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Injection Locking EECS 242 Lecture 26! Prof 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 • Injection locking is also known as frequency entrainment or synchronization! • Many natural examples including! - pendulum clocks on the same wall observed to synchronize 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 • Several metronomes (similar to pendulums) are initially excited in random phases. The oscillation frequencies are presumably 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. Ali M. Niknejad University of California, Berkeley Slide: 4 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 9, SEPTEMBER 2004 1415 A Study of Injection Locking and Pulling Unwanted Injectionin Oscillators Pulling/Locking Behzad Razavi, Fellow, IEEE One of Abstract—the difficultiesInjection locking characteristics in designing of oscillators area de- • rived and a graphical analysis is presented that describes injection fully integratedpulling in time and transceiver frequency domains. An identityis obtained from phase and envelope equations is used to express the requisite os- exactlycillator due nonlinearity to pulling and interpret / phasepushing noise reduction.! The be- havior of phase-locked oscillators under injection pulling is also • If the injectionformulated. signal is strong Index Terms—Adler’s equation, injection locking, injection enough,pulling, it will oscillator lock nonlinearity, the oscillatorsource. pulling, quadrature Otherwiseoscillators. it will “pull” the source and produce unwanted modulation! NJECTION of a periodic signal into an oscillator leads In the Ifirstto interesting example, locking orthe pulling transmitter phenomena. Studied by • Adler [1], Kurokawa [2], and others [3]–[5], these effects have is lockedfound to increasingly a XTAL greater importancewhereas for they the manifest them- receiverselves is in manylocked of today’s to transceivers the data and frequency clock. synthesis techniques. UnwantedThis paper coupling describes new (package, insights into injection locking and substrate,pulling Vdd/Gnd) and formulates the behaviorcan cause of phase-locked oscillators under injection. A graphical interpretation of Adler’s equation pulling.illustrates! pulling in both time and frequency domains while an identity derived from the phase and envelope equations • A PA isexpresses a classic the required source oscillator nonlinearityof trouble across the lock in a direct-conversionrange. transmitter Section II of the paper places this work in context and Fig. 1. Oscillator pullingSource: in (a) broadband [Razavi] transceiver and (b) RF transceiver. Section III deals with injection locking. Sections IV and V respectively consider injection pulling and the required oscil- Injection locking becomes useful in a number of applica- lator nonlinearity. Section VI quantifies the effect of pulling tions, including frequency division [8], [9], quadrature genera- on phase-locked loops (PLLs) and Section VII summarizes the tion [10], [11], and oscillators with finer phase separations [12]. experimental results. Injection pulling, on the other hand, typically proves undesir- able. For example, in the broadband transceiver of Fig. 1(a), Ali M. Niknejad University of California, Berkeley the transmit voltage-controlled oscillator, , is lockedSlide: to 5 I. GENERAL CONSIDERATIONS a local crystal oscillator whereas the receive VCO, , is Oscillatory systems are generally prone to injection locking locked to the incoming data and hence potentially a slightly or pulling. As early as the 17th century, the Dutch scientist different frequency. Thus, the two oscillators may pull each Christiaan Huygens, while confined to bed by illness, noticed other as a result of coupling through the substrate. Similarly, that the pendulums of two clocks on the wall moved in unison if the high-swing broadband data at the output of the transmitter the clocks were hung close to each other [6]. He postulated that may pull and as it contains substantial energy in the coupling of the mechanical vibrations through the wall drove the vicinity of their oscillation frequencies. the clocks into synchronization. It has also been observed that Fig. 1(b) depicts another example of undesirable pulling. The humans left in isolated bunkers reveal a “free-running” sleep- power amplifier (PA) output in an RF transceiver contains large wake period of about 25 hours [7] but, when brought back to spectral components in the vicinity of , leaking through the the nature, they are injection-locked to the Earth’s cycle. package and the substrate to the VCO and causing pulling. II. INJECTION LOCKING Manuscript received December 16, 2003; revised March 17, 2004. Consider the simple (conceptual) oscillator shown in Fig. 2, The author is with the Department of Electrical Engineering, University of California, Los Angeles, CA 90095 USA (e-mail: [email protected]). where all parasitics are neglected, the tank operates at the res- Digital Object Identifier 10.1109/JSSC.2004.831608 onance frequency (thus contributing no phase 0018-9200/04$20.00 © 2004 IEEE Authorized licensed use limited to: Univ of Calif Berkeley. Downloaded on April 26, 2009 at 19:53 from IEEE Xplore. Restrictions apply. Injection LockingInjection Locking is Non-Linear VCO |Vnoise(w)| |Vout(w)| Vnoise Vin Vout W W wo wo Δw -Δw Δw |V (w)| ! Noise close in |Vnoise(w)| out frequency to w W w W VCO resonant o o frequency can Δw -Δw Δw |V (w)| |Vout(w)| cause VCO noise frequency to W W wo wo shift when its Δw -Δw Δw amplitude |Vnoise(w)| |Vout(w)| becomes high W W enough w wo o Source: M. Perrott! Δw -Δw Δw MIT OCW 6.976 M.H. Perrott MIT OCW • For weak injection, you get a response at both side-bands! • As the injection is increased, it begins to “pull” the oscillator! • Eventually, for large enough injection, the oscillation locks to the injection signal Ali M. Niknejad University of California, Berkeley Slide: 6 Injection Locking in LC Tanks 1416 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 9, SEPTEMBER 2004 • Consider (a) a free-running 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 2π phase shift (or multiples) GmZT (ω0)=gmR =1 jφ0 Gme ZT (ω1)=1 Fig. 3. Phase difference between input and output for different values of and . jφ0 jφ0 Gme ZT (ω1) e− =1 | | Fig. 2. (a) Conceptual oscillator. (b)Source: Frequency [Razavi] shift due to additional phase which reaches a maximum of shift. (c) Open-loop characteristics. (d) Frequency shift by injection. ∠ZT (⇥1)= φ0 − (3) shift), and the ideal inverting buffer follows the tank to create a total phase shift of 360 around the feedback loop. What hap- if Ali M. Niknejad University of California,pens if Berkeley an additional phase shift is inserted in the loop, e.g.,Slide: as 7 depicted in Fig. 2(b)? The circuit can no longer oscillate at (4) because the total phase shift at this frequency deviates from 360 by . Thus, as illustrated in Fig. 2(c), the oscillation frequency Depicted in Fig. 3(c), these conditions translate to a 90 angle must change to a new value such that the tank contributes between the resultant and , implying that the phase differ- enough phase shift to cancel the effect of . Note that, if the ence between the “input,” , and the output, , reaches a buffer and contribute no phase shift, then the drain current maximum of . To compute the value of cor- of must remain in phase with under all condi- responding to this case, we first note that the phase shift of the tions. tank in the vicinity of resonance is given by (Section III-A) Now suppose we attempt to produce by adding a sinu- soidal current to the drain current of [Fig. 2(d)]. If the am- (5) plitude and frequency of are chosen properly, the circuit in- deed oscillates at rather than at and injection locking occurs. Under this condition, and must bear a phase and recognize from Fig. 3(c) that and difference [Fig. 3(a)] because: 1) the tank contributes phase at . It follows that , rotating with respect to the resultant current, , and 2) still remains in phase with and hence out (6) of phase with respect to , requiring that form an angle with . (If and were in phase, then would also be in phase with and thus with ). The angle formed be- tween and is such that becomes aligned with (This result is obtained in [3] using a different approach.) We (and ) after experiencing the tank phase shift, , at . denote this maximum difference by , with the understanding In order to determine the lock range (the range of across that the overall lock range is in fact around .1 which injection locking holds), we examine the phasor diagram The dependence of the lock range upon the injection level, of Fig. 3(a) as departs from . To match the increasingly , is to be expected: if decreases, must form a greater greater phase shift introduced by the tank, the angle between angle with so as to maintain the phase difference between and must also increase, requiring that rotate coun- and at [Fig. 3(d)]. Thus, the circuit moves closer to terclockwise [Fig. 3(b)]. It can be shown that the edge of the lock range.
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