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The secondary line constants can be used, for instance, to compare the characteristics of a waveguide to a copper line, whereas the primary constants have no meaning for a waveguide. The constants are conductor resistance and inductance, and insulator capacitance and conductance, which are by convention given the symbols R, L, C, and G ...
Equivalent circuit of an unbalanced transmission line (such as coaxial cable) where: 2/Z o is the trans-admittance of VCCS (Voltage Controlled Current Source), x is the length of transmission line, Z(s) ≡ Z o (s) is the characteristic impedance, T(s) is the propagation function, γ(s) is the propagation "constant", s ≡ j ω, and j 2 ≡ −1.
The primary line constants are normally taken to be constant with position along the line leading to a particularly simple analysis and model. However, this is not always the case, variations in physical dimensions along the line will cause variations in the primary constants, that is, they have now to be described as functions of distance.
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 voltage and current phasors on the line are related by the characteristic impedance as: = (+) (+) = () where the subscripts (+) and (−) mark the separate constants for the waves traveling forward (+) and backward (−). The rightmost expression has a negative sign because the current in the backward wave has the opposite direction to ...
In transmission line theory, α and β are counted among the "secondary coefficients", the term secondary being used to contrast to the primary line coefficients. The primary coefficients are the physical properties of the line, namely R,C,L and G, from which the secondary coefficients may be derived using the telegrapher's equation.
As an example, consider the advection equation (this example assumes familiarity with PDE notation, and solutions to basic ODEs). + = where is constant and is a function of and . We want to transform this linear first-order PDE into an ODE along the appropriate curve; i.e. something of the form
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.