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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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Feedback & Stability
A(jw)b(jw) must not encircle the point -1if you want a stable system
=
1 +
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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Feedback & Stability
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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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Feedback & Stability
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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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Feedback & Stability
How to realize ?
Both inverting and non-inverting amplifiertopologies are possible.
|Ab|=1 and arg(Ab)=180
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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Feedback & Stability
How to realize ?
A combination of positive and negative feedbackis also possible.
|Ab|=1 and arg(Ab)=180
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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!
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
-
+
b
A
in out
R1
C1
inout
R2
C2
Ab=-1A= positive real
arg(b) =-180o(only at =osc)
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
in outR1
C2
R2 R3
C1 C3
-
+
b
A
inoutAb=-1
A= positive real
arg(b) =-180o(only at =osc)
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
-
+
b
A
inoutAb=-1
A= positive real
arg(b) =-180o(only at =osc)
inR1
C2
R2 R3
C1 C3 outR4
C4
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
-
+
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
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
-
+
b
A
in outR1
C2
R2 R3
C1 C3
inout
A A A
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
A
in outR1
C2
R2 R3
C1 C3
A A A
Zin Zout
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
A
in outR1
C2
R2 R3
C1 C3
A A A
Zin Zout ZoutZin
7/29/2019 EL19 - Harmonic Oscillators (RW)
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University of TwenteEE B1-2A: Electronics
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RC Phase-shift oscillators
R1
C2
R2 R3
C1 C3A1 A2 A3
VTUNE
Ring oscillator
7/29/2019 EL19 - Harmonic Oscillators (RW)
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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