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The model is defined for a fixed set of listeners and a fixed set of event patterns: Listeners = { a , ~ , ~ ~ d ~ Pattern = {pall,pat23 The event manager is modeled by a set of REGISTER processes, each of which controls the re~stration and event propagation or a single, particular listener. ~ E ~ I S T E= IDLE, R IDLE = (regis~er[p:Pattern] M A T C ~ ~ p ] -> lannounce[Pattern] -> IDLE ), MATCH[p:Pattern] = (announce[a:Pattern]-> (a==p) then (eventia] -> MATCH[^^ deregister -> IDLE)

4. Your next steps will depend on the kind of filtering you want to make available in the PivotTable. Your objective is to associate specific data ranges with specific fields and assign descriptive names to them. Here s how: a. In the All Ranges list, select a range (one of the consolidation ranges you added earlier) to be included in a filter. b. In the Field one box, type a descriptive name for this filter. If a name has already been assigned to a range and you want to assign it to this range as well, you can select it from the drop-down list. c. If you are using more than one field, enter a name for this filter in the Field two, Field three, and Field four boxes. d. Return to Step 1 to add another range. e. Repeat until all desired filters have been defined. f. Click Next to go to the final step of the wizard.

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. . . . . . .

n c J P ( r i / O ) P ( r i / 1 )= ~ ( ~ P ( o l o ) p ( o ~Jlp)( l l o ) p ( l ( l ) ) 4i = l ri i=l

where W = 2R 0 + t/ r is the effective circumferential length of the patch and L = zm + t/ r is the effective axial length The actual dimensions of the patch are 2R 0 and zm An approximate formula for the input impedance can also be found using the cavity model [Luk et al 1989] Although the cavity model can be used to get an approximate estimation of the resonance frequency and input impedance, it does not incorporate the effect of the curvature and will not give an exact answer To include the curvature, a more rigorous model must be used In the next example, we will show how the resonant frequency and the input impedance depend on the curvature The results are obtained using the G1DMULT code [Sipus et al 1998] The following parameters apply for the substrate coating: t = 2.

3 mm, r = 285, and tan = 00073 The dimensions of the patch are L = 444 mm and W = 666 mm, yielding resonance at 21 GHz The position of the probe has been adjusted to achieve 50 input impedance for the isolated patch (the distance of the probe from the patch center is 135 mm for vertical polarization and 95 mm for horizontal polarization) Furthermore, an air gap (approximately 04 mm) between the PEC cylinder and the coating is included; see also Section 6632 Figure 661 shows the input impedance for this patch when mounted on a circular cylinder with different radii (RPEC = 2 , RPEC = 5 , and RPEC = 10 ) Both axially and circumferentially polarized patches are considered Figure 6.

At the jump x 1 the mean of the limits is /4. 4. The result suggests to consider (x) /2 (0 x 1) and to use (11). Then (10) gives

SOLUTIONS TO PROBLEM SET 18.6, page 774 2. Use (2). We obtain F(2) 4. Use (2). F(0) 6. By (3) with r0 0 1, 27 1 2

61 shows that the curvature does not affect the resonant frequency very much The axially polarized patch is more or less unaffected, whereas a slight change in resonant frequency is found for the circumferentially polarized patch The amplitude of the input impedance is also more or less unaffected by the change in curvature It should be pointed out, however, that the resonance resistance is sensitive to the air gap between the dielectric substrate and the metallic cylinder, in particular for cylinders with small radii Tam and coworkers [1995] reported a large difference between the calculated (rigorous formulation but no air gap) and measured (with air gap) resonance resistance for a cylinder with R 026 amounting to around 50% For the resonant frequency, however, only a small disagreement (less than 1%) was observed.

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