Aircraft Systems

Appendix BTheory of Transmission Lines and Waveguides

Wires used to carry oscillating signals from one place to another are generally referred to as transmission lines and can simply be a pair of wires as shown in Figure A2.1a or more commonly, a central conductor surrounded by hollow conducting cylinder (a coaxial cable) as shown in Figure A2.1b. When carrying a signal, there is an oscillating voltage between the wires and generally one of the conductors (the central one in the case of the coaxial cable) carries the current to the load. Either arrangement exhibits a capacitance per unit length, C, and an inductance per unit length, L.

Figure A2.1(a) Transmission line consisting of two parallel conductors. (b) Coaxial cable‐type transmission line.

Consider initially the line characterized in unit lengths each with a discrete capacitance C and a discrete inductance L forming the infinite network as illustrated in Figure A2.2a. The entire transmission line can be represented by a single impedance load at the input terminals, Z_c (Figure A2.2b) and since it is an infinite network adding a single unit in parallel to Z_c at the input will not change the load (Figure A2.2c). For a signal input with an angular frequency ω the impedance of L is Z₁ = iωL and the impedance of C is Z₂ = 1/iωC, thus with reference to Figure A2.2 we can write:

(A2.1)

giving

(A2.2)

Figure A2.2(a) Transmission ...