EL19 - Harmonic Oscillators (RW)

7/29/2019 EL19 - Harmonic Oscillators (RW)

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University of TwenteEE B1-2A: Electronics

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Harmonic Oscillators

Remco Wiegerink


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Electronics where are we?

9. Opamp internals8. Feedback (positive): oscillators6,7. Feedback (negative)5. Amplifier circuits4. Small signal equivalent circuits

3. Bias circuits2. PN junction, BJT, MOS0,1. Models & Circuit analysis

11. Digital Circuits10. RF


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Feedback & Stability

A(jw)b(jw) must not encircle the point -1if you want a stable system

=

1 +


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What happens if A(jw)b(jw) exactly crosses thepoint -1?

Im [A(w)b(w)]w=0=

-1Re [A(w)b(w)]SCARY!

SCARY!

A(jw)b(jw) = -1 for exactlyone frequency!

Nyquist:A(w)b(w) CROSSES -1: UNSTABLE


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What happens if A(jw)b(jw) exactly crosses thepoint -1?

Im [A(w)b(w)]w=0=

-1Re [A(w)b(w)]

A(jw)b(jw) = -1 for exactlyone frequency!

A(jw)b(jw) = -1

|Ab|=1 and arg(Ab)=180


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How to realize ?

Both inverting and non-inverting amplifiertopologies are possible.



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How to realize ?

A combination of positive and negative feedbackis also possible.



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Example: Wien bridge oscillator

-

+

A

bAb=1

|H|0 for w0|H|0 for w

inout

in out

b (e.g.):

R1 C1

R2 C2


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Wien bridge oscillator

|H|0 for w0|H|0 for win out

R1 C1

R2 C2

1122

22

//

//

CRCR

CR

ZZZZ

ZZ

H 221122

22

CRCRCR

CR

ZZZZZZ

ZZH

2

22

1

11

22

22

11/

/

Cj

CRj

Cj

CRjCjR

CjRH

ww

ww

w

w

22112212211 211 CRCRRCCRCRjRCj

H ww

|H|Re for w2121

CCRR

you have to be ableto derive that!


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Wien bridge oscillator

in out |H|0 for w0|H|0 for w

If e.g.

b=1/3 atw=1/R1R2C1C2then A=3

R1 C1

R2 C2

-

+

A

b inout


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Exercise: harmonic oscillator

Derive an expression for the oscillation (angular)frequency of this oscillator, expressed ine.g. A, C1, C2, R1, and R2.

Derive the value for the voltage A required forharmonic oscillation, expressed in e.g. C1, C2, R1,and R2.

1

2

2


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Answer

Calculate the loop gain, then find thefrequency at which the gain is a real value

The loop gain must be equal to 1, thisdefines the value of A

=

2

2

= 1 + 22


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Exercise: harmonic oscillator

Derive an expression for the oscillation (angular)frequency of this oscillator, expressed ine.g. A, C, L, R1, and R2.

Derive the value for the voltage A required forharmonic oscillation, expressed in e.g. C, L, R1, andR2.

1

2


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Answer

Calculate the loop gain, then find thefrequency at which the gain is a real value

The loop gain must be equal to 1, thisdefines the value of A

=

2

= 1 +

2


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RC Phase-shift oscillators

-

+

b

A

Ab=-1A= positive real

arg(b) =-180o(only at =osc)

in out

R1

C1

inout


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-

+

b

A

in out

R1

C1

inout

R2

C2

Ab=-1A= positive real



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in outR1

C2

R2 R3

C1 C3

-

+

b

A

inoutAb=-1

A= positive real



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-

+

b

A

inoutAb=-1

A= positive real


inR1

C2

R2 R3

C1 C3 outR4

C4


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-

+

b

A

Ab=-1

A= positive real

arg(b) =-180oinout

forRC

3

b=-1/8A=8

in out

R1

C1

in out

R1

C1

in out

R1

C1


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-

+

b

A

in outR1

C2

R2 R3

C1 C3

inout

A A A


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A

in outR1

C2

R2 R3

C1 C3

A A A

Zin Zout


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A

in outR1

C2

R2 R3

C1 C3

A A A

Zin Zout ZoutZin


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R1

C2

R2 R3

C1 C3A1 A2 A3

VTUNE

Ring oscillator


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University of TwenteEE B1 2A: El t ni

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Next...

Study Section 8.1 from the reader

Do assignment O 8.1 from the exercise

assignments

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EL19 - Harmonic Oscillators (RW)