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if TurnAmount > MaxTurnAmount TurnAmount = MaxTurnAmount endif //random turn direction if random(10000) < 5000 then TurnDirection = -1 elseif Sensors&3 and not(Sensors&24) //if painted area on right turn left //no need to check for left since turndir is set to //right by default TurnDirection = -1 elseif Sensors = 4 //if painted area is only straight ahead //randomize the direction if random(10000) < 5000 then TurnDirection = -1 endif endif //if not correct percent of time //turn off turning if random(100000) > 100000%TurnPercentTime TurnDirection = 0 endif //reset the %time for turning on occasion if random(100000) < 100000%ResetPercentTime TurnPercentTime = 0 endif //make the turn if required if TurnDirection <> 0 rTurn sign(TurnDirection)*TurnAmount endif Return //========================================================== //-- Creates 5 ground sensors //-- at +/-90, +/-45 and 0 degrees TestSensors: Sensors = 0 for i = 0 to 4 if rGroundA(90-i*45) = LnClr Sensors = Sensors | (2^i) endif next return //========================================================== CheckBorder: Swap BrdrClr,LnClr gosub TestSensors Swap BrdrClr,LnClr Borders = Sensors return //========================================================== Reverse: for i = 1 to (random(10)+10) if rBumper() & 1 then break rForward -1 next if random(1000) >= 500 rTurn 90-random(45) else
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practical scanning arrays, steps are taken to avoid this. A detailed discussion of arrays will be found in Kummer (1992). Arrays may be used directly as antennas, and details of a nine-horn array used to provide an earth coverage beam are given in Hwang (1992). Arrays are also used as feeders for reflector antennas, and such a horn array is shown in Fig. 6.28. 6.18 Planar Antennas A microstrip antenna is an antenna etched in one side of a printed circuit board, a basic patch antenna being as sketched in Fig. 6.29a. A variety of construction techniques are in use, both for the antenna pattern
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Case 2: D(x) is a product of linear factors, at least one of which is repeated. This is treated in the same manner as in Case 1, except that a repeated factor (x a)k gives rise to a sum of the form A2 Ak A1 + + + 2 x a (x a) (x a)k EXAMPLE
Dielectric substrate Ground plane (a)
(Continued )
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itself, and the feed arrangement, but the principles of operation can be understood from a study of the basic patch radiator. In Fig. 6.29a the feed is a microstrip line connecting to the patch, and the copper on the underside of the board forms a ground plane. The dielectric substrate is thin (less than about one-tenth of a wavelength) and the field under the patch is concentrated in the dielectric. At the edges of the patch the electromagnetic fields are associated with surface waves and radiated waves, the radiation taking place from the apertures formed in the substrate between the edges of the patch and the ground plane. The radiated fields are sketched in Fig. 6.29b. Figure 6.30 shows the patch of sides a and b situated at the origin of the coordinate system of Fig. 6.3. Approximate expressions for the radiation pattern in the principal planes at 0 and 90 are [see James et al., 1981, Eqs. (4.26a and b)]: g( , g( , 90 ) 0) cos2 a cos
rTurn -90+random(45) endif return //========================================================== WallFollow: rTurn TurnDir*random(150) while not rSense() while (rFeel() & 6) or (rBumper() &6) rTurn TurnDir wend if rBumper() &4 then return rForward 1 // forward always to prevent stall if rFeel()=1 or rFeel()=0 // too far from wall or no wall while not rFeel() // turn back quickly to find wall again rTurn -TurnDir*5 rForward 1 wend endif wend return //==========================================================
Multiply by (x l)2 (x 2), 3x + 1 = A1 (x 1)(x 2) + A2 (x 2) + A3 (x 1)2 Letting x = 1, 4 = 0 + A2 ( 1) + 0 Letting x = 2, 7 = 0 + 0 + A3 (1) or A3 = 7 The remaining numerator, A1 , is determined by the condition that the coef cient of x 2 on the right side of (2) be zero (since it is zero on the left side). Thus, A 1 + A3 = 0 or A1 = A3 = 7 or A2 = 4 (2) A3 3x + 1 A1 A2 + + = x 1 (x 1)2 x 2 (x 1)2 (x 2)
(6.41) (6.42)
where X ( a/l0)sin , and l0 is the free space wavelength. Equation (6.42) will be seen to be similar to Eq. (6.23). A plot of these functions, for a half wavelength patch is shown in Fig. 6.31. In practice the length of each side
(Continued )
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