CEM Workshop Lectures (4/11): CEM of High Frequency Methods

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CEM of High Frequency
Methods
Various methods to solve high frequency
electromagnetics

2
©ZeusNumerixPvtLtd:ConfidentialDocument
Overview
28-Sep-2012 Best Practices in CEM
 Introduction
 Comparison of Physical Optics with Geometric Optics
 Physical optics formulation (PO)
 Shadowing effects for PO
 Equivalent edge currents formulation (PTD)
 Shooting And Bouncing Ray methodology (SBR)
 Surface currents for PO, flash point analysis
 Conclusion
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Introduction
 When a perfectly conducting body is illuminated by an electromagnetic field, electric
currents are induced on the surface of the body.
 These currents act as new sources and create an electromagnetic field radiated
outward from the body.
 This field, called the scattered field, depends on the frequency and the polarization
of the incident field.
 Radar Cross Section (RCS), which is the fictitious area of the target, characterizes the
spatial distribution of the power of the scattered field.
 Among high frequency scattering techniques, Physical Optics (PO) and Geometric
Optics (GO) are the most popular methods.
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Comparison of GO and PO
 GO is based on the classical ray-tracing of incident, reflected and transmitted rays
while PO is based on the integration of induced currents predicted by GO.
 According to GO, RCS is given by a simple formula that involves the local radius of
curvature at the specular point. Prediction fails when radius of curvature becomes
infinite.
 The PO surface integral approach gives the correct result around the specular
direction.
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Theoretical Background (PO)
 PO uses the following steps in order to find the scattered field:
 The incident and reflected fields on the surface of the scatterer is found by
Geometrical Optics.
 The current excited on the surface of the scatterer is found by the tangential
components of the incident fields on the surface.
 The PO current for a conducting body is given by:
 Illuminated region:
 Shadowed region:
 Using radiation integrals, PO surface current is integrated over the surface of the
scatterer, to yield the scattered field
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𝐽𝑆 = 0
𝐽𝑆 = 0

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 The total PO field is given by the superposition of the incident and the scattered
fields:
 The incident electric and magnetic fields are given by the following expressions:
 Relation between incident magnetic and electric field:
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𝐻 𝑖
= ( 𝐸 𝜑
𝑖
𝜃 𝑖
− 𝐸 𝜃
𝑖
𝜑 𝑖
)(𝑒−𝑗𝑘 𝑟 𝑖. 𝑟
/𝜂)

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 Vector potential for scattered field:
 Scattered field is evaluated using the current computed with Physical optics:
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𝐴 𝑠 = (𝑒−𝑗𝑘𝑟𝑠 𝜇/4𝜋𝑟𝑠)
𝑆
𝐽𝑒 𝑗𝑘 𝑟𝑠. 𝑟 𝑑𝑠
𝐸 𝑠
= −(𝑗𝑤𝜇/2𝜋𝑟𝑠)𝑒−𝑗𝑘𝑟𝑠
𝑆
𝑛 × 𝐻 𝑖
𝑒 𝑗𝑘 𝑟𝑠. 𝑟
𝑑𝑆

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Shadowing Effects for PO
 When an electromagnetic wave is incident on a body, part of its surface is
illuminated and the rest is dark, depending on the direction of propagation with
respect to the body.
 Additionally, some parts of the body may be shadowed by other parts.
 In the PO solution, the contributions from these shadowed regions should be
discarded from the RCS calculations
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Shadowing Effects (Methodology)
 Considering surface triangulation meshing, each triangle is taken and checked if it is
shadowed by other triangles or not.
 More than one triangle may be in shadow because of a single triangle, depending on
the shape of the scatterer.
 Induced currents and hence the scattered field from shadowed triangles are not
considered.
 A very popular algorithm is the ‘Ray intersection’ algorithm for shadowing
implementation.
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Equivalent Edge Currents (PTD)
 When a body is illuminated by a plane wave, current is induced around the edges of
the body due to the diffraction of the incident field
 It involves finding currents that would, when integrated along the edge, give a known
value of radiated field at the observation point
 PTD approximates the edge contribution by subtracting the incident field and the PO
field from the exact solution for the total field
 The non-uniform part of induced current is called the fringe current and caused by
the presence of the edges
 Hence, the fields of fringe currents can be assumed to be caused by the equivalent
edge currents located along the edge
 This procedure of improving PO fields by the fringe fields of equivalent edge currents
is called PTD
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Scattering (PO + Fringe Wave Effect)
 Scattering from flat plates is considered.
 Scattering contributions are from the surface of the plate (PO) and the edges of the
plate (fringe wave effect).
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Formulation for PTD
 The current induced over the surface of the scatterer can be decomposed into PO
and non-uniform(fringe) component.
 Accordingly, the total scattered field is composed of two components: the Physical
Optics(PO) field and the fringe wave(FW) field.
 The exact solution of the total field is the sum of the PO contribution and the fringe
wave contribution.
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𝐽 𝑡𝑜𝑡 = 𝐽 𝑃𝑂 + 𝐽 𝐹𝑊
𝐸 𝑠
= 𝐸 𝑃𝑂 + 𝐸 𝐹𝑊

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Expression for Edge Contribution
 For the fringe wave contribution, scattering integral is evaluated over the near-edge
points.
 The contribution from the rest of the surface is negligible as it is accounted for in the
PO computation.
 For any far-field observation point, the total scattered field due to the induced
current on a surface S is given by
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  
Sedge
jkRFWPO
s
s
RsdeJRRjEE  4/))(ˆˆ(ˆ

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Shooting and Bouncing Ray (SBR)
 Combining Geometric Optics and Physical Optics methods, SBR begins the
computation by launching numerous rays from the source.
 Each ray then propagates through the computational domain and bounces between
the target surfaces under study using the GO method.
 The electromagnetic fields at each hit point are converted into surface currents using
the PO methods and re-radiated towards all observation points.
 Finally, the fields at each observation point are summed up to represent the final
electromagnetic field computed at the corresponding location of the computational
domain.
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SBR Implementation (Bounding Box Method)
 An advanced method is the bounding box method, which first encloses the target
structure in a volume.
 Then, rays are generated at equal spacing on the volume and launched towards the
volume.
 This is a dynamic way of generating the rays, as it guarantees that all of the
generated rays will be able to be incident at the structure.
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Hotspot Visualization (PO Application)
 Surface current distribution on the scatterer surface:
 Helps to identify regions that contribute more to RCS for a given source position.
 Has wide applications in designing low RCS objects, flash point analysis etc.
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Flash Point Analysis
 According to the high frequency phenomena, only some parts of the scatterer
contribute to the scattered field.
 Using the flash point visualization, localized reflected and diffracted currents are
extracted.
 Although PO technique is fast, RCS calculations for very large objects, may take long
period of time.
 Localizing the contributions of the surface current and calculating the PO integral
around these regions may shorten the calculation period.
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Conclusions
 PO is one of the high frequency techniques, and PTD is a correction term that is
added.
 GO traces all of the incident and reflected rays, whereas PO only calculates the
simple surface integral.
 PO for targets that have impedance surfaces yields RCS results that are lower than
the results of perfectly conducting surfaces.
 Hot spot visualization, an application of PO computation, is used for designing
objects to produce low RCS.
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www.zeusnumerix.com
+91 72760 31511
Abhishek Jain
abhishek@zeusnumerix.com
Thank You !

CEM Workshop Lectures (4/11): CEM of High Frequency Methods

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