Figure 1: Phase angle at various stage of RC network

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Dominic Anderson
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1 Name of The Expt: Construct a Phase-Shift Oscillator and Determine its of Oscillation. Objectives: After completing this experiment we will able to know- 1. How does an A.C. signal is produced by phase shift oscillator. 2. How a RC network does is used to phase shift. 3. Where can we use this circuit. 4. The designing procedure of a phase shift oscillator. Theory: Phase Shift Oscillator: An oscillator is a circuit, which generates ac output signal without giving any input ac signal. This circuit is usually applied for audio frequencies only. The basic requirement for an oscillator is positive feedback. The operation of the RC Phase Shift Oscillator can be explained as follows. The starting voltage is provided by noise, which is produced due to random motion of electrons in resistors used in the circuit. The noise voltage contains almost all the sinusoidal frequencies. This low amplitude noise voltage gets amplified and appears at the output terminals. The amplified noise drives the feedback network which is the phase shift network. Because of this the feedback voltage is maximum at a particular frequency, which in turn represents the frequency of oscillation. Furthermore, the phase shift required for positive feedback is correct at this frequency only. Phase shift oscillators are most commonly used in tremolo circuits in guitar amplifiers. They are used as the low-frequency oscillator (LFO) that generates the sinusoidal waveform which amplitude modulates the guitar signal to produce the characteristic tremolo amplitude variations. Rc Phase-Shift Network: Figure 1: Phase angle at various stage of RC network The circuit on the left shows a single resistor-capacitor network and whose output voltage "leads" the input voltage by some angle less than 90 o. An ideal RC circuit would produce a phase shift of exactly 90 o. The amount of actual phase shift in the circuit depends upon the values of the resistor and the capacitor, and the chosen frequency of oscillations with the phase angle ( Φ ) being given as:

2 Phase Angle In our simple example above, the values of R and C have been chosen so that at the required frequency the output voltage leads the input voltage by an angle of about 60 o. Then the phase angle between each successive RC section increases by another 60 o giving a phase difference between the input and output of 180 o (3 x 60 o ) as shown by the following vector diagram. Then by connecting together three such RC networks in series we can produce a total phase shift in the circuit of 180 o at the chosen frequency and this forms the bases of a "phase shift oscillator" otherwise known as a RC Oscillator circuit. We know that in an amplifier circuit either using a Bipolar Transistor or an Operational Amplifier, it will produce a phase-shift of 180 o between its input and output. If a RC phase-shift network is connected between this input and output of the amplifier, the total phase shift necessary for regenerative feedback will become 360 o, ie. the feedback is "in-phase". Then to achieve the required phase shift in an RC oscillator circuit is to use multiple RC phase-shifting networks such as the circuit below. Basic Rc Oscillator Circuit: Figure 2: Theoretical Circuit For Phase shift oscillator.

3 The RC Oscillator which is also called a Phase Shift Oscillator, produces a sine wave output signal using regenerative feedback from the resistor-capacitor combination. This regenerative feedback from the RC network is due to the ability of the capacitor to store an electric charge, (similar to the LC tank circuit). This resistor-capacitor feedback network can be connected as shown above to produce a leading phase shift (phase advance network) or interchanged to produce a lagging phase shift (phase retard network) the outcome is still the same as the sine wave oscillations only occur at the frequency at which the overall phase-shift is 360 o. By varying one or more of the resistors or capacitors in the phase-shift network, the frequency can be varied and generally this is done using a 3-ganged variable capacitor. If all the resistors, R and the capacitors, C in the phase shift network are equal in value, then the frequency of oscillations produced by the RC oscillator is given as: Where: ƒ is the Output in Hertz R is the Resistance in Ohms C is the Capacitance in Farads N is the number of RC stages. (in our example N = 3) Since the resistor-capacitor combination in the RC Oscillator circuit also acts as an attenuator producing an attenuation of -1/29th (Vo/Vi = β) per stage, the gain of the amplifier must be sufficient to overcome the losses and in our three mesh network above the amplifier gain must be greater than 29. The loading effect of the amplifier on the feedback network has an effect on the frequency of oscillations and can cause the oscillator frequency to be up to 25% higher than calculated. Then the feedback network should be driven from a high impedance output source and fed into a low impedance load such as a common emitter transistor amplifier but better still is to use an Operational Amplifier as it satisfies these conditions perfectly. Apparatus: 1. Transistor(C828) 2. Oscilloscope. 3. Power breadboard 4. Some Resistor(2.2,3.3,4.7,5.6,1.8,10,1,)KΩ 5. Capacitor (4.7n,23µ,10n)F 6. Trainer with bread board. 7. Connecting Wires. 8. Voltmeter Practical Circuit:

4 Figure 3: Practical Circuit For Phase shift oscillator(where+v=14v,r e =110Ω,C e =10nF) Procedure: a. Firstly we Cheek the transistor, power button of the trainer calibrate the oscilloscope. b. Then we arrange the all the components according to the practical circuit. c. Biasing voltage is fixed at 14V and we vary the variable resistor up to suitable signal appeared on the screen of the oscilloscope. d. Then we take readings at various stages by fixing capacitance and changing resistance and vice versa. e. These readings are taken at the following table-01 and table-02. Calculations: Here R 1 =R 2= R 3 =2.2KΩ & time period T mea =.34µs So Measured F mea =1/T mea = 2.94 KHz =1/ (2πRC ) KHz =1/ (2π ) = 2.93 KHz Error(%) = (- F mea )/ =.34% Table-01: For measuring the frequency of a oscillator sin phase shift arrangement when resistor is fixed. (R 1 =R 2 =R 3 =2.2KΩ No of Obs Capacitor C (F) Time period T mea µs =1/(2πRC ) F mea =1/T Error (%)= {(- F mea )/ } 01.01µ n n

5 Table-02: For measuring the frequency of a oscillator in phase shift arrangement when capacitor is fixed C=10nF. No. Of Obs. Resistor (R 1 =R 2 =R 3 =R) kω Time Period T mea µs =1/(2πRC ) F mea =1/T Error (%)= {(- F mea )/} Result & Discussion: From the above data table-01 we can observe that when resistance is fixed then there is maximum of 18.48% error is occurred. Again when capacitance is fixed then we can see that from data table-02 the maximum error is 7.75%. Its essential behavior is that it does not require transformers or inductors. It can be used to produce very low frequencies. This circuit provides good frequency stability. But in the arrangement is that the starting voltage is provided by noise, which is produced due to random motion of electrons in resistors used in the circuit. The noise voltage contains almost all the sinusoidal frequencies these may be not perfectly sinusoidal. These variations is also occurred due to following reasons Aging problem of the instruments Eye estimation. Di-electric loss in capacitor. Heating Problem. If these variations will be removed we will get error less phase shift oscillator. Precautions: a. We have to cheek all the connection as to practical circuit otherwise components may be destroyed. b. Supply voltage is fixed at not more than 15V.Connections is made rigidly. c. Connections are made rigidly. d. Calibrate the oscillator more accurately. e. Readings are taken attentively. Prepared by Sharat Chandra+Bhajan Saha Sess: Dept. of AECE. Islamic University,Kushtia, Bangladesh.

Figure 1: Closed Loop System

Figure 1: Closed Loop System SIGNAL GENERATORS 3. Introduction Signal sources have a variety of applications including checking stage gain, frequency response, and alignment in receivers and in a wide range of other electronics equipment.