Wien Bridge.

COLLEGE OF ENGINEERING AND TECHNOLOGY. SCHOOL OF ELECTRICAL AND ELECTRONICS ENGINEERING

UNIT NAME:

UNIT CODE:

TITLE:

ANALOGUE ELECTRONICS III

EEE 2302

WIEN - BRIDGE OSCILLATOR.

NAME: REG NO. 1. 2. 3. 4. 5. 6. 7. 8.

MWALE OSCAR LITEMBEKHO EN271-0571/2009 MICHAEL HENRY ODUOR EN271-0575/2009 OTIENO JOHN OUKO EN271-0577/2009 GIDEON MUASYA EN271-2179/2010 MOMANYI GEORGE KIMANGA EN271-0565/2009 CHESOLI DAVIS WANYAMA EN271-3408/2011 TONYA COLVIN NYAKUNDI EN271-0581/2009 OMBATI DEBORAH KEMUNTO EN271-0576/2009

LECTURER:

MR. OMBATI

DATE DUE:

10 TH AUGUST,2012.

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Contents OBJECTIVE OF THE EXPERIMENT...............................................................................2 EQUIPMENT......................................................................................................................2 1. THEORY.....................................................................................................................2 2. CIRCUIT DIAGRAM.................................................................................................3 3. PROCEDURE..............................................................................................................4 4. RESULTS....................................................................................................................4 4.1. Clipping.................................................................................................................5 4.2. Sample output waveforms obtained......................................................................5 5. DISCUSSION..............................................................................................................6 6. CONCLUSION............................................................................................................9 7. REFERENCE..............................................................................................................9

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OBJECTIVE OF THE EXPERIMENT To study, investigate and understand the operation of the Wein Bridge oscillator.

EQUIPMENT        

Resistors, 10K (3) Capacitors, 16nF (2) Rheostat, 50K (40%) IN4148 diodes (2) U741 Op-amp Signal generator CRO oscilloscope Connecting wires

1.THEORY A Wien bridge oscillator is the most commonly used type of oscillator because it gives better oscillations than RC phase shift oscillators. It can output a large range of frequencies. The basic Wien bridge oscillator comprises four resistors and two capacitors and it is known for its low distortion. The key to a low distortion oscillator is effective amplitude stabilization. The amplitude of electronic oscillators tends to increase until clipping or other gain limitation is reached. This leads to high harmonic distortion, which is often undesirable. A common way of stabilizing the amplitude is by using non-linear elements, such as diodes, to modify the resistance of the negative feedback network. As with other oscillators, the condition Avβ = 1 is required for oscillations to be initiated. For the oscillations to be sustained, then there must be positive feedback. Combining the two conditions gives the absolute condition for oscillations to be initiated and sustained at constant amplitude. Avβ = 1 0 ‫ﮮ‬° → Barkhausen condition.

However the practical condition is Avβ ≥ 1 0 ‫ﮮ‬° and an allowance of 5% is given. The frequency of oscillation is given by: JKUAT IS ISO 9001:2008 CERTIFIED

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In Wein bridge oscillator, Wein bridge circuit is connected between the amplifier input terminals and output terminals. The bridge has a series RC network in one arm and parallel network in the adjoining arm. In the remaining 2 arms of the bridge resistors R1and Rf are connected. To maintain oscillations total phase shift around the circuit must be zero and loop gain unity. First condition occurs only when the bridge is balanced. Assuming that the resistors and capacitors are equal in value, the resonant frequency of balanced bridge is given by FO = 0.159 RC

This circuit produces an extremely low distortion sine-wave, in spite of the non-linear devices used for amplitude limiting (D1 and D2). The reason is first that distortion (harmonics) are fed to the minus input of the op-amp with far less loss than to the plus input, severely attenuating them. Second, a Wien Bridge oscillator requires a gain of exactly 3.00: No more and no less. For lowest distortion, calculate the minimum and maximum available gain to just above and just below 3.00. In other words, use as little amplitude control as possible.

2.CIRCUIT DIAGRAM

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Fig.1: Circuit diagram for the Wien Bridge oscillator.

3.PROCEDURE 1. The circuit was connected as shown above, then the theoretical frequency of oscillation was calculated and then the experimental oscillation frequency was determined from the oscilloscope and compared with the theoretical one. 2. Simultaneously, both Vf and Vo were displayed on the dual slope oscilloscope and their peak-to-peak voltages were measured and their ratios were taken. The ratio was then compared with the theoretical value. 3. The waveforms of voltages Vo, Vx and Vf were displayed on the oscilloscope and their amplitude and phases were compared. 4. The variable resistor R1 was varied and the changes in the behavior of the output signal were observed. 5. The two diodes were disconnected from the circuit and variable resistor R1 was varied and the behavior of the output signal was observed and compared with the behavior when the diodes were connected. 6. R4 was exchanged with a variable resistor and varied then the changes in the signal generated were observed.

4.RESULTS Theoretical frequency of oscillation =

=1591.55HZ

Practical frequency of oscillation= 1430.5 HZ Vf(p-p) = 1.1 V, Vo(p-p) = 2.8 V VX = 1.9V Increase in R1 increases output amplification till clipping occurs. R R

=10k+RL=10+34=44k 1 clipping=10+37.5=47.5k 1 oscillation

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4.1. Clipping V o=18.5v V f = 6v Vx=10.8v After disconnecting diode clipping was 34.4k+RL+10K=78.4K Crossover distortion was observed.

4.2. Sample output waveforms obtained

Fig.2: The sample output waveform obtained upon connecting the circuit.

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Fig.3: Simultaneously displaying both Vf and VO on the dual oscilloscope

Fig.4: Simultaneously displaying the waveforms for VO, VX and Vf. Vf was displayed as a distorted sine wave

5.DISCUSSION AND ANSWERS TO QUESTIONS.

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A. Connect the circuit and confirm that the circuit oscillates. Compare the theoretical and experimental oscillation frequency. How do they compare? Explain the differences.

The theoretical frequency of oscillation was calculated as follows:

R1 = R2 = R = 10kΩ C1 = C2 = C = 10nF f = 1/ (2Ω x 10x103 x 10x 10-9) = 1.59 kHz The experimental oscillation frequency from the oscilloscope was; T = 0.7 ms F = 1/T = 1/0.7 x 10-3 = 1.43 kHz The values of the theoretical and the experimental frequencies were almost equal but the theoretical frequency of oscillation was slightly higher than the experimental frequency due to;  The tolerance of the resistors was not taken into consideration.  Parallax error in reading the accurate values from the oscilloscope.

B. Simultaneously display both Vf and VO on the dual oscilloscope. Measure the peak to peak voltage of the two voltages and take their ratio. Compare this ratio with the theoretical value. Explain any difference in the two values.

The measured peak-to-peak voltages (Vf and VO) were;

Vf(pp) = 1.1 V, Vo(pp) = 2.8 V Therefore measured ratio β = Vf(pp)/ VO(pp) = 1.1/2.8 = 0.39 The theoretical voltage ratio (β) is given by; β = Vf/ Vo = Z2/ (Z1+Z2)

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Equating j terms to zero, we have; β = ωoCR / 3ωoCR = 1/3 = 0.33333 The calculated value of β was slightly lower than the measured value due to;  The tolerance of the resistors was not taken into consideration,  Errors in reading the oscilloscope measurements.

C. Display the waveforms VO, VX and Vf. Compare the three waveforms (in terms of amplitude, phase, and e.t.c). Explain any difference in the three waveforms.

The amplitude of the output voltages Vo, Vf and Vx as measured from the oscilloscope were; a) Vo = Vx = 2.8V b) Vf = 1.1V

All the three voltages were in phase. Vo and Vx were both displayed in a square wave form but Vf was displayed as a distorted sine wave. This is because the wave forms of Vo and Vx were affected by the op-amp parameters while Vf was measured across the parallel RC circuit. D. Vary R1and observe any changes in the behavior of the output signal. Explain the changes observed when R1 is varied. Also explain how and why this method of varying R1 can be used to generate a square wave.

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As R1 is varied, the frequency of the output signal decreases with increase in resistance but the amplitude remains the same and vice versa. This is because varying R1 changes the operating frequency of the op-amp. In order to generate a square wave, the value of R 1 was increased.

E. Disconnect the two diodes, vary R1 and observe the behavior of

the output signal. Compare the same behavior when R1 is varied with the diodes in circuit and with the diodes disconnected. From the two behaviors, suggest the function of diodes D1 and D2.

With the diodes in the circuit the amplitude of the output signal was stable but when the diodes were disconnected, the amplitude of the output signal was unstable. Therefore the function of the two diodes is to stabilize the amplitude of the output signal by modifying the resistance of the negative feedback network.

F. Exchange R4 with a variable resistor. Vary R4 and observe any change in the signal generated. Comment on any change observed.

As R4 was varied, the output voltage Vo reduces with increase in R4, and vice versa and since gain (Av) = Vo/Vf, therefore a change in R4 affects the gain.

6.ERROR AND ARROR ANAYLYSIS This value is close to the experimental frequency which is 1550Hz. This difference in value can be attributed to the low sensitivity of the cathode ray oscilloscope. The time scale does not allow for very accurate readings and hence estimation has to be made. Errors in the experiment could be attributed to: 1. Reading errors of measuring instruments. 2. Resistor tolerances. 3. Loose terminal connections, thus increasing the effective resistance. 4. Noise in the d.c power supply.

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7.CONCLUSION The experiment was conducted successfully and the operation of the Wien Bridge oscillator was investigated and compared with the expected theoretical operation. The objective of the experiment was thus met. There were some deviations from the expected theoretical values expected due to error as above mentioned.

8.REFERENCE 1. Advanced techniques in power amplifier design by Steve .C. Cripps – 2002 Artech House INC. 2. Analog and digital circuits for electronic control systems applications by Jerry Luecke – Newnes, pages 69 – 71. 3. Electrical Technology by A. K. Theraja 4. Analogue Electronics 3 Lecturer’s Notes.

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