Capacitive position sensor with linearized output
An only slightly less simple followup circuit also ratios sensor capacitance to a reference capacitor to measure micrometers…this time linearly.
A few weeks ago, Design Ideas published a simple circuit of mine that provides an analog interface to capacitive position sensors. Figure 1 shows that basic design with its separate complementary outputs: Out and –Out.
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Figure 1 The U1a and U1b cross-coupled Schmidt trigger timers form a ~1MHz RC multivibrator. The Tsense pulse width is inversely proportional to sensor displacement (Tref/Tsen= Cref/Csen = d).
Figure 2 shows the “Simple Simon” method it offered for acquisition of the sensor position signal: passive RC averaging of the Tsense pulse train.
Figure 2 Passive RC averaging of the Tsense output yields the analog position output.
The resulting analog output, as shown in figure 3, provides good range and resolution but is nonlinear.
Figure 3 This graph shows the sensor performance when Out is connected to a 12bit ADC using +5V for its reference. The black curve (left axis) equals the plate separation (d) in millimeters. The red curve (right axis) equals the ADC lsb resolution in micrometers.
So, I got to thinking about linearization and the advantages it would provide, and wondering how tough it would be. It turned out to be not that difficult.
Figure 4 shows the resulting interface with added linearization circuitry. Just an added opamp, three resistors, and two non-critical caps did the trick. Here’s how it works.
Figure 4 Averaging integrator A1 linearizes the displacement sensing response. R5 is shown as a precision type, albeit just out of force of habit. It, like the ON resistances of U2’s switches, actually cancels out.
Each capacitance measurement cycle, the 500ns Tref pulse causes 4066 switch U2d to deposit a quantum of charge on integrator A1’s summing node of Qref = Tref/R5. Meanwhile the sensor-capacitance proportional Tsen pulse subtracts Qsen = Tsen(Vout – 1)/R5. The charge balance is forced by A1 to maintain Qsen = Qref, therefore Tsen(Vout – 1)/R5 = Tref/R5, and Vout – 1 = Tref/Tsen = Cref/Csen = d. Note that R5 magically (?) disappears from the math.
Figure 5 shows the straight-as-an-arrow-in-zero-gravity result.
Figure 5 In this graph of the enhanced circuit results, the black curve equates to the sensor readout d in mm, with red at a constant 1 mV per micron resolution.
Stephen Woodward‘s relationship with EDN’s DI column goes back quite a long way. Over 200 submissions have been accepted since his first contribution back in 1974. They have included best Design Idea of the year in 1974 and 2001.
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