Finite Active Arrays

In the previous chapter we studied surface waves on passive structures as for example finite FSSs. They were excited by an incident plane wave. We observed that a finite FSS in addition to the Floquet currents excited directly by the incident plane wave conld also snpport surface waves. These would radiate and thereby lead to an increase in the scattered field that is, the RCS could be larger than expected. The scattered field associated with the surface waves could be significantly rednced by resistively loading one or more columns at the edges of the finite FSS. This approach would leave the Floquet currents in the rest of the FSS unaffected that is, the transmission and reflection properties of the FSS were basically left intact. 

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The groundplane serves essentially two purposes. First of all it ensures that we have only a single mainbeam, not two. Second, as discussed in Chapter 2, the groundplane can lead to a significant reduction of the RCS of an active array. However, as discussed in Section 2.9, the area of the groundplane relative to the area of the active dipoles is crucial from an RCS point of view. Thus, the exact modeling of the finite groundplane becomes important. We shall discuss this issue in the next section. 

We shall next study surface waves on active arrays with a finite FSS ground-plane. Our model will be similar to the one used in the previous section—except that in order to properly study surface waves, the model must be considerably wider. 

The fundamental problem is now that all finite periodic structures may exhibit strong presence of surface waves at least at some frequencies as discussed in Chapter 4. We may envision that the finite FSS groundplane alone shows surface waves in one frequency band and the active array possibly in another. However, when the active array is placed adjacent to the FSS groundplane, we would expect both of these frequency bands to change and, possibly, to degenerate into a single frequency band. From a practical point of view, it is of course the surface waves on the combined structure that are most important. 

The basic approach of chemical theory to surface science is to model a surface with a cluster of a finite number of atoms, with one or more adsorbate atoms or molecules bonded to various sites on the cluster. In parallel with the chemical theory there is also the solid state physics approach. This starts from an extended surface surface model, where an array of atoms perfectly periodic in two dimensions represents both the substrate and any adsorbates. Many theoretical techniques have been developed for the extended-surface model. We can only refer the interested reader to the literature/87,88,89,90,91,92,93,94/ and remark that the relative merits of the cluster and extended-surface approaches are still very much under active debate. It is clear that certain properties, such as bonding, are very localized in character and are well represented in a cluster. On the other hand, there are properties that have a delocalized nature, such as adsorbate-adsorbate interactions and electrostatic effects, for which an extended surface model is more appropriate. 

The most prevalent effects of the new type of surface waves associated with finite periodic structures depend to an extent upon whether they are used passively as an FSS or actively as a phased array. 

In Chapter 1 we introduced the fundamental concepts concerning a new type of surface wave that can be excited only on finite periodic structures. It was pointed out that radiation could occur from such surface waves and therefore could lead to an increase in the RCS level in the backward direction. Similarly, if the structure was active—as, for example, for a phased array—this type of surface wave could lead to a very significant variation of the terminal impedance form element to element. This could make precise matching difficult, if not impossible. 

So far we have considered surface waves only on finite periodic structures without a groundplane. When a groundplane is added to an array of dipoles, it is usually driven actively. This case is in practice somewhat different from the passive case considered above by the fact that aU elements are connected to generators or amplifiers with impedances comparable to the scan impedances. As explained in Chapter 5, this leads to a highly desirable attenuation of any potential surface waves. 

We are now going to show how we can pinpoint exactly any scattering anomalies in an array and how to alleviate it. To illustrate our approach, we are again going to consider a finite array of active dipoles backed by a finite FSS groundplane as shown in Fig. 5.4, top. It is being exposed to an incident plane wave at broadside. 

Fig. 5.8 The backscattered fields from a finite array of 7 trieds plotted in the rectangular complex plane. All active dipoles are loaded with the same impedance equal to 235ohms. This value leads to nearly no backscatter for all the triads at f = 10.0 GHz except for the edge columns 4 and 4. By adjusting the loads for these two separately, the backscatter from these could also equal zero. (From Johnson [75].)...

CONTROLLING SURFACE WAVES ON FINITE ARRAYS OF ACTIVE ELEMENTS WITH FSS GROUNDPLANE... 

The second problem is actually more complex. When considering an infinite array, the terminal impedance will be the same from element to element in accordance with Floquet s Theorem. However, when the array is finite, it is well known that the terminal impedance will differ from element to element in an oscillating way around the infinite array value (sometimes denoted as jitter). We postulated that this phenomenon was related to the presence of surface waves of the same type as encountered in Chapter 4. However, there is a significant difference in amplitude of these surface waves in the passive and active cases. This is due to the fact that the elements in the former case in general are loaded with pure reactances (if any), while the elements in the latter case are (or should be) connected to individual amplifiers or generators containing substantial resistive components (as encountered when conjugate matched). 

We may conclude that use of parasitic columns either is ineffective or simply makes things worse. It appears prudent to recommend to excite all colnmns in a finite array and not try to improve upon the impedance by garnishing the active part of the array with all kinds of dummy elements located next to them. 

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