Oscillators produce a continuous output waveform using only a DC input voltage. There are several types of oscillators that produce either sinusoidal or non-sinusoidal outputs depending on the circuit design. Oscillators require positive feedback and conditions where the feedback gain is at least unity and the total phase shift around the feedback loop is zero degrees in order to sustain oscillations. Common oscillator circuits discussed in the document include RC oscillators, crystal oscillators, and LC oscillators such as the Colpitts and Hartley oscillators.

1. OSCILLATORS
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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.
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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.
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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.
Cppm/
T
o
oo d
d
ωω
ω
ω =






⋅
1
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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
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6. Conditions for
• 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
Oscillation
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7. •Three types of RC oscillators that
produce sinusoidal outputs will be
discussed :
1. Wienbridge oscillator
2. phase-shift oscillator
3. 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 frequenciesA Azhagu Jaisudhan RIT ECE

8. The Colpitts Oscillator
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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 :
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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.
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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
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12. Phase Shift Oscillator
Example
i. Determine the value of Rf necessary for the circuit above to
operate as an oscillator
ii. Determine the frequency of oscillation
Given:
C1=C2=C3= 0.001 uF
R1=R2=R3= 10 kΩ
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13. Phase Shift Oscillator
Solution
i. Acl = 29, B = 1/29 = R3/Rf, therefore :
ii. C1=C2=C3 and R1=R2=R3. Ttherefore :
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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.
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15. Wien-Bridge Oscillator
• Fundamental part : Lead-Lag circuit
Lag circuit : R1 & C1 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
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16. Wien-Bridge Oscillator (con’t..)
Positive feedback condition for
Oscillation
• To produce a sustained sinusoidal output (oscillate):
1. Phase shift around the positive feedback
loop must be 0o
2. 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
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17. Wien-Bridge Oscillator (con’t..)
Resonant Frequency :
At Resonant Frequency : R1 = R2 and XC1 = XC2
:
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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
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19. • where
•
22
22
'
p
s
C
j
jX
ωω
ωω
ω −
−
−=
( ) )/1/1(/1/1 '22
CCLLC ps +== ωω
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