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August 20, 2014

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This web page is part of a three-part tutorial on radar absorbing materials used for radar cross-section reduction.

Part one is on fundamentals of electro-magnetic waves

Part two is on radar cross-section physics

Part three is on radar absorbers and absorption mechanisms. You are here, and here is the index to this page!

Introduction

Electric-field loss mechanisms

Magnetic-field loss mechanisms

Generalities

Classic absorber design #1: Salisbury screen

Classic absorber design #2: Jaumann

### Introduction

Unfortunately absorbers usually come into the RCS reduction picture after all the shaping is done, but ideally they are an integral part of the design. Absorbers work by allowing the wave to penetrate into a region where the electric and/or magnetic fields experience loss.

Apart from Frangencite, Bolognium and Unobtanium, all other materials are constrained by the laws of physics! All lossy materials are frequency dependent, that dependence constrains the values the real and imaginary parts of the relative permittivity (R) and relative permeability (R) can take. In our universe we have freely mobile electric singularities called electrons, therefore the quantity called conductivity, , (mhos/m) exists down to DC. Conductivity is a loss mechanism, however it also folds into the material's impedance since -=/0. Thus a metal ( =107 mhos/m) is both highly lossy and highly reflective.

### Electric field loss mechanisms

Fortunately we have an abundance of cheap low conductivity material called carbon. It is possible to construct synthetic materials from carbon that can have tailored conductivity, from very poor (insulated grains of carbon black) to very high (connected chains of graphite). The only significant frequency dependence that enters into these synthesized absorbers is that introduced by the insulating resin (binder) between the carbon particles, which acts like a capacitor.

Carbon-based absorbers provide essentially an electric field loss mechanism. It is the induced currents that dissipate the energy into heat. The good news is that electric conductivity is a broadband loss mechanism. The bad news is that it has to be placed where the electric field is a maximum. We already saw that on a metallic surface the only electric field is vertical for off-normal incidence and it's difficult to use the vertical E-field for loss, that is, to absorb the wave.

At normal incidence:

### Magnetic field loss mechanisms

For a magnetic field to dissipate heat into a conducting material, the dimensions and conductivity of the material must be such that eddy currents can be set up (about two skin depths). A bulk material layer satisfying this requirement would be highly reflective to plane waves. Magram (magnetic radar absorbing material) is filled with particles that individually undergo eddy current relaxation but collectively create a bulk material that has low conductivity. Magnetic loss mechanisms are intrinsically narrow band. They arise from resonating simple harmonic oscillators inside the material, either magnetic domain walls
or entire domains of electron spins (Lorentz-like). A low-loss permeable conductor (that is one with intrinsically low )- can be made magnetically lossy if it is thick enough for eddy currents to be set up. This dispersion is Debye like.

### Generally valid generalities

Absorbers can be classified several ways:

Volumetric versus surface
Dielectric loss versus magnetic loss
Broadband versus wideband versus narrow band
Isotropic versus anisotropic

Now for some generalities:

• Thicker absorbers (volumetric) are more broadband than surface absorbers.
• Magnetic properties increase the bandwidth of absorbers.
• High dielectric constant reduces bandwidth.
• Magnetic properties are frequency dependent, especially in the UHF to GHz range.
• An absorber that is broadband in frequency is broadband in angle; conversely narrowband in frequency implies narrowband in angle.
• Broadband behavior requires grading the properties from light on top to heavy on the bottom.
• Wideband behavior can be obtained by using transformer/filter design concepts - a combination of interference and absorption.
• Most absorbers are backed by a conducting ground plane. Graphite reinforced epoxy is one example of this.
• Most RAS includes an unfortunately thick skin, plus chemical agent resistive coating (carc) plus paint on top; the high frequency behavior of the RAS is controlled by this skin structure.
• Skin cancellation is possible but it's not pretty.

Of course some generalities compete with others. For instance, an absorber that is electrically thin over its whole band of operation tends to behave the same way at all frequencies. High dielectric constant makes kz inside a material independent of angle of incidence so you can get internal behavior that is broad versus angle. A thick homogeneous layer of material has internal resonances that will make its behavior narrowband.

### Classic absorber design #1: Salisbury screen

Salisbury worked in the MIT RadLab in WWII, and this technique was named after him.

An easy way to use the ohmic loss mechanism is layered absorbers. The Salisbury screen consists of a sheet of resistive material placed /4 over ground. Magnetic loss mechanisms are intrinsically narrow band.

The Salisbury screen is narrowband in frequency and angle.

According to one of our generalities, to get more bandwidth you need to use multiple layers of R-Card separated by dielectric spacers. According to another, the dielectric constant of the spacers controls the maximum bandwidth of the design. The lower the permittivity the larger the bandwidth. But foam and honeycomb spacers give a physically thick sandwich structure. To get a composite skin you can lay up fiberglass and R-card layers and injection mold the whole thing.

### Classic absorber design #2: Jaumann

Johannes Jaumann worked in Germany before and during WWII, check him out in our Microwave Hall of Fame! His absorber design was first used on submarine periscopes to make them less visible to surface ships.

The Jaumann absorber can be designed using transformer concepts. Think of it as a shorted transmission line to which a sequence of shunt conductances are added separated from each other by quarter-wave transformers.

Conductances add in parallel, and the quarter-wave transformers can be used to invert the result. Work on a Smith Chart normalized to 377/R1/2. Start at infinite admittance (short circuit, right side of the Smith chart), then add a quarter-wave transformer to turn it into an open (zero admittance). Next add G1 to move past the center of the chart (here it's 377 ohms). Then add another quarterwave transformer to rotate back to the right side, then add G2, and so forth...

The result of this approach is a very deep null at center band, and twice the bandwidth of a Salisbury screen, using the same dielectric.

To get broadband design, think of the statement of the problem as being: "hide the groundplane." In other words, if we could eliminate all echoes behind the front face of the dielectric, the worst case echo would be the one from the front face of the dielectric. A dielectric of impedance = 0/2 has a front-face reflection coefficient of about '10 dB. Let's come up with a scheme for gently erasing everything else.

Note that after you accomplish this you can convince your customer to add an anti-reflection layer to the design and you'll do a lot better than '10 dB

The approach: imagine the energy entering this material as it passes G3, G2 and G1, hits the groundplane and returns again through G1, G2, G3. Every time the wave interacts with a G sheet it loses energy. How much energy does it lose? Well if you treat it as a local phenomenon (kind of time domain thinking - not frequency domain) then consider a sheet of G in a sea of Ym.

By considering the rest of the medium to the right as a load Ym behind G

It follows that: = (Ym-(G+Ym))/(Ym+(G+Ym))

That is, = -G/(G+2*Ym)

Thus, T=2*Ym/(G+2*Ym).

In this simple problem T is the transmitted E field at the sheet and therefore that of the transmitted wave behind the sheet. Therefore the power transmitted is lower than the power incident by the factor: P=4Ym2/(G+2Ym)2.

At each interface you now have a power loss factor and a local reflection coefficient.

Looking at the "ray" that makes it all the way to the ground and reflects back..

The incident ray, Ray 1, is down in power by:

Ray number 2 is the one that crosses G3 and G2 reflects off G1 and travels all the way back:

Ray 3 only crosses G3 and reflects off G2 and crosses G3 again:

Finally Ray 4 just reflects off G3:

Experience with the anti-reflection coating tells us that the way to get deep nulls and good cancellation is to make the various echoes have the same strength so that when they are out of phase with each other they cancel exactly out.

This means, starting with Rays 1 and 2, that |P12| = |1|. Therefore:

In this example Ym=2/377

Solving this for G1 gives: G1= 1.235Ym

From this we can calculate: 1 = 0.38

Now for Rays 2 and 3 to be equal P22*1=2, or:

Again a quadratic equation that yields: G2=0.5897Ym

For Rays 1 and 2 to be equal, P32*2=3

Because G2 yields 2 = 0.22

Again a quadratic equation that yields: G3=0.3711Ym

Implementing these:

And so there is a closed form procedure for designing "gentle Jaumanns" that reduce the reflection coefficient to that of the supporting dielectric. The Jaumann is broadband in angle as well as frequency. In fact the degradation with angle in TE is simply the increased reflectivity of the TE case of Fresnel's equations.

Like so many microwave circuits, with the Jaumann absorber you can trade off bandwidth for performance:

So there is a design procedure, but with exceptions.

Note that this design is upside down: The top sheet (G3 because we are not using G4) is the highest and the one next to the groundplane is the lowest in conductance

The End!

Much of the technical material on this page was prepared by Dr. Rudy Diaz of Arizona State University, for ARC Technologies, Inc.

Author: The Unknown Editor