Extension of Capacitance Measurement Function for Digital Multimeters
1 On‑line Capacitance Measurement
Based on the characteristics of differential‑integral circuits, capacitance measurement can be converted into voltage measurement.
The core of the circuit adopts a simple active RC inverting differential and integral circuit for the Cₓ/V conversion. A Wien‑bridge oscillator generates an AC reference signal Vᵣ of fixed frequency, which excites the Cₓ/V conversion circuit and produces an AC output voltage V₀ (V₁) proportional to the measured capacitance Cₓ. After filtering out spurious components outside the fixed‑frequency band by a second‑order band‑pass filter, the signal passes through an AC/DC converter to yield a DC output voltage V proportional to Cₓ.
When the AC signal Vᵣ drives the Cₓ/V circuit, the output voltage of the inverting amplifier is proportional to the measured capacitance Cₓ, thus realizing the Cₓ‑to‑V conversion. To match the basic capacitance range with the 2 V range of the digital multimeter, the Wien‑bridge oscillator is set to operate at 400 Hz with an RMS output voltage of 1 V. R₁ is 20 kΩ and C₁ is 0.1 μF. R₂ is switched among 200 Ω, 2 kΩ, 20 kΩ, 200 kΩ and 2 MΩ, corresponding to capacitance measuring ranges of 20 μF, 2 μF, 200 nF, 20 nF and 2 nF respectively.
2 Measurement of Small‑value Capacitance
Ordinary 3½‑digit digital multimeters provide capacitance ranges from 2000 pF to 20 μF and cannot measure tiny capacitances below 1 pF. Small‑capacitance measurement can be realized by the capacitive‑reactance method with high‑frequency excitation signals. The measuring circuit is shown in Figure 2. Cₓ denotes the capacitance under test and Rբ is the feedback resistor at the inverting input terminal. When a sinusoidal input signal Vᵢ of frequency f is applied, an impedance appears across Cₓ, and the gain of the operational amplifier is determined accordingly. With fixed amplifier gain A and feedback resistance Rբ, the frequency f of the sinusoidal signal is inversely proportional to the measured capacitance Cₓ. Therefore, high‑frequency signals are adopted for measuring small capacitances.
The block diagram of the implemented measuring circuit is presented in Figure 2(b). In the measurement procedure: a high‑frequency sinusoidal signal generated by a high‑frequency oscillator is applied to the device‑under‑test capacitance Cₓ, converting Cₓ into capacitive reactance Xc. A C‑to‑AC‑voltage transformation converts Xc into an AC voltage, which is amplified and fed via an isolation transformer to a phase‑sensitive demodulator. The second input of the phase‑sensitive demodulator is a square‑wave demodulation signal, derived from the high‑frequency sine wave through a wave shaper; the two input signals share identical frequency and phase. The demodulated signal is processed by a low‑pass filter to obtain a DC voltage proportional to Cₓ, which is sent to a DC voltmeter for direct readout of the measurement result.
The wave shaper consists of an inverting zero‑crossing comparator, which converts the standard 1 MHz high‑frequency sine wave from the Wien‑bridge oscillator into a complementary square‑wave reference. Since the output of the phase‑sensitive demodulator is a pulsating DC voltage containing high‑order harmonics, a π‑type filter is employed to suppress harmonic components and deliver stable, constant DC output.
