Harmonic Distortion

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series teaches you a specific topic of common measurement applications by explaining the theory and giving practical examples. This tutorial covers an introduction to RF, wireless, and high-frequency signals and systems.

For the complete list of tutorials, return to the NI Measurement Fundamentals main page, or for more RF tutorials, refer to the NI RF Fundamentals main subpage. For more information about National Instruments RF products, visit www.ni.com/rf.

Harmonic Distortion

In an ideal system, the fast Fourier transform (FFT) of a sinusoid would result in a single peak at a specific frequency. However, in real-world systems, non-linearity and noise result in imperfections. When a signal of a particular frequency f₁ passes through a nonlinear system, the output of the system consists of f₁ and its harmonics. The following figure demonstrates this relationship.

Figure 1. Fundamental Frequency f₁ With Second and Third Harmonics

Harmonic distortion is a measure of the amount of power contained in the harmonics of a fundamental signal. Harmonic distortion is inherent to devices and systems that possess nonlinear characteristics—the more nonlinear the device, the greater its harmonic distortion.

Calculating Harmonic Distortion

Harmonic distortion can be expressed as a power ratio or as a percentage ratio. Use the following formula to express it as a power ratio.

where P_HD is the power of the harmonic distortion in dBc, P_fund is the fundamental signal power in dB or dBm, and P_harm is the power of the harmonic of interest in dB or dBm.

Convert power to voltage and use the following equation to express harmonic distortion as a percentage ratio.

In some applications, the harmonic distortion is measured as a total percentage harmonic distortion (THD). This measurement requires the power summation of all the harmonics in the spectrum band, as defined in the following equation:

Testing for Harmonic Distortion

A typical setup to perform a harmonic distortion measurement is shown in the following figure. A lowpass filter or bandpass filter passes the fundamental signal to the unit under test (UUT) while suppressing its harmonics. This setup injects a clean sinusoidal signal into the UUT. Any harmonic content at the UUT output is assumed to be generated by the UUT rather than the signal source.

Figure 2. Typical Harmonic Distortion Measurement Setup

Harmonic distortion can be effectively reduced in any real-world system through the use of lowpass or bandpass filtering.

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Conclusion

For the complete list of tutorials, return to the NI Measurement Fundamentals main page, or for more RF tutorials, refer to the NI RF Fundamentals main subpage. For more information about National Instruments RF products, visit www.ni.com/rf.

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