Understanding harmonic distortion measurements

Harmonics and harmonic distortion measurements

The amplitude of a harmonic decreases as the harmonic order increases. For example, the second harmonic has a lower amplitude than the fundamental. Theoretically, there can be an infinite number of harmonics, but eventually, the harmonics became so small that they fall below the noise floor, at which point they can be safely ignored.

There are a few cases when harmonics can be useful or desirable. For example, harmonic mixers can be used to intentionally generate harmonics, which are then used to downconvert microwave or millimeterwave signals to a lower intermediate frequency. However, these are exceptional cases. Harmonics are usually undesirable and should be kept as low as possible. Low-pass filtering is the most common way in which harmonics are suppressed or attenuated.

Harmonic distortion measurements are used to measure the amplitudes of harmonics, and in radio frequency (RF) applications, this is done using a spectrum analyzer. The device under test (DUT) is connected to the analyzer, which uses something called zero span mode to measure the power of the fundamental and each harmonic individually.

The spectrum analyzer should have high linearity to avoid harmonics being generated within the analyzer itself, and the analyzer should also have low noise and a high dynamic range, since the difference in amplitudes between the fundamental and highest order harmonic of interest can be quite large.

Some DUTs, such as amplifiers, require an input, so a signal generator may also be a necessary part of the measurement setup. Like the spectrum analyzer, the signal generator must have good performance, especially low output harmonics. In some cases, it may be necessary or advantageous to use an external low pass filter to further reduce any harmonics present in the generator output.

Zero span mode

You can measure the fundamental and the harmonics with a spectrum analyzer’s zero span mode. Zero span means that instead of sweeping across a frequency range, the spectrum analyzer measures at a single, fixed frequency, usually starting at the fundamental and then at each calculated harmonic frequency. At each of these frequencies, the power is measured only within a user-definable resolution bandwidth, which is usually chosen to be slightly wider than the harmonic. This helps ensure that you are measuring the power of the harmonic with minimal contribution from the surrounding noise.

This width of each harmonic is scaled or multiplied by the harmonic order, so the resolution bandwidth may also need to be increased with the harmonic order.

Finally, the measurement time at each frequency is typically also user-definable, with longer measurement times providing more accurate measurement results.

In many modern spectrum analyzers, all of these functions are integrated into an automated measurement function: the user simply provides a few configuration values, and the analyzer measures and reports the results automatically.

Harmonic distortion measurement results

Harmonic distortion measurements are provided in two ways:

• Amplitudes of individual harmonics: These are normally reported as powers relative to the fundamental, so units are typically dBc, or decibels down from the (fundamental) carrier. This data is often provided in tabular format.
• Total harmonic distortion (THD): This is the harmonic distortion quantified as the combined power in multiple harmonics relative to the power of the fundamental. It is reported either as a percentage or in dB.

Calculating total harmonic distortion (THD) and THD+N

THD is usually automatically calculated by the measuring spectrum analyzer, once the user defines the number of harmonics to include in the measurement. But here is how you would do the calculation manually:

• Convert any relative powers in dBc into absolute powers in dBm. Recall that spectrum analyzers normally report powers in units of dB, i.e., on a logarithmic scale.
• Convert the dBm values into linear units, i.e., into watts.
• Calculate the total harmonic distortion in percent.
• If necessary, convert THD in percent to THD in dB.

It goes without saying that, especially when there are many harmonics, it is much easier to have the analyzer perform these calculations.

THD+N is a special variant of THD. In some applications, particularly audio applications, the effect of noise is very important, and a measurement of THD plus noise is desirable. In this case, power is measured over a bandwidth, as opposed to only at each discrete harmonic. Like total harmonic distortion, THD+N is also reported in percent or in dB.

Prior to the development of modern spectrum analyzers, THD+N was actually an easier measurement to make: a filter was used to “notch out” the fundamental, and then measurements were made over the bandwidth of interest.

Note: THD+N is essentially the inverse of “signal-to-noise and distortion” (SINAD), another common measurement of noise and distortion.