How to measure MLCC capacitance that varies with bias voltage

Designers often ignore the characteristics of high-capacity, multilayer ceramic capacitors (MLCCs) that vary with their DC voltage. This phenomenon exists in all high dielectric constant or class II capacitors (B/X5R R/X7R and F/Y5V characteristics). However, the amount of variation of different types of MLCC is very different. Mark Fortunato once wrote an article on this topic, and he concluded that: You should check the data of the capacitor to confirm that the value of the capacitor changes with the bias voltage. But what if this information is not provided in the data sheet? How do you determine how much the capacitance has become smaller under specific application conditions?

The theory of characteristic analysis of the relationship between capacitance and bias voltage

Figure 1 shows a circuit for measuring DC bias characteristics. The circuit is the operational amplifier U1 (MAX4130). The op amp is used as a comparator, and the feedback resistors R2 and R3 increase hysteresis. D1 sets the bias higher than GND, so there is no need for a negative supply voltage. C1 and R1 are connected from the feedback network to the negative input terminal, making the circuit work as an RC oscillator. Capacitor C1 is the object under test (DUT), as the C in the RC oscillator; the potentiometer R1 is the R in the RC oscillator.

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Figure 1: A circuit for characteristic analysis of the relationship between capacitance and bias voltage.

The voltage waveform Vy at the output pin of the operational amplifier and the voltage Vx at the connection point between R and C are shown in Figure 2. When the output of the op amp is 5V, C1 is charged through R1 until the voltage reaches the upper limit, and the output is forced to 0V; at this time, the capacitor is discharged until Vx reaches the lower limit, thereby forcing the output to return to 5V. This process occurs repeatedly, forming a stable oscillation.

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Figure 2. Oscillation voltage of VX and VY.

The oscillation period depends on R, C, and the upper threshold VUP and lower threshold VLO:

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Since 5V, VUP and VLO are fixed, T1 and T2 are proportional to RC (usually called RC time constant). The comparator threshold is a function of Vy, R2, R3, and D1 forward bias (Vsub>Diode):

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In the formula, VUP is the threshold when Vy = 5V, and VLO is the threshold when Vy = 0V. Given the parameters, the result of these thresholds is approximately: VLO is 0.55V and VUP is 1.00V.

The circuit around Q1 and Q2 converts the cycle time into a proportional voltage. The working principle is as follows. MOSFET Q1 is controlled by the output of U1. During T1, Q1 turns on, clamping the voltage of C3 to GND; during T2, Q1 turns off, allowing constant current sources (Q2, R5, R6, and R7) to linearly charge C3. As T2 increases, the voltage of C3 increases. Figure 3 shows the C3 voltage for three cycles.

The average value of C3 voltage (VC3) is equal to:

"Because I, C3, α, and β are all constants, the average voltage of C3 is proportional to T2, and therefore proportional to C1.

The low-pass filter R8/C4 filters the signal, and the low-offset op amp U2 (MAX9620) buffers the output, so any voltmeter is allowed for measurement. Before measurement, the circuit needs to be simply calibrated. First install the DUT into the circuit and set VBIAS to 0.78V (the average of VLO and VUP), so the actual average (DC) voltage on the DUT is 0V. When the potentiometer R1 is adjusted, the output voltage changes accordingly. Adjust R1 until the output voltage reads 1.00V. Under this condition, the peak voltage of C3 is approximately 2.35V. The bias voltage can be changed, and the output voltage will display the percentage of change in the capacitance value. For example, if the output voltage is 0.80V, the capacitance value at a specific bias voltage will be 80% of the value when the bias is 0V.

Build the circuit of Figure 1 on a small PCB. First use a 10μF capacitor for measurement. Figures 4 and 5 show the signals under 0V and 5V bias conditions, respectively.

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Figure 4: Measurement results when VBIAS = 0V, Ch1 = Vx; Ch2 = Vy; Ch3 = VC3. Adjust R1 so that the voltmeter reads 1.000V.

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Figure 5. Measurement results when VBIAS = 5V. Due to the reduced capacitance value, the oscillation period has been significantly shortened. Ch1 = Vx; Ch2 = Vy; Ch3 = VC3. The voltmeter reads 0.671V.

When 　　 is biased at 0V, adjust the potentiometer R1 to make the voltmeter read 1.000V. When 5V is biased, the voltmeter reads 0.671V, indicating that the capacitance value is 67.1% of the original. Using the high counter, the total period T is also measured. The T under 0V bias voltage is 4933?s, and under 5V bias voltage is 0V, indicating that the capacitance value is 66.5% of the original (that is, 3278μs/4933μs). These values are very consistent, which proves that the circuit design can measure the relationship between the capacitance value and the bias voltage.

Now perform the second measurement, extract a 2.2μF/16V capacitor (model GRM188R61C225KE15) from the sample provided by Murata. In this measurement, the capacitance value was recorded in the entire working range of 0V to 16V. Determine the relative capacitance by measuring the output voltage of the circuit and the actual oscillation period. In addition, data is collected from the Murata Simsurfing tool; this tool can provide the DC bias characteristics of a specific device based on Murata's measurements. The result is shown in Figure 6. The results shown in the two measurement data curves are almost identical, which proves that the time-voltage conversion circuit works well in a larger dynamic range. There is a certain difference between the data obtained by the Simsurfing tool and our measurement results, but the shape of the curve is similar.

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Figure 6: The relationship between the relative capacitance of a 2.2μF/16V MLCC and the bias voltage. The capacitance value is normalized to the capacitance value under a bias voltage of 0V. The blue curve is based on the measured value of the output voltage of the circuit; the red curve is based on the measured value of the oscillation period; the green curve is based on the characteristic data provided by the Murata Simsurfing tool.

  to sum up

Using the introduced circuit, dual power supply and voltmeter, it is easy to measure the DC bias characteristics of a high-capacitance MLCC. A simple laboratory test can prove that the capacitance value changes with the bias voltage.