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Entry  Sun Jun 6 08:08:05 2010, rana, sanjit, Summary, Electronics, Capacitor Bridge Test CapacitanceBridge.png
    Reply  Mon Jun 7 07:39:38 2010, Alberto, Omnistructure, Electronics, Capacitor Bridge Test 
Message ID: 3052     Entry time: Sun Jun 6 08:08:05 2010     Reply to this: 3053
Author: rana, sanjit 
Type: Summary 
Category: Electronics 
Subject: Capacitor Bridge Test 

To get a feel for the Capacitive Bridge problems, we setup a simple bridge using fixed (1 nF) caps on a breadboard. We used an SR830 Lock-In amplifier to drive it and readout the noise.


We measured the cap values with an LCR meter. They were all within a few % of 0.99 nF.

With a 0.5 V drive to the top of the bridge, the A-B voltage was ~2 mV as expected from the matching of the capacitors.

(** Note about the gain in the SR830: In order to find the magnitude of the input referred signal, one has to divide by G. G = (10 V)/ Sensitivity. 'Sensitivity' is the setting on the front panel.)

  1. Directly measuring from Vs to ground gives 0.5 V, as expected. This is done to verify the calibration later on.
  2. Shorting the A and B wires to ground gives ~0 V and lets us measure the noise. On the spectrum analyzer it was ~400 nV/rHz at 100 Hz and rising slowly to 4 uV/rHz at 100 mHz. In this state, the sensitivity was 10 mV, so the overall gain was 1000. That gives an input referred level of ~0.4 nV/rHz at the input.
  3. Hooking up now to A-B: the signal is ~10x larger than the 'dark' noise everywhere. 2 uV/rHz @ 100 Hz, 10 uV/rHz @ 10 Hz, 50 uV/rHz @ 1 Hz. The spectrum is very non-stationary; changing by factors of several up and down between averages. Probably a problem with the cheapo contacts in the breadboard + wind. The gain in this state was still 1000. So at 1 Hz, its 50 nV/rHz referred to the input.

To convert into units of capacitance fluctuation, we multiply by the capacitance of the capacitors (1 nF) and divide out by the peak-peak voltage (1 V). So the bridge sensitivity is 50e-9 * 1e-9 = 5 x 10^-17 F/rHz.

If we assume that we will have a capacitive displacement transducer giving 1 nF capacitance change for a 0.1 mm displacement, this bridge would have a sensitivity of 5 x 10^-12 m/rHz @ 1 Hz. We would like to do ~50-100x better than this. The next steps should be:

  1. Solder it all together on a PCB to have less air current sensitivity and decent contacts.
  2. Use a low-noise FET input. Since the impedance of the bridge is ~5 kOhms at this frequency, we are probably current noise limited.
  3. Estimate the oscillator amplitude noise sensitivity.
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