Feedback (and control) systems -...
Transcript of Feedback (and control) systems -...
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-1/23
Feedback (and control) systemsStability and performance
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-2/23
Behavior of Under-damped System
00
2 22
2( )
2n
n n
bs y s yMY sb k s ss sM M
Damping ratio Natural frequency
21 2, 1n ns s
If
< 1
21 2, 1n ns s j
j
21nj
21nj
2 n
n
n
1cos
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-3/23
Nyquist Plot
• Example 8.10
– Consider an amplifier with frequency independent feedback
and an open- loop transfer function given by
3
4
4
10( )1
10
A ss
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-4/23
Nyquist Plot
• Example 8.10
– Consider an amplifier with frequency independent feedback
and an open-loop transfer function given by
– The Nyquist plot of this system for
= .01 is
3
4
4
10( )1
10
A ss
s j
0s
![Page 5: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/5.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-5/23
Nyquist Plot
3
4
4
10( )1
10
A ss
180s j
• Example 8.10
– Consider an amplifier with frequency independent feedback
and an open- loop transfer function given by
– The Nyquist plot of this system for
= .01 is
![Page 6: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/6.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-6/23
Nyquist Plot
3
4
4
10( )1
10
A ss
• Example 8.10
– Consider an amplifier with frequency independent feedback
and an open- loop transfer function given by
– The Nyquist plot of this system for
= .005 is
Gain < 1 when phase shift = -180o
![Page 7: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/7.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-7/23
Stability and Pole location
( ) o n nt j t j tv t e e e
• Consider a system with poles at s = o + jn
• Transient response is
j
o < 0
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-8/23
Stability and Pole location
( ) o n nt j t j tv t e e e
• Consider a system with poles at s = o + jn
• Transient response is
j
o = 0
![Page 9: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/9.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-9/23
Stability and Pole location
( ) o n nt j t j tv t e e e
• Consider a system with poles at s = o + jn
• Transient response is
j
o > 0
![Page 10: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/10.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-10/23
Feedback Amplifier Poles
1 ( ) ( ) 0A s s
• Poles of closed loop feedback system are determined by:
A(s)
(s)
+in out
-
+
![Page 11: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/11.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-11/23
Feedback Amplifier Poles
0( )1
p
AA s s
• Consider a system with a single pole in the open loop response
A(s)
(s)
+in out
-
+
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-12/23
Feedback Amplifier Poles
• Consider a system with a single pole in the open loop response
0( )1
p
AA s s
A(s)
(s)
+in out
-
+
0
0
0
1( )1
(1 )
f
p
AAA s s
A
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-13/23
Feedback Amplifier Poles
• Consider a system with a single pole in the open loop response
0( )1
p
AA s s
A(s)
(s)
+in out
-
+
0
0
0
1( )1
(1 )
f
p
AAA s s
A
Gain of feedback systemis reduced
Frequency characteristic of feedback systemis changed
![Page 14: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/14.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-14/23
Feedback Amplifier Poles
0
0
0
1( )1
(1 )
f
p
AAA s s
A
0( )1
p
AA s s
A(s)
(s)
+in out
-
+
dB
log()
A(s)
p
|Ao |
|Af0 |
pf
j
ppf
0(1 )pf p A
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-15/23
Approximating system response
dB
log()
|Af0 |
pf
0For ( )pf f fs A s A
0( )1
ff
pf
AA s s
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-16/23
Approximating system response
dB
log()
|Af0 |
pf
0For ( ) f pfpf f
As A s
s
0( )1
ff
pf
AA s s
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-17/23
Approximating system response
0( )1
ff
pf
AA s s
0For ( )pf f fs A s A dB
log()
|Af0 |
pf
0For ( ) f pfpf f
As A s
s
![Page 18: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/18.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-18/23
System with two pole response
0
1 2
( )1 1
p p
AA ss s
![Page 19: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/19.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-19/23
System with two pole response
21 2 0 1 21 0p p p ps s A
Closed loop response poles:
21 11 2 1 2 0 1 22 2 4 1p p p p p ps A
0
1 2
( )1 1
p p
AA ss s
Solving for poles:
![Page 20: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/20.jpg)
Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-20/23
System with two pole response
1 2
2p p
j
p1p2
21 11 2 1 2 0 1 22 2 4 1p p p p p ps A
Root-locus diagram
![Page 21: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/21.jpg)
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Pole quality
21 2 0 1 21 0p p p ps s A
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-22/23
Pole quality
21 2 0 1 21 0p p p ps s A
2 200 0s s
Q
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Copyright ©2007-2008Stevens Institute of Technology - All rights reserved 22-23/23
Pole quality
0 1 2
1 2
1 p p
p p
AQ
2 200 0s s
Q
j
0
2Q
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1
Signal Generators and Signal Generators and WaveformWaveform--shaping Circuitsshaping Circuits
Ch 17Ch 17
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2
Input summing, output sampling voltage amplifier
Series voltage summing Shunt voltage sensing
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3
Using negative feedback system to create a signal generator
A
| ( ) | 1( )
AA
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4
Basic oscillator structure
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5
Basic oscillator structure
( )( )1 ( ) ( )f
A sA sA s s
With positive feedback
![Page 30: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/30.jpg)
6
Basic oscillator structure
( )( )1 ( ) ( )f
A sA sA s s
With positive feedback
( ) ( )A s s
Loop gain
![Page 31: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/31.jpg)
7
Basic oscillator structure
( )( )1 ( ) ( )f
A sA sA s s
With positive feedback
( ) ( )A s s
Loop gain
Define loop gain L(s)
( ) ( ) ( )L s A s s
![Page 32: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/32.jpg)
8
Basic oscillator structure
( )( )1 ( ) ( )f
A sA sA s s
With positive feedback
( ) ( )A s s
Loop gain
Define loop gain L(s)
( ) ( ) ( )L s A s s
Characteristic equation
1 ( ) 0L s
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9
Criteria for oscillation
( ) ( ) ( ) 1o o oL j A j j The Barkhausen criteria:
For oscillation to occur at o
At o , the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback)
![Page 34: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/34.jpg)
10
Criteria for oscillation
( ) ( ) ( ) 1o o oL j A j j The Barkhausen criteria:
For oscillation to occur at o
At o , the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback)
1
f o
f o
o o
x x
Ax x
A x xA
![Page 35: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/35.jpg)
11
Criteria for oscillation
( ) ( ) ( ) 1o o oL j A j j The Barkhausen criteria:
For oscillation to occur at o
At o , the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback)
1
f o
f o
o o
x x
Ax x
A x xA
If gain is sufficient, frequency of oscillation is determined only by phase response
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12
Oscillation frequency dependence on phase response
A steep phase response ( () ) produces a stable oscillator
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13
Oscillator amplitude
j
j
|L(jo ) < 1
|L(jo ) > 1
0 1 2 3 4 5
2
0
2
f t( )
ta 0.2
0 1 2 3 4 5
2
0
2
f t( )
ta 0.2
![Page 38: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/38.jpg)
14
Oscillator amplitude
j
|L(jo ) = 1
0 1 2 3 4 5
2
0
2
f t( )
ta 0
How do you stabilize the oscillator so the output level remains constant
If the oscillator is adjustable, how is this possible across the full range?
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15
Nonlinear oscillator amplitude control
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16
Nonlinear oscillator amplitude control
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17
Nonlinear oscillator amplitude control
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18
Nonlinear oscillator amplitude control
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19
Wein-Bridge oscillator (without amplitude stabilization)
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20
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
![Page 45: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/45.jpg)
21
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
2
1
2
1
( ) ( )
1
( )
( ) 1
p
p s
p
p s
L s A sRAR
Zs
Z Z
ZRL sR Z Z
![Page 46: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/46.jpg)
22
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
2
1
2 1 2 1
2 1
2 1
( ) 1
1 1( )1 1
1( )1
1( )1 11
p
p s
p s s p
s p
ZRL sR Z Z
R R R RL sZ Z Z Z
R RL sZ Y
R RL sR sC
sC R
![Page 47: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/47.jpg)
23
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
2 1
2 1
2 1
1( )1 11
1( ) 11
1( )13
R RL sR sC
sC RR RL s R sCsCR
R sCR sCR RL j
j CRCR
![Page 48: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/48.jpg)
24
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
2 11( )13
R RL jj CR
CR
1
1
oo
o
CRCR
CR
Oscillation at o if
![Page 49: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/49.jpg)
25
Wein-Bridge oscillator (without amplitude stabilization)
A
(s)
2 11( )13
R RL jj CR
CR
Oscillation if
2 1
2 1
1( )3
2
R RL j
R R
![Page 50: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/50.jpg)
26
Wein-Bridge oscillator (with amplitude stabilization)
A
(s)
stabilization
![Page 51: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/51.jpg)
27
Wein-Bridge oscillator (with amplitude stabilization)
9 3
0
1
1(16 10 F)(10 10 )6250 rad/sec
f 1000 Hz
o
o
o
CR
2 1
2 1
220.3 10 2.03
R RR R
![Page 52: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/52.jpg)
28
Wein-Bridge oscillator (with alternative stabilization)
D1 and D2 reduce Rf at high amplitudes
![Page 53: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/53.jpg)
29
Phase shift oscillator-A
(s)
![Page 54: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/54.jpg)
30
Phase shift oscillator-A
(s)
Phase shift of each RC section must be 60o to generate a total phase shift of 180o
K must be large enough to compensate for the amplitude attenuation of the 3 RC sections at o
![Page 55: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/55.jpg)
31
Quadrature oscillator
![Page 56: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/56.jpg)
32
Quadrature oscillator
Limiting circuit
Integrator 2
Integrator 1
![Page 57: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/57.jpg)
33
Quadrature oscillator
Limiting circuit
Integrator 2
Integrator 1
2 2 2
0
1( )
1
L ss C R
CR
![Page 58: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/58.jpg)
34
Quadrature oscillator
0sin( )t
0cos( )t
![Page 59: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/59.jpg)
35
LC oscillator
Colpitts oscillator
![Page 60: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/60.jpg)
36
LC oscillator
Hartley oscillator
![Page 61: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/61.jpg)
37
LC oscillator
Colpitts oscillator Hartley oscillatorFrequencydetermining
element
![Page 62: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/62.jpg)
38
LC oscillator
Colpitts oscillator Hartley oscillatorGainstage
![Page 63: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/63.jpg)
39
LC oscillator
Colpitts oscillator Hartley oscillatorFeedback
voltage divider
![Page 64: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/64.jpg)
40
LC oscillator
Colpitts oscillator Hartley oscillator
0
1 2
1 2
1
C CLC C
01 2
1L L C
![Page 65: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/65.jpg)
41
Practical LC (Colpitts) oscillator
![Page 66: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/66.jpg)
42
Piezoelectric oscillator
Quartz crystalschematic symbol
![Page 67: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/67.jpg)
43
Piezoelectric oscillator
Quartz crystalschematic symbol
Equivalentcircuit
![Page 68: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/68.jpg)
44
Piezoelectric oscillator
Quartz crystalschematic symbol
Equivalentcircuit
Reactance
![Page 69: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/69.jpg)
45
Piezoelectric oscillator
Seriesresonance
Parallelresonance1
ssLC
1p
s p
s p
C CL
C C
![Page 70: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/70.jpg)
46
Piezoelectric oscillator
Seriesresonance
Parallelresonance1
ssLC
1p
s p
s p
C CL
C C
r << |ZL |
![Page 71: Feedback (and control) systems - personal.stevens.edupersonal.stevens.edu/~bmcnair/EE359-S11/lecture16.pdf · the phase shift is 0 (for positive feedback) 1. f o f o oo. x x Axx ...](https://reader033.fdocument.pub/reader033/viewer/2022051722/5aa8d6c47f8b9a6c188c0640/html5/thumbnails/71.jpg)
47
Pierce crystal oscillator
LPF to discourageharmonic/overtone
oscillation
Frequencydetermining
elements(but CS dominates)
DC bias circuit(near VDD /2)
CMOS inverter(high gain amplifier)