RC Phase Shift Oscillator

RC Phase Shift Oscillator

AU : May-06, 11, 14, 16, 17, Dec.-ll, 12, 14, 16, 17, 18

• It consists of an amplifier and feedback network consisting of resistors and capacitors.

• An amplifier can be BJT, FET or operational amplifier.

 

1. Analysis of RC Circuit

The Fig. 10.5.1 (a) shows basic RC network. The output is taken across resistor R.

• The capacitive reactance X_C is given by X_C = 1 / 2πfC Ω where f is frequency of the input.

• The total impedance of the circuit is,

• The current I flowing in the circuit is, ViZ0° _ ViZ0°

• The equation (10.5.2) shows that current I leads input voltage by angle ϕ

• The output voltage is drop across R hence

V_o = V_R = I_R         ... (10.5.3)

• The output voltage is in phase with current hence it leads input voltage by angle ϕ

• Thus R-C circuit introduces a phase shift ϕ between input and output which depends on R, C and frequency f.

 

2. RC Feedback Network for Phase Shift

• In RC phase shift oscillator, amplifier introduces a phase shift of 180°.

• Thus the feedback network must introduce a phase shift of 180° to satisfy Barkhausen condition.

• The RC feedback network consists of three RC sections, with each RC section contributing 60° phase shift.

• Hence in RC phase shift oscillator, the feedback network consists of three RC sections, as shown in the Fig. 10.5.2.

• In all the three sections, resistance values and capacitance values are same so that at a particular frequency, each section produces precisely 60° phase shift. This is operating frequency of oscillator.

 

3. Transistorised RC Phase Shift Oscillator

• The Fig. 10.5.3 shows RC phase shift oscillator which uses BJT amplifier stage which is single stage amplifier in common emitter configuration.

• A phase shift network has three RC sections.

• The output of CE amplifier is connected as input to the RC phase shifting network.

• The output of RC phase shifting network is connected as input to the amplifier.

• Due to common emitter amplifier it introduces a phase shift of 180° between its input and output.

• The RC phase shift network contributes further 180° phase shift so that phase shift around a loop is 360°.

• From the Fig. 10.5.3, neglecting R1 and R2 we can write,

h_ie = Input impedance of the amplifier stage

• Thus to have all three resistance values in three RC sections equal, resistance in the last section is selected as R₃ so that R₃ + h_ie = R.

 

• When gain A of the amplifier stage and feedback factor β are adjusted to give |A β | = 1, then the circuit works as an oscillator, satisfying both the Barkhausen conditions.

 

4. Derivation of Frequency of Oscillations

• Replacing the transistor by its approximate h-parameter model, the equivalent circuit of RC phase shift oscillator is as shown in the Fig. 10.5.4

• It is known that R = h_ie + R₃ and replace current source by equivalent voltage source.

• The ratio of resistance R_C to R is k.

R_C / R = k

• The modified equivalent circuit is as shown in the Fig. 10.5.5.

• Applying KVL to the three loops,

 

5. Minimum Value of h_fe

For satisfying Aβ = 1, the expression for the value of h_fe of the transistor used in RC phase shift oscillator is given by,

Thus for the circuit to oscillate, the transistor must be selected with h_fe greater than 44.54.

 

Ex. 10.5.1 Find the capacitor C and /yg for the transistor to provide a resonating frequency of 10 kHz of a transistorised phase shift oscillator. Assume R₁ =25 kΩ, R₂ =57kΩ R_C = 20Ω, R = 7.1kΩ  and h_ie = 1.8kΩ

Sol. :

 

6. Advantages of RC Phase Shift Oscillator

• The advantages of R-C phase shift oscillator are,

1. The circuit is simple to design.

2. Can produce output over audio frequency range.

3. Produces sinusoidal output waveform.

4. It is a fixed frequency oscillator.

 

7. Disadvantages of RC Phase Shift Oscillator

1. To vary the frequency, values of R and C of all three sections are to be varied simultaneously which is practically difficult. Hence frequency can not be varied.

2. Frequency stability is poor due to changes in the values of various components due to effect of temperature, aging etc.

 

Ex. 10.5.2 Design a RC phase shift oscillator to generate 5 kHz sine wave with 20 V peak to peak amplitude. Draw the designed circuit. Assume h_fe = 150.

Sol. : For RC phase shift oscillator,

• Neglecting effect of biasing resistances assuming them to be large and selecting transistor with h_ie = 2 kΩ ,

R_i = 2 kΩ

Last resistance in phase shift network

R₃ = R - R_i = 12 - 2 = 10 kΩ

• Using the back to back connected zener diodes of 9.3 V (V_z) each at the output of emitter follower and using this at the output of the oscillator, the output amplitude can be controlled to 10 V i.e. 20 V peak to peak. The zener diode 9.3 V and forward biased diode of 0.7 V gives total 10 V.

• The designed circuit is as shown in the Fig. 10.5.6.

 

Ex. 10.5.3 In an RC phase shift oscillator, if R₁ = R₂ =R₃ =200kΩ and C₁ =C₂ = C₃ =100 pF. Find the frequency of the oscillator.

Sol. : R = 200 kΩ, C = 100 pF

 

Ex. 10.5.4 Design a RC phase shift oscillator to generate 5 kHz sine wave with 20 V peak to peak amplitude. Assume h_fe = β = 150, C = 1.5 nF, h_ie = 1.2 kΩ.

Sol. : Refer Ex. 10.5.2 for the procedure and verify the values as :

R = 8.06 kΩ , RC = 1.86 kΩ, R3 = 6.86 kΩ.

Review Questions

1. With a neat diagram, explain the construction and working of BJT RC phase shift oscillator.

AU : Dec.-ll, 12, 14, 18, May-16, 17. Marks 8

2. Find C and h_fe of a transistor to provide a resonating frequency of 10 kHz of a transistor phase shift oscillator. R₁ = 24 kΩ, R₂ = b8 kΩ, R_C = 18 kΩ, R = 6.8 kΩ = and h_ie = 2 kΩ.

(Ans.: 575 pF ≥  44.543)

3. State the advantages and disadvantages of RC phase shift oscillator.

4. Derive the expression for the frequency of oscillations of RC phase shift oscillator. Hence obtain the expression of amplifier gain required for the oscillations.

AU : May-14, 16, Marks 8

5. Design an oscillator to operate at a frequency of 10 kHz which gives an extremely pure sine wave output, good frequency stability and highly stabilized amplitude. Discuss the operation of this oscillator as an audio signal generators.

AU : May-17, Marks 15

6. Explain the working of a phase shift oscillator. Discuss its advantages and disadvantages.

AU : Dec.-17, Marks 8

7. Explain the working of phase shift oscillator.