Lecture 37 Feedback, stability and oscillation

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Lecture 37Feedback, stability and oscillation

• Amit Kumar Mishra
• ECE, IIT G

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Barkhausens Criteria for Oscillation.

• For sinusoidal oscillations,
• Barkhausens criteria state-
• Phase shift around feedback loop should be zero
  degrees and magnitude of loop gain must be unity.
• Loop gain greater than unity causes distorted
  oscillations.

Or even multiples of 3600

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Oscillators with Frequency-Selective RC Networks
Phase-Shift Oscillator
Phase shift will be zero if
0, At ?0
Use node equations at v1 and v2 To find the
relation between V2 and Vo
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Oscillators with Frequency-Selective RC Networks
Wien-Bridge Oscillator (HP 200A)?
Phase shift will be zero if
0, At ?0 1/RC This oscillator is used for
frequencies upto few MHz, limited primarily by
characteristics of amplifier. (variable freq.?)
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Amplitude Stabilization

• Loop gain of oscillator changes due to power
  supply voltage, component value or temperature
  changes.
• If loop gain is too small, desired oscillation
  decays and if it is too large, waveform is
  distorted.
• Amplitude stabilization or gain control is used
  to automatically control loop gain and place
  poles exactly on jw axis.
• At power on, loop gain is larger than that
  required for oscillation.As oscillation builds
  up, gain is reduced to minimum required to
  sustain oscillations.

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Amplitude Stabilization in RC Oscillators Method
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R1 is replaced by a lamp. Small-signal resistance
of lamp depends on temperature of bulb
filament. If amplitude is large, current is
large, resistance of lamp increases, gain is
reduced. If amplitude is small, lamp cools,
resistance decreases, loop gain increases.
Thermal time constant of bulb averages signal
current and amplitude is stabilized.
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Amplitude Stabilization in RC Oscillators Method
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Thus, when diodes are off, op amp gain is
slightly gt3 ensuring oscillation, but, when one
diode is on, gain is reduced to
slightlylt3. Same method can also be used in
phase shift oscillators.
For positive signal at vo, D1 turns on as voltage
across R3 exceeds diode turn-on voltage. R4 is in
parallel with R3, loop gain is reduced. D2
functions similarly at negative signal peak.
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LC Oscillators Colpitts Oscillator
?0, collect real and imaginary parts and set
them to zero.
At ?0
Generally more gain is used to ensure oscillation
with amplitude stabilization.
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LC Oscillators Hartley Oscillator
?0, collect real and imaginary parts and set
them to zero.
G-S and G-D capacitances are neglected, assume no
mutual coupling between inductors.
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Crystal Oscillators
Crystal A piezoelectric device that vibrates is
response to electrical stimulus, can be modeled
electrically by a very high Q (gt10,000) resonant
circuit. L, CS, R represent intrinsic series
resonance path through crystal. CP is package
capacitance. Equivalent impedance has series
resonance where CS resonates with L and parallel
resonance where L resonates with series
combination of CS and CP.
Below ?S and above ?P, crystal appears
capacitive, between ?S and ?P it exhibits
inductive reactance.
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Crystal Oscillators Example

• Problem Find equivalent circuit elements for
  crystal with given parameters.
• Given data fS5 MHz, Q20,000 R 50 W, CP 5 pF

Analysis
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Crystal Oscillators Topologies
Colpitts Crystal Oscillator
Crystal Oscillator using BJT
Crystal Oscillator using CMOS inverter as gain
element.
Crystal Oscillator using JFET
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Our experiments with truth

• Some experimental error!

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Many Thanks