1. PLANE WAVE PROPAGATION
Fields and Waves
Lesson 5.2
PLANE WAVE PROPAGATION
Lossless Media
Lale T. Ergene

2. Time Harmonic Fields
EM wave propagation involves electric and magnetic fields having more than one component, each dependent on all three coordinates, in addition to time.
e.g. Electric field
instantaneous field
vector phasor
Valid for the other fields and their sources

3. Maxwell’s Equations in Phasor Domain
time domain
remember

4. Complex Permittivity complex permittivity
For lossless medium σ=0 ε’’= εc =ε’=ε

5. Wave Equations (charge free)
Homogenous wave equation for
propagation constant

6. Plane Wave Propagation in Lossless Media
There are three constitutive parameters of the medium: σ, ε, μ
If the medium is nonconducting σ=0 α=0 LOSSLESS
εc =ε’=ε
Wavenumber k
(for a lossless medium)

7. Transverse Electromagnetic Wave
Electric and magnetic fields that are perpendicular to each other and to the direction of propagation
They are uniform in planes perpendicular to the direction of propagation x
At large distances from physical antennas and ground, the waves can be approximated as uniform plane waves
Direction of propagation z y

8. Transverse Electromagnetic Wave
Spatial variation of and at t=0

9. Traveling waves The Electric Field in phasor form (only x component)
General solution of the differential equation
Amplitudes (constant)

10. Uniform Plane waves
In general, a uniform plane wave traveling in the +z direction, may have x and y components
The relationship between them
Do Problem 1

11. Intrinsic impedance (η) of a lossless medium
Similar to the characteristic impedance (Z0) of a transmission line
Defines the connection between electric and magnetic fields of
an EM wave
[Ω]
Phase velocity
[m/s]
wavelength
[m]
If the medium is vacuum : up=3x108 [m/s], ηc=377 [Ω]
Do Problem 2

12. Electromagnetic Power Density
Poynting Vector , is defined
[W/unit area]
is along the propagation direction of the wave
Total power
[m/s]
[W] OR
[W]
Average power density of the wave
[W/m2]

13. Plane wave in a Lossless Medium
[W/m2]
Do Problem 3