Capacitance sensors measure a wide variety of physical quantities, such as position, acceleration, pressure and fluid level. The capacitance changes are often much smaller than stray capacitances, especially if the sensor is remotely placed. I needed to make measurements with a 50 pF cryogenic fluid level detector, with only 2 pF full-scale change, hooked to several hundred pF of varying cable capacitance. This required a circuit with high stability, sensitivity and noise rejection, but one insensitive to stray capacitance caused by cables and shielding. I also wanted battery operation and analog output for easy interfacing to other instruments. Two traditional circuit types have drawbacks: integrators are sensitive to noise at the comparator and voltage-to-frequency converters typically measure stray as well as sensor capacitance. The capacitance bridge presented here measures small transducer capacitance changes, yet rejects noise and cable capacitance.
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| Figure 1. | A simple, high performance capacitance bridge. |
The bridge, shown in Figure 1, is designed around the LTC1043 switched-capacitor building block. The circuit compares a capacitor, CX, of unknown value, with a reference capacitor, CREF. The LTC1043, programmed with C1 to switch at 500 Hz, applies a square wave of amplitude VREF to node A, and a square wave of amplitude VOUT and opposite phase to node B. When the bridge is balanced, the AC voltage at node C is zero, and
Balance is achieved by integrating the current from node C using an op amp (LT1413) and a third switch on the LTC1043 for synchronous detection. With CREF = 500 pF and VREF = 2.5 V, this circuit has a gain of 5 mV/pF, and when measured with a DMM achieves a resolution of 10 fF for a dynamic range of 100 dB. It also rejects stray capacitance (shown as ghosts in Figure 1) by 100 dB. If this rejection is not important, the switching frequency f can be increased to extend the circuit’s bandwidth, which is
COUT should be larger than CREF.
The circuit operates from a single 5 V supply and consumes 800 µA. If the capacitances at nodes A and C are kept below 500 pF, the LT1078 micropower dual op amp may be used in place of the LT1413, reducing supply current to just 160 µA.
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| Figure 2. | A bridge with increased sensitivity and noise performance. |
If the relative capacitance change is small, the circuit can be modified for higher resolution, as shown in Figure 2. A JFET input op amp (LT1462) amplifies the signal before demodulation for good noise performance, and the output of the integrator is attenuated by R1 and R2 to increase the sensitivity of the circuit. If ΔCX << CX, and CREF ≈ CX, then
With CREF = 50 pF, the circuit has a gain of 5 V/pF and can resolve 2 fF. Supply current is 1 mA. The synchronous detection makes this circuit insensitive to external noise sources and in this respect shielding is not terribly important. However, to achieve high resolution and stability, care should be taken to shield the capacitors being measured. I used this circuit for the fluid level detector mentioned above, putting a small trim cap in parallel with CREF to adjust offset and trimming R2 for proper gain.
Bridge circuits are particularly suitable for differential measurements. When CX and CREF are replaced with two sensing capacitors, these circuits measure differential capacitance changes, but reject common mode changes. CMRR for the circuit in Figure 2 exceeds 70 dB. In this case, however, the output is linear only for small relative capacitance changes.
