Characterizing High-Q 100 pF Capacitors with the Zurich Instruments MFIA

Introduction

In the last impedance blog post we discussed how the MFIA could be used to investigate 3000 F capacitors, here we turn to the other end of the spectrum to investigate 100 pF capacitors. Specifically, this blog post looks at high-Q (low loss) commercially available SMD capacitors, both ceramic and polymer-film. A wide range of dielectrics are available for use in capacitors, but we focus on a selection of class I ceramic and polymer-film capacitors.

Figure 1: Q-Factors of common capacitor dielectrics. Adapted from Wikipedia.

The value 100 pF was selected as it sits nicely in the middle of the range of SMD capacitors most commonly used in today’s circuits. We have measured a range of eight commercially available 100 pF capacitors, ranging from cheap low-Q to higher-end high-Q capacitors. The capacitors come from well-known manufacturers, such as Johanson, Murata, ATC and AVX. Table 1 shows an overview of the 100 pF capacitors selected for characterization in this blog post:

Table 1: List of the 100 pF capacitors selected for characterization in the blog post.

Experimental Setup

Each capacitor tested in this blog post was solder-mounted onto a low-capacitance carrier (1 fF, see photo in figure 2). We then ran each impedance sweep (300 points) from 200 Hz to 1 MHz in twelve minutes with a driving voltage of 800 mV. All settings were kept constant for each capacitor in order to be able to compare between each component. The path of the sweep is illustrated on the reactance chart in figure 2 by an orange arrow running along the 100 pF diagonal from 200 Hz to 1 MHz. From this chart, we see that the MFIA achieves its optimum accuracy of 0.05% along this path. Figure 2 also shows the phase-accuracy of the MFIA (Right hand chart).

Figure 2: Reactance chart of the MFIA (left hand figure) with an overlaid orange arrow showing the path of the impedance sweep used to characterize the 100 pF capacitors. The accuracy along this sweep ranges from 0.1% down to 0.05%. The right-hand figure shows the phase-accuracy of the MFIA.

Easy-to-use fixture compensation

A key feature of the MFIA is the easy-to-use compensation-advisor which guides the user when compensating for parasitics coming from the fixture. The user-compensation can be run in a matter of minutes in standard mode, but for the data in this blog post we opted to run a high-precision user-compensation. The high-precision user-compensation allows the user to select both the frequency range and the number of points measured during the user-calibration.  Further, the high-precision user-compensation uses longer averaging and settling times, which gives less noise in the compensation.

Figure 3: Photo of 100 pF SMD capacitor mounted on a low-capacitance (1fF)  carrier inserted into the MFITF fixture.

The most important factors when characterizing the electrical performance of a capacitor are the quality factor (Q) and the equivalent series resistance (ESR). The phase between the current and the voltage is also of fundamental interest, so we present the phase traces from each capacitor.

The Q-factor and ESR are related by:

$Q = \frac{Xc}{ESR}$,

where Xc is the capacitive reactance. Although Q and ESR are inter-related, each parameter is generally used in its own right, and so we present both of the parameters in separate figures for clarity.

Starting with the Q-Factor, we see from the above equation that it is inversely proportional to the ESR. To be more general, the Q-Factor gives us the ratio of energy stored to the energy lost due to the ESR. A perfect capacitor with zero ESR would have an infinite Q-factor. The Q-Factor is also strongly frequency-dependent due to its dependence on both reactance and ESR (which themselves are dependent on frequency). Both Q and ESR are typically measured by using a resonant line at a single frequency such as 1 MHz, but this blog shows how the MFIA can be used to measure these important parameters in a continuous sweep from low frequency to 1 MHz.

Figure 4 shows a screenshot of the LabOne software which controls the MFIA. The Sweeper module, which can be seen on the lower part of the figure, displays eight color-coded traces of the Q-factor for each of the eight candidate capacitors. The traces are color-coded as described in the legend in the lower right part of the figure.  Looking in general at the Q-factor traces, we see there is a strong frequency dependence of the Q-Factor in all but one capacitor; namely, the NP0 from Murata (yellow trace). All the other capacitors show an increase in Q to 1 kHz, and a decrease after 10 kHz. The clear winner when it comes to Q-Factor is the 1111 capacitor from AVX. The pink trace shows Q-Factors in excess of 60,000 (the uppermost horizontal cursor line is set to 60,000).

Figure 4: Screenshot of LabOne showing an Impedance sweep of Q-Factor (Q) of eight commercial capacitors. The traces of the eight capacitors are color coded as shown in the legend on the right. Cursor lines within the sweeper show Q factors in excess of 60,000 (Pink trace).

The next parameter we’ll look at is the equivalent series resistance (ESR). This is a measure of the series resistance of the capacitor at a certain frequency. Perfect capacitors would have zero resistance, and the voltage would lag the current by exactly 90 degrees. However, in the real world, an ESR exists due to the leads, connections and housing of the capacitor, and also due to the insulating dielectric. It is modeled as a resistor in series with the capacitor, hence the name ESR. The lower the ESR, the less power is dissipated in the circuit, meaning less overheating and longer battery life. ESR is typically quoted at a single frequency of 1 MHz, but this does not sufficiently describe the frequency-dependent behavior. The data in this blog shows the ESR behavior from 200 Hz to 1 MHz, as shown in figure 5.  Figure 5 shows ESR values starting at 2500 Ohms at 200 Hz on the right hand side of the sweeper window, they then drop down to 400 mOhms 1 MHz in the case of the Johanson capacitor (orange trace). In the case for both the  Murata (pink trace) and the P90 from ATC (blue trace), we see they have ESR below 200 mOhm, although the traces show that the ESR is not yet fully saturated.

Figure 5: Impedance sweep of equivalent series resistance (ESR) of eight commercial capacitors. The traces of the eight capacitors are color coded as shown in the legend on the right.

Finally, we move onto the phase between the current and the voltage. As we saw earlier in the blog post, a perfect capacitor would exhibit 90 degree phase between current and voltage. The capacitors we are measuring may not be perfect, but they do get very close to the 90 degree phase shift. This means that our impedance analyser needs to be able to measure phases of within 5 millidegrees of 90 degrees. Figure 6 shows the phase of all eight components under test. If we take the orange trace as an example, we see the Johanson NP0 gets to within 5 millidegrees of 90 degrees at a frequency of 6 kHz. With increasing frequency, measuring the phase becomes more challenging, as even a small delay between current and voltage will result in a large phase error.

Figure 6: LabOne Screenshot showing the phase between the voltage and current of each of the capacitors. The traces of the eight capacitors are color coded as shown in the legend on the right.

Conclusion

The MFIA impedance analyser has been used to measure the Q, ESR and phase of eight commercially available high-Q 100 pF capacitors. We measure Q-Factors in excess of 60,000, ESR down to 200 mOhms and phases within 5 millidegrees of 90 degrees. The MFIA achieves this by leveraging the state-of-the-art lock-in technology on which it is based. Furthermore, the low parasitics of the MFITF fixture, combined with a high-precision user-compensation give best possible phase measurements.