Impedance groundplane

Fig. 6.2 Typical terminal impedance Za = 2Rao + S a be negative direction. The interelement spacing is varied from Dx/X = 0.75 to 0.25. The groundplane impedance Zr+ is purely imaginary that is, it is located on the rim of the Smith charts as shown.

Fig. 6.5 Top The equivalent circuit for an array of wire dipoles backed by a groundplane. Bottom The groundplane impedance at the rim of the Smith chart is being connected In parallel with 2Rao to the left and denoted 2Rao Zi+. Finally, adding the antenna reactance JX in series is seen to produce a more compact terminal impedance 2Rao Zi+ + jX than without a groundplane.

Fig. 6.6 Top The equivedent circuit for an array of wire dipoles with a dielectric slab in front and a groundplane in the back. Bottom From the array we look left through the dielectric slab and see Zr. Then we connect the groundplane impedance Zi+ in parallel and obtain Zi- Z,+. Finally, we connect the antenna reactance jX in series and obtain the compensated terminal impedance curve Zr Zi+ +P(a-...

It is interesting to compare the nondielectric case in Fig. 6.5 with the dielechic case shown in Fig. 6.6. A casual inspection indicates that the latter has a greater potential for yielding a wider bandwidth or lower VSWR than the former. The reason is of course that the groundplane impedance Zi+ is partly canceled by the reactive part of Zi at higher as well as lower frequencies. In contrast to the nondielectric case in Fig. 6.5, the Zi impedance remains equal to 2Rao without any reactive part at any frequency and will consequently not reduce the effect of the variation of Zi+ as a function of frequency. 

Fig. 6.10 Single dielectric slab. The input impiedance as seen through the dielectric slab at the array in the negative direction is denoted Zi-. As shown in the schematic, we then connect the groundplane impedance Z + in parallel and obtain Zi- Z). Finally, we add the antenna reactance JXa in series and obtain the comp isated terminal impedance cunre Zi. Zf++/Xy,.

Fig. 6.15 Typical antenna impedance = 2Rao +JXa in the negative direction for a long wire antenna like a flat spiral without the effect of a groundplane. At lower frequencies the groundplane impedance Zi+ is inductive as shown on the rim of the Smith chart. The total antenna may improve if jXa is capacitive but get worse If Inductive. Thus, no broadband compensation will take place.

The Moving Groundplane (That Moves Too Fast ) We considered above an array of spirals in front of a groundplane. We observed how the antenna reactance Xa was incompatible with the groundplane impedance Zi+ and therefore would not lead to a consistently lower VSWR. However, one may... 

Certainly, we have produced a loaded groundplane impedance Zi+ that does not go through zero over a considerable frequency range. However, we have in effect merely produced an absorber, or more precisely a circuit analog absorber. For an in-depth discussion about this type, see Chapter 9 in reference 102. 

Thus, the groundplane impedance will typically remain infinite at the center frequency and inductive and capacitive at the lower and higher frequencies, respectively. Consequently, only certain types of elements are suitable for broadband arrays. The flat spiral, for example, is not a good choice because its impedance changes repeatedly as a function of frequency between the inductive and capacitive region (this is typically for all long wire antennas like the two arms in a flat spiral). 

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. 

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. 

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 next show the same three cases as in Figs. 5.13, 5.14, and 5.15, but at the middle frequency /m = 7.8 GHz. More specifically. Figs. 5.16 and 5.17 show the lightly loaded FSS groundplane with active load impedances Rl = 100 ohms and 200 ohms, respectively. This time we observe a significant reduction of the... 

Furthermore, Rao denotes the radiation resistance of the array when located in an infinite free space and with no groundplane. Similarly, Ra denotes the radiation resistance of the same array without a groundplane and located in an infinite medium with intrinsic impedance Zi. 

To start, let us consider an array of dipoles with a groundplane and no dielectric slabs in front From Fig. 6.1 we readily obtain the equivalent circuit for this case as shown in the insert of Fig. 6.2. We shall point out various impedance... 

The determination of the locus for the scan impedance for a single slab in Fig. 6.10 and a double slab in Fig. 6.11 is only qualitative. However, the reduction of VSWR and to some extent an increase in bandwidth in the double-slab case is quite obvious. Inspection of the figures of the two cases shows that the primary reason is that the double-slab case produces a smaller variation of the real part of the scan impedance while the imaginary part must be balanced very carefully with the groundplane reactance Z2+ and the antenna reactance In other words, a parametric study of actual calculated curves should be undertaken. A typical example will be given in the next section. 

CALCULATED SCAN IMPEDANCE FOR ARRAY WITH GROUNDPLANE AND TWO DIELECTRIC SLABS... 

Note in particniar that we are not interested in an array that without a ground-plane has a constant impedance over a broad band. On the contrary, we need an array impedance with a reactive part that can at least partly cancel the groundplane reactances at the npper and lower frequencies, respectively. 

The groundplane reactance Zi+ is obviously not affected by the dielectric. Thus, we have in effect a lower array impedance in parallel with the same groundplane reactance which is equivalent to a larger bandwidth. 

Thus, the scan impedance for an infinite array without a groundplane is... 

Fig. D.3 The scan impedance for an infinite x infinite array without a groundplane obtained from the PMM program. The array dimensions are identical to the broadband array in Chapter 6 (see insert) but includes only the underwear" (see Dieteclric Profile above). Also included is a small transmission line matching section as was the case in Chapter 6 (see text).

Fig. D.5 The stick self-impedance 7P ° for an array without a groundplane. Eiement dimensions identical to the case in Fig. D.3 (see insert). Obtained from the SPLAT program. The dieiectric underwear is rrxxleled by placing dielectric shells around the elements. Diameter approximately equal to total thickness of the underwear, includes a matching transformer (see text).

Finally we show in Fig. D.14 a variation of the frontal approach. Here all elements in the array backed by a groundplane are simply terminated in the same load impedance Zi (this requires no connectors). A plane wave E with direction of propagation Si is incident upon this aperture. It is being reflected in the specular direction r with reflection constant F. The reflection coefficient observed from the terminals looking in the direction of r (or S ) has the same magnitude as F (not phase in general). 

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