  A novel room temperature capacitance-to-phase transducer is described, which
uses a modified All-Pass filter architecture combined with a simple series
resonant tank circuit with a moderate Q-factor. It is fashioned from a discrete
inductor with small dissipation resonating with a grounded capacitor acting as
the sensor, to obtain a relative resolution equal to or better than 10-11 in a
1 Hz bandwidth. The transducer converts the change in capacitance to the change
in the phase of a carrier signal at the resonance frequency and is configured
to act as a close approximation of the almost ideal All-Pass filter. This
cancels out the effects of amplitude modulation when the carrier signal is
imperfectly tuned to the resonance. When used as a mechanical
displacement-to-phase transducer, the predicted position noise was
approximately 3 femtometre/rootHz. Other applications of the proposed circuit
include the measurement of the electric field, where the sensing capacitor
depends on the applied electric field. In addition, the circuit can be easily
adapted to function with very small capacitance values (1 - 2 pF) as is typical
in MEMS-based transducers.
