Higher harmonic generation in CMOS/SOS ring oscillators

Harmonic generation is found with 101-stage ring oscillators. Harmonics have not been observed for the usual ring oscillators with a small number of stages. If one mistakes the higher harmonic generation for the fundamental, he obtains a wrong propagation delay which is shorter than the real one. It is shown experimentally and theoretically that only odd harmonics are generated for the ring oscillators with an odd number of stages. The propagation delay t
pd
of the nth harmonic oscillation is given by
t_{pd} = n \cdot T/2N
where
T
is the observed repetition period and
N
the number of stages. Computer simulation shows that a ring oscillator with an even number of stages can also oscillate if every inverter is the same, and that the oscillation decays if there is asymmetry in the inverter chain. If
N
is large and the effects of the deviations of the transistor parameters cancel one another, the harmonic oscillation that happens to be generated can continue.