A negative impedance generator, the "negatron" in Fig 1, solves a common problem with capacitive sensors. These sensors have some initial capacitance, C₀, which is typically several times more than the sensor's incremental capacitance, dC. The use of specialized circuits to reduce C_o is common. The overall goal is to increase the frequency output's relative sensitivity, dF/F_o. One technique, which calls for a frequency subtraction, requires a reference fixed oscillator and frequency subtractor. However, Fig 1's alternative approach is simpler. This circuit performs subtraction not of the output frequencies but of the sensor capacitance itself using the negatron's equivalent negative impedance.

Fig 1 consists of two parts: the negatron and measuring oscillator. The equivalent impedance of the negatron between its input and ground, is as follows:

Thus, this circuit ideally produces the equivalent negative lossless capacitance. Applying this capacitance to the sensor reduces the total initial capacitance to a final capacitance of C_o-C_EQ.

Test results show that without the negatron and with an F_o of 13 kHz, the relative sensitivity dF/F_o was -7.7%, and dC=5 pF. Table 1 shows the increased sensitivity that adding the negatron produces (dC is again 5 pF). Adjusting the value of R₁ varies F_o, and, as Table 1 indicates, R₃ varies the sensitivity.

Be aware that the magnitude of F_o and dF/F_o will differ from their theoretical values because of the op amps' input capacitances and the stray capacitance of the circuit. Also, you have to account for any nonlinearity of the input capacitance of the op amps vs input voltage. The circuit may not be stable when the positive and negative capacitance are nearly equal.

The LTC1124 op amp was selected because its input capacitance doesn't exceed 2 pF and its low-voltage single-supply operation. Good results were also obtained using the rail-to-rail TLC2272. (DI#1680)