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12. We do (a) and (b). (a) (b) 1 02 2 2 2 2 e + 2 e 1 + 2 e 2 + 2 e 3 + e 4 2 1/2 cos(e 2 ) + 2 cos(e 3/2 ) + + 2 cos(e 3/2 ) + cos(e 2 ) 2

Part III:

Linear Model of Single DOF System The procedures that are described here are based on the linear, lumped parameter model shown in Fig. 5.23. It is composed of a single mass and massless springs and dampers. Such a model is usually satisfactory in addressing the dynamic effects of general camfollower mechanisms (Barkan, 1953; Chew et al., 1983; Freudenstein et al., 1983; Kanzaki and Itao, 1972; Wiederrich and Roth, 1975). Further, follower models consisting of one or two degree-of-freedom systems will be adequate because the dynamic response of most cam-follower systems is dominated by the fundamental frequency and probably the second harmonic of the cam-follower system (Barkan, 1965). In fact, it has been shown (Koster, 1974) that a cam-follower system can be modeled by a single degree-of-freedom system without introducing signi cant errors if the system has a natural frequency equal to the frequency of the actual cam-follower system. As a consequence, single degree-of-freedom systems have been studied by most authors (Barkan, 1953; Chen, 1981; Chew et al., 1983; Freudenstein, 1960; Hrones, 1948; Kanesaka et al., 1978; Kanzaki and Itao, 1972; Kwakernaak and Smit, 1968; Mercer and Holowenko, 1958; Rees Jones and Reeves, 1978; Tesar and Matthew, 1976; Wiederrich and Roth, 1975) who have made general investigations of output motions or who have designed cam pro les. The general, simple model used in this work is shown in Fig. 5.23. Although it will not be explained here, the single degree-of-freedom can be extended to include nonlinear Coulomb friction damping

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The loss in received optical power due to a weather condition is expressed in terms of dB and is computed as 10 times the Log of the factor by which the received optical power is reduced The loss of an optical signal due to weather conditions has been well studied Table 91 provides a list of various weather conditions and the loss caused per km on a typical optical wireless signal Loss at other distances can be derived simply by multiplying the loss per km listed in the table by the desired distance in km For example, heavy rain results in signal loss of about 4 dB/km, which means an FSO system operating at 05 km would experience an additional signal loss of 2 dB during heavy rain The dB loss/km for the IR signal of FSO is also correlated to visibility during these weather conditions.

A sample data correlating visibility and weather conditions with dB/km attenuation of 850 nm signal is provided in Table 91 The data can be used to compute the link margin of a 850-nm FSO link in various weather conditions For example, according to the table, a moderate fog, which has a visibility of 500 m, causes an attenuation of about 21 dB/km This means an FSO link operating at 1 km would need 21 dB of link margin for it to be able to overcome atmospheric attenuation during conditions of moderate fog An FSO link at 500 m would need half that amount, 105 dB of margin, for it to be able to overcome the same weather condition In order for an optical wireless system to be immune to all weather conditions, its link margin during the worst condition has to be at least 0 dB.

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Figure 8-13

From Table 91, it is evident that the worst weather condition, dense fog, can produce a loss of as much as 270 dB/km In order for an FSO link at 1 km to be immune from all weather conditions, it needs to have a clear weather margin of 270 dB Just to put this number in perspective, for a typical commercially available FSO system to have a margin of 270 dB at 1 km, it needs to be transmitting at least 1020 watts of optical power, a number that is not even a theoretical possibility Therefore, such FSO systems at 1 km may never be immune from all weather conditions..

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