Phase Noise and Oscillators

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Phase Noise and Oscillators

• Stephen Powell

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What is an Oscillator?

• Produces a signal at a particular frequency
• They are everywhere!
• watches, radios, computers, in most electronic
  circuits
• Uses?
• Generates signals for transmission
• Frequency translation
• Provides timing references

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How to build an Oscillator!

• Need a feedback loop
• Oscillates at frequency ?0 when
• 1-A(j?0)B(j?0) 0 (Barkhausen criteria)
• Unstable device!

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Simple LCR Oscillator

• L,C,R forms an impedance tank
• Impedance has same form as the loop equation
• Voltage across tank oscillates

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Effect of Resistance
Without R
With R
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Phase Noise

• Oscillator output V(t) Csin(?0t?(t))
• Suppose ?(t) ? sin(pt) ? model one component of
  white noise then

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Origins of Phase Noise

• Three types of contributing noise
• Flicker Noise power inversely proportional to
  frequency, AKA 1/f noise
• Shot Noise due to random charge carriers,
  proportional to current
• Thermal Noise present in all resistors, wide
  band, AKA Johnson noise

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Aggregate Phase Noise

• All three types together

?1/f 3
log(L(??))
?0/2Q
Shot Noise
Thermal Noise
Flicker Noise
log(??)
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Modified Leeson Model

• Tries to account for traits seen in spectrum
• Loosely based on principle of time-invariance
• F, ?1/f3 are empirically calculated
• Not good for prediction!

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Lee Model

• Based on time-variance
• No empirical variables
• Corresponds well to observations

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Lee Model (continued)
Region of 1/f3 (Flicker Noise)
Region of 1/f2 (Shot Noise)
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Effects of Phase Noise

• In the time domain Timing Jitter
• bad if you want to synchronize a signal, or
  sample a signal

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Effects of Phase Noise

• In the frequency domain Reciprocal Mixing
• bad for interference immunity

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So, what did I learn again?

• Oscillators are unstable (but very important!!)
  devices
• Phase noise is bad
• Spreads the frequency spectrum
• Causes timing jitter
• Two models can be used to provide insight in
  reducing phase noise