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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Positive Feedback, Oscillators and Stability
Introduction
Oscillators
Stability
Chapter 24
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Introduction
Earlier we looked at feedback in general terms
in particular we concentrated on negative feedback
In this chapter we will considerpositive feedback
this is used in both analogue and digital circuits
it is used in the production of oscillators
positive feedback can occur unintentionally within
circuits when it has implications for stability
24.1
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Oscillators
Earlier we looked at a generalised feedback system
We also derived the closed-loop gain Gof this
24.2
)1( AB
AG
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Baukhausen criterion FOR OSCILATING
Looking at the expression
we note that when AB= -1, the gain is infinite
this represents the condition for oscillation
The requirements for oscillation are described by theBaukhausen criterion:
1. The magnitude of the loop gain ABmust be 12. The phase shift of the loop gain ABmust be 180,
or 180 plus an integer multiple of 360
)1( AB
AG
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
RCor phase-shift oscillator
one way of producing a phase shift of 180 is to usean RCladder network
this gives a phase shift of 180 when
at this frequency the gain of the network is
621
CRf
29
1
i
o
v
v
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
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Therefore the complete oscillator is
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Wien-bridge oscillator
uses a Wien-bridge network
this produces a phase-shift
of 0 at a single frequency,and is used with an invertingamplifier
the selected frequency is
when the gain is 1/3
CRf
2
1
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
A complete oscillator might look like
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Amplitude stabilisation
in both the oscillators above, the loop gain is set bycomponent values
in practice the gain of the active components is veryvariable if the gain of the circuit is too high it will saturate
if the gain of the circuit is too low the oscillation will die
real circuits need some means of stabilising the
magnitude of the oscillation to cope with variability inthe gain of the circuit
see Section 24.2.3 in the course text for morediscussion of this topic
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Digital oscillators
many examples, for example the relaxation oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Crystal oscillators
frequency stability is determined by the ability of thecircuit to select a particular frequency
in tuned circuits this is described by the quality factor, Q
piezoelectric crystals act like resonant circuits with avery high Q as high as 100,000
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
A typical crystal oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Stability
Earlier we used a general expression for the gain of
a feedback network
So far we have assumed that A and Bare real gains
the gain of a realamplifier has not only a magnitude,
but also a phase angle
a phase shift of 180 represents an inversion and sothe gain changes polarity
this can turn negativefeedback into positivefeedback
24.3
)1(AB
AG
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
The gain of all real amplifiers falls at high frequenciesand this also produces a phase shift
All multi-stage amplifiers will produce 180 of phase
shift at somefrequency
To ensure stability we must ensure that the
Baukhausen conditions for oscillation are notmet
to guarantee this we must ensure that the gain fallsbelow unity before the phase shift reaches 180
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Gain andphase margins
these are a measure
of the stability of acircuit
8/4/2019 FEEDBACK Stabilization in Oscillator
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Unintended feedback
stability can also be affected by unintended feedbackwithin a circuit
this might be caused by stray capacitance orstray inductance
if these produce positive feedback they can causeinstability
a severe problem in high-frequency applications
must be tackled by careful design
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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#
Key Points
Positive feedback is used in analogue and digital systems
A primary use is in the production of oscillators
The requirement for oscillation is that the loop gain AB
must have a magnitude of 1, and a phase shift of 180
(or180 plus some integer multiple of 360)
This can be achieved using a circuit that produces a phaseshift of 180 together with a non-inverting amplifier
Alternatively, it can be achieved using a circuit that
produces a phase shift of 0 with an inverting amplifier For good frequency stability we often use crystals
Care must be taken to ensure the stability of all feedbacksystems