ELEC 241 Lab

Background

The Communication Equation

Free Wave Propagation.

Suppose we have a source (transmitter) of power

that is radiating isotropically (i.e. uniformly in all directions). Then at a distance

the power is spread uniformly over the surface of a sphere and the power density (in $\rm W/m^2$ ) is $\displaystyle S_{ISO}(r)=\frac{P_T}{4\pi r^2}$

Transmitter Antenna Gain.

If the transmitter antena could focus all of the radiated power into a beam, then the power outside the beam would be zero, but the same total power would be concentrated into a smaller angle, so the power density inside the beam will be higher. In particular, if the beam is uniform, of solid angle $\Omega$ , then $\displaystyle S(r)=\frac{P_T}{\Omega r^2}$ Define the transmitter antenna gain to be $\displaystyle G_{TA}=\frac{4\pi}{\Omega}$ . Then $\displaystyle S(r)=\frac{P_T G_{TA}}{4\pi r^2}$

Receiver Antenna Gain.

What is the power available at the receiver? If the power density at the receiver is $S\: \rm W/m^2$ and the receiver antenna has an effective area of $A_{eff}\: \rm m^2$ then $\displaystyle P_{rec}= S\cdot A_{eff} = \frac{P_T G_{TA}}{4\pi r^2} A_{eff}$ This is one form of the communication equation and it tells us what we can do to increase the range of our optical communication system.