Lecture 3 Oscillator

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Lecture 3 Oscillator

• Introduction of Oscillator
• Linear Oscillator
• Wien Bridge Oscillator
• RC Phase-Shift Oscillator
• LC Oscillator
• Stability

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Oscillators

• Oscillation an effect that repeatedly and
  regularly fluctuates about the mean value
• Oscillator circuit that produces oscillation
• Characteristics wave-shape, frequency,
  amplitude, distortion, stability

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Application of Oscillators

• Oscillators are used to generate signals, e.g.
• Used as a local oscillator to transform the RF
  signals to IF signals in a receiver
• Used to generate RF carrier in a transmitter
• Used to generate clocks in digital systems
• Used as sweep circuits in TV sets and CRO.

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Linear Oscillators

• Wien Bridge Oscillators
• RC Phase-Shift Oscillators
• LC Oscillators
• Stability

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Integrant of Linear Oscillators
For sinusoidal input is connected Linear
because the output is approximately sinusoidal A
linear oscillator contains - a frequency
selection feedback network - an amplifier to
maintain the loop gain at unity
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Basic Linear Oscillator
and
If Vs 0, the only way that Vo can be nonzero
is that loop gain A?1 which implies that
(Barkhausen Criterion)
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Wien Bridge Oscillator
Frequency Selection Network
Let
and
Therefore, the feedback factor,
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? can be rewritten as
For Barkhausen Criterion, imaginary part 0,
i.e.,
Supposing, R1R2R and XC1 XC2XC,
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Example
By setting , we get Imaginary
part 0 and
Due to Barkhausen Criterion, Loop gain
Av?1 where Av Gain of the amplifier
Wien Bridge Oscillator
Therefore,
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RC Phase-Shift Oscillator

• Using an inverting amplifier
• The additional 180o phase shift is provided by an
  RC phase-shift network

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Applying KVL to the phase-shift network, we have
Solve for I3, we get
Or
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The output voltage,
Hence the transfer function of the phase-shift
network is given by,
For 180o phase shift, the imaginary part 0,
i.e.,
Note The ve sign mean the phase inversion from
the voltage
and,
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LC Oscillators

• The frequency selection network (Z1, Z2 and Z3)
  provides a phase shift of 180o
• The amplifier provides an addition shift of 180o
• Two well-known Oscillators
• Colpitts Oscillator
• Harley Oscillator

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For the equivalent circuit from the output
Therefore, the amplifier gain is obtained,
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The loop gain,
If the impedance are all pure reactances, i.e.,
The loop gain becomes,
The imaginary part 0 only when X1 X2 X30

• It indicates that at least one reactance must be
  ve (capacitor)
• X1 and X2 must be of same type and X3 must be of
  opposite type

With imaginary part 0,
For Unit Gain 180o Phase-shift,
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Hartley Oscillator
Colpitts Oscillator
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Colpitts Oscillator
Equivalent circuit

• In the equivalent circuit, it is assumed that
• Linear small signal model of transistor is used
• The transistor capacitances are neglected
• Input resistance of the transistor is large enough

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At node 1,
where,
Apply KCL at node 1, we have
For Oscillator V? must not be zero, therefore it
enforces,
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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.

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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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Wien-bridge oscillator with bulb stabilization
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Wien-bridge oscillator with diode stabilization
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Twin-T Oscillator
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Bistable Circuit
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A Square-wave Oscillator