COMSOL 6.4 - Fast Asymptotic Radar Cross-Section Analysis of a Conductive Sphere

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Fast Asymptotic Radar Cross-Section Analysis of a Conductive Sphere

This example uses asymptotic techniques to study the radar cross-section (RCS) response of a conductive sphere. The selected physics interface transforms the incident plane-wave field on the boundaries to the far-field using the Stratton–Chu formula. The computed results are compared to the well-known asymptotic RCS value of a conductive sphere in the optical region. The optical region is one of three scattering regions used in radar terminology. The other regions are the Rayleigh and Mie regions. See Table 1 below for a discussion of the characteristic sphere size a for the three scattering regions.

Table 1: Radar terminology scattering regions
Region	size of a Sphere
Rayleigh	r0 << λ0
Mie	Between Rayleigh and optical region
Optical	r0 >> λ0, conventionally 2πr0/λ0 > 10

Figure 1: The background field incident on the surface of a PEC sphere is plotted with the 3D RCS pattern that is partially transparent.

Model Definition

The Electromagnetic Waves, Asymptotic Scattering physics interface is useful when approximating the scattered far-field of an object configured only by a perfect electric conductor (PEC) boundary condition. The incident background field is a z-polarized wave propagating along the positive x-axis. Only PEC is available in this physics interface. So, the sphere is set to a PEC by default. The far-field calculation feature transforms the surface background field on the metallic scatterer to the far-field. There is no need to add a surrounding air domain and absorbing boundary condition as in a typical finite element analysis.

Results and Discussion

After computation, two default plots are generated. They are the surface plot of the background field on the sphere (Figure 2) and the 1D plot of the RCS (Figure 3). Figure 2 shows the z-component of the background field projected on the conductive sphere. The field has a sinusoidal spatial variation with a wavelength corresponding to the simulation frequency 30 GHz.

Figure 2: The z-component of the background electric field on the surface of a metallic sphere modeled as perfect electric conductor.

The default RCS plot is modified to show the logarithmic value of the bistatic RCS. When calculating the monostatic RCS, the incident angle of the background field increases corresponding to every RCS observation angle. Here, the bistatic analysis is simpler: the propagation direction of the background field is fixed at one angle while measuring the RCS at each angle of observation. For an electrically large sphere in the optical region, the reference RCS value can be calculated by

where r0 is the radius of a sphere.

Figure 3: The dB-scaled bistatic RCS plot with the known asymptotic RCS value of the sphere in the optical region.

Notes About the COMSOL Implementation

The Compute action does not perform a real computation. Instead, it is a preprocess for the far-field transformation used in the results plot. At the moment you click one of the generated default plots, the postprocessing of a far-field expression is conducted. Though it is a fast asymptotic method, it still takes time to visualize the 3D far-field response of a finely meshed structure, which is an electrically large scatterer in terms of wavelengths.

The usage of this specific physics interface is limited to a convex-shaped scatterer where multiple reflections are not expected.

RF_Module/Scattering_and_RCS/rcs_sphere_asymptotic

Modeling Instructions

From the menu, choose .

In the window, click

.

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In the window, click

.

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In the tree, select > .

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4

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In the tree, select > .

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Global Definitions

1

In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
f0	30[GHz]	3E10 Hz	Frequency
lda0	c_const/f0	0.0099931 m	Wavelength
r0	5*lda0	0.049965 m	Sphere radius

Step 1: Frequency Domain

Define the study frequency ahead of performing any frequency-dependent operation such as building mesh. The physics-controlled mesh uses the specified frequency value.

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In the window, under click .

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In the window for , locate the section.

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In the text field, type f0.

Sphere 1 (sph1)

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In the toolbar, click

.

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In the window for , locate the section.

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In the text field, type r0.

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Electromagnetic Waves, Asymptotic Scattering (ewas)

Use the default settings. The z-polarized plane-wave background field is propagating in the positive x direction in vacuum.

In the window, under right-click and choose .

In the toolbar, click

.

Background Electric Field (ewas)

This is the background electric field (z-component) illuminating the sphere.

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In the window, expand the > node, then click .

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In the window for , type RCS, xy-plane in the text field.

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Locate the section. Find the subsection. In the text field, type 720.

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Click to expand the section. Select the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
Using far-field transformation

RCS, known asymptotic in the optical region

1

Right-click and choose .

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In the window for , type RCS, known asymptotic in the optical region in the text field.

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Locate the section. In the text field, type 10*log10(pi*r0^2).

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Locate the section. In the table, enter the following settings:


Legends
Known asymptotic

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Click to expand the section. Find the subsection. From the list, choose .

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Find the subsection. From the list, choose .

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In the text field, type 1.

Radar Cross Section (ewas)

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In the window, click .

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In the window for , locate the section.

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Select the checkbox.

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In the text field, type -50.

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In the toolbar, click

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The computed bistatic radar cross-section (RCS) results are compared to the known asymptotic backward scattering RCS value in the optical region.