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.