Wireless Communication

Lecture 5 – Large-scale Path Loss – Friis transmission equation

Text sections: 4.1-3

Types of Transmission:

Line of Sight (Friis transmission equation)

Sky Wave (reflection)

Ground Wave (refraction)

Large-Scale Path Loss = predicting average power at some distance far from the TX

Small-Scale Path Loss = predicting power as it changes over a very small scale, may be in the near or far field.

Isotropic Radiator:

Radiates equally in all directions. Must be “infinitesimally” small. Does not exist in practice, but is a good starting point.

Transmitted power will radiate in a large sphere:

Antenna Directivity:

If an antenna transmits more power in one direction than another, it is called “directional”. The directivity of the antenna is measured “far” from the antenna, and does not depend on distance. It is:

D = Pr(maximum) << power received at some angle the received power is maximum

Pr(isotropic) << power that would have been received at that location if the same power was sent through an isotropic antenna

Antenna Efficiency:

Accounts for loss in the antenna itself, but does not include impedance mismatch of the antenna.

Antenna Gain:

Gain = Directivity * Efficiency = power received (maximum) / power received (lossless isotropic antenna)

For large antennas this can be approximated:

dBi: = Gain of antenna with respect to isotropic antenna given in dB = 10 log (power max / power isotropic)

dBd = Gain of antenna with respect to a dipole antenna given in dB = 10 log (power max/ / power max of half-wave dipole antenna)

Gain of dipole is 1.64 = 2.15 dB, so dBi is always 2.15 dB greater than dBd

Received power considering antenna gains:

Received Power considering antenna and other mismatches:

Received Power considering attenuation in the path (trees,atmosphere etc.): FRIIS TRANSMISSION EQUATION

Atmospheric Loss

Water vapor absorbs most at 22 GHz (negligible below 15 GHz)

Oxygen absorbs most at 60 GHz (negligible below 30 GHz)

Effective Isotropic Radiated Power (EIRP)

EIRP = maximum power radiated in the direction of maximum antenna gain, as compared to an isotropic radiator = Pt Gt

Effective Radiated Power (ERP)

ERP = maximum power radiated in the direction of maximum antenna gain, as compared to a dipole antenna = EIRP (dB) – 2.15 dB

Path Loss = signal attenuation due to the path spreading

Far Field = Fraunhofer region

Electric Field of infinitesimal dipole

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Note 1/r,1/r², 1/r³ regions.

Power = E² / 377 for far field plane wave lossless

Sources of Change in the wave direction or magnitude:

Reflection (from large objects or the ground)

Diffraction (around corners)

(Rough Surface) Scattering

Review Reflection Section 3.5.1

L5a -- Sectoring\L5a-sectoring.htm