1. Part B-5
OSCILLATORS: Condition for oscillations. RC-phase oscillator with transistor and FET, Hartley and colpitts oscillators, Wien bridge oscillator, Crystal oscillators, Frequency and amplitude stability of oscillators.

2. The oscillators
Oscillator is a circuit that produce a continuous signal/waveform on its output with only the dc supply voltage as an input.
The output voltage can be either sinusoidal or non sinusoidal depending on the type of oscillator.

3. Instabilities, Oscillations and Oscillators
If positive feedback is applied to an amplifier, the feedback signal is in phase with the input, a regenerative situation exists.
If the magnitude of the feedback is large enough, an unstable circuit is obtained.
To achieve the oscillator circuit function, we must ensure an unstable situation. In addition we need to develop the oscillatory power at a desired frequency, with a given amplitude and with excellent constancy of envelope amplitude and frequency.
The design of good oscillators can be quite demanding because the governing equations of an oscillator are nonlinear, differential equations. Consequently oscillator analysis and design are not as advanced as that for linear circuits.
Typical oscillator analysis involves reasonably simple approximate analyses of linearized or piecewise-linear-circuit models of the oscillator together with perturbations and power series techniques.
There are a few oscillator circuits that can be solved exactly.

4. Frequency Stability
The frequency stability of an oscillator is defined as
Use high stability capacitors, e.g. silver mica, polystyrene, or Teflon capacitors and low temperature coefficient inductors for high stable oscillators.

5. Amplitude Stability
In order to start the oscillation, the loop gain is usually slightly greater than unity.
LC oscillators in general do not require amplitude stabilization circuits because of the selectivity of the LC circuits.
In RC oscillators, some non-linear devices, e.g. NTC/PTC resistors, FET or zener diodes can be used to stabilized the amplitude

6. Conditions for Start-Up Conditions
Oscillation
Phase shift around the feedback loop must be 0o
Voltage gain, Acl, around the closed feedback loop (loop gain) must equal 1 (unity) – The voltage gain around the closed feedback loop (Acl) is the product of amplifier gain (Av) and the attenuation (B) of the feedback circuit
Acl = Av B
Start-Up Conditions
For oscillation to begin, Acl around the positive feedback loop must be greater than 1 so that the output voltage can build up to a desired level.
Then Acl decrease to 1 and maintains the desired magnitude

7. Three types of RC oscillators that produce sinusoidal outputs will be discussed :
Wienbridge oscillator
phase-shift oscillator
twin-T oscillator.
Generally RC oscillators are used for frequencies up to about 1 MHz
Wienbridge oscillator is most widely used for this range of frequencies

8. The Colpitts Oscillator

9. The Colpitts Oscillator
Uses an LC circuit in the feedback loop :
To provide necessary phase shift
To act as a resonant filter that passes only the desired frequency
Approximate frequency of oscillation :

10. The Colpitts Oscillator
The input impedance of transistor amplifier acts as a load on the resonant feedback circuit and reduce the quality factor, Q of the circuit
When Q > 10, frequency =
If Q < 10, fr is reduced significantly
FET can be used in place of BJT to minimize the loading effect of the transistor’s input impedance.
When connected to external load, fr may decrease because of a the reduction in Q.

11. The Hartley Oscillator
The Hartley oscillator is similar to the Clapp and Colpitts. The tank circuit has two inductors and one capacitor. The calculation of the resonant frequency is the same.
For Q > 10 :
Attenuation, B :
Loading of the tank circuit same as in Colpitts: Q is decreased and thus fr decrease

12. Phase Shift Oscillator
Example
Given:
C1=C2=C3= uF
R1=R2=R3= 10 kΩ
i. Determine the value of Rf necessary for the circuit above to operate as an oscillator
ii. Determine the frequency of oscillation

13. Phase Shift Oscillator
Solution
i. Acl = 29, B = 1/29 = R3/Rf, therefore :
ii. C1=C2=C3 and R1=R2=R3. Ttherefore :

14. Phase Shift Oscillator
The phase shift oscillator utilizes three RC circuits to provide 180º phase shift that when coupled with the 180º of the op-amp itself provides the necessary feedback to sustain oscillations.
The gain must be at least 29 to maintain the oscillations.
The frequency of resonance for the this type is similar to any RC circuit oscillator.

15. Lag circuit : R1 & C1 Lead circuit : R2 & C2
Wien-Bridge Oscillator
Fundamental part : Lead-Lag circuit
Lag circuit : R1 & C Lead circuit : R2 & C2
At resonant frequency, fr, phase shift through the circuit is 0o and the attenuation is 1/3
Below fr the lead circuit dominates and the output leads the input
Above fr, the lag circuit dominates and output lags the input

16. Wien-Bridge Oscillator (con’t..)
Positive feedback condition for Oscillation
To produce a sustained sinusoidal output (oscillate):
Phase shift around the positive feedback loop must be 0o
Gain around the loop must be at least unity (1)
0o phase-shift condition - met when the frequency is fr because the phase shift through the lead-lag circuit is 0o & no inversion from non inverting (+) input of the op-amp to the output

17. Wien-Bridge Oscillator (con’t..)
Resonant Frequency :
At Resonant Frequency : R1 = R2 and XC1 = XC2 :

18. Crystal Oscillators
If a piezoelectric crystal, usually quartz, has electrodes plated on opposite faces and a potential is applied between these electrodes, forces will be exerted on the bound charges within the crystal. If this device is properly mounted, deformations takes place within the crystal, and an electromechanical system is formed which will vibrate when properly excited. Frequencies ranging from a few kHz to a few hundred MHz. Q values range from several thousand to several hundred thousand. The equivalent circuit of a crystal is shown below L,C and R are analogs of mass, compliance (reciprocal of spring constant) and viscous-damping factor of the mechanical system. If we neglect R the impedance of the crystal is

19. where