feedback stabilization in oscillator

8/4/2019 FEEDBACK Stabilization in Oscillator

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Storey: Electrical & Electronic Systems Pearson Education Limited 2004 OHT 24.#

Positive Feedback, Oscillators and Stability

Introduction

Oscillators

Stability

Chapter 24


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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


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Oscillators

Earlier we looked at a generalised feedback system

We also derived the closed-loop gain Gof this

24.2

)1( AB

AG


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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


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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


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Therefore the complete oscillator is


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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


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A complete oscillator might look like


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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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Digital oscillators

many examples, for example the relaxation oscillator


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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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A typical crystal oscillator


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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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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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Gain andphase margins

these are a measure

of the stability of acircuit


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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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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

feedback stabilization in oscillator

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