EECS 142 Oscillator Phase Noise Prof Ali M Niknejad University of California Berkeley Copyright A M Niknejad c 2009 by Ali M Niknejad University of California Berkeley EECS 242 p 1 61 p 1 61 Oscillator Output Spectrum Ideal Oscillator Spectrum Real Oscillator Spectrum The output spectrum of an oscillator is very peaked near the oscillation frequency but not infinitely so It s not a pair of delta function Why If we ignore noise the closed loop gain of the system is infinite since Al 1 But in practice there is noise in any real oscillator A M Niknejad University of California Berkeley EECS 242 p 2 61 p 2 61 Phase Noise versus Amplitude Noise Upper and Lower Sidebands Shown Separately Sum of Upper and Lower Sidebands SSB DSB AM PM a b c d Source The Designer s Guide Community www desingers guide org Noise in Mixers Oscillators Samplers and Logic by J Philips and K Kundert Notice that noise at offset frequency can be modeled as a phasor rotating around the rotating carrier phasor It rotates because it s at a different frequency offset The upper side band rotates in the same direction with frequency whereas the lower sideband rotates clockwise or with frequency A M Niknejad University of California Berkeley EECS 242 p 3 61 p 3 61 Graphical Picture of AM and PM In general the two side bands are completely uncorrelated meaning their amplitude and phase will vary randomly from one another When summed together they trace an ellipse whose size and shape and orientation shifts randomly If the noise is cyclostationary there is correlation between the two sidebands which reduces the random shifting of the shape and orienation For perfect correlation the shape and orienation will remain unchanged and the size shifts randomly Note that for a stationary noise source the AM and PM components are equal If we pass the signal through a limiting amplifier the AM noise is rejected This produces an output with only PM We shall see that for an oscillator the AM noise is rejected Oscillators generate phase noise AM component rejected which traces a perpundicular line A M Niknejad University of California Berkeley EECS 242 p 4 61 p 4 61 Phase Noise Why do we say that the noise in the spectrum is due to phase noise rather than amplitude noise An oscillator has a well defined amplitude which is controlled by the non linearity of the circuit If there is an amplitude perturbation it is naturally rejected by the oscillator This occurs because the oscillation occurs at a frequency when the loop gain is unity If the amplitude grows due to compressive characteristics of the non linearity the loop gain decreases and the oscillation amplitude dampens Likewise if the amplitude drops the loop gain goes over unity due to expansive characterisitcs of the non linearity and the amplitude grows back The phase of the oscillator on the other hand is free running Any phase shifted solution to the oscillator is a valid solution So if a perturbation changes the phase of the oscillator there is no restoring force and the phase error persists A M Niknejad University of California Berkeley EECS 242 p 5 61 p 5 61 Phase Noise Measurement log If we zoom into the carrier on a log scale the relative power at an offset frequency f from the carrier drops very rapidly For the case shown above at an offset of 100kHz the power drops to 100dBc P dBc Hz P0 1 f 3 80 1 f 2 100 1kHz 10kHz 100kHz 1MHz f There is clearly a region where the slope is 20dB dec But this range only holds until the noise flattens out Also very near the carrier the slope increases to approximately 30dB dec A M Niknejad University of California Berkeley EECS 242 p 6 61 p 6 61 Phase Noise In TX Chain Phase Noise Leakage PA VCO CH 1 CH 2 CH 3 CH 4 CH 5 CH 6 Channel Spacing 200 kHz Phase noise in a transmit chain will leak power into adjacent channels Since the power transmitted is large say about 30dBm an adjacent channel in a narrowband system may only reside about 200kHz away GSM placing a stringent specification on the transmitter spectrum A M Niknejad University of California Berkeley EECS 242 p 7 61 p 7 61 Phase Noise In RX Chain Interferer Desired IF LO RF1 RF2 In a receive chain the fact that the LO is not a perfect delta function means that there is a continuum of LO s that can mix with interfering signals and produce energy at the same IF Here we observe an adjacent channel signal mixing with the skirt of the LO and falling on top of the a weak IF signal from the desired channel A M Niknejad University of California Berkeley EECS 242 p 8 61 p 8 61 Phase Noise In Digital Communication Q In a digital communication system phase noise can lead to a lower noise margin Above we see that the phase noise causes the constellation of a 4 PSK system to spread out I In OFDM systems a wide bandwidth is split into sub channels The phase noise leads to inter carrier interference and a degradation in the digital communication BER A M Niknejad University of California Berkeley EECS 242 p 9 61 p 9 61 Feedback Model of Phase Noise In a simple linear model for an oscillator the closed loop transfer function is given by H f Y f X f H f 1 This goes to infinity at oscillator since by definition H f 1 for osicllation to occur Barkhausen condition At a frequency offset from the carrier assuming the loop gain varies smoothly we have dH H f H f0 f df so that H f0 dH Y f f df f X f f H f0 dH df f 1 A M Niknejad University of California Berkeley EECS 242 p 10 61 p 10 61 Feedback Model cont Since H f0 1 and assuming dH df f 1 for practical situations near the carrier Y f f X f f 1 dH df f This shows that for circuits containing white noise sources the noise voltage current is inversely proportional to f while the noise power spectral density is proportional to f 2 This simplistic picture already gives us some insight into the shape of the noise spectrum But the noise does not blow up near the carrier Also why does all the noise go to phase noise and not amplitude noise Clearly an LTI model is too simple A M Niknejad University of California Berkeley EECS 242 p 11 61 p 11 61 Limit Cycle Model of Phase Noise The figure above shows that the non linearity in the oscillator tends to reject AM noise The noise is very small so why is a linear model not valid There are two reasons for this First the transfer function that the noise sees is a periodically time varyng function similar to a mixer Second we must be careful and correctly model the noise transfer …