oscillator is shown in Fig. 6-3.
SINE/COSINE OSCILLATOR
If we integrate or differentiate a sine wave, as was discussed in Chapter 3, we can generate a cosine wave
(i.e., a sine wave that is 90o out-of-phase). However, if we use a dual op-amp, such as a 747 or 5558 with
both sections connected as integrators as shown in Fig. 6-4, we are then able to generate simultaneous sine
and cosine outputs. Such a circuit is also called a quadrature oscillator.
The output frequency is given by:
fo=
1
2πRC
(Eq.6-3)
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ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
Fig. 6-3. A 500-Hz sine-wave oscillator circuit.
Resistor R1 is made slightly less than R to make sure that the oscillator starts immediately when the power
is applied. Usually there is a form of limiting circuitry, as shown in the partial schematic of Fig.6-5, applied
to the second op-amp A2 to control the amplitude of the cosine output at the zener voltage, ±VZ . Table 6-2
lists the common types of zener diodes and their voltages.
Table 6-2. Common Zener Diodes and Voltages
Zener Diode
Vz
1 N746
3.3V
1N751
5.1
1 N4734
5.6
1 N4735
6.2
1N4736
6.8
1 N5236
7.5
1N4738
8.2
1N757
9.0
1N4742
12.0
SQUARE AND TRIANGLE GENERATORS
The basic square-wave generator, shown in Fig. 6-6, is also called a relaxation oscillator, as the circuit
oscillates without an external
Fig. 6-4. Sine/cosine (quadrature) oscillator.
Fig. 6-5. Zener diode limiting.
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ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
Fig. 6-6. Square-wave generator.
signal. The output is fed back to both inputs, so that the output frequency is set by the charging and
discharging of capacitor C through R, so that:
fo ≈
1
2R
2 RC ln( 1 + 1)
R2
(Eq. 6-4)
Resistors R1 and R2 are chosen so that R1 is approximately 1/3 R and R2 is 2 to 10 times R1.
Another oscillator that produces square waves along with simultaneous triangular waves is shown in Fig. 67. Op-amp A2 is wired as an integrator while A1 is essentially wired as a comparator whose reference
voltage is zero.
Fig. 6-7. Square/triangle wave generator.
The output amplitude of the square wave is set by the output swing of A1, and the ratio R1/R2 sets the
triangle’s amplitude. For both waveforms, the frequency of oscillation is given by:
fo =
1  R2

4 RC  R1



(Eq. 6-5)
With the advancement of solid-state technology, it is now common to design waveform generators with
integrated circuits manufactured for this purpose. There are two chips that generate variable frequency sine,
square, and triangle waveforms.
Another popular chip is the 555 timer, which is capable of generating variable frequency square waves with
adjustable duty cycles. In addition, triangular and sine waves are also possible with some external circuitry,
as outlined in:
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ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
THE STAIRCASE GENERATOR
In Fig. 6-8, we have the circuit for a linear staircase generator. An input square wave, having a peak-topeak voltage V1, charges capacitor C1, with a charge equal to:
Q=CV.
(Eq. 6-6)
= C1(V1 —0.7)
When the switch across C2 is open, capacitor C2 is charged by each input cycle in equal voltage steps ∆V0
so that:
∆Vo =
(V1 — 1.4) C1/C2
(Eq. 6-7)
In the limit, the maximum height of the staircase, which goes negative because of the input signal being
applied to the op-amp’s inverting input, is determined by the supply voltage.
Fig. 6-8. Staircase generator.
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ELT 215 Operational Amplifiers (LECTURE)
Chapter 6
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