Electrical lengthening

In telecommunications and electrical engineering, electrical length (or phase length) refers to the length of an electrical conductor in terms of the phase shift introduced by transmission over that conductor at some frequency.

Depending on the specific usage, the term "electrical length" is used rather than simple physical length to incorporate one or more of the following three concepts:

The first usage of the term "electrical length" assumes a sine wave of some frequency, or at least a narrowband waveform centered around some frequency f. The sine wave will repeat with a period of T = 1/f. The frequency f will correspond to a particular wavelength λ along a particular conductor. For conductors (such as bare wire or air-filled coax) which transmit signals at the speed of light c, the wavelength is given by λ=c/f. A distance L along that conductor corresponds to N wavelengths where N= L / λ.

In the figure at the right, the wave shown is seen to be N=1.5 wavelengths long. A wave crest at the beginning of the graph, moving towards the right, will arrive at the end after a time 1.5T. The electrical length of that segment is said to be "1.5 wavelengths" or, expressed as a phase angle, "540°" (or 3π radians) where N wavelengths corresponds to φ = 360°•N (or φ = 2π•N radians). In radio frequency applications, when a delay is introduced due to a transmission line, it is often the phase shift φ that is of importance, so specifying a design in terms of the phase or electrical length allows one to adapt that design to an arbitrary frequency by employing the wavelength λ applying to that frequency.

In a transmission line, a signal travels at a rate controlled by the effective capacitance and inductance per unit of length of the transmission line. Some transmission lines consist only of bare conductors, in which case their signals propagate at the speed of light, c. More often the signal travels at a reduced velocity κc, where κ is the velocity factor, a number less than 1, representing the ratio of that velocity to the speed of light.

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