Transmission line theory: quick summary (part A)
The mathematics of transmission line theory is complicated and so is given in the "Transmission line details" appendix at end of this tutorial. The essential results are:
1. Signal and return conductors can always be considered to constitute a transmission line.
2. The transmission line characteristic impedance Z is determined by the physical layout of the conductors together with certain physical constants (permittivity of vacuum, permeability of vacuum, dielectric constant). The characteristic impedance of practical transmission lines is in the range of 25 to 300 Ohms. Various commercially available cables are designed to be transmission lines with precise characteristic impedances. This precision is obtained by maintaining constant geometric properties along the length of the line (e.g., constant separation between conductors). Examples of commonly used transmission lines and their characteristic impedances are:
(i) RG-59 coaxial cable often used in laboratories, Z =50 ohms,
(ii) cable television coaxial cable, Z =75 ohms,
(iii) Category 5 data cable, Z =100 ohms,
(iv) now-obsolete twin wire ribbon once used for home television, Z =300 ohms.
The reason for the relatively limited range of Zc is that Zc~ sqrt(m/e) ln (b/a) where m= 4p x10^-7 is the permeability of vacuum, e is the dielectric constant of the insulation between the two conductors (for vacuum evac = 8.85x10^-12 , for typical plastics e~2 x evac), b is the large and a is the small characteristic perpendicular dimension of the transmission line. For twin conductors b would be the inter-conductor separation and a the individual radius, while for coaxial cables b and a would be the outer and inner radii.
->continue to Part B (next page)