Improvement of the circuit for measuring capacitance using DT9205 multimeter

Improvement of the Capacitance Measurement Circuit in DT 9205 DMM

CAO Lijian, CHEN Xiaozhen

(Dept. of Electronics Science and Engineering,
Nanjing University, Na njing 210093, China)

Key words: digital multimeter; capacity; measurement; error

The capacitance measurement circuit in the DT9205 multimeter is shown in Figure 1. Many other models of multimeters also use this circuit. This circuit converts the capacitance value into an AC voltage with a frequency of about 400Hz, which is then converted into a DC voltage by the rectifier circuit in the multimeter. Finally, the 3.5-bit A/D conversion and display driver circuit ICL7106 converts the DC voltage value into a digital value and sends it to the display. The above circuit can be divided into four stages, as shown in Figure 2.
The first stage consists of C1, C2, R1, R2, R3, R4 and op amp N3A3, which is a typical Wien bridge oscillator. When R1=R2, C1=C2, the fundamental frequency of the output waveform of the circuit can be estimated as

Its negative feedback gain

Since the circuit does not have the ability to automatically adjust from A1F＞3 to A1F=3, the output of the circuit is a limited "sine wave" in steady state, with large harmonic distortion, that is, in addition to f1, there are also harmonic components such as f2=2f1≈812Hz and f3=3f1≈1218Hz. The waveform obtained by EWB simulation is shown in Figure 3, and its peak value V01m≈VCC, where VCC is the DC bias voltage of the op amp.

R7 is an adjustable resistor. Adjusting R7 can adjust the gain of the amplifier circuit, which is used for calibration of the entire capacitance measurement circuit. The amplification factor of this stage is 0.02~0.04, and the output V02 is an approximate square wave with an amplitude of tens of millivolts.
The third stage is composed of D1, D2, D3, D4, R8, R9, R10, R11, R12 and N3A1 to form an active differential circuit. The output

Rn is the resistor selected by the band switch, and Cx is the capacitor to be measured. It can be seen from formula (4) that if V02 is a sine wave, the effective value of V03 is proportional to Cx. Therefore, the measurement of capacitance is converted into the measurement of the effective value of AC voltage. In the actual circuit, the four diodes make the input waveform of this stage further tend to a square wave. The advantage of this is that the entire capacitance measurement circuit has better thermal stability.
Considering the frequency characteristics of the op amp, the op amp is regarded as a first-order unit, and the differential circuit is a second-order system. Since the open-loop gain of the op amp is very large, the quality factor Q value of the closed-loop circuit is very high, which can reach several tens, and its amplitude-frequency characteristic curve has a large peak. Take Rn=1kΩ, Cx=1μF, and use EWB simulation to obtain the amplitude-frequency characteristic of the differential circuit. There is a peak at f=12.2kHz. The gain at this peak is about 30dB higher than the gain of the amplitude-frequency characteristic curve of the ideal differential circuit. When the frequency is greater than 12.2kHz, the gain drops sharply. The frequency band of the limited "sine wave" output by the first-stage Wien bridge oscillator is very wide. The high-order harmonic components in the limited "sine wave" after differentiation have a greater gain than the fundamental wave, which causes serious distortion of the waveform and obvious oscillation of the time domain waveform.
The fourth stage is composed of C3, C4, R13, R14, R15 and op amp N3A2, which is an infinite gain multi-feedback active second-order bandpass filter circuit with a center frequency of

If the filter can filter out the high-order harmonics in V03, then in principle, the capacitance measurement method is error-free. However, the quality factor of the actual filter

can only reduce the high-order harmonic components in V03, but cannot basically filter them out, which causes errors in capacitance measurement.
In addition, the capacitance measurement range of this circuit can only reach 2μF. Due to the limited output current of ordinary op amps, there are other problems in the 200μF range, which will not be discussed here.

According to the above analysis, the ways to improve the capacitance measurement circuit are: using sine wave as the measurement signal; improving the differential circuit so that its amplitude-frequency characteristics are similar to those of the ideal differential circuit; using narrow-band filters, etc. Based on the comprehensive consideration of factors such as the power supply of the multimeter, manufacturing cost, and technical difficulty, the solution of using a sine wave generator instead of a square wave generator is selected to improve the capacitance measurement circuit in the multimeter, that is, the waveform generator output waveform is changed from wideband to single frequency. The improved circuit is shown in Figure 4. The first part of this circuit is changed to a sine wave oscillator. That is, a diode that can adjust the amplification factor is added to the original circuit. The frequency of the output sine wave remains unchanged. When the amplitude is stabilized, A1F = 3, the parallel equivalent resistance of D1, D2 and R5 is R′5 = 3.9kΩ. If the conduction voltage of the diode is set to 0.7V, the amplitude of the output voltage can be estimated as:

The experimentally measured second harmonic distortion of the output sine wave is 0.5%.
Since a nonlinear diode is used in the sine wave generator, and the temperature characteristic of the diode is about -2.5mV/℃, the temperature effect must be improved. The effect of temperature on the circuit is shown in Table 1.

When R4 does not change much, the relationship between V01m and R4 simulated by EWB is shown in Table 2. As can be seen from Table 2, R4 has an approximately linear relationship with V01m when it is between 8.2kΩ and 9.1kΩ.

If an 8.2kΩ thermistor is used, the temperature coefficient is 0.00113. The results of the EWB simulation after improvement are shown in Table 3. =?0.000758V/℃, even if the temperature changes from -13℃ to 37℃, the V01m error is within 0.7% (change 10℃), which can fully meet the requirements. In fact, R4 can be replaced by a thermistor and an ordinary resistor in parallel, and the appropriate parallel resistance value can be selected according to the temperature coefficient of the thermistor. R3 can also be changed to a thermistor and an ordinary resistor in parallel, and the calculation of the resistance value and temperature coefficient is the same as the above method.
The second part is a voltage follower. Its input and output relationship is: R7 is used to adjust the amplification factor. The voltage is attenuated by 10 to 20 times. The third part is a differential circuit, and the fourth part is a second-order bandpass filter circuit, which is not modified.

The data in Table 4 are obtained by simulating Figure 4 with EWB. The data of actual capacitance measured with the improved circuit are shown in Table 5, where the capacitance value is measured with the TH7128 RLC bridge. The second row of the table is measured with the 200nF range, and the fourth row is measured with different ranges.