You can improve a capacitive-sensor circuit with a modulator and an RF transmitter (Reference 1) by modifying the modulator portion to obtain better accuracy. More improvements result from adding a "negatron" circuit, a configuration that uses equivalent negative capacitance. Reference 2 gives some insight into the uses of negative impedance. The circuit in Figure 1 works with the RF transmitter of Reference 1 (Figure 2) as follows: The modulator uses op amp IC₁ in a standard flip-flop configuration (with the addition of the bias resistor R₄, because of single-supply operation). The negatron portion of the circuit uses op amp IC₂. The output frequency, f, of the modulator without the negatron is a function of the time constant τ_M=R₃C_S. Thus, the frequency is a function of the physical value of the input (for example, pressure or humidity). The potential accuracy and stability of the modulator in Figure 1 are greater than those of the modulator in Reference 1 because of the low input capacitance and temperature coefficient of the LTC1124 op amp and the high stability of the R₄-R₆ voltage threshold.

Adding the negatron portion in Figure 1 increases the relative sensitivity of the frequency modulator. The equivalent capacitance of the negatron is C_N=–C₁(R₂/R₁). Assuming the physical value of the input causes the change ΔC (compared with the sensor's initial capacitance, C₀), the relative output-frequency change without the negatron (for small ΔC) is Δf/f₀=ΔC/C₀. With the negatron added, the equation is: Δf/f₀=ΔC/(C₀–C₁(R₂/R₁)). The result is higher relative sensitivity because of the reduction in the denominator value. The value of C_N is approximately –100 pF for the circuit in Figure 1. In other words, a given change in the input value causes a greater relative-frequency deviation. Note that adding the negatron changes the equivalent time constant: τ=R₃(C_S–C₁(R₂/R₁)). You can make value adjustments in R₃ to obtain the desired initial frequency, f₀. Also, note that the measured values of f₀ and Δf may differ from the calculated ones because of parasitics and the input capacitance of the op amp.

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