*Modern test and measurement instruments go from simple DMMs to handheld oscilloscopes to very sophisticated spectrum and harmonic analyzers.*

The variety of test and measurement products available today can boggle the mind. They go from the mundane to the exotic. These amazing instruments can practically lead you by the hand. But, if you don't have a full understanding of the measurements you're getting, you can be confused and even mislead others. Let's take a brief walk through this potential mine field and discuss some important instrument measurements and performance characteristics.

**Alternating rms current.** Looking at Fig. 1 (In the original article; this is a standard representation of a sinusoidal wave, with 30 degree increments shown. 90 degrees is a quarter cycle, 180 degrees a half cycle, and so on), we see the current waveform starting at zero, reaching a peak on the positive side of the zero axis, returning to zero, continuing onto another peak on the negative side of this axis, and then returning to zero again. One combination positive and negative loop represents one cycle. In the United States, 60 Hz-current goes through 60 complete sets of this loop in 1 sec.

So, if current reverses itself 60 times in 1 sec, how can we measure it? After all,equal positive and negative values cancel each other. The net result, then, is zero amperes.

The answer: We don't measure the actual current of the sine wave. Instead, we measure its heating effect. The equipment of choice is our trusty ammeter, whether it's a clamp-on or handheld digital multimeter (DMM) with a current transformer (CT). The unit manufacturer calibrates the ampere scale in effective amperes. Another term used is root-mean-square (rms) amperes.

Let's expand on the concept of heating effect. When you pass a direct current through a given resistance, this current produces heat. A car cigarette lighter is a good example of this phenomenon. Now, if you pass an alternating current through this same resistance, it will also produce heat.

For both direct and alternating currents, their respective heating effects are proportional to I2R. In other words, their heating effects vary as the square of their respective currents for the specific resistance. The larger the current, the more heat produced in the given circuit.

So, you don't base the value of alternating current on its average; instead, you base it on its heating effect. In fact, the definition of an alternating current ampere is "that current which, when flowing through a given ohmic resistance, will produce heat at the same rate as a direct current ampere"

Let's look at an example for clarification. Suppose we have one ampere of direct current and one rms ampere of alternating current. Because the magnitude of rms alternating current equals the magnitude of direct current, the former is equal in heating to the latter. If we square the alternating current by squaring each of its instantaneous values for both its positive and negative loops, we generate an I2 waveform. Since negative quantities squared are positive, the I2 wave for the negative loop of alternating current appears above the zero axis.

As you see, the average value of the I2 wave is one ampere. As discussed, heating varies as the square of the current (I2). The square root of one is one, so the one rms ampere of effective current is equal to the square of one ampere of direct current.

**Crest factor.** This is the ratio of peak current value to the rms current value of a waveform. In a pure, undistorted current sine wave, the instantaneous peak current equals to 1.414 times the rms amperes. So, this waveform has a crest factor of 1.414.

A "true-rms" measuring instrument typically has a crest factor performance specification. It relates to the amount of peaking this instrument measures without error. The higher the performance number, the better the performance of the device. You'll find these specification numbers in the range of 2.0 to 7.0. A typical DMM will have a crest factor number of 3.0, which is adequate for most distribution measurements.

**Total harmonic distortion.** Presence of harmonic currents will distort sinusoidal waveforms. The main culprit of power distribution harmonic problems is voltage distortion. As harmonic currents pass through a power distribution system's total impedance, they create voltage distortion. This is a simple application of Ohm's Law (Vh4Ih2Zh), where Vh is the voltage at Harmonic h, Ih is the current at Harmonic h, and Zh is the system impedance at Harmonic h. The cumulative effect of these drops at each harmonic frequency produces voltage distortion.

Total harmonic distortion (THD) indicates the amount of waveform distortion. Voltage THD (VTHD) is the root mean square of all harmonic voltage drops. Current THD (ITHD) is the root mean square of all the harmonic currents. Percent harmonic distortion is the ratio of the square root of the sums of the squares of all rms harmonic voltages and currents to the fundamental.

You can characterize harmonic distortion at any point by the frequency spectrums of the voltages and currents present. But, take measurements over time and determine statistical characteristics of the harmonic components. This is where spectrum and harmonic analyzers come into play. (This information is from IEEE paper "Interpretationand Analysis of Power Quality Measurements" by Christopher Melhorn and Mark McGranaghan, IEEE Transactions on Industry Applications, Vol.31, No. 6, Nov./Dec. 1995.)

IEEE Std. 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems, lists current distortion limits for general distribution systems.

**Methods of meter calculations.** All multimeters and DMMs are calibrated to give rms indication. However, depending on the voltage or current signal you're measuring, the different methods used in instruments to calculate rms value may yield vastly different measurements. Let's look at the most popular types to see how they arrive at rms values.

Peak method. Meters using this method read the peak of the measured signal and divide the result by 1.414 to obtain rms value of that signal. So, if the signal waveform is undistorted, this method gives relatively accurate measurements.

Averaging method. With this method, a meter determines the average value of a rectified signal. For a clean sinusoidal signal, it relates to the rms value by the constant k (1.1). As with the peak method, it gives accurate measurements if there's no waveform distortion.

True rms-sensing method. It uses an rms converter that does a digital calculation of rms value. It squares the signal on a sample-by-sample basis, averages the result, and takes the square root of the result. It gives accurate measurements, regardless of waveform distortion.