# Essay on Osc: Feedback and Phase Shift

Submitted By kokujampo
Words: 1349
Pages: 6

3/22/2011

Instructor: Shahab Ardalan http://www.ardalan.ws EE-227

Oscillator*
 “Design of Integrated Circuit for Optical Communications”, B. Razavi
 “High Speed Communication Circuits and System”, MIT, M. H. Perrot

Oscillator
 Oscillators are one of the important blocks of PLL, CDR system.
 A simple oscillator produce a periodic output, usually in form of voltage.  Negative feedback system may oscillate.
 An oscillator is a badly designed feedback amplifier.

Vout
H ( s)
( s) 
Vin
1  H ( s)
2

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Negative feedback
 Large phase shift at high frequency then the overall feedback becomes positive.
 s= jω0 and H(jω0) = , then the closed-loop gain approaches infinity at ω0  At this condition, circuit will amplifies its own noise at ω0

VX  V0  H ( j0 ) V0  H ( j0 ) V0  H ( j0 ) V0  ...
2

VX 

V0

1  H ( j0 )

3

H ( j0 )  1

H ( j0 )  1
3

Negative feedback oscillation condition
 Barkhausen Criteria

H ( j0 )  1
H ( j0 )  180
 With total phase shift of 360 degree the oscillation can be happened.

4

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Oscillator types
 Ring Oscillator
– Small area, poor phase noise

 LC Oscillator
– low phase noise large area

5

Ring Oscillator

 Gain is set to 1 by saturating characteristic of inverters
 Phase equals 360 degrees at frequency of oscillation – Assume N stages each with phase shift of
ΔΦ

2 N  360   

180
N

 Alternative, N stages with delay Δt

2 Nt  T  t 

T 2
N
6

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Ring Oscillators
 CS Stage with feedback

 Open loop circuit contains only one pole, thereby providing a maximum freq.-dependent phase shift is 90 degree.
 Another 180 degree phase shift from gate and drain
 The maximum total phase shift is around 270, then the loop sustain oscillation growth
7

Two stage

 It has two significant poles
– Phase shift of 180 degrees

 Circuit has two stable point and it will not oscillate
 Increase in VE => falls in VF => M1 is going to cut-off region
 M1 is getting OFF and then VE increases => …

8

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Modify two-stage gain block

 It will provide a negative gain at zero frequency and eliminate the latch-up issue.
 Freq. dependent phase shift can reach 180 but at a frequency of infinity, where the gain is vanished
 Circuit is not satisfy gain condition of Barkhausen’s criteria

9

Three stage, Ring Oscillator

 Total phase shift around the loop is -135 at ω=ωp,E (= ωp,F = ωp,G) and -270 at ω equals to infinity.
 Phase can be equaled to 180 if the ω is less than infinity and larger than ωp,E and loop gain can be larger than one

H ( s) 

A03

 s 
1  
 0 

3

10

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Three stage, Ring Oscillator
osc
tan
 60
0
1

Bode Diagram
20

Magnitude (dB)

 Circuit will oscillate if the phase shift is 180

osc  0 3

-40

Phase (deg)

-60
0

-90

-180

-270

A03
2

osc
 1 

   

0 

0

-20

3

 1  A0  2

5

6

10

10

7

10

11

Exceed gain
Vout
 A03
H ( s)
( s) 

Vin
1  H ( s) (1  s 0 )3  A03

(1 

s

0

)3  A03  (1 

s

0

 A0 )[(1 

s

0

) 2  (1 

s

0

) A0  A03 ]

s1  ( A0  1)0
 A (1  j 3 )  s2 , 3   0
 10
2

12

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Gain more than 2!
6

Root Locus

x 10
1 0.93

Vout (t )  ae

A0  2
0 t
2

0.64

0.46

0.24

0.6 0.97
0.4
0.992
0.2

2.5e+006
0

 Neglecting the s1:

0.78

0.8

Imaginary Axis

 A0> 2 then two complex poles exhibits a positive real part and hence give rise to a growing sinusoid.

0.87

2e+006

1.5e+006

1e+006

5e+005

-0.2
0.992
-0.4
-0.6 0.97

A 3 cos( 0 0t )
2

-0.8
0.87

-1 0.93
-2.5

-2

0.78
-1.5

Then the exponential envelope grows to infinity

0.64
-1

0.46
-0.5

0.24
0

Real Axis

0.5
6

x 10

In reality, as the oscillator amplitude increases, the stages in the signal path experience nonlinearity and eventually saturation, limiting the maximum amplitude. 13

LC Oscillators
 Monolithic inductors making it possible to design oscillators based
on…