Understanding Total Harmonic Distortion
Total harmonic distortion represents the ratio of harmonic energy to fundamental frequency energy in a signal. When a device amplifies, transmits, or converts a signal, nonlinear behaviour introduces unwanted harmonic frequencies absent from the original input.
- THD as a percentage: Expresses the proportion of distorted signal relative to the pure fundamental. A 1% THD means 1% of the output signal comprises spurious harmonics.
- Attenuation in decibels: A logarithmic representation showing how much the harmonic content is suppressed relative to the fundamental. More negative values indicate cleaner signals.
- Practical significance: Audio systems require THD below 0.5% for high fidelity; switching power supplies often operate at 5–20% THD; grid-connected equipment may be specified at 3–5% depending on voltage class.
THD and Decibel Conversion Formula
The relationship between THD percentage and attenuation in decibels is logarithmic. This formula converts between the two representations of the same phenomenon: signal degradation from nonlinear distortion.
a = 20 × log₁₀(THD / 100)
THD = 100 × 10^(a / 20)
a— Distortion attenuation in decibels (always ≤ 0 for physical signals)THD— Total harmonic distortion as a percentage (0–100%)
Why Measure Harmonic Distortion?
Harmonic distortion degrades equipment performance and interacts with power systems in measurable ways:
- Audio equipment: Speakers, amplifiers, and microphones with low THD reproduce source material with minimal coloration or artefacts.
- Power electronics: Switching converters, inverters, and variable frequency drives inject harmonics into electrical distribution networks, affecting transformer efficiency and cable heating.
- Regulatory compliance: EN 61000-3-2 (Europe) and IEEE 519 (North America) set harmonic limits for connected devices to protect grid stability.
- Measurement standards: Professional audio uses EN 60268; power quality assessment uses IEC 61000-4-30.
From Theory to Measurement
Real-world harmonic measurement uses a spectrum analyser or power quality meter. The instrument measures voltage and current at each harmonic frequency (50 Hz or 60 Hz fundamental, plus multiples: 100 Hz, 150 Hz, etc.), calculates RMS values, and computes THD automatically.
In audio, a pure sine wave has 0% THD. A square wave, by contrast, contains all odd harmonics and exhibits approximately 48% THD. Most signals fall between these extremes. When designing a product or troubleshooting audio issues, comparing THD values in both percentage and decibel form helps you quickly assess whether a specification has been met and by what margin.
Common Pitfalls and Practical Notes
When working with harmonic distortion measurements, several subtleties can affect interpretation:
- Logarithmic scale masks small changes — A 1% THD equals −40 dB; a 0.1% THD equals −60 dB. Small percentage changes near zero produce large dB swings. Conversely, at high THD values (>10%), dB changes become small. Always check which scale your specification uses.
- THD summation method varies — Some standards sum harmonics linearly; others sum them as root-mean-square (RMS). IEC 61000-3-2 uses RMS; older audio specs sometimes use linear. Confirm the method to avoid mismatches between calculated and measured values.
- Fundamental frequency dependency — THD definitions assume a known, stable fundamental. In variable-speed motors or adjustable-frequency drives, the fundamental shifts, and THD can appear to change even if harmonic magnitudes remain constant. Use tracking measurements for time-varying signals.
- Signal-to-noise ratio interaction — Very low THD values (<0.01%) approach the noise floor of typical test equipment. Measurement uncertainty becomes significant; report THD with its measurement tolerance to avoid false precision.