A waveguide is a special form of transmission line consisting of a hollow, metal tube. The tube wall provides distributed inductance, while the empty space between the tube walls provide distributed capacitance. Wave guides conduct microwave energy at lower loss than coaxial cables.

Transmission lines are used to transfer electromagnetic energy from one point to another with minimum losses over a wideband of frequencies. There are three major types of transmission lines: transverse electromagnetic (TEM) mode, transverse electric (TE) mode and transverse magnetic (TM) mode.

1(b) and taking the limit as Δz→0 the transmission line equations are. ∂v(z,t)∂z=−Ri(z,t)−L∂i(z,t)∂t∂i(z,t)∂z=−Gv(z,t)−C∂v(z,t)∂t.

Propagation Constant of a Transmission Line Z = R + iωL is the series impedance of line per unit length.

Solution α|Np=0.1151×α|dB=0.1151×(10 dB/m)=1.151 Np/m,β=50 rad/m. Propagation constant, γ=α+ȷβ=(1.151+ȷ50) m−1. γ=√(R+ȷωL)(G+ȷωC), and Z0=√(R+ȷωL)/(G+ȷωC), therefore Z0=γ/(G+ȷωC); ω=2π⋅2×109 s−1; G=0; C=100×10−12 F, so Z0=39.8−ȷ0.916Ω.

Transmission Line Power If you want to calculate this, you can use Poynting's vector from electromagnetic theory, but EE's normally just use the relation P = I x V.