 Total harmonic distortion

Total harmonic distortion measures the root-sum-square amplitude of the selected higher harmonic components relative to the fundamental amplitude. For nonzero $A_1$ and one common amplitude convention,Peak amplitudes or root mean square amplitudes give the same ratio when used consistently for all sinusoids. The finite upper order $M$, measurement bandwidth, and treatment of noise must be specified. The primary Anritsu procedure distinguishes this fundamental-normalized definition from normalization by the full harmonic component sum.^[ref]

For an original example, let a waveform have fundamental peak amplitude $2\mathrm{V}$, second harmonic component $0.06\mathrm{V}$, and third harmonic component $0.08\mathrm{V}$, with no other components. ThenA logarithmic amplitude-ratio report is $20{\log }_{10}(0.05)\approx -26.02\mathrm{dB}$. The phases do not enter this RMS sum because distinct integer harmonic components are orthogonal over a full period.

If the denominator instead includes the fundamental and all included harmonic components, excluding DC, the resulting ratio isabout $4.994\%$ in the example. The two conventions are close at low distortion but differ markedly when higher harmonic components are large; only the latter is bounded by one. A quoted percentage without its denominator convention is incomplete. Broadband noise is a different contribution and is not silently included in the displayed THD formula.

A motivating apparatus uses a clean sinusoidal source, the device under test, and calibrated receivers tuned to the fundamental and harmonic component frequencies. Anritsu's worked system calibrates the receiver over those frequencies before combining separate measurements.^[ref] With an FFT-based instrument, spectral leakage bias in harmonic distortion measurements can misassign a strong fundamental to harmonic component bins; aliasing and insufficient receiver bandwidth can also hide or relocate components. Small THD therefore describes a stated test and analysis, not every possible waveform or operating level.