How Phase Shift Oscillator work ? find your answer from here

RC Phase shift oscillator

An oscillator is a circuit that produces an output without an input. More specifically it is a circuit that produces a signal at a desired frequency with the aid of a dc source.

An oscillator can be classified on the bases of output waveform, circuit elements used, and the range of frequency that it produces. An oscillator which uses RC network for producing oscillations are called as an RC oscillator. RC phase shift oscillator is a type of RC oscillator in which RC phase shift networks are employed for producing successful oscillations.

Circuit diagram:



Working :
The RC phase shift oscillators basically consist of an amplifier and feedback network. The feedback network consists of resistors and capacitors arranged in cascade to produce oscillations. For a circuit to act as an oscillator certain criteria's need to be satisfied. This criterion is called Barkhausen Criteria. According to this criteria an amplifier stage will act as an oscillator if

1) The signal feedback from the output to the input is in same phase with the actual input and

2) The factor AB =1, where A is the amplifier gain and B is the feedback factor

Most commonly used RC oscillator circuit is shown in the figure. The amplifier part is formed by the components R1, R2, Rc, Re, Q1 and Ce and the phase shift network consist of C and R combination

The components R1, R2, Rc, Re, Q1, and Ce form a common emitter inverting amplifier. In this circuit the BJT is given a voltage divider bias. The resistors R1 and R2 form the voltage divider network. Rc is used for providing collector bias and it act as the load the Re resistor provide thermal stabilization. The capacitor Ce is called the bypass capacitor as it is used to bypass frequency components produced at the emitter terminal to the ground. This capacitor have a great role in gain stability because if frequency components were allowed to pass through Re resistor then the drop in Re increases and this could result in negative feed backing and can reduce the gain of the amplifier.

When the vcc is provided any circuit imbalance could produce small base current and this will be amplified at the collector terminal with 180 degree phase shift. The collector terminal is connected with 3 phase shift networks (RC) which produce approximately 60 degree phase shift each and to their combined effect produces another 180 degree phase shift. The last resistor R is connected to the base of the amplifier. This act as the feedback path so the signal feedback from the phase shift stage is now (360 degree phase different or) in phase with the input hence the Barkhausen Criterion 1 is satisfied. The phase feedback network is designed to make the product AB=1 and hence both the criteria's were satisfied and the circuit act as an oscillator

From the derivations the frequency of an RC oscillator can be obtained as F=1/(2∏RC√ (6+4Rc/R)) and the hFE of the transistor required is given by hFE >= 23+29(Rc/R)+4(R/Rc) from this equation the minimum hFE required is 29

Design of a practical RC phase shift oscillator

Output requirement: Sine wave with 10Vpp and frequency 500Hz

Selection of BJT : Select transistor BC 107 as its minimum hFE is 100

Design of Rc and Re : Let the Vcc is chosen to be 20% more than the required output swing therefore Vcc=12v . Let this voltage be divided as follows 40% across Rc, 50% across BJT and 10% across Re therefore VRc=4.8V ,VRe=1.2V, VCE=6V , Ic =2mA(collector current from datasheet)
Rc=VRc/Ic =4.8V/2mA=2.4KΩ, use 2.2K standard
Re=VRe/Ie=VRe/Ic=1.2/2=600Ω, use 680Ω standard

Design of R1 and R2: Let the current through R1 be 10 Ib and current through R2 be 9 Ib this assumption is made in order to prevent loading of the voltage divider by the base current
Ib=Ic/hFE =2mA/100=20uA
VR2=VBE+VRe=.6+1.2=1.8V
VR1=Vcc-VR2=12-1.8=10.2V
R1=VR1/10 Ib=10.2V/(10*20uA)=51K , use 47k standard
R2=VR2/9 Ib=1.8V/(9*20uA)=10K ,use 10K standard

Design of Ce: Ce is the bypass capacitor let the lowest frequency that it bypass should be 100Hz
The impedance of the capacitor XCe<=Re/10 (standard rule) The resonant frequency of any RC network is given by F=1/ (2∏RC)
Here R=Re/10=68 ,F=100Hz
so from this C=Ce>=1/(2∏FRe) =1/(2∏*100*68)=23uF , use 22uF standard

Design of Phase shift network:
Since our required frequency of oscillation is 500Hz the phase shift network should provide 180 degree phase shift to this frequency.
From the frequency equation of the phase shift network F=1/(2∏RC√ (6+4Rc/R)) where F=500Hz , Take R =4.7K to limit collector current from this equation C can be found out
C=1/(2∏RF√ (6+4Rc/R))=1/(2∏4.7K*500Hz√ (6+4*2.2K/4.7K)) =0.024uF use 0.022uF standard

Practical circuit diagram:



Output waveform:



The output produced by the oscillator may not produce the designed amplitude.There is a chance for slight variations due to the standardised values of components. The output wave amplitude can be fine adjusted by using a 4.7K pot instead of 4.7K resistor in the last stage.

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