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Suppose a linearly polarized wave produces an electric field E at the receiver antenna when no Faraday rotation is present The received power is proportional to E2 A Faraday rotation of qF degrees will result in the copolarized component (the desired component) of the received signal being reduced to Eco E cos qF, the received power in this case 2 being proportional to Eco The polarization loss (PL) in decibels is PL 20 log Eco (519).

or crosses the robot s perimeter. If it had done so we could have used a better avoidance mechanism such as the one in Fig. 9.3. Can you modify the subroutine to give the Violation a value that indicates the place where the robot s body is touching the boundary line (instead of just true or false)

E sinqF is created,

1 a2

(5.20)

HINT: Calculate the angle an intercept point makes in relation to the robot s center point and its center line (left [ ] and right [ ]) and set Violation to that value [you can use PolarA() with additional calculations]. However, this will slow the program appreciably.

Maximum values quoted by Miya (1981) for Faraday rotation are 9 at 4 GHz and 4 at 6 GHz. In order to counter the depolarizing effects of Faraday rotation, circular polarization may be used. With circular polarization, a Faraday shift simply adds to the overall rotation and does not affect the copolar or cross-polar components of electric field. Alternatively, if linear polarization is to be used, polarization tracking equipment may be installed at the antenna.

he robot in RobotBASIC has a feature that facilitates many possibilities for innovation. This feature is a pen at its center that can be lowered to allow the robot to leave a trace on the oor as it moves (you have seen some uses of this feature in previous chapters). With the proper program we can convert the robot into a device for drawing vector graphics (meaning we specify a line to be drawn with a starting point, an angle, and a length). This feature can be used for a variety of projects: Draw and write on the oor. Show area covered by the robot for a sweeper simulation. Display the effectiveness of an algorithm by showing the path taken. Solve mazes by leaving a breadcrumbs trail.

5.6 Rain Depolarization The ideal shape of a raindrop is spherical, since this minimizes the energy (the surface tension) required to hold the raindrop together. The shape of small raindrops is close to spherical, but larger drops are better modeled as oblate spheroids with some flattening underneath, as a result of the air resistance. These are sketched in Fig. 5.12a and b. For vertically falling rain, the axis of symmetry of the raindrops will be parallel to the local vertical as shown in Fig. 5.12b, but more realistically, aerodynamic forces will cause some canting, or tilting, of the drops. Thus there will be a certain randomness in the angle of tilt as sketched in Fig. 5.12c. As shown earlier, a linearly polarized wave can be resolved into two component waves, one vertically polarized and the other horizontally polarized. Consider a wave with its electric vector at some angle t relative to the major axis of a raindrop, which for clarity is shown horizontal in Fig. 5.13. The vertical component of the electric field lies parallel to the minor axis of the raindrop and therefore encounters less water than the horizontal component. There will be a difference therefore in the attenuation and phase shift experienced by each of the electric field components. These differences are termed as the differential attenuation and differential phase shift, and they result in depolarization of the wave. For the situation shown in Fig. 5.13, the angle of polarization of the wave emerging from the rain is altered relative to that of the wave entering the rain. Experience has

CHAP. 37]

Figure 5.12 Raindrops: (a) small spherical, (b) flattening resulting from air resistance, and (c) angle of tilt randomized through aerodynamic force.