AURIGA: the capacitive transducer


The conversion of the mechanical signal of the bar vibration into an usable electromagnetic signal is accomplished by the transducer. AURIGA is equipped with a capacitive transducer. Essentially it is a plane plate capacitor, with unperturbed capacitance C0, biased at constant electrical field E0. The transducer is attached to one of the bar end faces. The bar is counter-loaded by a calibrator on the end face opposite the transducer.

One of the capacitor plates is fixed to (i.e. co-moving with) the bar end-face while the other is a resonant body (called resonant transducer) having the same resonant frequency of the bar. The bar-transducer system thus behaves as the system of two tuned harmonic oscillators coupled together: within a beat time the elastic energy of the main resonator is transferred to the lighter transducer producing a resonant plate displacement larger than the bar displacement by a factor equal to the square root of the bar-transducer effective mass ratio.

Any displacement x(t) of the bar end face produces a modulation of the transducer capacitance C(t): at first order in x(t) the voltage signal V(t) developed across the capacitor is:

V(t)=Q(t)/C(t) ~ E0 x(t) + q(t)/C0

where q(t) is the time dependent transducer charge. The vibration signal is thus transformed (i.e. 'transduced') into an electrical signal whit efficiency E0.

In order take full advantage of having a transducer which is resonant with the bar, the filter used for data analysis should have an integration time at least equal to the beat time. As the integration time is suitable for an optimization, an optimal transducer mass function of the noise sources amplitudes is required. The present AURIGA transducer resonant mass is 0.3 kg.

exploded drawing transducer

Scale drawing of the AURIGA capacitive transducer The lower part of the transducer is the resonator which is directly bolded to the bar end face. The resonator is made out in the same aluminum alloy (namely Al5056) as the bar. The capacitor plate co-moving with the bar is here indicated as charged plate. A teflon (PTFE) spacer guarantees the electrical insulation between the two plates.

A scale drawing of the AURIGA transducer is reported in fig.1. The resonator is an Al5056 shell "mushroom" shaped: its first flexural mode is coupled to the bar longitudinal mode. The mechanical resonance is at about 923 Hz and the mechanical quality factor is more than 1.5x 106 at 4.2 K temperature.

A problem to face with capacitive transducer is the relatively large mismatch between the transducer output impedance 1/(w C0) (approx = 100kOhm) and the SQUID input impedance w Lsq (approx = 10 mOhm). Here Lsq is the SQUID input coil and w is the angular frequency. Optimal signal transfer is obtained inserting an high ratio matching transformer between the transducer and the SQUID (see fig. 2). The transformer is made by superconducting wires and is housed in a superconducting box: this is done so not to worsen the overall Q-factor and so to preserve high sensitivity.

Scheme of the AURIGA readout

A scheme of the AURIGA readout The transducer output is connected to a superconducting matching transducer whose primary coil self-inductance is Lp = 5.5 H. The secondary coil Ls = 2.4x10-6 H is directly connected to the SQUID input coil Lsq= 1.9x10-6 H. The transducer capacitance forms a third resonator with the transformer primary coil: this resonator is an electrical one with characteristic frequency of 1254 Hz and with estimated Q-factor of about 4x105.

Main figures of the AURIGA transducer are listed in the following.

Transducer effective mass 0.3 kg Transducer capacitance C0 2.7nF
Transducer capacitance gap 80 m Transducer bias voltage 300 600 V

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