wein bridge oscillators - 1

8/8/2019 Wein Bridge Oscillators - 1

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Wien-Bridge OscillatorCircuits


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Why Look At the Wien-

Bridge? It generates an

oscillatory output

signal withouthaving any input

source


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Basics About the Wien-

Bridge Uses two RC

networks

connected to thepositive terminal toform a frequencyselective feedbacknetwork

CausesOscillations toOccur


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Basics About the Wien-

Bridge Amplifies the

signal with the two

negative feedbackresistors


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Modification to Circuit


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Analysis The loop gain

can be found by

doing a voltagedivision

V o s( ) V 1 s( )Z 2 s( )

Z 1 s( ) Z 2 s( )+


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Analysis The two RC

Networks must

have equalresistors andcapacitors

Z1 s( ) R1

s C+

Z2 s( )

R1

s C

R1

s C

+


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Analysis

Operational amplifier gain

GV1 s( )

Vs s( )1

R2

R1+

V o s( ) V 1 s( )

Z 2 s( )

Z 1 s( ) Z 2 s( )+

Need to find the Gain over the whole Circuit:Vo/Vs

V o s( ) G V s s( )s R C

s2 R2 C2 3 s R C+ 1+

Solve G equation for V1 and substitute in for above eq


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Analysis

T s( ) V o s( )V s s( )

s R C G

s2

R2

C2

3 s R C+ 1+

We now have an equation for the overall circuitgain

T j( )j R C G

1 2

R2

C2

( ) 3 j R C+

Simplifying and substituting jw for s


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AnalysisIn order to have a phase shift of zero,

1 2

R2

C2

0

This happens at = 1/RC When =1/RC, T(j) simplifies to:

T j( )G

3

If G = 3, oscillations occur

If G < 3, oscillations attenuate

If G > 3, oscillation amplify


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Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms

V(R5:2)

-4.0V

0V

4.0V

G = 3

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms

V(R5:2)

-4.0V

0V

4.0V

G = 2.9

Time

0s 100us 200us 300us 400us 500us 600us

V(R5:2)

-20V

0V

20V

G =3.05


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Ideal vs. Non-Ideal Op-

Amp Red is the ideal op-amp.

Green is the 741 op-amp.

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms

V(R1:2) V(R5:2)

-4.0V

0V

4.0V


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Making the Oscillations

Steady Add a diode

network tokeep circuitaround G =3

If G = 3,diodes areoff


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Steady When output

voltage ispositive, D1turns on andR9 is switched

in parallelcausing G todrop


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Steady When output

voltage isnegative, D2turns on andR9 is switched

in parallelcausing G todrop


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Results of Diode Network

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms

V(D2:2)

-4.0V

0V

4.0V

With the use of diodes, thenon-ideal op-amp can produce

steady oscillations.


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Frequency Analysis By changing the resistor and

capacitor values in the positive

feedback network, the outputfrequency can be changed.R 10k := C 1nF:=

1

R C:= 1 105

rad

sec=

f

2 := f 15.915kHz=


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Frequency Analysis

Frequency

0Hz 10KHz 20KHz 30KHz 40KHz

V(D2:2)

0V

2.0V

4.0V(15.000K,2.0539)

Fast Fourier Transform ofSimulation


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Frequency Analysis Due to limitations of the op-

amp, frequencies above 1MHz

are unachievable.


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Conclusions No Input Signal yet Produces

Output Oscillations

Can Output a Large Range ofFrequencies

With Proper Configuration,

Oscillations can go onindefinitely

wein bridge oscillators - 1

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