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

Oscillator*

*Slides are adopted from

“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

1

3/22/2011

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 ( j0 ) V0 H ( j0 ) V0 H ( j0 ) V0 ...

2

VX

V0

1 H ( j0 )

3

H ( j0 ) 1

H ( j0 ) 1

3

Negative feedback oscillation condition

Barkhausen Criteria

H ( j0 ) 1

H ( j0 ) 180

With total phase shift of 360 degree the oscillation can be happened.

4

2

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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 Nt T t

T 2

N

6

3

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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

4

3/22/2011

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

5

3/22/2011

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

Frequency (rad/sec)

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

10

2

12

6

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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