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These relationships are given for reference only and will not be used further in this book. An important parameter for carrier systems is the ratio of the average carrier power to the noise power density, usually denoted by [C/N0]. The [Eb/N0] and [C/N0] ratios can be related as follows. The average carrier power at the receiver is PR W. The energy per symbol is therefore PR/Rsym J, with Rsym in symbols per second. Since each symbol contains m bits, the energy per bit is PR/mRsym J. But mRsym Rb, and therefore, the energy per bit, Eb, is Eb PR Rb (10.22)

notation f + g is a function such that ( f + g)(x) = f (x) + g(x) for every x that is in both the domain of f and the domain of g. Similarly, ( f g)(x) = f (x) g(x) for all x common to the domains of f and g.

As before, let N0 represent the noise power density. Then Eb/N0 PR/RbN0. But PR/N0 is the carrier-to-noise density ratio, usually denoted by C/N0, and therefore, Eb N0 C/N0 Rb (10.23)

are very helpful and informative The Boe-Bot can easily serve as the basis for our realworld robot even though the basic kit does not have all the functions provided by our simulation The photograph in Fig 171 as well as others in this chapter that depict Parallax products are courtesy of Parallax, Inc The discussions that follow, offer suggestions for customizing the Boe-Bot to enhance its abilities Remember, our simulated robot has all the sensory capability most hobbyists would ever want on a mobile robot Use the simulator to determine what you would like the robot to do and to establish what capabilities it needs to accomplish your target project When you are ready to build a real robot you can purchase only the sensors you need for the projects you wish to do.

Rearranging this and putting it in decibel notation gives c C d N0 c Eb N0 d [Rb] (10.24)

Thus, the slope of the tangent line at (x, 1/x) is 1/x 2 . (b) From part (a), the slope of the tangent line at (2, 1 ) is 2 1 1 1 2 = 2 = 4 x 2 Hence, the slope-intercept equation of the tangent line L has the form 1 y = x+b 4

Furthermore, if you have utilized the simulator effectively, you can feel con dent that the money you spend on the hardware project will result in an operational robot with the desired capabilities 1721 WHEEL AND BASE ASSEMBLY RobotBASIC s simulated robot is a circular robot (no corners to hook things) that can turn around its center This movement has the advantage of allowing the robot to turn within its footprint without having to worry about bumping objects around it Since the robot is round and rotates around its center, if it is not in contact with an object before it turns, it will not hit an object as it turns The robot in the Boe-Bot kit has two side-by-side wheels and one caster to keep the robot from tipping If both wheels turn in the same direction at the same speed the robot will move forward (or backward).

It should be noted that whereas [Eb/N0] has units of decibels, [C/N0] has units of dBHz, as explained in App. G.

the required [Eb /N0] at the ground station receiver is 9.5 dB. Calculate the required [C/N0].

If one wheel turns forward while the other turns backward, the robot will rotate around its center In order to generate the motions described above, each wheel has its own motor We could have successfully used DC motors, stepper motors, or servomotors but both DC and stepper motors require external drive circuitry Servomotors (similar to those used in model airplanes) are easy to control with digital logic because the drive-circuitry is built into the servo itself This is the type of motor supplied with the kit..

CHAP. 11]

The transmission rate in decibels is [Rb]

NOTE:

10 log(61

106)

11.4 (a) Find a formula for the slope of the tangent line at any point of the graph of the function f such that f (x) = 3x 2 6x + 4. (b) Find the slope-intercept equation of the tangent line at the point (0, 4) of the graph. (c) Draw the graph of f and show the tangent line at (0, 4).

Standard servomotors have a xed range of motion and are not suitable for driving the wheels of a mobile robot. Servos that can rotate continuously can be purchased from Parallax or standard servos can be modi ed.