# Summary

- A
*transmission line*is a device used for transmission of electromagnetic energy guided by two conductors in a dielectric medium. *Transmission-line mode*is the distinct pattern of electric and magnetic field induced on a transmission line under source excitation.- Transverse ElectroMagnetic (TEM) mode
- Quasi-TEM mode
- Waveguide mode

- A transmission line can be characterized by four distributed parameters: resistance (in Î©/m), inductance (in H/m), capacitance (in F/m), and conductance (in S/m). These four distributed parameters are constant for a particular transmission line and are known as
*primary line constants*of a transmission line. - Apart from these primary line constants, there are few other constants related to a transmission line. These include the characteristic impedance (
*Z*_{0}), the propagation constant (*Î³*), attenuation constant (*Î±*), and phase constant (*Î²*). These constants are known as the*secondary line constants*. - Transmission line voltage and current equations, known as telegrapherâ€™s equations, are given as,
*Characteristic impedance*of a transmission line is defined as the ratio of positively travelling voltage wave to current wave at any point on the line. It is given as,- A transmission line is said to be
*lossless*if- the conductors of the line are perfect, i.e., the conductors have infinite conductivity and zero resistance (
*Ïƒ*= âˆž, R = 0), and - the dielectric medium between the conductors is ideal, i.e., the medium has zero conductivity and infinite resistance (
*Ïƒ*= 0, G = 0).

- the conductors of the line are perfect, i.e., the conductors have infinite conductivity and zero resistance (
- A
*distortionless*if it has no frequency and phase distortions. - The
*input impedance*at any point on the transmission line is given by the ratio of voltage to current at that point. *Reflection coefficient*of a transmission line is the ratio of the reflected voltage (or current) to the incident voltage (or current), when a transmission line is terminated in an impedance (*Z*_{R}) not equal to the characteristic impedance (*Z*_{0}) of the line. The reflection coefficient as a function of position can be written as,- The reflection coefficient at the load (
*z*= l) is, *Standing wave ratio*in a transmission line is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current) of a line having standing waves.- The input impedance as a function of position at any point along a general transmission line is given as,
- A Smith chart is a useful graphical tool used to calculate the reflection coefficient and impedance at various points on a (lossless) transmission line system.