ECE - 342 : EXPERIMENT VII Week 15 (5/01/07)
SINUSOIDAL OSCILLATORS
Purpose:
To investigate the conditions for oscillation, frequency of oscillation for a phase-shift and Wein bridge oscillators, and to investigate the rule of build up for the latter.
Parts:
1 - LM741 Op-Amp
Figure 1
Theory:
1. Introduction - If a linear feedback amplifier contains reactive elements, and at some frequency the loop gain Ab = -1, sinusoidal oscillations will be obtained. The sine wave oscillators investigated in this experiment consist essentially of two separate but connected parts; the amplifier part and the frequency determining part. Probably the simplest type of feedback oscillator is shown in figure 1. Here the amplifier function is the ratio, V2 / V1 = - R2 / R and through the phase shift circuit, the ratio V1/V2 is a function of frequency. In other words the amplifier yields a phase inversion of 180° and a 180-degree phase-shift-circuit is used to produce a zero loop phase shift.
Figure 2
An analysis of the phase shift circuit, figure 2, shown that when V1 is exactly out of phase with V2
(1) and occurs at a frequency of 
(2)
Figure 3
An oscillator circuit in which a balanced bridge is used as the feedback network is the Wien-bridge oscillator shown in figure 3. The "bridge" is clearly indicated in figure 4.
Figure 4
The four arms of the bridge are Z1, Z2, R3 and R4. The input to the bridge is the output Vo of the op. amp., and the output of the bridge between nodes 1 and 2 supplies the differential input to the op. amp. There are two feedback paths in figure 3, positive feedback through Z1 and Z2, whose components determine the frequency of oscillation, and negative feedback through R3 and R4, whose elements effects the amplitude of oscillation. The loop gain is given by -b A where:
(3)
It can be found that, with a = w RC
(4)
The Barkhausen condition that Ab = -1 requires that a = 1 and
(5)
The maximum frequency of oscillation is limited by the slew rate of the amplifier. Continuous variation of frequency is accomplished by varying simultaneously the two capacitors. Changes in frequency range are accomplished by switching in different values for the two identical resistors R1 and R2.
2. Preliminary Questions
a. Verify equations (1) and (2)
b. Verify equations (3), (4), and (5)
c. Calculate the value of R4 in figure 3, which will just produce oscillation.
Procedure:
1. Phase-shift oscillator.
a. Set up the phase-shift oscillator and adjust R4 for the best output wave-form (sinusoid). Record the value of R4.
b. Observe the waveform of the signal at all nodes of the phase shift circuit.
c. Using the signal generator, determine the frequency for which the phase-shift of the phase-shift network is p radians. Record the ratio of Vin/Vout.
2. Wein-Bridge Oscillator
a. Condition For Oscillation: With an ohmmeter, adjust the potentiometer of R4 to the calculated value in preliminary question 3, and turn the circuit on. Vary the potentiometer setting and note the effect on the oscillation waveform. At what setting of R4 does the output appear most sinusoidal? What R4 just sustains oscillation. Check with an ohmmeter and compare with your calculated value.
Figure 5b. Rate Of Build Up Of Oscillation: Modify the circuit as shown in figure 5. The transistor Q1 acts as a switch and stops the oscillation when the square wave generator output is positive. When the generator output goes negative, oscillation begins to build up. The scope is also triggered at this point. So the build up can be observed. Vary the time base until the build is visible on the screen.
What is the effect of R4 on build up rate? If a rise time is defined as the time required for the output to reach ±10 volts in magnitude, determine the rise time for R4 = 2, 2.5k, 3k, 3.5k, 4k, 4.5k, 5k, and ¥ (open circuit). Compare these values with the theoretical time constant of build up. The two values should be proportional.
c. Steady State Oscillation: Return the circuit to the original configuration; and observe the oscillator output. Vary R4 and note the effect. Open R4 and observe the waveform. What is causing the change in waveform? What is the best value of R4 in terms of distortion?
TO HAND IN ON DAY OF LAB
Do a PSpice simulation of the circuit in Figure 2. Assume 0° phase for the input V2. Plot the phase at nodes 1, 2, 3, 4 and the magnitude of V1 as a function of frequency. Plot over a frequency interval of 10 Hz to 1 MHz.
