Surface waves active arrays

From a practical point of view, the question is of course whether these surface waves can hurt the performance of a periodic structure when used either passively as an FSS or actively as a phased array. And if so, what can be done about it. 

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 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. 

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). 

These resistive components cause significant attenuation of potential surface waves along the structure. In fact, they will in general be so weak that the surface wave radiation from active arrays can be ignored in contrast to the FSS case discussed in Chapter 4. However, they may be strong enough to produce jitter of the terminal impedance. 

However, in cases where we are working with FSS s, the element loads, if there are any, will in general be entirely reactive that is, no attenuation of a potential surface wave will take place. Nor is it a good idea to place even small resistors in each element since that would lead to reflection and transmission loss of the principal mode. In that case only a small number of edge columns should be resistively loaded. This is not as effective a way to control surface waves as resistors placed in each element, but then again FSS s are more forgiving in that respect than are the active arrays. 

Automated droplet-based manipulation methods described in this article include electrowetting, dielectrophoretic, thermocapillary, surface acoustic wave (SAW), and pressure-driven channel-based droplet systems. Fabrication of arrays of elements to control these droplet manipulation methods typically involves the use of photolithography. The methods of addressing of the elements have become increasingly sophisticated with several efforts to utilize passive- and active-matrix control strategies. Trends and issues associated with each method are described. 

The former case is intriguing since the discrete active electrode site is a micro-electrode . The radial diffusion gives rise to steady-state sigmoidal voltammetric waves, but since mass transport is very efficient, the current that is obtained from an array of sites need not be greatly lower than that obtained for a uniformly active surface. For a reversible electrode reaction the potential E1/2 at which half-maximal current is obtained is equivalent to the formal reduction potential E°. 

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