Harmonic Distortion: Principles and Measurement
In the world of signal processing, maintaining the purity of a waveform is essential for high-fidelity transmission and reproduction. Harmonic distortion occurs when a system adds unwanted harmonics to a signal, altering its original shape and quality. This phenomenon is most evident when a purely sinusoidal signal—a smooth, repetitive mathematical curve—is processed through a device that introduces non-linearities.
When this distortion occurs, a series of harmonics are superimposed on the original signal. These additional frequencies can be identified and measured using specialized diagnostic equipment.
The Mathematics of Signal Distortion
To understand how harmonic distortion works, we must look at the relationship between the input and the output signals. If we start with a pure input signal represented as:
fi = a1 ⋅ sin(ωt)
The resulting normalized output signal becomes a composite of the original frequency and its multiples:
fo = a1 ⋅ sin(ωt) + a2 ⋅ sin(2ωt) + a3 ⋅ sin(3ωt) + ...
In this equation, a1 represents the amplitude of the fundamental frequency, while a2, a3, and subsequent values represent the amplitudes of the second, third, and higher-order harmonics.
[ไม่มีภาพประกอบ]Measuring Total Harmonic Distortion (THD)
The most common way to quantify this effect is through Total Harmonic Distortion (THD). THD is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency.
The mathematical formula for THD is expressed as:
THD = √ (a22 + a32 + ...) / a1
Depending on the industry or application, this ratio is typically reported in one of two formats: as a percentage or in decibels (dB).
Key Facts
- Harmonic distortion is the addition of harmonic frequencies to a primary signal.
- It is most easily detected when the input is a pure sine wave.
- THD measures the ratio between the harmonics and the fundamental frequency.
- Results are commonly expressed in percentage (%) or decibels (dB).
| Term | Definition | Role in Signal |
|---|---|---|
| Fundamental Frequency | The original input frequency (a1) | The primary signal component |
| Harmonics | Integer multiples of the fundamental (a2, a3, etc.) | The distorting components |
| THD | Total Harmonic Distortion | The overall measure of signal impurity |
Frequently Asked Questions
What exactly is harmonic distortion?
Harmonic distortion is the process where a system adds additional frequencies, known as harmonics, to an original sinusoidal signal, resulting in a distorted output waveform.
How is THD calculated?
THD is calculated by taking the square root of the sum of the squares of the harmonic amplitudes (a2, a3, etc.) and dividing that value by the amplitude of the fundamental frequency (a1).
In what units is Total Harmonic Distortion measured?
THD is typically expressed either as a percentage or in decibels (dB).
What happens to a pure sine wave during harmonic distortion?
A pure sine wave is superimposed with a series of harmonics, meaning the output signal contains the original frequency plus multiple higher-frequency components.