Total Harmonic Distortion (THD) Calculator

Calculate total harmonic distortion in audio systems and power supplies to measure signal quality and interference.

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What is Total Harmonic Distortion (THD)?

Total Harmonic Distortion (THD) is a measurement that quantifies how much a signal has been distorted by a system. When a pure signal (like a sine wave) passes through an electronic circuit, imperfections in the system can create additional frequencies called harmonics. THD measures the ratio of the sum power of all harmonic components to the power of the fundamental frequency.

THD is usually expressed as a percentage or in decibels (dB). Lower THD values indicate cleaner signals with less distortion, which is generally desirable in most audio and power applications.

How THD is Calculated

The mathematical formula for calculating THD as a percentage is:

THD (%) = (√(V₂² + V₃² + V₄² + ... + Vₙ²) / V₁) × 100

Where:

  • V₁ is the RMS amplitude of the fundamental frequency (first harmonic)
  • V₂, V₃, etc. are the RMS amplitudes of the higher harmonics

THD can also be expressed in decibels (dB):

THD (dB) = 20 × log₁₀(√(V₂² + V₃² + ... + Vₙ²) / V₁)

Negative dB values indicate that the harmonic content is lower than the fundamental frequency, which is usually the case in audio and power systems.

THD in Audio Applications

In audio systems, THD is a critical specification that directly affects sound quality. Lower THD values mean the amplifier or audio device is reproducing sounds more accurately with less added distortion.

THD RangeAudio QualityTypical Applications
<0.01%ExceptionalHigh-end audiophile equipment, professional studio gear
0.01% - 0.1%ExcellentQuality home audio systems, professional equipment
0.1% - 0.5%Very GoodGood consumer audio products
0.5% - 1%GoodAverage consumer electronics
1% - 3%AcceptableBudget audio equipment, car audio
>3%PoorLow-quality equipment, may have audible distortion

It's worth noting that some audio equipment, particularly guitar amplifiers, intentionally introduce harmonic distortion as a desired effect to create specific tones for musical expression.

THD in Power Systems

In electrical power systems, THD measures how much a voltage or current waveform deviates from a perfect sine wave. High THD in power systems can cause:

  • Increased heating in electrical equipment
  • Reduced efficiency and capacity in power systems
  • Malfunctions in sensitive electronic equipment
  • Interference with nearby equipment
  • Shorter equipment lifespan

Power quality standards like IEEE 519 typically recommend keeping THD below 5-8% for voltage and below specific limits for current based on the system size.

Causes of Harmonic Distortion

Several factors can contribute to harmonic distortion in electronic systems:

  • Non-linear components - Components like transistors, diodes, and transformers can distort signals when they don't maintain a linear relationship between input and output.
  • Clipping - When an amplifier is overdriven and cannot reproduce the peaks of a waveform, it "clips" the tops of the waveform, introducing significant harmonic distortion.
  • Power supply issues - Inadequate power supplies can cause distortion when amplifiers demand more current than is available.
  • Non-linear loads - In power systems, devices like switch-mode power supplies, LED drivers, and variable frequency drives draw current in a non-sinusoidal way, introducing harmonics.
  • Intermodulation - When multiple frequencies interact in a non-linear system, they can create additional harmonic components.

Measuring and Reducing THD

THD is typically measured using specialized equipment such as:

  • Audio analyzers
  • Distortion analyzers
  • Spectrum analyzers
  • Power quality analyzers

To reduce THD in systems:

  • In audio systems: Use higher-quality components, implement negative feedback, operate amplifiers within their linear range, and ensure adequate power supply.
  • In power systems: Install passive or active harmonic filters, use phase-shifting transformers, implement active power factor correction, and isolate sensitive equipment from harmonic sources.

THD vs. THD+N

While THD only measures harmonic distortion, THD+N (Total Harmonic Distortion plus Noise) includes both harmonic distortion components and noise in the measurement. THD+N is often used in audio equipment specifications as it provides a more comprehensive picture of overall signal quality.

THD+N is always equal to or higher than THD alone, and it offers a more realistic assessment of the actual degradation of the signal that a listener might experience.

See Also

Frequently Asked Questions

Total Harmonic Distortion (THD) is a measurement that quantifies the level of harmonic distortion present in a signal. It's expressed as a percentage or in decibels (dB) and represents the ratio of the sum of all harmonic components to the fundamental frequency. Lower THD values indicate cleaner signals with less distortion.

THD is crucial in audio systems because it directly affects sound quality. Lower THD values mean the amplifier or audio device is reproducing sounds more accurately with less added distortion. Excessive harmonic distortion can cause audio to sound harsh, unclear, or fatiguing to listen to. High-quality audio equipment typically aims for THD values below 0.1% or even 0.01% at normal listening levels.

In power supplies, THD measures how closely the output voltage or current matches a pure sine wave. High THD in power systems can cause equipment overheating, reduced efficiency, interference with sensitive electronics, and potentially shorter component lifespans. For critical applications, power supplies with THD under 5% are often recommended.

While THD only measures harmonic distortion components, THD+N (Total Harmonic Distortion plus Noise) includes both harmonic distortion and random noise in its measurement. THD+N provides a more comprehensive picture of signal quality but doesn't distinguish between distortion and noise sources. In professional applications, both measurements are useful for different analyses.

High THD can result from multiple factors including: Clipping (when amplifiers are overdriven), nonlinearities in circuit components, power supply issues, thermal problems, poor circuit design, component aging, and impedance mismatches. In professional audio, distortion can sometimes be intentionally added for creative effects, particularly in guitar amplifiers.

To reduce THD in an audio system: Avoid overdriving amplifiers (keep volume at reasonable levels), use higher quality components and equipment, ensure proper impedance matching between components, maintain adequate power supply capacity, reduce interference from other electronic devices, use balanced connections when possible, and consider adding power conditioning for cleaner electrical supply.

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