Groundplane

In another task a pointing theodolite and a video theodolite of the Leica company (see fig. 4.2) were used, to monitor deformations of a building with a circular groundplane. The diameter of the building was about 100 m. 

Wagner, W.H., Jr., Origin and philosophy of the groundplan-divergence method of cladistics, Syst. Bot, 5, 173-193, 1980. 

So far we have merely tacitly approved of the standard practice, namely the use of infinite array theory to solve finite periodic structure problems, at least in the case of an FSS with no loads and no groundplane. However, even in that case we may encounter a strong departure from the infinite array approach. In short, we may encounter phenomena that shows up only in a finite periodic structure and never in an infinite as will be discussed next. 

Most readers will say no. They typically base their answer on well-documented facts about the most commonly used antennas such as a single dipole or monopole, the horn, the flat spiral, the corner reflector, the polyrod, the patch, the log periodic, the helical with a groundplane, and many more. These are all lacking in their ability to produce a low RCS over a broad frequency range when properly matched. Thus, we shall in this chapter instead concentrate on one of the few concepts that can truly produce invisibility in the backward sector, namely the large flat aperture in the form of an array backed by a groundplane and with uniform aperture illumination. The tapered case will also be discussed and it will be shown that also in that case, invisibility is conceptually compatible with 100% efficiency. 

The reaction to this suggestion is typically something like Well, we have measured dipoles, horns, parabolic dishes, flat spirals as well as helical antennas with groundplane, and what not, and we have never come across an antenna with no residual scattering. In fact we are not even sure whether an antenna without residual scattering violates certain fundamental rules ... 

In many respects it makes a significant difference whether the array has a groundplane or not. Thus we shall look in detail at each of these cases separately. 

Fig. 2.8 A large array without a groundplane seen edge-on for three load conditions. Left The terminals are open-circuited, that is, r = +7. Middle The terminals are loaded with a conjugate match, that is, r = 0. Right the terminals are short-circuited, that is, r = -1.

Obviously, (2.11) supports the statement made several times earlier (see Section 2.2), namely that an array without a groundplane has about as much residual as antenna mode scattering. 

Finally we consider the case to the right in Fig. 2.8. We have here loaded the array at its terminals with short circuits thus F = — 1 as indicated in the Smith chart underneath the array. The total backscattered field is proportional to F - -C —1 — 1 = —2 [see (2.9)]. However, when viewed as an FSS of elements with length 21 A./2, we also know that such a surface reflects as a groundplane. Thus the reflection coefficient for an incident wave is Ff s = — 1. In other words, F - -C = —2 produces a reflection coefficient equal to Ffss = —1, and consequently the matched case in the middle with C = — 1 will produce a reflection coefficient equal to Ff s = — 1 /2. 

We now add a groundplane to our array of dipoles as shown in Fig. 2.9. This will distinctly change the antenna impedance Za, but that is of no particular concern for our present purpose. 

Fig. 2.9 A large array with a groundplane seen edge-on. It can be shown that for conjugate match the three plane waves denoted by their directions 1," 2," and 3" will add up to zero that is, everything is absorbed.

This result is surprising to many readers. However, it has actually been known by implication for at least half a century. As any classical textbook about antennas will tell you [51], the receiving area of a large array with uniform aperture distribution and no groundplane is half its physical size. Thus, when conjugate-matched, such an array will receive half the power incident upon it. The other half (i.e., down 3dB) will be radiated equally in the forward and backward directions—that is, down another 3 dB. Thus we have simply verified the 6-dB Rule introduced earlier. 

Furthermore, it is also well known that if a large array is provided with a groundplane, the receiving area is simply eqnal to the physical area [52]. In other words, an array with a groundplane and conjugate match will receive all the energy incident upon it and will consequently not scatter any energy in the backward direction (Remember Only for uniform aperture distribution. The tapered aperture distribution is discussed in Section 2.11.2). 

Fig. 2.10 Left A plane wave is incident upon a large array without a groundplane. As seen from the equivalent circuit below, it will have no backscatter only for Zl = oo that is, we will receive no power. For Zl conjugate matched, r = -112 [see (2.12)]. Right Same situation as before but the array has a groundplane. When Zi is conjugate-matched, the Incident wave is completely absorbed that is, the RCS equals zero. Note These equivalent circuits are valid only in the principal planes.

Note that the spacing d between array and groundplane can be anything but nk/2. See also discussion about this subject in Section 6.12.2. 

We finally note that an array with a groundplane and resistive loads actually belongs to a simple form of circuit analog absorbers. This relationship was pointed out in reference 54 and is also discussed in a different context in Section 6.12.1.4. 

Example I Large Dipole Array without Groundplane... 

Fig. 2.12 The transmitting, receiving, and scattering pattern. Top An array of dipoles without a groundplane. Middle An array of dipoles with a groundplane. Bottom An array of dipoles with an oversized groundplane.

Example II Large Dipole Array with Groundplane... 

In Fig. 2.12, middle, we show a large finite array of dipoles backed by a finite groundplane as large as the array. When fed from constant current generators, we obtain the currents under transmitting condition, and the transmit pattern Paf is obtained in the traditional way based on these currents and their approximate images in the finite groundplane. 

Let us first examine the backward sector. If we assume that the load impedance Zl is conjugate-matched to the antenna impedance Z, all the energy incident upon this array with a groundplane will (as shown in Section 2.6.2) basically be absorbed. Thus, for this load condition the scattering pattern will simply be given by a number of low-level sidelobes due to the finiteness of the array. For an actual calculated example of what happened when Zl Z, see Section 5.3. 

Let us finally consider an array with the same number of elements as in Examples 1 and 11 but where the finite groundplane is somewhat larger than the dipole area as shown in Fig. 2.12, bottom. 

However, the transmitting (or receiving) pattern is radically different from the scattering pattern, and it radiates more in the backward than in the forward direction. And when open-circuited an incident field will essentially see just the groundplane and consequently exhibit a very large RCS. Thus, for conjugate match the Thevenin circuit will correctly account for the absorbed and scattered power but fail completely for = oo. See also Eigs. 5.2 and 5.3 for exact calculations. 

A large array of fuU-wave dipoles without a groundplane will scatter approximately as much power as it receives when conjugate-matched (for no grating... 

Fig. 2.14 An array of full-wave dipoles without a groundplane will have transmitting and scattering patterns that took alike and scatters the same amount in front and back. However, when Zl =

A uniform aperture with groundplane can basically absorb all the incident energy and will consequently have no backscatter (see Section 2.6.2). In contrast, a tapered aperture is capable of absorbing only part of the incident energy. Thus, some of the power not being absorbed by Zl wiU be either reradiated, most likely in the backscatter direction but not necessarily so, or absorbed by some other absorbing mechanism (see Section 2.13). 

Fig. 2.15 Top A uniform aperture with a groundplane simitar to Exampiell in Fig. 2.12. Bottom A tapered aperture will absorb less power than the uniform case, above however, the scattering in the forward direction will basically be the same. Thus, it scatters more than it absorbs and is thus not an MSA.

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