Wireless Communication

Lecture 6 – Ground Reflection

Text Section 4.5,6

Reflection from Dielectrics

This is a review from basic EM. If you need additional information on this topic, please consult a basic electromagnetics text from the library.

Dielectric properties of materials

TABLE 4.1

Complex Permittivity

Characteristic impedance

Parallel and Perpendicular Polarization

Plane of Incidence: contains the rays marking the direction of propagation for the incident, transmitted, and reflected fields.

FIGURE 4.4 Plane of incidence is the paper/board

Parallel Polarization: E field is parallel to plane of incidence (A)\

Perpendicular Polarization: E field is perpendicular to plane of incidence (B)

Note Polarization of transmitted and reflected E fields

Direction of Transmitted and Reflected waves:

From E field boundary conditions:

From Snell’s Law:

1=air

2=dielectric (ground or building)

(Note change of DEFINITION of angles from the ECE3170 textbook!)

Reflection and Transmission Coefficients

(these may be complex)

Ground Reflection at Grazing Angles

When TX and RX are far apart, most of the ground bounces occur at “grazing” incidence (grazing the ground, both TX and RX nearly parallel to ground, very small qi)

Then G_|| = 1 and G_^ = -1

See Example3.4

Two-Ray Ground Bounce Model

(Ray-tracing theory … this is extended using computer programs to many rays, and can be combined with diffraction theory from the next section)

FIGURE 4.7

Eo = electric field a distance do from the transmitter

do = some small distance from the transmitter that is in the far field of the transmitter

E(d,t) = some electric field that we want to calculate

d = distance from the transmitter where we will calculate the field

t = instantaneous time where we are calculating the field

E(d,t) = (Eodo/d) cos(w_c (t- d/c)) for d>do

Direct Path (LOS = Line of Sight)

E(d’,t) = (Eodo/d’) cos(w_c (t- d’/c))

Path reflected off ground

E(d’’,t) = G (Eodo/d’’) cos(w_c (t- d’’/c))

For d large:

G= -1 (perfect conductor, perpendicular polarization)

Total electric field

E_total = E_LOS + E_ground

(this gives an exact equation for any t,d)

Approximation:

FIGURE 4.8

Difference in distance between the two paths…

First, no approximation:

Approximation:

Phase difference as a result of this difference in distance:

Time delay

For large distances, assume that the magnitudes of the waves stay the same, and only the phase changes:

Then the total field using the above approximations is:

(This is the time t that the field from the ground reflection arrives…)

Then the magnitude of this (approximate) total field is:

When q_D is small

Then

Notes about Power Loss:

(1) This means that the power for a 2-ray model is falling off as d⁴ which is faster than the free-space value of d²

To analyze the power equation in dB instead of linearly:

Path Loss (dB)= (inverse of Pr)