Part
one is on fundamentals of electro-magnetic waves.
Part two is on radar cross-section
physics You are here!
Part
three is on radar absorbers and absorption mechanisms.
Here is the index to this page
(part two):
Radar
cross-section physics
Basic
RCS reduction approaches
Metals
and dielectrics
Reflection
coefficient
Click
here to go to our main page on absorbing materials.
Introduction
Before we can discuss radar
cross-section reduction, we first must examine the physics behind
radar cross-section.
In directional antenna systems,
most of the radiated power is sent into a forward cone:
The power density (S) reaching
a target is equal to :
Where GT
is the gain of the antenna.
The incident wave
excites currents on the scatterer (the target you are trying to
illuminate) which then becomes an antenna re-radiating with its
own antenna pattern. The power returned (PR) is measured
by the radar cross-section (RCS), denoted 
.
We define
as the area of an ideal "mirror" that reflects that
amount of power back to the source.
Here AR
is the receiving area of the antenna. The echo goes as 1/R4.
To drop the detection range by a factor of two, the required return
loss off of the object can be calculated:
Microwaves101 Rule of Thumb
An absorber with
–12 dB return loss allows the scatterer to get twice as close
to the radar before being detected, compared to an object with
0 dB return loss.
Radar cross-section
is dominated by shape, because it's the shape that governs how
much of the incident power is captured and sent back, as illustrated
in the three examples below, where the objects are assumed to
be large compared to the incident wavelength. The example on the
left illustrates mirror-like reflection or specular reflection,
here the reflection is proportional to 1/
2.
The middle example shows the amplitude of the reflections from
a vertical cylinder. Looking straight onto the cylinder produces
maximum backscatter. However, at certain angles other than 90
degrees there can be also considerable reflection as shown. For
a cylinder, the reflected signal is proportional to 1/.
On the right is a sphere, which also reflects back a signal proportional
to the radius of the sphere (and not a function of wavelength).
Orientation of
the shape is critical. The worst case when the wave is incident
perpendicular to a flat part of the surface, which results in
specular reflection. Canting the surfaces redirects this echo.
Beware of "corner
reflectors" when you are designing for low radar cross-section,
as shown below. Inside corners can increase your radar cross-section
much more than you'd imagine.
If the specular
echo is redirected, the remainder is the next greatest contributor
to radar cross-section. It is due to diffraction, which is caused
by discontinuities of the surface. Discontinuities imply a change
in the boundary conditions; and boundary conditions are what
govern the distribution of the fields in the first place. Metals
at radio frequency behave nearly like perfect electric conductors
(PECs). This invokes a well-known boundary condition of Maxwell's
equations: the tangential E-field must go to zero on the surface
of a conductor.
Where did the
energy go if total ETE =>0? It goes into the H-field:
On metal surfaces,
E total is always perpendicular to the surface, and H total is
parallel to the surface. On the shadow side the E-field attaches
and travels along the surface at the speed of light. Equal and
opposite charges created at the leading edge create almost no
scatter. On the illuminated side we get a running (traveling)
wave consisting of incident and reflected waves until it runs
out of surface. Then it scatters strongly.
V-Pol, TM incidence
on wing
For horizontal polarization
(H-pol) it is the leading edge of an object such as of an aircraft
wing that scatters strongly. The leading edge gets a very strong
current induced in it whose job is to create the wave that exactly
cancels the E field tangential to the metal. Clearly the radar
cross-section reduction job is different for leading edges and
trailing edges. Because Etotal = 0, there is no significant
diffraction off the trailing edge.
The color figures
below show two-dimensional finite-difference time domain simulatons.
The white rectangle surrounding the target is a teleportation
boundary separating the total field region from the scattered
field region outside. This is a standard way of examining scattering
phenomena because we are interested in the field scattered by
the object out to the far field. Inside the total field region,
in the illuminated side, you will see standing waves, the interference
between the incident and scattered field. Inside the total field
region then you will also see the "apparent wavelengths".
If the wave is running at an angle to the surface, the apparent
wavelength is longer (the wave is fast) compared to free space
(similar to the guide wavelength
in waveguide). But in the shadow side, the only waves are creeping
waves and diffracted waves whose wavelength is that of free space.
The figures show the field
strength of the field perpendicular (out of) the figure. For TE
it is E field strength for TM it is H field strength. The colors
indicate + and - so you can visualize the wavelength (one full
red and one full blue region). The color has been saturated to
highlight the phasefronts rather than given a continuous spectrum
of color from red to blue.
Scattered field
view, 45o incidence onto a perfect electrical conductor,
TM incidence:
Scattered field
view, 45o incidence onto a perfect electrical conductor,
TE incidence:
Total field
view, 45o TM incidence onto a hole in a PEC:
Total field
view, 45o TE incidence onto a hole in PEC:
Diffraction is
a challenge because it can go in many directions. The only general
rule that edge diffraction obeys is that angle of incidence =
angle of re-radiation cone. Shaping helps to some extent but the
forward scattered rays can be reflected downstream and come back
as backscatter. Therefore the discontinuity must be softened or
the surface covered with a surface wave absorber.
Basic
RCS reduction approaches
Softening with
resistive cards (R-cards) is one method of RCS reduction. A tapered-conductivity
R-card breaks up scattering into many small echoes instead of
a large single one.
The best surface-wave
absorber is magram (magnetic radar absorbing material). There
are two fields available to defeat at the surface of a PEC: the
normal E-field, and the tangential H-field. Magram attacks the
strong tangential H-field. Magram works very fast in a few inches,
but magram is very heavy, it contains iron particles embedded
in synthetic rubber. The actual weight depends on the application
and is frequency-specific: magram at cell-phone frequencies can
be 0.3 inches (1 centimeter) thick! Higher frequencies permit
thinner magram.
A surface of resistive
hairs would have loss in the right direction to take advantage
of the vertical E-field, but too little current flows along the
hairs because the hairs end in a open circuit. Thus such an absorber
requires a longer distance to attenuate a creeping wave… several
feet, and is not practical.
As seen in the
upper figure below, the trailing edge echo always contains the
reverberations (multiple reflections of surface traveling waves)
of the plate. These reverberations create interference as they
radiate from both ends of the strip. The r-card kills the surface
wave, so there is no more distortion of the field after it is
generated the first time at the edge itself. Therefore, we see
the smooth, cylindrical backscatter in the second figure below.
For TE there are no TE surface
waves on metal so we see no reverberations. The leading edge echo
is clearly damped immediately by the graded resistive edge.
R-Card on leading
edge:
Ideal magram covering
the whole object for TM incidence:
Metals
and dielectrics
The behavior of a material
is governed by the impedance of the material:
Impedance Z or 
=377 ohms x (
R/
R)1/2
A perfect electrical conductor
(metal) has ,
”
~ infinity (
= ’-j
”,
where ”=/
0,
and
is conductivity mhos/m). Therefore a PEC is a zero impedance object.
What about nonmetal objects?
If R>1
and R
~ 1, a dielectric is a low impedance object: Z<377 ohms. Dielectrics
tend to behave like PECs, because their impedance can be quite
low depending on the dielectric constant.
If R>R
, Z>377 ohms, and you are considering a magneto-dielectric,
high impedance object. You can likewise define magnetic conductivity
as given by m”=m/0,
where m
is magnetic conductivity (ohms/m) and a PMC has ,
”~
=infinity.
Reflection
coefficient
For PECs or PMCs , 
(the reflection coefficient) = 100% or 0 dB. At normal incidence
on a half-space of the material,
Note that
< 0 for dielectrics, and
> 0 for magnetics. The sign tells you whether the tangential
E field flips in phase or not . For Teflon (R
= 2), gamma~ -15 dB. For FR4 (R
= 4.8),
~ = -8.5 dB
Things get even more interesting
off normal.
Fresnel’s Laws point out the
difference between TE and TM incidence on a dielectric interface.
The reason for the dependence on angle of incidence is that the
boundary conditions of Maxwell’s equations apply to the tangential
fields. Relative to the material surface, a TM wave has part of
its E-field tangential and all its H-field tangential. A TE wave
has part of its H-field tangential and all its E-field tangential.
Therefore the impedance that matters is the so-called transverse
impedance.
Define a coordinate system
and plane of incidence:
The transverse
or tangential impedance is the ratio of the tangential fields.
Then the reflection coefficient is defined the same way as before.
But because kz changes with angle of incidence the two impedances
(to and from) also change, but at different rates.
This behavior is often plotted
as ||
versus angle. This emphasizes that for dielectrics the TM front
face reflectivity drops with angle except near grazing.
Fresnel’s Laws mean radomes
depolarize antenna radiation. They also mean that when a material
or structure (RAS) is specified for off-normal performance, TM
is always easier because the wave gets into the absorbing material
easier, to be converted from RF energy into
heat.
In addition to reflecting and
refracting a wave, a dielectric can trap a wave. These are called
surface waves and they travel at a speed between the speed of
light in air and the speed of light in the dielectric, carrying
a significant amount of energy in the air outside. A creeping
wave on metal always sheds energy away and gets weaker. A surface
guided wave on a dielectric skin can travel a long distance losing
almost no energy and then hit a discontinuity and re-radiate.
If there is underlying metal (or graphite epoxy) then only the
TM wave is bound. It must be attenuated.
For instance, put a dielectric
coating on the bottom side of the PEC plate. The echo is brighter
because the creeping wave doesn't just leave the plate, it reflects
and bounces around.
Time to summarize some radar
cross-section phenomena: specular reflection means 100% reflection
off metal, <100% off dielectric. Specular reflection can be
redirected by shaping, avoiding corner reflectors, and the use
of broadband absorbers. Diffraction off discontinuities can be
redirect by shaping, shed off by bending or employing magram or
tapered R-cards. Traveling waves include direct illumination running
wave, creeping wave on metal, trapped guided wave on dielectric.
Magram can counter traveling waves, or you can consider making
the guiding dielectric lossy.
There is one more thing to consider: resonant scatterers are a
combination of discontinuities that allow the echo to buildup.
Natural resonators include antennas and cavities. In the figures
below a wave of wavelength = 10 cells in FDTD is incident at 45
degrees onto a metal groundplane with two notches (perhaps seams
at a door). The apparent wavelength (y)along
the surface is then about 14 cells (1.414*10) . Let's examine
the scattered field. When the distance between the notches is
comparable to half of the apparent wavelength along the surface
we get strong scattering, as shown in the third picture (separation=
8 cells).
To damp the resonance
you can cover the notches with magram. You can see in the figure
below that the backscatter is reduced.
Much of the technical material
on this page was prepared by Dr. Rudy Diaz of Arizona State
University, for ARC Technologies, Inc. This Microwaves101 page
was contributed and sponsored by:
