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The telegrapher's equations (or just telegraph equations) are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. [1] The equations and their solutions are ...
Applying the transmission line model based on the telegrapher's equations as derived below, [1] [2] the general expression for the characteristic impedance of a transmission line is: = + + where R {\displaystyle R} is the resistance per unit length, considering the two conductors to be in series ,
They were developed by Oliver Heaviside who created the transmission line model, and are based on Maxwell's equations. Schematic representation of the elementary component of a transmission line. The transmission line model is an example of the distributed-element model. It represents the transmission line as an infinite series of two-port ...
Two approximations can be made to simplify things: assume a lossless Transmission Line (a decent assumption as very low resistance conductor is typically used) and neglecting any capacitance on the line (a fair assumption for 200kV lines and lower). This reduces the Line impedance to just a reactance, and results in the real and reactive power ...
A wave travelling rightward along a lossless transmission line. Black dots represent electrons, and arrows show the electric field. The lossless line approximation is the least accurate model; it is often used on short lines when the inductance of the line is much greater than its resistance. For this approximation, the voltage and current are ...
There are several approaches to understanding reflections, but the relationship of reflections to the conservation laws is particularly enlightening. A simple example is a step voltage, () (where is the height of the step and () is the unit step function with time ), applied to one end of a lossless line, and consider what happens when the line is terminated in various ways.
The following example shows how a transmission line, terminated with an arbitrary load, may be matched at one frequency either with a series or parallel reactive component in each case connected at precise positions. Smith chart construction for some distributed transmission-line matching.
The transmission system usually does not have a large buffering capability to match loads with generation. Thus generation has to be kept matched to the load, to prevent overloading generation equipment. Multiple sources and loads can be connected to the transmission system and they must be controlled to provide orderly transfer of power.