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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 ...
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 ...
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 ,
From the definition of (angular) wavenumber for transverse electromagnetic (TEM) waves in lossless media, = = For a transmission line, the telegrapher's equations tells us that the wavenumber must be proportional to frequency for the transmission of the wave to be undistorted in the time domain. This includes, but is not limited to, the ideal ...
Heaviside's model of a transmission line. A transmission line can be represented as a distributed-element model of its primary line constants as shown in the figure. The primary constants are the electrical properties of the cable per unit length and are: capacitance C (in farads per meter), inductance L (in henries per meter), series resistance R (in ohms per meter), and shunt conductance G ...
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.
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.
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 ...