Bistatic scattering

In the first case we will observe a significant increase in the bistatic scattering. In the second case we will observe a variation of the terminal impedance as we move from column to column. Let us look upon these two phenomena separately. 

Fig. 1.4 The bistatic scattered fieid in the H plane from a finite x infinite array of 25 columns...

If used as an FSS, it can lead to a significant increase in the bistatic scattering. In particular, we may observe a sizeable increase in the RCS of objects comprised of FSS without freatment. 

Similarly to Example I above, we shall feed these elements via a harness containing hybrids in order to decouple the elements internally from each other (see Section 2.12). Thus, our scattering model will merely consist of elements loaded with identical load impedances Zl as shown. We seek the bistatic scattering pattern based on the element currents when exposed to an incident... 

Receiving incident field resulting in bistatic scattering pattern Pat... 

Fig. 4.1 The array considered here consists of a finite number of infinitely long columns (stick arrays) with axial elements. Voltages are induced in all elements by an incident plane wave propagating in the direction S = kSx+ Sy + Is. We seek the bistatic scattered pattern.

THE BISTATIC SCATTERED FIELD FROM A FINITE ARRAY... 

First we show in Fig. 4.6 the bistatic scattering pattern of the Floquet currents only when a signal is incident upon an array of 50 columns at 45° angle of incidence. We obtain main beams in the forward as well as the specular directions and note that the sidelobe level looks clean as expected (sin x/x function). 

Fig. 4.6 The bistatic scattering pattern for the Fioquet currents only. Angle of incidence Is 45°.

Furthemore, we show in Fig. 4.7 the bistatic scattering pattern of the two surface waves. We observe that they are identical except for amplitude and direction of propagation. Note that the ratio between the pattern amplitudes of the two surface waves is close to the ratio between the two surface waves amplitudes given in Fig. 4.5. 

Furthermore, we show in Figs. 4.8 and 4.9 the bistatic scattering pattern associated with the end currents only and the residual currents, respectively. Comparing Figs. 4.7 and 4.8 with their sum in Fig. 4.9 indicates that the surface and end currents are basically out of phase. However, see also Section 4.9. 

Fig. 4.7 The bistatic scattering pattern for the left- and right-going surface wave. Angie of incidence is 45°.

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. 

Fig. 4.9 The bistatic scattering pattern of the residuat currents (i.e., Total-Floquet s). Angle of incidence is 45°.

We will illustrate this result in Fig. 4.13. We here show the calculated scattering pattern for an array of columns and vary the angle of incidence from 45.5° to 41.0° in steps of 0.2°. We then selected the bistatic scattering pattern with the strongest residual pattern, namely Fig. 4.13a for 9 = 45.2° and the weakest residual pattern as shown in Fig. 4.13c for 9 — A9 = 41.8°. Thus to obtain a... 

This estimate has been checked out by calculating the bistatic scattering pattern for arrays where the number of columns vary from 50 to 55 in increments of one. In Fig. 4.14a we show the case where the residual pattern is close to a maximum for N = 51 columns, and in Fig. 4.14b we show the case where it is close to a... 

Fig. 4.14 The bistatic scattered fieid from arrays with (a) 51 columns and (b) 55 columns. Fuii tine denotes fieid from Fioquet currents oniy, and broken iine denotes fieid from the residuai currents oniy. Angie of incidence is 45°. Note that the fieids from the residuai currents are maximum for 51 columns and minimum for 55 coiumns.

By inspecting several calculated bistatic scattering patterns in this chapter, discuss the loss of the reflection coefficient in the bistatic direction. Is this problem serious ... 

Fig. 5.2 Calculated bistatic scattered field obtained from the Sf LATprogram of a finite array of dipoles backed by a finite FSS groundplane" for an incident plane wave eariving at broadside (0°). Two curves One for the driven dipoles short-circuited. C.) and another when loaded withZi =315 ohms.

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. 

Furthermore, in Fig. 5.3 we show the bistatic scattered field when Zl = 195 + 7 75ohms—that is, conjugate-matched. We also repeat the case Zl = 315 ohms to facilitate comparisons. 

It is, however, very instructive to observe how the field is scattered in all directions when the incident field is arriving from a fixed direction. Thus, we show at the top of Figs. 5.26 through 5.29 the bistatic scattered field at / = 5.7, 7.8, 10.0, and 12.0 GHz, respectively, for a typical triad (no. 25). 

ON THE BISTATIC SCATTERED FIELD FROM A LARGE ARRAY Bistatic Field from Triad 25. Normal Incidence... 

Fig. 5.27 Top The bistatic scattered fieid from a singie typicai triad (no. 25). Bottom The bistatic scattered fieid from the entire array of 50 triads. Normal angle of incidence, f =7.8 GHz.

If all the triads had identical bistatic scattering patterns, we could next obtain the total bistatic scattered field for the entire array by multiplication with the array factor. A typical example of this factor at 10 GHz is shown in Fig. 5.30. At other fi equencies they look similar except for the beamwidth and are therefore not shown. 

However, the bistatic scattering patterns are as implied earlier not quite the same for the triads located close to the edges (see Figs. 5.22 and 5.25). Thus, simple array theory strictly speaking does not apply, although it is actually fairly accurate for large arrays with compensated edges as noted later. 

Next, in Figs. 5.31 through 5.34 we show the bistatic scattered field for the same array as above but for angle of incidence equal to -30°. At the top we... 

---