Phase Noise and Oscillators

Phase Noise and Phase Noise and OscillatorsOscillators

Stephen PowellStephen Powell

What is an Oscillator?What is an Oscillator?

Produces a signal at a particular Produces a signal at a particular frequencyfrequency

They are everywhere!They are everywhere!• watches, radios, computers, in most watches, radios, computers, in most

electronic circuitselectronic circuits Uses? Uses?

• Generates signals for transmissionGenerates signals for transmission• Frequency translationFrequency translation• Provides timing referencesProvides timing references

How to build an Oscillator!How to build an Oscillator!

A(jω)

β(jω)

X Y

Need a feedback loopNeed a feedback loop Oscillates at frequency Oscillates at frequency ωω00 when when

1-A(j1-A(jωω00)B(j)B(jωω00) = 0 (Barkhausen criteria)) = 0 (Barkhausen criteria) Unstable device!Unstable device!

Simple LCR OscillatorSimple LCR Oscillator

L,C,R forms an impedance “tank”L,C,R forms an impedance “tank” Impedance has same form as the loop Impedance has same form as the loop

equationequation Voltage across tank oscillatesVoltage across tank oscillates

V(t)

I∂(t)

Effect of ResistanceEffect of Resistance

Without R With R

Phase NoisePhase Noise Oscillator output: Oscillator output: VV((tt) = ) = CC·sin(·sin(ωω00t+t+θθ(t)(t))) Suppose Suppose θθ((tt) = ) = θθ sin(sin(ptpt)) model one model one

component of white noise… then:component of white noise… then:

Origins of Phase NoiseOrigins of Phase Noise

Three types of contributing noise:Three types of contributing noise:

• Flicker NoiseFlicker Noise: power inversely : power inversely proportional to frequency, AKA 1/f noiseproportional to frequency, AKA 1/f noise

• Shot NoiseShot Noise: due to random charge : due to random charge carriers, proportional to currentcarriers, proportional to current

• Thermal NoiseThermal Noise: present in all resistors, : present in all resistors, wide band, AKA Johnson noisewide band, AKA Johnson noise

Aggregate Phase NoiseAggregate Phase Noise All three types together…All three types together…

log(∆ω)

log(L(∆ω))

ω1/f 3

ω0/2Q

Thermal Noise

Shot Noise

Flicker Noise

Modified Leeson ModelModified Leeson Model

Tries to account for traits seen in spectrum Tries to account for traits seen in spectrum Loosely based on principle of time-invarianceLoosely based on principle of time-invariance FF, , ωω1/f1/f33 are empirically calculated are empirically calculated

• Not good for prediction!Not good for prediction!

Lee ModelLee Model Based on time-varianceBased on time-variance No empirical variablesNo empirical variables Corresponds well to observationsCorresponds well to observations

0 2 4 6 8 10 12 14 16 18 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Impulse

0 2 4 6 8 10 12 14 16 18 20-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Impulse

Lee Model (continued)…Lee Model (continued)…

Region of 1/f2

(Shot Noise)

Region of 1/f3

(Flicker Noise)

Effects of Phase NoiseEffects of Phase Noise

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

sample a signalsample a signal

Effects of Phase Noise…Effects of Phase Noise…

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

ω

Δω

Δω

ω0ω2 ω1Δω

So, what did I learn again?So, what did I learn again?

Oscillators are unstable (but very Oscillators are unstable (but very important!!) devicesimportant!!) devices

Phase noise is badPhase noise is bad• Spreads the frequency spectrumSpreads the frequency spectrum• Causes timing jitterCauses timing jitter

Two models can be used to provide Two models can be used to provide insight in reducing phase noiseinsight in reducing phase noise