1. Lecture 2

2. Derive the transmission line parameters (R, L, G, C) in terms of the electromagnetic fields Rederive the telegrapher equations using these parameters  1.4 Field analysis of transmission lines Example: Voltage : V 0 e  j  z Current: I 0 e  j  z

3. Work (W) and power (P) H* Multiplies the two sides of the first Maxell’s equation: E Multiplies the two sides of the conjugated second Maxell’s equation: Add the above two equations and utilize We obtain (J=Js+σE): Integrate the above formula in volume V and utilize divergence theory, we have the following after reorganize the equation

4. Poynting law: Source power P s : Output power P 0 : Loss power P l : Stored magnetic energy W m : Stored electric energy W e : (Time averaged)

5. Calculate the time-average stored magnetic energy in an isotropic medium ( the results valid for any media ) Calculate magnetic energy

6. Surface resistance and surface current of metal Energy entering a conductor: The contribution to the integral from the surface S can be made zero by proper selection of this surface. Therefore, From vector identity, we have The energy absorbed by a conductor:

7. Transmission line parameter: L The time-average stored magnetic energy for 1 m long transmission line is  1.4 Field analysis of transmission lines And circuit line gives. Hence the self inductance could be identified as

8. Appendix 1: Calculate the time-average stored magnetic energy in an isotropic medium ( the results valid for any media )

9. Transmission line parameter: C  1.4 Field analysis of transmission lines Similarly, the time-average stored electric energy per unit length can be found as Circuit theory gives, resulting in the following expression for the capacitance per unit length:

10. Transmission line parameter: R  1.4 Field analysis of transmission lines The power loss per unit length due to the finite conductivity of the metallic conductors is The circuit theory gives, so the series resistance R per unit length of line is (R s = 1/  is the surface resistance and H is the tangential field)

11. Transmission line parameter, G  1.4 Field analysis of transmission lines The time-average power dissipated per unit length in a lossy dielectric is Circuit theory gives, so the shunt conductance per unit length can be written as

12. Homework 1. The fields of a traveling TEM wave inside the coaxial line shown left can be expressed as where  is the propagation constant of the line. The conductors are assumed to have a surface resistivity R s, and the material filling the space between the conductors is assumed to have a complex permittivity  =  ’ - j  " and a permeability μ = μ 0 μ r. Determine the transmission line parameters (L,C,R,G). x y aρ φ b μ,μ, 2. For the parallel plate line shown left, derive the R, L, G, and C parameters. Assume w >> d. d rr  y z x w