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Normally, the frequency rather than wavelength will be known, and the substitution l c/f can be made, where c 108 m/s. With frequency in megahertz and distance in kilometers, it is left as an exercise for the student to show that the free-space loss is given by [FSL] 32.4 20 log r 20 log f (12.10)

The battery must be removed from many robots in order to charge it. However, it would be more convenient if the robot s battery could be charged by just plugging the robot into some mechanism without having to remove the battery at all. There are many situations where it would be desirable for the robot to be self-charging. If the robot is to be fully autonomous it certainly ought to be able to:

Abscissa, 8 Absolute extremum (maximum, minimum), 111 tabular method, 113 Absolute value, 2 Absolute value function, 50 Acceleration, 173 due to gravity, 173 Amplitude, 218 Angle, directed, 199 Angle of inclination, 232 Angle measure, 197 Antiderivative, 235 Approximation Principle, 164 Arc cosecant, 315 Arc cosine, 312 Arc cotangent, 313 Arc length, 267 Arc length formula, 268 Arc secant, 314 Arc sine, 311 Arc tangent, 313 Area: between curves, 264, 265 circle, 119 under a curve, 243 equilateral triangle, 119 trapezoid, 259 Argument, 49 Asymptote: horizontal, 74 vertical, 73

Equation (12.8) can then be written as [PR] [EIRP] [GR] [FSL] (12.11)

1. 2. 3. 4. 5. 6.

The received power [PR] will be in dBW when the [EIRP] is in dBW, and [FSL] in dB. Equation (12.9) is applicable to both the uplink and the downlink of a satellite circuit, as will be shown in more detail shortly.

Average, 254 Average speed (velocity), 145 Average value of a function, 255 Axis of symmetry, 44 b (y-intercept), 29 Base (of logarithm), 293, 299 Chain rule, 124 power, 123 Change of variable in an integral, 255, 257 Circle, 17 area, 119 circumference, 119 standard equation of, 17 Closed interval, 52 Collinear points, 32 Common logarithm, 299 Completing the square, 18 Complex roots of a polynomial, 56 Composite function, 122 Composition, 122 Concave: downward, 178 upward, 178 Concavity, 178 Continuity, 82 over a closed interval, 84 on the left, 84 393

Example 12.3 The range between a ground station and a satellite is 42,000 km. Calculate the free-space loss at a frequency of 6 GHz.

Recognize that its battery needs a charge. Abandon any action it is currently performing to seek a recharging station. Reach the charging station promptly. Orient it self correctly and dock with the charging outlet. Monitor the charge level and wait until the battery is fully recharged. Go back to performing its duties.

[FSL]

1321 FINDING THE STATION To enable the robot to nd the charging station it can be marked with a beacon that is visible to the robot from wherever it is likely to be while performing its duties Another way is to give the robot the GPS (global positioning system) coordinates of the station The robot can then use its GPS system to reach the station In either case, the robot may have to negotiate around obstacles and avoid objects while it is making progress toward the station Going from one spot to another while avoiding obstacles and objects was covered in Chap 12, and we will see how to negotiate around a complicated environment, such as a house or of ce in Chap 15.

20 log 42,000

one-sided, 83 on the right, 83 on a set, 83 Continuous function, 82, 83 Continuously compounded interest, 300 Coordinate systems: on a line, 2 in a plane, 8 Coordinates: on a line, 1 polar, 206 Cosecant, 227 Cosine, 203 Cotangent, 227 Critical number, 112 Cross-section formula, 276 Cylindrical shell formula, 275 Decay constant, 303 Decreasing function, 138 De nite integral, 245, 246 De nition by cases, 51 df, 165 Degree, 197 Demand equation, 42 Derivative, 97 rst, 171 higher-order, 171 left-hand, right-hand, 103 second, 171