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The current distortion factor is the ratio $D_I=I_1/I_{\mathrm{rms}}$, where $I_1$ is the root mean square magnitude of the fundamental electric current component and $I_{\mathrm{rms}}>0$ is the root mean square magnitude of the complete electric current. Its square is the fraction of the current's mean square supplied by the fundamental component. This ratio is distinct from displacement power factor, which measures the relative phase of the fundamental potential difference and current.

Use a Fourier series at fundamental frequency $\omega /(2\pi )$:Here $I_0$ is the DC component and the $I_n$ are RMS magnitudes of harmonic components. Averaging over a complete period, orthogonality and the Parseval identity giveFor purely sinusoidal electric potential difference $v(t)=\sqrt{2}V\cos \omega t$, only the fundamental electric current contributes to active power:Thus a displacement power factor of one can coexist with a lower total power factor.

For $I_1>0$, use fundamental-normalized current total harmonic distortion, ${\mathrm{THD}}_I=\sqrt{{\sum }_{n\ge 2}{I}_n^2}/I_1$. The relation between current distortion factor and THD with DC current isWith zero DC component, this reduces to $D_I=(1+{\mathrm{THD}}_I^2{)}^{-1/2}$. The definition of RMS here includes the DC component. For example, a 10 ampere fundamental and 3 ampere DC component, with no higher harmonic components, have zero total harmonic distortion but $D_I=10/\sqrt{109}\approx 0.9578$.

For an original zero-mean waveform, take a 230 volt RMS sinusoidal supply, $I_1=10\mathrm{A}$, $\cos {\varphi }_1=0.8$, and RMS third/fifth harmonic components of 6 and 3 amperes. ThenThe active power is 1840 watts, apparent power is about 2769.57 volt-amperes and total power factor is about 0.6644. This is an illustrative waveform model, not a measurement of a particular rectifier.

Terminology requires care. Overview of Functions: Harmonic Measurements by Schneider Electric uses distortion factor for the ratio of power factor to the fundamental cosine. Power Quality Considerations by Schneider Electric uses the label for harmonic content relative to the fundamental, or total harmonic distortion. The defining ratio identifies the intended quantity.

If the supply also contains harmonic components, use the harmonic active power sum:with matching voltage/current phase conventions. The fundamental-only factorization above assumes a purely sinusoidal supply.

The relation between current distortion factor and THD with DC current accounts for the mean component omitted from the usual fundamental-normalized total harmonic distortion. For a periodic electric current, let $I_0$ be its signed DC component, $I_1>0$ the fundamental RMS magnitude, and $I_n$ the RMS magnitudes of higher harmonic components. The Parseval identity givesDefine ${\mathrm{THD}}_I=\sqrt{{\sum }_{n\ge 2}{I}_n^2}/I_1$ and current distortion factor $D_I=I_1/I_{\mathrm{rms}}$. Division by $I_1^2$ provesThe root mean square in this expression includes the mean, while the stated total harmonic distortion excludes it. An instrument reporting AC-only RMS or a differently normalized distortion quantity requires a correspondingly different conversion.

For an original example, take $I_1=4\mathrm{A}$, $I_0=3\mathrm{A}$ and combined higher-harmonic RMS magnitude $2\mathrm{A}$. Then ${\mathrm{THD}}_I=0.5$, $I_{\mathrm{rms}}=\sqrt{29}\mathrm{A}$ and $D_I=4/\sqrt{29}\approx 0.7428$. Neglecting the DC component would instead predict $1/\sqrt{1.25}\approx 0.8944$. In the same conductor electrical resistance $R$, the actual heating is $29R$, while that omission would predict $20R$.

For a zero-mean sinusoidal supply of $100\mathrm{V}$ RMS and an in-phase fundamental current, the example absorbs $400\mathrm{W}$. Its apparent power is approximately $538.52\mathrm{VA}$, so total power factor is $0.7428$ despite a displacement power factor of one. The DC component carries no average power from that particular zero-mean supply, but it still increases mean-square electric current. If the supply itself has a DC component, its contribution $V_0{I}_0$ must be included through the harmonic active power sum.

As $I_1$ tends to zero the defining current distortion factor can tend to zero, but fundamental-normalized total harmonic distortion is undefined at $I_1=0$. Do not evaluate the boxed relation there by silently dividing by zero. The manufacturer's documentation also uses differing labels for distortion ratios, reinforcing the need to state the defining normalization.^[ref][ref]

Spectral leakage bias in harmonic distortion measurements occurs when a finite record spreads a strong component into bins interpreted as distinct harmonics. A waveform can have zero physical total harmonic distortion while a naive FFT-bin ratio reports otherwise. Confining a sinusoid to a finite interval creates spectral sidelobes; the pinned primary guide derives this leakage from the finite-time Fourier transform.^[ref]

For an exact discrete calculation, take $x_m=A\cos (2\pi \nu m/N+\varphi )$, where $\nu$ is the number of cycles in the record. With the unscaled forward discrete Fourier transform, a finite geometric sum giveswherewhenever the denominator is nonzero, with the finite-sum limit elsewhere. Integer-cycle coherent sampling makes the unwanted integer bins cancel; a noninteger cycle count generally does not. The negative-frequency contribution also matters because the input is real.

For an original pure-tone example, let $A=1$, $\varphi =0$, $N=128$ and $\nu =5.3$. Its true higher-harmonic amplitudes are zero. Yet choosing the nearest bins $5$, $11$, and $16$ for the fundamental, second and third harmonic givesA naive result would be about $6.58\%$ distortion from this undistorted sinusoid. This is an exactly specified record calculation, not an instrument's measured distortion floor.

A window reduces some sidelobes at the cost of a broader main lobe and a changed amplitude normalization. Its coherent gain of a window must be treated consistently, and one cannot assume that one selected bin captures a noncoherent tone's full amplitude. Zero padding samples the same finite-record spectrum more densely; it does not restore missing observation time or remove leakage.

A measurement can instead synchronize the source and acquisition for an integer number of cycles, fit a justified sinusoidal model, or use a validated window/band-integration method. The finite-record phasor extraction with coherent sampling gives a particularly transparent exact case. Calibrated receiver response and actual harmonic coverage remain necessary, as in the primary Anritsu apparatus.^[ref] Power spectral density and squared-amplitude spectrum outputs also have different units; an arbitrary square root of a density bin is not a calibrated harmonic amplitude.^[ref]

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.