Pre-Phase A Report - Lisa - Nasa

3.2 The inertial sensor 69
and the level of the disturbing effects resulting from the presence of the instrument cage
near the mass. Currently selected are gaps of 1 to 2 mm for the Z-axis electrodes and of
0.3 mm for the X and Y axes.
Then, the setting of the configuration parameters results from the trade-off between the
position sensing resolution and the back-actions induced on the proof-mass motion by the
detection voltage, i.e. a negative electrostatic stiffness and an electrostatic acceleration
when the configuration is not fully symmetric.
As presented in Figure 3.9, the sensitivity of the capacitive position sensor can be adjusted
according to the three following parameters: the amplitude of the sine wave detection
voltage, Vd, applied to the proof mass via injection electrodes, the gain of the electronics
that collect the detection signal through the two sensing electrodes corresponding to the
sensor, and the distance between the electrodes and the proof mass.
As a matter of fact, the capacitive sensor resolution is mainly driven by the thermodynamic
noise of the capacitive bridge formed by the proof mass, the opposite sensing
electrodes and the differential transformer, and it can be expressed by:
Cn(f) = 1
Vd
2kTCe
πfdQ
(F/ √ Hz) , (3.8)
with Ce the whole capacitance seen at the transformer input and with Q the quality factor
of the LC detection circuit. With a detection voltage level of 5 Vrms and a sensitivity of
50 V/pF a resolution of 1.2×10 −7 pF/ √ Hz has been obtained with space qualified hybrids.
Using a reduced detection voltage of only 1 Vrms and a gap of 1 mm, in order to minimise
the effects of the negative electrostatic stiffness, a resolution of 2×10 −10 m/ √ Hz should
be achieved. Moreover, recent improvements of the resolution of the capacitive sensor
could be beneficial to the CAESAR electronics development: the corner frequency of the
1/f sensor noise can be lowered under certain conditions to frequencies below 10 −4 Hz.
Figure 3.8 Electrodes set configuration.
Corrected version 2.08 3-3-1999 9:33