Electrical length

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In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor.^[1][2][3] In other words, it is the length of the conductor measured in wavelengths. It can alternately be expressed as an angle, in radians or degrees, equal to the phase shift the alternating current experiences traveling through the conductor.^[1][3]

Electrical length is defined for a conductor operating at a specific frequency or narrow band of frequencies. It is determined by the construction of the cable, so different cables of the same length operating at the same frequency can have different electrical lengths. A conductor is called electrically long if it has an electrical length much greater than one; that is it is much longer than the wavelength of the alternating current passing through it, and electrically short if it is much shorter than a wavelength. Electrical lengthening and electrical shortening means adding reactance (capacitance or inductance) to an antenna or conductor to increase or decrease the electrical length,^[1] usually for the purpose of making it resonant at a different resonant frequency.

This concept is used throughout electronics, and particularly in radio frequency circuit design, transmission line and antenna theory and design. Electrical length determines when wave effects (phase shift along conductors) become important in a circuit. Ordinary lumped element electric circuits only work well for alternating currents at frequencies for which the circuit is electrically small (electrical length much less than one). For frequencies high enough that the wavelength approaches the size of the circuit (the electrical length approaches one) the lumped element model on which circuit theory is based becomes inaccurate, and transmission line techniques must be used.^{[4]: p.12–14}