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This is a very large loss. Suppose that the [EIRP] is 56 dBW (as calculated in Example 12.1 for a radiated power of 6 W) and the receive antenna gain is 50 dB. The receive power would be 56 50 200.4 94.4 dBW. This is 355 pW. It also may be expressed as 64.4 dBm, which is 64.4 dB below the 1-mW reference level. Equation (12.11) shows that the received power is increased by increasing antenna gain as expected, and Eq. (6.32) shows that antenna gain is inversely proportional to the square of the wavelength. Hence, it might be thought that increasing the frequency of operation (and therefore decreasing wavelength) would increase the received power. However, Eq. (12.9) shows that the free-space loss is also inversely proportional to the square of the wavelength, so these two effects cancel. It follows, therefore, that for a constant EIRP, the received power is independent of frequency of operation. If the transmit power is a specified constant, rather than the EIRP, then the received power will increase with increasing frequency for given antenna dish sizes at the transmitter and receiver. It is left as an exercise for the student to show that under these conditions the received power is directly proportional to the square of the frequency.

In this chapter we will assume that the robot is in the same general area as the station and will only handle moving around obstacles 1322 THE CHARGING STATION There can be many schemes to couple a robot to a charging station; the variety of methods is only limited by your ingenuity A simple method is to place electrodes on the back of the robot at the same height as corresponding terminals on a battery charging station In order to make it easy for the robot to make contact with the terminals you could make each terminal a 1-in2 copper or aluminum plate mounted on a spring The spring ensures a good connection when the robot backs into the charging station until its rear bumper triggers, letting the spring-tension hold the terminals together The 1-in2 sized terminals would allow the robot a reasonable tolerance when approaching the station.

to the earth station, while the command subsystem receives command signals from the earth station, often in response to telemetered information The command subsystem demodulates and, if necessary, decodes the command signals and routes these to the appropriate equipment needed to execute the necessary action Thus attitude changes may be made, communication transponders switched in and out of circuits, antennas redirected, and station-keeping maneuvers carried out on command It is clearly important to prevent unauthorized commands from being received and decoded, and for this reason, the command signals are often encrypted Encrypt is derived from a Greek word kryptein, meaning to hide, and represents the process of concealing the command signals in a secure code This differs from the normal process of encoding which converts characters in the command signal into a code suitable for transmission.

Difference of cylindrical shells, 279 Differentiable function, 97 Differential, 165 Differentiation, 97 higher-order implicit, 172 implicit, 133 logarithmic, 289 Directed angle, 199 Discontinuity, 82 removable, 83 Displacement, 145, 242 Disk formula, 273 Distance formula, 10 Distance from a point to a line, 42 Division of polynomials, 61 Domain, 50 Double-angle formula, 208 e, 293 Ellipse, 17 Epsilon delta de nition, 69 Even function, 53 Exponential decay, 303 Exponential functions, 292, 293 tables, 354 Exponential growth, 303 Exponents, 124 Extreme-value theorem, 111 Extremum, absolute, 111 relative, 111 First derivative, 171 First-derivative test, 182 Free fall, 146 Frequency, 215 Function, 49 argument, 49 composite, 122 continuous, 82 decreasing, 138 differentiable, 97 domain, 50 even, 53 increasing, 138 integrable, 246 odd, 54 one-one, 309 periodic, 206 range, 50 rational, 76 step, 57 trigonometric, 203, 227 value, 49 Fundamental theorem of algebra, 56 Fundamental theorem of calculus, 254

Tracking of the satellite is accomplished by having the satellite transmit beacon signals which are received at the TT&C earth stations Tracking is obviously important during the transfer and drift orbital phases of the satellite launch Once it is on station, the position of a geostationary satellite will tend to be shifted as a result of the various disturbing forces, as described previously Therefore, it is necessary to be able to track the satellite s movement and send correction signals as required Tracking beacons may be transmitted in the telemetry channel, or by pilot carriers at frequencies in one of the main communications channels, or by special tracking antennas Satellite range from the ground station is also required from time to time This can be determined by measurement of the propagation delay of signals especially transmitted for ranging purposes.