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Oscillator Circuits

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II. Oscillator OperationFor self-sustaining oscillations:

• the feedback signal must positive• the overall gain must be equal to one (unity gain)

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If the feedback signal is not positive or the gain is less than one, then the oscillations will dampen out.

If the overall gain is greater than one, then the oscillator will eventually saturate.

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Types of Oscillator Circuits

A. Phase-Shift OscillatorB. Wien Bridge OscillatorC. Tuned Oscillator CircuitsD. Crystal OscillatorsE. Unijunction Oscillator

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A. Phase-Shift Oscillator

Frequency of the oscillator: (the frequency where the phase shift is 180º)

Feedback gain β = 1/[1 – 5α2 – j (6α – α3) ] where α = 1 / (2πfRC)Feedback gain at the frequency of the oscillator β = 1 / 29

The amplifier must supply enough gain to compensate for losses. The overall gain must be unity. Thus the gain of the amplifier stage must be greater than 1/β, i.e. A > 29

The RC networks provide the necessary phase shift for a positive feedback. They also determine the frequency of oscillation.

621

0 πRCf =

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Example of a Phase-Shift Oscillator

FET Phase-Shift Oscillator

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Example 1

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BJT Phase-Shift Oscillator

C

Cfe R

RR

Rh 42923 ++>

iehRR −=′

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Phase-shift oscillator using op-amp

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B. Wien Bridge Oscillator

So frequency of oscillation is ( )22110 2

1CRCRπ

f =

1

1

1

1

4

3

2

143

4

21

2

+−

+=

+−

+=

−==

RR

ZZRR

RZZ

ZV

VVVVβ

a

bd

o

i

2 and ,2

1

then and When

4

30

2121

≥=

====

RR

πRC f

CCCRRRfrequency noscillatio theat phase zero have should i.e., ,2

1

21

2

ZZ

ZZZ+

1

2

2

1

4

3 0CC

RR

RR

+=⇒=β

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Calculate the resonant frequency of the Wien bridge oscillator shown aboveHz7.3120

)101)(1051π(21

21

930 =××

== −πRCf

Example 2

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C. Tuned Oscillator Circuits

Tuned Oscillators use a parallel LC resonant circuit (LC tank) to provide the oscillations.

There are two common types:

• Colpitts – The resonant circuit is an inductor and two capacitors.• Hartley – The resonant circuit is a tapped inductor or two inductors and one

capacitor.

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Colpitts Tuned Oscillator Circuit

FET based Colpitts Oscillator

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21 where ,2

10 CC

CCCLCπ

f eqeq +

==Frequency of oscillations:

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Transistor Colpitts oscillator.

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Op-amp Colpitts oscillator.

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Hartley Tuned Oscillator Circuit

FET Hartley Oscillator

1221 2 where ,2

10 LLLL

CLπf eq

eq++==Frequency of oscillations:

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BJT based Hartley Oscillator

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D. Crystal Oscillators

The crystal appears to the rest of the circuit as a resonant circuit.

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Crystal Resonant Frequencies

The crystal has two resonant frequencies:

Series resonant: RLC determine the resonant frequency. The crystal has a low impedance.Parallel resonant: RL and CM determine the resonant frequency. The crystal has a high impedance.

The series and parallel resonant frequencies are very close, within 1% of each other.

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Series Resonant Crystal Oscillator

FET Crystal Oscillator

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Parallel Resonant Crystal Oscillator

BJT Crystal Oscillator

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Crystal Oscillator using Op-amp

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E. Unijunction Oscillator

Frequency of oscillations:

where η = 0.4 to 0.6 η is a rating of the unijunction transistor.

[ ]η)(CRf

T T −=

11ln1

0

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Unijunction Oscillator Waveforms

The unijunction oscillator (or relaxation oscillator) produces a sawtooth waveform.

DBBBP

BBBB

VVηVVVVV

++=−=

1

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Unijunction transistor (UJT): basic construction.

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UJT – Unijunction Transistor

The UJT is also basically a switching device.

Schematic Symbol:

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UJT Basic OperationEven though the UJT is a switching device it works very differently from the SCR variety of devices.

The equivalent circuit indicates that the UJT is like a diode and a resistive voltage divider circuit. The resistance exhibited by RB1 is variable; it is dependent on the value of current IE.

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UJT Characteristic Curve

A voltage is applied across the UJT (VBB) and to the Emitter input (VE). Once VE reaches a peak value (Vp) the UJT begins to conduct. At the point where VE = Vp, the current IE is at minimum. This is the threshold value of VE that puts the UJT into conduction. Once conducting, IE increases and VE decreases. This phenomenon occurs because the internal resistance labeled RB1 in the equivalent circuit decreases as the UJT conducts more and more. This is called negative resistance.