EEL 6509 - Wireless Communications

Dr. John M. Shea

Spring 2001

Copy your student ID (preferred) or other photograph of yourself. Write on that sheet the name you would like to be called, the country you are from (optional), and whether you are a Master's or Ph. D. student. If you are a FEEDS student, please write the name, division, and location of the company that you work for. Do not write anything else on that page.

On a separate sheet (or sheets) of paper, do:

Consider two ideal isotropic antennas. Use the Friis free-space equation (3.1 in the book) with L=1 to show that the received power in dBW can be expressed as

\begin{eqnarray*}\left[ P_r (d) \right]_{dBW} = \left[ P_t \right]_{dBW} - A \log_{10} d - B \log_{10} f + C \mbox{dB},

where A, B, and C are constants. Give the values for A, B, and C explicitly.

Consider the following two cases:

1) ht = 30 m, hr= 1.5 m, d=450 m,

2) ht= 40 m, hr=2 m, d=10 km.

Assume that the transmitter frequency is 900 MHz for each case.

For each case find the following:

The exact path distances (d' and d'') for the line-of-sight and reflected paths

The exact path difference $\Delta$
The approximate path difference $\tilde{\Delta}$, which is given by equation (3.41) in the book.
The exact angle of incidence $\theta_i$, shown in Figure 3.7.

The exact phase difference $\Theta_\Delta$, given by (3.42).

The approximate phase difference $\tilde{\theta}_\Delta$ given by (3.49).
Determine if (3.50) holds. Is (3.52) a valid approximation for this case?

About this document ...

EEL 6509 - Wireless Communications

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John Shea