A variety of different measurement techniques can be used to evaluate the equivalent series resistance (ESR) of high-frequency capacitors and inductors, with varying results.
Capacitor and inductor improvements have resulted in lower equivalent-series-resistance (ESR) values for these circuit elements. In turn, measurements of ESR for capacitors and inductors have become even more difficult. ESR measurements errors are caused either by the minimum (or absolute value) of the ESR or the phase of the complex signal vector, both of which can present very significant measurement challenges. While error-correction techniques can be used to minimize them, at some point the limitations of physics limit their feasibility. Understanding measurement-technique limitations, frequency dependencies, and fixture-error correction can greatly help the designer apply the proper processes to get the best possible results.
Several techniques are used to measure ESR. The best approach for a given situation depends primarily on the measurement frequency. Resonant techniques or the autobalancing bridge are used for low-frequency measurements, while the resonant method using a cavity, a reflection test set with a vector network analyzer (VNA) or the RF current-voltage (I-V) method with dedicated impedance measuring equipment are used for high-frequency measurements.
For low-frequency measurements, the autobalancing bridge measurement technique (Fig. 1) includes an AC source to supply current through a device under test (DUT). The voltage across the DUT is measured by V1 and the current through the DUT is derived from V2/R2. It is important to remember that V1 and V2 are vector voltmeters, which means that they measure both the magnitude and phase of the AC signal. To achieve this, they actually measure the magnitude of the signal at 0 deg. (representing the real part) and the magnitude of the signal at 90 deg. (for the imaginary part). These measurements are made using mixers with very high dynamic ranges.
Although the real part will represent the ESR value of the DUT, most low-ESR components also have a relatively high reactive part. The ratio of the two is called the quality factor, Q (or inversely D or tan δ, and is the ratio of the imaginary to real parts. Since ceramic capacitors with Q over 10,000 are quite common, the mixer must attempt to separate the real portion (ESR) in the presence of a very large input signal that is almost entirely reactive, which is a significant challenge.
Most impedance measurement techniques use some form of vector separation. This inherently limits the accuracy of very low ESR measurements. Recent advances have been made in mixer design and new instrumentation that allow measurements of even-lower ESR values to be measured by the autobalancing bridge technique.
However, another method called the resonant technique does not rely on vector separation, and has been used for many years in the form of the Q-meter (Fig. 2). Although this technique is cumbersome, it can provide the most accurate Q measurement results when the Q is very high (more than 10,000), as long as extreme care is taken in performing the measurement.
For high-frequency ESR measurements, Q-meters usually operate up to the tens of megahertz, and autobalancing bridge technology now allows measurements to 110 MHz. However, in many cases, ESR must be measured at higher frequencies where three techniques—the RF-IV technique with dedicated impedance measuring equipment, the resonant technique using a cavity, and the reflection test set with network analyzer—are available.
The RF-IV technique (Fig. 3) is very different from the autobalancing bridge approach, although it appears quite similar according to the simple schematic. Both methods require two vector voltmeters: one for current and one for voltage, each of which has the same basic operating principles and consequently the same limitations as when used in low-frequency ESR measurements. The technique that employs a VNA and reflection test set does not work well for very low or very high impedances and results in very large ESR measurement errors. Figure 4 offers a comparison of the RF-IV (solid-line) and VNA (dotted-line) methods.
Calibration Standards
All measurements will have error caused by the quality and traceability of the calibration standards as well as the process used for calibration. In the autobalancing bridge technique, the process and stability of the instrument is very high, and calibration is performed at a calibration lab once a year.
High-frequency techniques require the user to establish the calibration plane with traceable standards or working standards (i.e., devices in which the user has a high degree of confidence). Since low-ESR devices typically have relatively high Q (although a rectangular metal block may have low ESR and low Q), most measurements are made on devices with low ESR and high Q. While high-frequency techniques also usually employ open/short/load calibration, using only these standards will result in significant ESR error because the phase of these standards is not well known. Because of this limitation, impedance analyzers and impedance-capacitance-resistance (LCR) meters using the RF-IV technique support an additional calibration standard called the low-loss capacitor. This additional calibration device provides a well-known phase reference to the calibration process, which produces much more accurate ESR measurements (Fig. 5).
A typical fixture model (Fig. 6) is used for both low-frequency and high-frequency measurement situations, but as frequency decreases, port extension phase shift becomes insignificant. In general, a 1-m port extension can be ignored at frequencies below 100 kHz, and a 10-cm extension can be ignored below 1 MHz.
The first step is to remove the fixture errors, excluding the port extension (phase shift). The fixture model includes a series resistor and inductor and a shunting resistor and capacitor. The open/short compensation process requires that if the value of each of the four elements can be determined and the combination of the DUT with these elements (i.e., the DUT in the fixture) can be measured, the actual value of the DUT can be determined by mathematically removing the effect of the elements. This is theoretically very straightforward but presents some challenges in practice.
To measure the shunting C (B) and R (G) values, open compensation is performed. This simply requires the component to be removed and the contacts to be left in the same position as they would be with the component inserted. The short compensation method is used to measure the series inductance and resistance values. In this case, the DUT measurement contacts must be shorted, which is difficult because while only the fixture's series R and L should be measured, the short will also have a series resistance and inductance. In low-frequency cases, it may be possible to move the contacts to perform a better short compensation, but in high-frequency cases moving the contacts will cause very large errors. Shorting block inductance is also extremely critical at higher frequencies.
A recent improvement has been made in modern impedance measuring equipment that allows the user to enter non-zero short values (for the L and R of the shorting block). This allows all subsequent measurements to be made properly without the need for additional calculations. If the user's measuring equipment does not have this feature, the data can be corrected on a personal computer.
The potential phase error inherent in the model of Fig. 6 (caused by a significant port extension) can be corrected depending on the type of extension, type of measuring equipment, and measurement frequency. Phase shift even causes errors at relatively low frequencies. ESR measurement data has been taken on both a low-frequency impedance analyzer and an RF impedance analyzer. Measurements were made of a 0.01-µF ceramic capacitor on a model 4294A impedance analyzer from Agilent Technologies (Santa Rosa, CA) with and without a 30-cm port extension. At 1 MHz, the correct ESR value was 390 mΩ, and with the 30-cm port extension it showed 360 mΩ (about 10-percent error). At 10 MHz, the error increased to about 30 percent. An RF impedance analyzer was used to measure the same device, and in this case, the incorrect measurements were performed with about 1 cm of uncorrected port extension.
Another consideration that must be made is how the port extension is to be performed. In the high-frequency case, the complete measuring environment is a single coaxial cable, so any port extension performed after the calibration plane should have minimal loss. Either a delay can be added to the analyzer (typically determined by applying a short and adding the proper delay to return to zero on the Smith chart), or by using a working standard calibration.
In the low-frequency case, other options may exist if using a four-terminal measuring instrument. All of Agilent's autobalancing bridges use the four-terminal pair (4TP) technique that provides superior ESR measurements at higher frequencies. Standard four-wire or five-wire techniques still have mutual coupling (transformer effect) that cannot be eliminated by electrostatic shields. The 4TP system actively drives equal but opposite current in the shield conductors compared to the current flowing in the center conductors. This eliminates the mutual coupling effect that is critical when making low-impedance measurements like ESR.
When making 4TP port extensions, consideration must be given to the degree of coupling and to the measurement frequency. For large devices such as aluminum-can electrolytic capacitors, an attempt should be made to reduce the coupling affect by bringing the current source and voltage sensing leads together at the DUT at right angles to each other.
Fixture contacts play a very important role in the measurement of ESR. All of the discussions of ESR measurement accuracy are related to a perfectly-contacted DUT. In the case of a 4TP system, there are two contacting options. When measuring low-value capacitors (e.g., 10 pF), the total D (ESR) error will be greater with a four-wire contact than with a two-wire contact. Until recently, the four-wire option was used either for very large DUTs measured at low frequencies (usually with alligator clips) or required custom fixtures. The model 16044A fixture from Agilent Technologies brought four-wire contact to SMD devices for the first time. The low ESR values of many of today's capacitors and inductors require that attention be paid to correcting the many sources of error. Fortunately, by understanding the limitations of measurement technique, frequency dependencies, and techniques for fixture-error correction, excellent measurement results can still be obtained.
FOR FURTHER READING
The Effect of Fixturing on ESR Measurements; CARTS Proceedings, 2001.
