Distortion and Locking Range of a Pulse Synchronized Linear LC(t) Circuit

Exact conditions for the synchronization of the Oscillations of a linear resistanceless
LC(t)
circuit to a harmonic/subharmonic of the frequency of the capacitance variation are derived for the case of a periodically pulsed capacitance. It is shown that the magnitude of the largest undesired spectral component relative to that of the desired output is given by
-A_{0}(N) + 20 \log N_{\pi \nu} (dB)
, where
A_{0}(N)
is determined by numerical computation for several
N
, and
\nu
is the fractional offset of the resonant frequency from the Nth harmonic of half the synchronization frequency.