INTRODUCTION
Oscillator is a circuit that produces a continuous signal or waveform on its output with only the dc supply voltage as an input. Depending on the type of oscillator, the output voltage can be either sinusoidal or non- sinusoidal.
Oscillators are often characterized by the freq of their output signal:
A low-freq oscillator (LFO) is an electronic oscillator that generating freq below 20 Hz. To distinguish it from an audio freq oscillator this term is used in the field of audio synthesizers
An audio oscillator produces frequencies , about 16 Hz to 20 kHz in the audio range.
An RF oscillator produces signals of frequencies of about 100 kHz to 100 GHz in the radio freq (RF) range..
There are three basic types of oscillators such as RC Oscillator, LC Oscillator and Crystal Oscillator.
1. RC Oscillators: Resistance-capacitance network os used to determine the oscillator freq. They are suitable for low (audio range) and moderate freq applications (5Hz to 1MHz).
2. LC Oscillators : Inductors and capacitors are used either in series or parallel to determine the freq. They are more suitable for radio freq(1 to 500 MHz) . They are further classified as:
Hartley
Colpitts
Clapp
Armstrong Oscillators
3. Crystal Oscillator : Like LC oscillators it is suitable for radio freq applications. Though it has accuracy and very high degree of stability as compared to other oscillators.
RC Oscillators can be further divided as:
RC PSO
Wien Bridge Oscillator
Twin-T Oscillator
RC Phase Shift Oscillator :
The basic RC Oscillator which is also known as a PSO, produces a sine wave output signal using regenerative feedback obtained 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. By varying one or moreof the resistors or capacitors in the phase-shift network, the freq can be varied.Generally this is done by keeping the resistors the same and 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 freq of oscillations produced by the RC oscillator is given as:
F = 1/(2πRC√2N)
Where:
ƒr is the Output Frequency in Hertz
R is the Resistance in Ohms
C is the Capacitance in Farads
N is the number of RC stages
The loading effect of the amplifier on the feedback network has an effect on the freq of oscillations and can cause the oscillator freq to be up to 25% higher than calculated. One of the most important features of an RC Oscillator is its freq stability which is its ability to provide a constant freq sine wave output under varying load conditions. By cascading three the stability of the oscillator can be greatly improved.
As the feedback is connected to the inverting input, the operational amplifier is therefore connected in its “inverting amplifier” configuration which produces the required 180o phase shift while the RC network produces the other 180o phase shift at the required freq (180o + 180o).
fig.1.1 Inverting Input
The phase shift represents the movement of the waves based on the amplitude and periods. The general graph of y = sin (t – c) is obtained by the operation of shifting the graph of y = sin t by horizontally with the c units. If c is considered as positive, the graph is shifted c units from right and if c is considered as the negative, the graph is shifted c units from left. The number c is called as the phase shift.
fig. 1.2 Phase Shift Graph
The sine function will complete one cycle when its argument varies from 0 to 2π. The function will start out when the argument is equal to 0.
By connecting together three such RC networks in series we can produce a total phase shift in the circuit of 180o at the chosen freq and this fors the bases of a “PSO” also known as a RC Oscillator circuit.
fig. 1.3 Vector Diagram
The gain of the amplifier must be sufficient to overcome the circuit losses. 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. Therefore, in our three stage RC network above the amplifier gain must be greater than 29.
fig. 1.4 Phase Shift and Gain
In an amplifier circuit either using a Bipolar Transistor or an Operational Amplifier, it will produce a phase-shift of 180o between its input and output. Op-Amp has been used here. If a three-stage RC phase-shift network is connected between this input and output of the amplifier, the total phase shift necessary for regenerative feedback will become 3 x 60o+ 180o = 360o.
Op-amp is a very high gain DC differential amplifier that uses one or more external feedback networks to control its response and characteristics. We can connect external resistors or capacitors to the op-amp in a number of different ways to form basic “Building Block” circuits such as, Inverting, Non-Inverting, Voltage Follower, Summing, Differential, Integrator and Differentiator type amplifiers.
A very large number of operational amplifier IC’s available to suit every possible application. Op-amps are available in IC packages of either single, dual or quad op-amps within one single device. The most commonly available and used of all operational amplifiers in basic electronic kits and projects is the industry standard μA-741.
fig.1.5 741 IC
PRINCIPLE
Op-Amp acts as an inverting amplifier. A PSO works on the principle that a fraction of the output single-stage amplifier is passed through a phase-shift network before feeding back to input.
fig. 2.1 Three-Stage Feedback Network
It not only amplifies the input signal but also shifts its phase by 180º. However, to produce oscillations, we must have positive feedback of sufficient amount.
Positive feedback occurs only when the fed back voltage is in phase with the original input signal. This condition can be achieved when we take a part of output and pass it through a phase shift network (feedback circuit) giving another phase-shift of 180° in addition to the phase-shift of 180° introduced by the amplifier. Thus, we get total phase shift of 180º + 180º = 360º ( which is equal to 0°) as signal passes through the amplifier and the phase shift network.
fig.2.2 Total Phase Shift
DESIGN
The resistance Rf of the inverting amplifier is designed by making current through it much larger than the input bias current of the op-amp. Good freq stability and waveform can be obtained from oscillators employing resistive and capacitive elements.
COMPONENT USED VALUE
Op-amp 741 IC
Capacitors 0.01µF
Resistors 1.2 KΏ , 1.2 KΩ , 1.2 KΩ
Potentiometer 47 KΩ
Table.1 Components Used
fig. 2.3 Circuit Diagram
Connections on Breadboard:
Connections on PCB:
OPERATION OF PSO
The RC PSOs 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, Barkhausen Criteria need to be satisfied.
According to this criteria, 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.
2) The factor AB =1, where A is the amplifier gain and B is the feedback factor.
When ac voltage is applied to such a network, the voltage across R leads the applied voltage by certain angle ɸ called phase angle. This angle depends on the values of R and C.
fig. 2.4
If R=0Ω then angle will be 90°.But making R=0 Ω is impractical because if R=0Ω then the voltage across it would also become zero.
Therefore R is adjusted such that ɸ becomes 60°.Adjusting R= Ω provides 60° phase shift to the RC feedback network. Total phase shift produced by whole network is 180°.
Calculations:
C = 0.01 µF R= 1.2 KΩ
Frequency of Oscillation (F):
F = 1/(2πRC√2N)
= 1/(2πRC√2×3)
= 1/(2 × 3.14 × 1.2×〖10〗^3 × 0.01×〖10〗^(-6) × √6)
= 1/(0.1845 × 〖10〗^(-3) )
= 〖10〗^3/0.1845
= 5.4 KHz
Percent Error in output freq
= ( Expected Value – Theoretical Value)/(Expected Value) ×100
= (5 – 5.4 )/5 ×100
= 8 %
Rf = R × 29
= 1.2 × 29
= 34.8 KΩ
Percent Error in Rf
= ( Expected Value – Theoretical Value)/(Expected Value)×100
= (47 – 34.8)/47 ×100
= 25 %
Observations:
Table.2 Observation Table
Parameter Theoretical Expected % Error
Output Freq 5.4 KHz 5 KHz 8 %
Rf 34.8 KΩ 47 KΩ 25 %
Result:
Theoretical output frequency = 5.4 KHz
Expected output frequency = 5 KHz
Theoretical Rf = 34.8 KΩ
Expected Rf = 47 KΩ
Output:
ADVANTAGES
It doesn't require transformers and inductors that's why it is less bulky.
It is cheap and simple circuit as it contains resistors and capacitors only.
It can produce output over wide freq range.
It can produce pure sinusoidal waveform since only one freq can fulfill the Barkhausen phase shift requirement.
DISADVANTAGES
The output is small due to smaller feedback.
It is difficult for the circuit to start oscillation.
The freq stability is not so good.
It requires high voltage for larger feedback.
PHASE SHIFT v/s WEIN-BRIDGE OSCILLATOR
PSO WEIN BRIDGE OSCILLATOR
This oscillator is used for low freq range since it is RC oscillator. This oscillator is also used for low freq range since both are RC oscillator.
Feedback network provide 180° phase shift. Feedback network do not provide any phase shift.
Op-amp is used in inverting mode. Op-amp is used in non-inverting mode.
Op-amp introduces 180° phase shift. Op-amp does not introduce 180° phase shift.
Amplifier gain |A| ≥29 Amplifier gain |A| ≥ 3
3RC section in feedback. 2RC section in feedback.
Difficult to adjust freq variation.
F = 1⁄(2πRC√6) Easy adjustment of freq by varying both capacitors.
F = 1⁄(2πRC√6)
fig.3.1(i) 3-RC Feedback Network
fig.3.2(ii) 2-RC Feedback Network
APPLICATIONS
RC PSOs are used for musical instruments, oscillators, voice
synthesis, and GPS units.
RC PSOs are mostly used at audio frequencies. Other than this, electronic organs makes use of this oscillator such as electronic musical instruments like pianos.
Also used in equipment that emits beeps. Example, many GPS units beeps when they performs an action.
Also used in voice synthesis.
APPENDIX
References
https://books.google.co.in/books?id=8fmUCgAAQBAJ&pg=PA232&dq=phase+shift+oscillator+consists&hl=en&sa=X&ved=0ahUKEwjrpbOE3NzNAhUDrI8KHerKAtk4FBDoAQgyMAI#v=onepage&q=phase%20shift%20oscillator%20consists&f=false
https://books.google.co.in/books?id=-zAe0P33BAcC&pg=SA9-PA50&dq=phase+shift+oscillator+operation&hl=en&sa=X&ved=0ahUKEwj_wen79zNAhUMrI8KHc8_AHQQ6AEITjAE#v=onepage&q=phase%20shift%20oscillator%20operation&f=false
https://books.google.co.in/books?id=lc1d_aghlFYC&pg=PR6&dq=phase+shift+oscillator+operation&hl=en&sa=X&ved=0ahUKEwiNmKXJj97NAhVJImMKHRTqB804ChDoAQg9MAI#v=onepage&q=phase%20shift%20oscillator%20operation&f=false
http://www.electronics-tutorials.ws/oscillator/rc_oscillator.html
http://wikieducator.org/Sinusoidal_Oscillator