Applications Dictate Capacitance Measurements

Figure 1 shows a fairly complete capacitor model. I say “fairly complete” because not only do the effects of each component vary with frequency, but the values of the components themselves also may vary with frequency. In a perfect model, the values of the components don’t change with frequency.

Fortunately, you often don’t need to account for all of a capacitor’s characteristics when designing one into a circuit because not all characteristics will significantly change how the device performs in your application. In a timing circuit or a sample-and-hold circuit, for example, a capacitor’s series inductance (L_s) and series resistance (R_s) are usually insignificant because the frequency of the voltage applied across the capacitor is relatively low (DC–10 kHz). But parallel leakage resistance (R_p) and perhaps the effects of C_d and R_d (the dielectric absorption network) can significantly change a circuit’s timing. These components will cause some low-frequency current to leak through the device.

In a capacitor used as a switching power supply’s filter, R_p and the dielectric absorption network have negligible effects on circuit performance. But L_s and R_s can change a capacitor’s characteristics. As frequency increases, the impedance of L_s increases until it overwhelms the impedance of the ideal capacitance (C). At frequencies above the point where C and L_s resonate, the capacitor acts like an inductor.

Choose Your Model
You can divide capacitor applications into two models—admittance and impedance. In the timing circuit example, the admittance model (Fig. 2a) describes the capacitor’s performance. A parallel resistance across capacitor C_p will force some current to bypass the capacitor, causing a timing error in the circuit. The admittance model reduces the full model to two components, C_p and R_p. C_p is an equivalent value of ideal capacitance that combines all the capacitive components of the full model. The ideal capacitance is the predominant element in the full model that affects C_p.

In a switching power supply filter, though, a series resistance can alter an ideal capacitor’s characteristics. In an impedance model (Fig. 2b), you can reduce the capacitor to components C_s and R_s. C_s represents the equivalent capacitance of the device, which includes the effects that L_s has on the device. Resistance, R_s, often called equivalent series resistance (ESR), places a limit on the capacitor’s minimum impedance no matter how high the input frequency gets.

Remember that admittance and impedance are inversely proportional. A low admittance implies a high impedance, and vice versa. In choosing a model, use the admittance model when you want a low admittance (high impedance) load on the low-frequency test signal. Use the impedance model when you want a low impedance (high admittance) load on the high-frequency test signal.

Capacitance meters and LCR meters use both models to measure and calculate a capacitor’s characteristics. Because the admittance and impedance models are not full models, the values of the components are frequency dependent and are valid at one frequency only—the frequency of the excitation signal you use in your measurement. The values you read for C_p and R_p or C_s and R_s on a capacitance meter will vary with frequency.

A capacitance meter or LCR meter applies an AC voltage across the DUT, then measures the amplitude and phase of both the voltage across and the current through the DUT. The meter then calculates the phase difference. Knowing the current, the voltage, and the difference in phase, a meter can calculate impedance (and therefore admittance), and then use that value to calculate the values of C_p and R_p (admittance model) or C_s and R_s (impedance model).

Figure 3. Use the guarded two-wire method to measure capacitors modeled by the admittance model.

Figure 4. Use the four-wire method to measure capacitors modeled by the impedance model.

When using the admittance model, use the guarded two-wire measurement shown in Figure 3. This setup is highly accurate for admittance tests at lower frequencies, typically below 100 kHz depending on the value of the DUT. Above 100 kHz, the accuracy deteriorates. The guarded two-wire setup works well for measuring capacitors less than 1000 pF. The shielded cables eliminate stray capacitance in the test leads that can add to C_p, which would produce a measurement that’s too high.

For the impedance model, use a four-wire measurement setup similar to the one in Figure 4. The additional two leads let the meter sense the DUT’s impedance right at the device, which eliminates the losses caused by lead resistance and lead inductance. Otherwise, the losses in the wires will add to the measurement result. Use shielded wires here, too, to eliminate the effects of stray capacitance in the wires. Use the four-wire setup for capacitors above 1000 pF. Although you can use the four-wire method to measure capacitors below 1000 pF, it offers no advantage over the guarded two-wire setup.

In the admittance model, a low test frequency (typically 1 kHz or 10 kHz) makes C_p look like an open circuit, which accentuates the influence of R_p, and the meter can calculate the value of C_p. For the impedance model, a high test frequency (typically 100 kHz or 1 MHz) makes C_s appear like a short, letting the meter measure R_s. If your meter lets you adjust excitation frequency, you should perform your tests at the frequency that the DUT will most likely encounter in its application. If your meter only lets you test at fixed frequencies, use the nearest one. T&MW