This is a good background color and a good text color

1
Lumped, Inductorless Oscillators How Far Can
They Go?
Reza Navid, Thomas H. Lee and Robert W.
Dutton Center for Integrated Systems
(CIS) Stanford University, Stanford, CA
2
Outline of Presentation

• Background
• Minimum Achievable Phase Noise
• Mathematical Formulation
• Frequency and Power Dissipation
• Jitter
• Phase Noise
• Experimental Results
• Conclusion

3
Phase-Noise in Communication Systems
a) RF systems
Interference
Received Signal
IF Filter
Signal of Interest
w
wRF
wRFDw
Local Oscillator
w
wIF
w
wRF wIF
4
Phase noise in Communication Systems (cont.)
b) High-speed communication systems
Signal
Ideal clock
1101001
5
The Race for Low-Phase-Noise Integrated
Oscillators

• The race is on

(Photo courtesy of the Equine Museum of Japan)
, but is there a FINISH line?
6
Time Constant in Oscillators

• A stable time constant is required

F
v
R
l
a) Transmission-line-based oscillators
b) Inductor-based
c) Lumped inductorless
7
Minimum Achievable Phase Noise in RC Oscillators

• All resistors are noisy.
• Fluctuation dissipation theorem
• In equilibrium

in(nA)
Noiseless Resistor
t(ns)
There is always a finite amount of noise, hence
phase noise.
Real Resistor
8
A Model for Lumped, Inductorless Oscillators
9
Outline of Presentation

• Background
• Minimum Achievable Phase Noise
• Mathematical Formulation
• Frequency and Power Dissipation
• Jitter
• Phase Noise
• Experimental Results
• Conclusion

10
Frequency and Power Dissipation
vC
v2
tRC
tRC
v1
t
T1
T2
To1/fosc
11
Voltage Noise and Jitter
vC
v2
v1
t
T1
0
12
Voltage Noise and Jitter
vC
v2
v1
t
T1
0
13
Voltage Noise and Jitter (Cont.)
vC
v2
tRC
tRC
v1
Only need to calculate the voltage noise dvC
t
T1
T2
To1/fosc
14
Problem Definition
15
Voltage Fluctuations
in(nA)
t(ns)
16
Cycle-to-Cycle Jitter
Assumptions
17
Minimum Jitter
Multiplication Factor
v10.24vdd
For minimum jitter
v20.76vdd
18
Minimum Jitter
v10.24vdd
For minimum jitter
v20.76vdd
19
Minimum Jitter, Power Dissipation and Phase Noise
20
Outline of Presentation

• Background
• Minimum Achievable Phase Noise
• Mathematical Formulation
• Frequency and Power Dissipation
• Jitter
• Phase Noise
• Experimental Results
• Conclusion

21
Relaxation Oscillators
From B. Razavi, JSSC Mar. 1996
Minimum Achievable Phase Noise
Measurement Results
Phase Noise (dBc/Hz)
20.6dB
21.6dB
Offset Frequency (MHz)
22
Relaxation Oscillators (Cont.)
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Relaxation Oscillators vs. Ring Oscillators
Current consumption only on switching
Nearly continuous current consumption
24
Ring Oscillators (Cont.)
Form Hajimiri et al, JSSC Jun. 1999 (Df1MHz)
Much Smaller wastefulness factor compared to
relaxation oscillators
Wastefulness Factor
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Conclusion

• The minimum phase noise of lumped, inductorless
  oscillators is limited by the first principles of
  the thermodynamics.
• A simple model representing these oscillators is
  introduced.
• Analytical formulation of minimum achievable
  phase noise for this model is presented.
• The wastefulness factor of relaxation oscillators
  is larger than ring oscillators.

26
Acknowledgements

• This work is supported under an SRC customized
  research project from Texas Instrument and MARCO
  MSD center