![](https://csdnimg.cn/release/download_crawler_static/12143380/bg13.jpg)
HONG AND HAJIMIRI: GENERAL THEORY OF INJECTION LOCKING AND PULLING IN ELECTRICAL OSCILLATORS—I 2121
[25] S. Verma, H. R. Rategh, and T. H. Lee, “A unified model for injection-
locked frequency dividers,” IEEE J. Solid-State Circuits, vol. 38, no. 6,
pp. 1015–1027, Jun. 2003.
[26] L. J. Paciorek, “Injection locking of oscillators,” Proc. IEEE, vol. 53,
no. 11, pp. 1723–1727, Nov. 1965.
[27] A. Mirzaei, M. E. Heidari, R. Bagheri, S. Chehrazi, and A. A. Abidi,
“The quadrature LC oscillator: A complete portrait based on
injection locking,” IEEE J. Solid-State Circuits, vol. 42, no. 9,
pp. 1916–1932, Sep. 2007.
[28] B. Hong and A. Hajimiri, “A phasor-based analysis of sinusoidal
injection locking in LC and ring oscillators,” IEEE Trans. Circuits Syst.
I, Reg. Papers, vol. 66, no. 1, pp. 355–368, Jan. 2019.
[29] A. Mirzaei and H. Darabi, “Mutual pulling between two oscillators,”
IEEE J. Solid-State Circuits, vol. 49, no. 2, pp. 360–372, Feb. 2014.
[30] X. Lai and J. Roychowdhury, “Capturing oscillator injection locking
via nonlinear phase-domain macromodels,” IEEE Trans. Microw. Theory
Techn., vol. 52, no. 9, pp. 2251–2261, Sep. 2004.
[31] X. Lai and J. Roychowdhury, “Automated oscillator macromodelling
techniques for capturing amplitude variations and injection locking,” in
Proc. IEEE/ACM Int. Conf. Comput.-Aided Des. (ICCAD), Nov. 2004,
pp. 687–694.
[32] G. R. Gangasani and P. R. Kinget, “Time-domain model for injection
locking in nonharmonic oscillators,” IEEETrans.CircuitsSyst.I,Reg.
Papers, vol. 55, no. 6, pp. 1648–1658, Jul. 2008.
[33] H. A. Tanaka, A. Hasegawa, H. Mizuno, and T. Endo, “Synchronizability
of distributed clock oscillators,” IEEE Trans. Circuits Syst. I, Fundam.
Theory Appl., vol. 49, no. 9, pp. 1271–1278, Sep. 2002.
[34] P. Maffezzoni, “Analysis of oscillator injection locking through phase-
domain impulse-response,” IEEE Trans. Circuits Syst. I, Reg. Papers,
vol. 55, no. 5, pp. 1297–1305, Jun. 2008.
[35] T. Nagashima, X. Wei, H.-A. Tanaka, and H. Sekiya, “Locking range
derivations for injection-locked class-E oscillator applying phase reduc-
tion theory,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 61, no. 10,
pp. 2904–2911, Oct. 2014.
[36] M. A. Tiebout, “A CMOS direct injection-locked oscillator topology
as high-frequency low-power frequency divider,” IEEE J. Solid-State
Circuits, vol. 39, no. 7, pp. 1170–1174, Jul. 2004.
[37] C.-C. Chen, H.-W. Tsao, and H. Wang, “Design and analysis of CMOS
frequency dividers with wide input locking ranges,” IEEE Trans. Microw.
Theory Techn., vol. 57, no. 12, pp. 3060–3069, Dec. 2009.
[38] R. J. Betancourt-Zamora, S. Verma, and T. H. Lee, “1-GHz and
2.8-GHz CMOS injection-locked ring oscillator prescalers,” in Symp.
VLSI Circuits Dig. Tech. Papers, Jun. 2001, pp. 47–50.
[39] J. C. Chien and L. H. Lu, “Analysis and design of wideband injection-
locked ring oscillators with multiple-input injection,” IEEE J. Solid-State
Circuits, vol. 42, no. 9, pp. 1906–1915, Sep. 2007.
[40] A. Mirzaei, M. E. Heidari, R. Bagheri, and A. A. Abidi, “Multi-
phase injection widens lock range of ring-oscillator-based frequency
dividers,” IEEE J. Solid-State Circuits, vol. 43, no. 3, pp. 656–671,
Mar. 2008.
[41] D. Dunwell and A. C. Carusone, “Modeling oscillator injection locking
using the phase domain response,” IEEETrans.CircuitsSyst.I,Reg.
Papers, vol. 60, no. 11, pp. 2823–2833, Nov. 2013.
[42] A. Hajimiri and T. H. Lee, “A general theory of phase noise in electrical
oscillators,” IEEE J. Solid-State Circuits, vol. 33, no. 2, pp. 179–194,
Feb. 1998.
[43] A. Hajimiri and T. H. Lee, “Design issues in CMOS differential LC
oscillators,” IEEE J. Solid-State Circuits
, vol. 34, no. 5, pp. 717–724,
May 1999.
[44] A. Hajimiri, S. Limotyrakis, and T. H. Lee, “Jitter and phase noise
in ring oscillators,” IEEE J. Solid-State Circuits, vol. 34, no. 6,
pp. 790–804, Jun. 1999.
[45] A. Hajimiri and T. H. Lee, The Design of Low Noise Oscillators.
Norwell, MA, USA: Kluwer, 1999.
[46] S. Levantino, P. Maffezzoni, F. Pepe, A. Bonfanti, C. Samori, and
A. L. Lacaita, “Efficient calculation of the impulse sensitivity function
in oscillators,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 59, no. 10,
pp. 628–632, Oct. 2012.
[47] J. A. Sanders, F. Verhulst, and J. Murdock, Averaging Methods in
Nonlinear Dynamical Systems. New York, NY, USA: Springer, 2007.
[48] B. Hong, “Periodically disturbed oscillators,” Ph.D. dissertation, Dept.
Elect. Eng., California Inst. Technol., Pasadena, CA, USA, 2018. doi:
10.7907/W0A7-4258.
[49] A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering
and Science. New York, NY, USA: Springer, 2000.
Brian Hong (S’11) received the B.S. degree (summa
cum laude) in electrical engineering from the Uni-
versity of California at Los Angeles (UCLA),
Los Angeles, CA, USA, in 2013, and the M.S.
and Ph.D. degrees in electrical engineering from
the California Institute of Technology (Caltech),
Pasadena, CA, USA, in 2014 and 2018, respectively.
His research interests include the mathematical
and physical modeling of various electronic systems,
with a particular emphasis on the theory of injection
locking and pulling in electrical oscillators.
Dr. Hong was a recipient of the JPL Undergraduate Scholarship in 2008,
the Rose Hills Foundation Fellowship in 2013, and the Analog Devices
Outstanding Student Designer Award in 2014.
Ali Hajimiri (S’94–M’98–SM’09–F’10) received
the B.S. degree in electronics engineering from the
Sharif University of Technology, Tehran, Iran, in
1994, and the M.S. and Ph.D. degrees in electrical
engineering from Stanford University, Stanford, CA,
USA, in 1996 and 1998, respectively.
From 1993 to 1994, he was with Philips Semicon-
ductors, Sunnyvale, CA, USA, where he worked on a
BiCMOS chipset for Global System for Mobile com-
munications (GSM) and cellular units. In 1995, he
was with Sun Microsystems, Sunnyvale, working on
the UltraSPARC microprocessors cache RAM design methodology. In 1997,
he was with Lucent Technologies (Bell Labs), Murray Hill, NJ, USA, where
he investigated low-phase-noise integrated oscillators. In 1998, he joined
the faculty of the California Institute of Technology (Caltech), Pasadena,
CA, USA, where he is currently a Bren Professor of electrical engineering
and medical engineering, the Director of the Microelectronics Laboratory,
and a Co-Director of the Space Solar Power Project. In 2002, he was a
Co-Founder of Axiom Microdevices Inc., Irvine, CA, USA, whose fully inte-
grated CMOS PA shipped close to 400 million units and which was acquired
by Skyworks Inc. in 2009. He is the author of The Design of Low Noise
Oscillators (Boston, MA, USA: Springer), and he has authored or coauthored
more than 200 refereed journal and conference technical articles. He holds
more than 100 U.S. patents and has many more pending applications. His
research interests include high-speed and high-frequency integrated circuits
for applications in sensors, photonics, biomedical devices, and communication
systems.
Dr. Hajimiri is a fellow of the National Academy of Inventors. He has
served as a member of the Technical Program Committee for the IEEE
International Solid-State Circuits Conference (ISSCC) and the International
Conference on Computer-Aided Design (ICCAD). He was selected to the
TR35 top innovator’s list (formerly TR100) in 2004. He has received a
number of teaching awards from Caltech, including the Richard P. Feynman
Prize for Excellence in Teaching, the Graduate Student Council Teaching
and Mentoring Award, and the Associated Students of the California Institute
of Technology (ASCIT) Undergraduate Excellence in Teaching Award. He
was the Gold Medal winner of the National Physics Competition, Iran,
and the Bronze Medal winner of the 21st International Physics Olympiad,
Groningen, the Netherlands. He has been recognized as one of the top-
10 contributors to ISSCC. He was a co-recipient of the IEEE Journal of Solid-
State Circuits Best Paper Award of 2004, the ISSCC Jack Kilby Outstanding
Paper Award, the RFIC Best Paper Award, and the CICC Best Paper Award
(twice). He has received the National Science Foundation CAREER Award
and the Okawa Foundation Award, and he is a three-time winner of the IBM
Faculty Partnership Award. He has served as an Associate Editor for the
IEEE J
OURNAL OF SOLID-STATE CIRCUITS and the IEEE TRANSACTIONS
ON
CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS,aGuestEditorofthe
IEEE T
RANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,and
a member of the Guest Editorial Board for the Transactions on Electronics
of the Institute of Electronics, Information and Communication Engineers
(IEICE), Japan. He has also served as a Distinguished Lecturer for the IEEE
Solid-State and Microwave Societies.