Injection Locking EECS 242 Lecture 26 Prof Ali M Niknejad Outline Injection Locking Adler s Equation locking range Extension to large signals Examples GSM CMOS PA Low Power Transmitter Dual Mode Oscillators Clock distribution Quadrature Locked Oscillators Injection locked dividers Ali M Niknejad University of California Berkeley Slide 2 Injection Locking http www youtube com watch v IBgq NJCl0 locking is also known as frequency entrainment or Injection synchronization Many natural examples including clocks on the same wall observed to synchronize pendulum over time fireflies put on a good light show Injection locking can be deliberate or unwanted Ali M Niknejad University of California Berkeley Slide 3 Injection Locking Video Demonstration http www youtube com watch v W1TMZASCR I metronomes similar to pendulums are initially excited Several in random phases The oscillation frequencies are presumably Ali M Niknejad very close but vary slightly due to manufacturing imperfections When placed on a rigid surface the metronomes oscillate independently When placed on flexible table with springs coke cans they couple to one another and injection lock University of California Berkeley Slide 4 A Study of Injection Locking and Pulling Unwanted Injection Pulling Locking in Oscillators Behzad Razavi Fellow IEEE of the difficulties in designing a One fully integrated transceiver is Abstract Injection locking characteristics of oscillators are derived and a graphical analysis is presented that describes injection pulling in time and frequency domains An identity obtained from phase and envelope equations is used to express the requisite oscillator nonlinearity and interpret phase noise reduction The behavior of phase locked oscillators under injection pulling is also formulated exactly due to pulling pushing If the injection signal is strong Index Terms Adler s equation injection locking injection enough it will lock the source pulling oscillator nonlinearity oscillator pulling quadrature oscillators it will pull the source Otherwise and produce unwanted modulation NJECTION of a periodic signal into an oscillator leads to interesting locking orthe pullingtransmitter phenomena Studied by In the I first example Adler 1 Kurokawa 2 and others 3 5 these effects have is locked a XTAL whereas found to increasingly greater importance for theythe manifest themselvesisin locked many of today s transceivers and frequency synthesis receiver to the data clock techniques Unwanted coupling This paper describes new package insights into injection locking and pulling Vdd Gnd and formulates the behavior of phase locked oscillators substrate can cause under injection A graphical interpretation of Adler s equation pulling illustrates pulling in both time and frequency domains while derived from the phase and envelope equations A PA isanexpresses aidentity classic source of trouble the required oscillator nonlinearity across the lock range in a direct conversion transmitter Section II of the paper places this work in context and Section III deals with injection locking Sections IV and V respectively consider injection pulling and the required oscillator nonlinearity Section VI quantifies the effect of pulling on phase locked loops PLLs and Section VII summarizes the experimental results Ali M Niknejad Fig 1 Source Razavi Oscillator pulling in a broadband transceiver and b RF transceiver Injection locking becomes useful in a number of applications including frequency division 8 9 quadrature generation 10 11 and oscillators with finer phase separations 12 Injection pulling on the other hand typically proves undesirable For example in the broadband transceiver of Fig 1 a is lockedSlide to University of California Berkeley the transmit voltage controlled oscillator 5 I GENERAL CONSIDERATIONS Injection Locking is Non Linear 0 1 2 3 142 5 0 012 3 3 3 012 4 54 367 8 9 6 4 4 4 Ali M Niknejad 0 0 0 Source M Perrott MIT OCW 6 976 For weak injection you get a response at both side bands As the injection is increased it begins to pull the oscillator for large enough injection the oscillation locks to the Eventually injection signal University of California Berkeley Slide 6 Injection Locking in LC Tanks 1416 IE a a free running Consider oscillator consisting of an ideal positive feedback amplifier and an LC tank Now suppose b we insert a phase shift in the loop We know this will cause the oscillation frequency to c shift since the loop gain has to have exactly 2 phase shift or multiples Gm ZT 0 gm R 1 Gm ej 0 ZT 1 1 Gm ej 0 ZT 1 e j 0 1 ZT 1 0 Ali M Niknejad Fig Source Fig 2 a Conceptual oscillator b Frequency Razavi shift due to additional phase shift c Open loop characteristics d Frequency shift by injection wh shift and the ideal inverting buffer follows the tank to create a total phase shift of 360 around the feedback loop What hap if University of California pens if Berkeley an additional phase shift is inserted in the loop e g Slide as 7 Injection Locking in LC Tanks cont phase shift in the tank will cause the oscillation frequency to Achange in order to compensate for the phase shift through the tank impedance The oscillation frequency is no longer at the resonant frequency of the tank Note that the oscillation amplitude must also change since the loop gain is now different tank impedance is lower Maximum phase shift that the tank can provide is 90 In a high Q tank the frequency shift is relatively small since 1 5 1 0 d Q 2 d 0 5 0 0 2 Q 0 5 1 1 5 8 9 25 10 Ali M Niknejad 8 9 5 10 University of California Berkeley 8 9 75 10 9 1 10 9 1 025 10 9 1 05 10 9 1 075 10 9 1 1 10 Slide 8 Phase Shift for Injected Signal interesting to observe that if a signal is It s injected into the circuit then the tank current is Ali M Niknejad a sum of the injected and transistor current Assume the oscillator locks onto the injected current and oscillates at the same frequency Since the locking signal is not in general at the resonant center frequency the tank introduces Source Razavi a phase shift Fig 2 a Conceptual oscillator b Frequency shift due to additional phase shift c Open loop characteristics d Frequency shift by injection In order for the oscillator loop gain to be equal to unity with zero phase shift the sum of the shift andinjected the ideal inverting buffer follows the tank to create a current of the transistor and the total phase shift of 360 around the feedback loop What hapcurrents must have the proper phase shift to pens