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In the lossless case, it is possible to show that = + + and = + where in this special case, is a real quantity that may depend on frequency and is the characteristic impedance of the transmission line, which, for a lossless line is given by = and and are arbitrary constants of integration, which are determined by the two boundary conditions ...
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 ...
The analysis of lossless lines provides an accurate approximation for real transmission lines that simplifies the mathematics considered in modeling transmission lines. A lossless line is defined as a transmission line that has no line resistance and no dielectric loss. This would imply that the conductors act like perfect conductors and the ...
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 ...
Looking towards a load through a length l of lossless transmission line, the normalized impedance changes as l increases, following the blue circle. At l=λ/4, the normalized impedance is reflected about the centre of the chart. Standing waves on a transmission line with an open-circuit load (top), and a short-circuit load (bottom).
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 ...
Versions of the transmission-line equation may be similarly derived for the admittance loss free case and for the impedance and admittance lossy cases. The Smith chart graphical equivalent of using the transmission-line equation is to normalise Z L , {\displaystyle \,Z_{\mathsf {L}}\,,} to plot the resulting point on a Z Smith chart and to draw ...
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.