Expanding Capacitance Measurement on Digital Multimeters
Based on the characteristics of differential and integral circuits, capacitance measurement can be converted into voltage measurement.
The core part of the circuit, CX/V, uses a simple active RC inverting differentiator and integrator. A Wien bridge oscillator generates an AC signal Vr at a fixed frequency, which excites the CX/V conversion circuit to produce an AC voltage V0(V1) proportional to CX. After removing noise outside the fixed frequency by a second-order band-pass filter, an AC/DC conversion yields a DC output voltage V proportional to CX.
When the AC signal Vr excites the CX/V circuit, the output voltage of the inverting integrator is:
That is, the measured capacitance CX is proportional to the output voltage V0, thus realizing the CX→V conversion.To match the basic capacitance range with the 2V range of the digital multimeter, the Wien bridge oscillator is set to 400 Hz with an RMS voltage of 1 V, R1=20 kΩ, and C1=0.1 μF.By varying R2 as 200 Ω – 2 kΩ – 20 kΩ – 200 kΩ – 2 MΩ, the corresponding capacitance measurement ranges are 20 μF – 2 μF – 200 nF – 20 nF – 2 nF.
2 Measurement of Small Capacitances
Typical 3½-digit digital multimeters have a capacitance measurement range of 2000 pF ~ 20 μF and cannot measure tiny capacitances below 1 pF.Using the capacitive reactance method with high-frequency signals enables measurement of minute capacitances, as shown in Figure 2.Let CX be the measured capacitance and Rf the feedback resistor at the inverting input. For a sinusoidal input signal Vi at frequency f, the impedance of CX and the gain of the op-amp are given by:With fixed A and Rf, the frequency f of the sinusoidal signal is inversely proportional to CX. High-frequency signals are therefore used to measure small capacitances.
The block diagram of the measurement circuit is shown in Figure 2(b).The measurement process is as follows:A high-frequency sinusoidal signal from a signal generator is applied to the measured capacitance, converting CX into capacitive reactance XC.This XC is converted into an AC voltage via a C/ACV converter, amplified, and sent through an isolation transformer to a phase-sensitive demodulator.The other input to the demodulator is a square wave (reference signal) derived from the high-frequency sine wave through a waveform converter, with the same frequency and phase.The demodulated signal is filtered by a low-pass filter to produce a DC voltage proportional to CX, which is sent to a DC voltmeter for direct display.
The waveform converter is an inverting zero-crossing comparator that converts the standard 1 MHz high-frequency sine wave from the Wien bridge oscillator into a standard inverted square wave.Since the output of the phase-sensitive demodulator is a pulsating DC voltage containing high-frequency harmonics, a π-filter is used to remove harmonics and obtain a stable, constant DC output.The corresponding average voltage is then sent to the DC voltmeter.
To match the basic capacitance range with the 2V range of the digital multimeter, the high-frequency sinusoidal signal is set to 1 MHz (high enough to avoid distributed parameter effects at excessive frequencies) with an RMS voltage of 1 V.The product of the circuit gain and feedback resistor Rf is set such that the 200 mV DC range of the multimeter corresponds to 0.2 pF, and 2 V corresponds to 200 pF.
