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
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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 ( 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
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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
5
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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
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