In unbounded media, wave propagation is supposed to be unguided. The existence of uniform plane wave is considered to be all through the space. Electromagnetic energy related with the wave stretched over a broad area. In TV and radio broadcasting, unbounded medium propagation of the wave is required. Here transmission of information is destined for one and all who may be interested. Another way of transmitting information is by guided media. Guided media acts to direct the transmission of energy from transmitter to receiver. Transmission lines are usually used in low frequency power distribution and in high frequency communications as well as in the ethernet and internet in computer networks. Two or more parallel conductors may be used to construct a transmission line, which connects source to a load. Typical transmission lines consist of coaxial line, waveguide, microstrip line, coplanar waveguide, etc. In this chapter, problems related with transmission lines are solved with the help of EM field theory and electric circuit theory.
TopCoaxial Line
The most extensively used TEM transmission line is the coaxial cable [Collin,R.E 1960, Liboff, R.L, and Dalmon G,C 1985] represented in Figure 1. It comprises of two conductors with inner conductor of radius a and outer conductor of radius b. The gap between two conductors is filled with dielectric material such as Teflon.
Figure 1. Configuration of coaxial line
The problems related to electrostatic can be explained expediently in cylindrical coordinate ρ, ϕ́. The Laplace equation has been satisfied by potential φ́ (ρ, ϕ́).
The corresponding problems related to electrostatic can be explained expediently in cylindrical coordinates ρ, φ́. The Laplace’s equation can be satisfied by potential ϕ́ (ρ, φ́):
The potential is independent on the azimuthal angle φ́ due to cylindrical symmetry. Therefore
where two constants of integration are A and B. Considering the condition that the outer conductor is grounded and the voltage of the inner conductor is held to be V́. The constants A=-Bln b and B=-V́ ln(b/a), resulting the potential:
It seems that radial component is associated with the electric field Eρ́ and azimuthal component is related with magnetic field Hφ́.
To achieve the current integrate Hϕ́ around the inner conductor:
Therefore the inductance and capacitance per unit length can be written as:
By solving above equations one can state the magnetic field in the form of:
Using Ampere’s law around a closed circular wire of radius ‘ρ’ surrounded by the conductor kept inside, the same expression can be obtained. The transmitted power Pt can be stated either in terms of voltage V́ or in terms of the highest value of electric field which take place at ρ=a,