1. Phase Noise and Oscillators Stephen Powell

2. What is an Oscillator?  Produces a signal at a particular frequency  They are everywhere! watches, radios, computers, in most electronic circuitswatches, radios, computers, in most electronic circuits  Uses? Generates signals for transmissionGenerates signals for transmission Frequency translationFrequency translation Provides timing referencesProvides timing references

3. How to build an Oscillator!  Need a feedback loop  Oscillates at frequency ω 0 when 1-A(jω 0 )B(jω 0 ) = 0 (Barkhausen criteria) 1-A(jω 0 )B(jω 0 ) = 0 (Barkhausen criteria)  Unstable device!

4. Simple LCR Oscillator  L,C,R forms an impedance “tank”  Impedance has same form as the loop equation  Voltage across tank oscillates

5. Effect of Resistance Without R With R

6. Phase Noise  Oscillator output: V(t) = C·sin(ω 0 t+θ(t))  Suppose θ(t) = θ sin(pt)  model one component of white noise… then:

7. Origins of Phase Noise  Three types of contributing noise: Flicker Noise: power inversely proportional to frequency, AKA 1/f noiseFlicker Noise: power inversely proportional to frequency, AKA 1/f noise Shot Noise: due to random charge carriers, proportional to currentShot Noise: due to random charge carriers, proportional to current Thermal Noise: present in all resistors, wide band, AKA Johnson noiseThermal Noise: present in all resistors, wide band, AKA Johnson noise

8. Aggregate Phase Noise  All three types together… log(∆ω) log(L(∆ω)) ω 1/f 3 ω 0 /2Q Thermal Noise Shot Noise Flicker Noise

9. Modified Leeson Model  Tries to account for traits seen in spectrum  Loosely based on principle of time- invariance  F, ω 1/f 3 are empirically calculated Not good for prediction!Not good for prediction!

10. Lee Model  Based on time-variance  No empirical variables  Corresponds well to observations

11. Lee Model (continued)… Region of 1/f 2 (Shot Noise) Region of 1/f 3 (Flicker Noise)

12. Effects of Phase Noise  In the time domain: Timing Jitter bad if you want to synchronize a signal, or sample a signalbad if you want to synchronize a signal, or sample a signal

13. Effects of Phase Noise…  In the frequency domain: Reciprocal Mixing bad for interference immunitybad for interference immunity

14. So, what did I learn again?  Oscillators are unstable (but very important!!) devices  Phase noise is bad Spreads the frequency spectrumSpreads the frequency spectrum Causes timing jitterCauses timing jitter  Two models can be used to provide insight in reducing phase noise