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In an electric power system, a harmonic of a voltage or current waveform is a sinusoidal wave whose frequency is an integer multiple of the fundamental frequency.Harmonic frequencies are produced by the action of non-linear loads such as rectifiers, discharge lighting, or saturated electric machines.
As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series . The term is employed in various disciplines, including music, physics, acoustics , electronic power transmission, radio technology, and other fields.
To understand a system with an input and an output, such as an audio amplifier, we start with an ideal system where the transfer function is linear and time-invariant.When a sinusoidal signal of frequency ω passes through a non-ideal, non-linear device, additional content is added at multiples nω (harmonics) of the original frequency.
Harmonic balance is a method used to calculate the steady-state response of nonlinear differential equations, [1] and is mostly applied to nonlinear electrical circuits. [2] [3] [4] It is a frequency domain method for calculating the steady state, as opposed to the various time-domain steady-state methods. The name "harmonic balance" is ...
Animation of the additive synthesis of a triangle wave with an increasing number of harmonics. See Fourier Analysis for a mathematical description.. It is possible to approximate a triangle wave with additive synthesis by summing odd harmonics of the fundamental while multiplying every other odd harmonic by −1 (or, equivalently, changing its phase by π) and multiplying the amplitude of the ...
(Odd) harmonics of a 1000 Hz square wave Graph showing the first 3 terms of the Fourier series of a square wave Using Fourier expansion with cycle frequency f over time t , an ideal square wave with an amplitude of 1 can be represented as an infinite sum of sinusoidal waves: x ( t ) = 4 π ∑ k = 1 ∞ sin ( 2 π ( 2 k − 1 ) f t ) 2 k ...
Devices that utilize rectifier-capacitor front ends (such as switch-mode power supplies for computers, office equipment and the like) introduce third order harmonics. Third harmonic currents are in-phase on each of the supply phases and therefore will add together in the neutral which can cause the neutral current in a wye system to exceed the ...
The harmonic number with = ⌊ ⌋ (red line) with its asymptotic limit + (blue line) where is the Euler–Mascheroni constant.. In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] = + + + + = =.