  A new approach to investigate noise spikes due to regeneration in a
relaxation oscillator is proposed. Noise spikes have not been satisfactorily
accounted for in traditional phase noise models. This paper attempts to explain
noise spikes/jump phenomenon by viewing it as phase change in the thermodynamic
system(for example, from gas to liquid or magnetization of ferromagnet). Both
are due to regeneration (positive feedback in oscillator as well as alignment
of spin due to positive feedback in ferromagnet). The mathematical tool used is
the partition function in thermodynamics, and the results mapped between
thermodynamic system and relaxation oscillator. Theory is developed and formula
derived to predict the magnitude of the jump, as a function of design parameter
such as regeneration parameter or loop gain. Formulas show that noise increases
sharply as regeneration parameter/loop gain approaches one, in much the same
way when temperature approaches critical temperature in phase change.
Simulations on circuits (Eldo) using CMOS as well as Monte Carlo simulations
(Metropolis) on ferromagnet (Ising model) were performed and both show jump
behaviour consistent with formula. Measurements on relaxation oscillators
fabricated in 0.13um CMOS technology verify such behaviour, where the sharp
increase in noise when regeneration parameter/loop gain is close to one,
matches closely with the theoretical formula. Using the formula the designer
can quantify the variation of noise spikes dependency on design parameters such
as gm (device transconductance), R, I0, via their influence on regeneration
parameter/loop gain.
