SPLAT program

We have calculated the element currents only at / = 10 GHz—that is, close to the resonant frequency of the array. Let us now explore the situation at a frequency approximately 25% lower, namely at / = 7.8 GHz. From the SPLAT program we obtain the element currents shown in Fig. 1.3c, while the PMM program gives us element currents equal to 0.045 mA as shown in Fig. 1.3c, close to what would be expected based on the resonant value of 0.055 mA (see Fig. 1.3a). 

It was primarily for that reason that Usoff decided to work in the spatial domain when he wrote the SPLAT program. He further used a shanks transform to obtain faster convergence [24]. It became a most wonderful and versatile program. In fact, it is the workhorse for our research into finite arrays. 

This is not necessarily the way we actually calculate the element currents. In fact this was done by direct calculations of the currents in the finite array in question by using the SPLAT program discussed in Chapter 3. Typical examples have already been presented in Figs. 1.3b and 1.3c. Clearly the currents in Fig. 1.3c are seen to be highly erratic. To find out what current components actually are contained in such a distribution, we simply ran a Fourier analysis and obtained the current spectrum shown in Fig. 4.5f. While the current spike at Tex = 0.707 is easy to associate with the Floquet currents obtained for an infinite array exposed to a plane wave incident at 45°, the two other spikes at Tex = 1.25 remained somewhat of a mystery until the explanation in Section 4.6 above was introduced. 

Note Sometimes the reader perceives the introduction of the two semi-infinite arrays with negative Floquet currents as an inadequate approximation. As discussed in detail in Section 4.19 (Common Misconceptions), this is not the case. However, even if some inaccuracies were present in our explanation, it really would not matter since the currents in Fig. 4.5f were obtained by direct calculation of the actual currents obtained from the SPLAT program applied to a finite array. 

In the previous section we gave a physical explanation of how various current components on finite arrays came about. Furthermore, we used the SPLAT program in conjunction with a Fourier analysis to determine the actual element currents on a finite array. We decomposed these according to their phase velocities and found one strong component at Tcx = = 0.707 for 45° angle of... 

Finally, we show in Fig. 4.10 (broken Une) the bistatic scattering pattern of the actual current on the finite array as obtained from the SPLAT program—that is, the sum of the Floquet currents, the surface waves, and the end currents. This pattern should be compared with the Floquet pattern shown in Fig. 4.6. It has been redrawn in Fig. 4.10 (solid line) for easy comparison. We readily observe that the main beams are unaffected and so is the location of the sidelobes. However, the sidelobe level is 5-7 dB higher when we include the radiation from the residual currents. 

We shall present several practical examples obtained by use of the SPLAT program discussed earlier. 

Finally we recall that the SPLAT program is structured to have the finite dimension along the x axis and the infinite along the z axis. Thus, the array... 

Fig. 4.32 Modification of the array when changing from H-plane to E-plane scan, (a) The original array used for H-plane scan. If we scan this array in the E plane, grating lobes will start too early, namely at 9.38 GHz. (b) By interlacing adjacent columns as shown, the onset of grating lobes can be delayed to a much higher frequency, (c) To comply with the structure of the SPLAT program the array in (b) is rotated 90° and the x and z axis interchanged as explained in the text.

An example of actual calculated double surface waves are shown in Fig. 4.35. We clearly observe the Floquet current at Sx = -0.707 while we also observe a pair of right-going surface waves at = 1.015 and 1.165 as well as left-going surface waves at Sx = -1.015 and -1.165. It is noteworthy that the column currents in Fig. 4.35 were produced by a simple Fourier transform of the actual calculated currents obtained directly from the SPLAT program. Thus, their validity can hardly be in doubt. Therefore, even if one does not accept the physical explanation presented above, the facts speak fairly loudly. There will, however, always be those who refuse to believe anything they do not readily understand because things are explained somewhat differently than they are used to. And that is of course their right. 

We finally remind the reader that the discussion above merely serves the purpose of explaining the mechanism of finite arrays. The actual decomposition into Floquet and surface wave currents as well as end currents is done by applying a Fourier analysis of the actual calculated currents obtained from the SPLAT program. Thus, whether one accepts the explanation above or not, the results speak for themselves. 

The other group can exist whether a dielectric is presented or not, but the structure must be finite. Thus, it shows up only in programs based on finite array theory like, for example, the SPLAT program and not when using the PMM program. 

This encapsulation can actually be done in the SPLAT program as written by Usoff [24],... 

Fig. 5.3 Calculated bistatic scattered field of a finite array of dipoles backed by a finite FSS groundplane for an incident plane wave arriving from

A plane wave is incident broadside to this array—that is, at 0°. The bistatic scattered field is obtained from the SPLAT program in the entire range fi om —90° to 270°. Furthermore, we show the bistatic fields for various load conditions of the active elements. 

By inspection of Fig. 5.9 we chose the frequency 5.7 GHz (more or less arbitrarily) as a representative of a range of frequencies with strong surface waves. The actual column currents obtained from the SPLAT program are shown in Fig. 5.10. Indeed, we observe very strong surface waves at that frequency. 

The field in the forward sector can basically be obtained approximately by integration of the incident field over the aperture width as discussed in Section 2.9.2. Note, however, that the entire pattern in Fig. 8.1 was obtained from the SPLAT program and therefore is as exact as the method of moments. In other words, the effect of edge currents is rigorously observed. See also Section 8.5. 

Our investigation here has primarily been focused around the two-dimensional cylindrical parabola. This case could be solved exactly and efficiently by using the SPLAT program. However, it is readily extended to explain the scattering mechanism for the parabolic disk as well. 

We have calculated the stick self-impedance Z for an array without ground-plane with dimensions as used in Chapter 6 as obtained from the SPLAT program. This program cannot handle dielectric slabs however, it will approximate the effect of the dielectric underwear [136] by placing cylindrical dielectric shells around each element. The thickness of these dielectric coatings should be approximately equal to the thickness of the underwear. ... 

Thus, we show in Fig. D.5 an example of the stick self-impedance Z° ° with dimensions as shown in the insert and as obtained from the SPLAT program (includes a matching transmission hne). 

Furthermore, we show in Fig. D.6 the embedded stick impedance Zemb stk as given by (D.IO) as also obtained from the SPLAT program and with dimensions as given in the insert (includes matching transmission line). 

It is therefore of interest to investigate just a single stick array when we feed only a single pair of terminals while the rest are loaded with the same load impedances Z. We have denoted the terminal impedance for this case for the embedded element stick impedance Zemb eie stk- Examples are shown in Fig. D.7. The array has the same dimensions as nsed in the previons section (see insert). The calcnlations were obtained from the method of moment program ESP [137]. Similar to the SPLAT program nsed to obtain the resnlts in Figs. D.5 and D.6, it uses dielecttic cylinders placed aronnd each element. 

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).

Fig. D.6 The embedded stick impedance Zemb stk as given by. 10) (no groundpiane). The center stick array is driven whiie the two outer stick arrays are Just haded with Zl = 100 ohms. Array dimensions as in Figs. D.3 and D.4 (see insert). From the SPLAT program, inciudes matching transformer (see text).

Fig. D.9 The scan Impedance for the center column when all three columns are fed with identical voltage generators with generator impedances equal to 100 ohms (to suppress surface waves). Dielectric cylinders are placed around the elements to model the undenwear. Includes matching section (see text). From the SPLAT program.

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