

Synchronizability of Distributed Clock Oscillators
HisaAki Tanaka, Akio Hasegawa, Hiroyuki Mizuno, and Tetsuro Endoh
IEEE Transactions on Circuits and Systems  I: Fundamental Theory and Applications, 2002.
Keyword
Clock distribution network, impulse sensitive
function, phase equation, ring oscillator, synchronization,
voltagecontrolled oscillator.
Abstract
We analyze the synchronizability of synchronous distributed
oscillators (SDOs) [3], a novel clocking scheme for microprocessors.
A computeraided perturbation analysis is developed
for such systems, where analytically tractable equations of
the clock phases are reduced from experimental data reflecting all
circuit details. Using this reduction, a theory is constructed to explain
the underlying mechanism of the synchronization in SDOs.
It systematically explains the observed phenomena, the existence
and stability of the (mutually) synchronized states, and the transition
from the inphase synchronized state to the outofphase (but
still synchronized) state. Furthermore, the present theory of phase
reduction provides a new design principle of coupled oscillators
based on “the equation”; a precise delay control (less than the gate
delay) circuit can be designed in a simple and general form.
Download PDF
Figures at a glance
References
 G. A. Pratt and J. Nguyen, “Distributed synchronous clocking,” IEEE
Trans. Parallel Distrib. Syst., vol. 6, pp. 314328, Feb. 1995.
 V. Gutnik and A. Chandrakasan, “Active GHz clock network using distributed
PLLs,” in ISSCC Dig. Tech. Papers, Feb. 2000, pp. 174175.
 H. Mizuno and K. Ishibashi, “A noiseimmune GHzclock distribution
scheme using synchronous distributed oscillators,” in ISSCC Dig. Tech.
Papers, Feb. 1998, pp. 404405.
 A. Hajimiri and T. H. Lee, “A general theory of phase noise in electrical
oscillators,” IEEE J. SolidState Circuits, vol. 33, pp. 179194,
Feb. 1998.
 J. M. Rabaey, Digital Integrated Circuits; A Design Perspective.
Upper Saddle River, NJ: PrenticeHall, 1996, pp. 5760.
 P. Antognetti and G. Masobrio, Eds., Semiconductor Device Modeling
with SPICE. New York: McGrawHill, 1988.
 J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical
Systems, and Bifurcation of Vector Fields. New York: Springer, 1982,
pp. 166180.
 J. G. Maneatis and M. A. Horowitz, “Precise delay generation using coupled
oscillators,” IEEE J. SolidState Circuits, vol. 28, pp. 12731282,
Dec. 1993.
 K. Ishibashi, “A 300 MHz 4Mb wavepipeline CMOS SRAM using a
multiphase PLL,” in ISSCC Dig. Tech. Papers, vol. 28, Feb. 1995, pp.
308309.
 Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence. Berlin,
Germany: Springer, 1975, vol. 39. Lecture Notes in Physics, 1984.
 G. B. Ermentrout and N. Kopell, “Multiple pulse interactions and averaging
in systems of coupled neural oscillators,” J. Math. Biol., vol. 29,
pp. 195217, 1991.
 N. Mellen, T. Kiemel, and A. H. Cohen, “Correlational analysis of fictive
swimming in the lamprey reveals strong functional intersegmental
coupling,” J. Neurophys., vol. 73, pp. 10201030, Mar. 1995.
 M. Kawato and R. Suzuki, “Analysis of entrainment of circadian oscillators
by skeleton photoperiods using phase transition curves,” Biol.
Cybern., vol. 40, pp. 139149, 1981.
 N. Ikeda, “Model of bidirectional interaction between myocardial pacemaker
based on the phase response curve,” Biol. Cybern., vol. 43, pp.
157167, 1982.


