Transcript Wire Modeling

NEC Features
INPUT
Geometry
Wires & Patches
Environment
Free Space

Perfect Ground
Real Earth
Sources
Voltage & Current
Plane Wave
C
U
R
R
E
N
T
D
I
S
T
R
I
B
U
T
I
O
N

OUTPUT
I & Q Distributions
ZIN YIN PIN
Power Budget
PIN PRAD PLOSS
Efficiency
Fields
Near & Far
Gain
Power, Directive,
Average
1
NEC Features (Continued)
INPUT
LOADING
Lumped Impedance
Networks
Transmission Lines
OUTPUT
Patterns
Transmitting &
Receiving
Port Currents
Network Voltages
Coupling Information
Scattered Fields
2
NEC Input Options

Titles
Group of Comments and
descriptions
Structure Specifications
Wires
GW
Surface Patches
SP
Geometry Moves & Replications
Move, Rotate, Duplicate
Rotate, Duplicate (Z-Axis)(w/Symm)
Reflect in Coordinate Planes (w/Symm)
Scale Dimensions
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CM
GA
SM
CE
GC
SC
GM
GR
GX
GS
3
NEC Input Options

Performance Parameters
Alters Matrix
Frequency Stepping (Linear, Multipl.)
Ground Conditions (P.G., R.C., SOMM)
Structure Loading (Lumped, Distrib.)
Alters Currents
Excitations (XMT or RCV)
Networks (Non-Radiative)
Transmission Lines (Balanced)
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FR
GN
LD
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EX
NT
TL
4
NEC Input Options
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Performance Selection
Radiation Patterns/Far Fields/Gain
Near Fields
Coupling
Additional Ground Conditions (Patterns)
Receive Currents
Charges
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RP
NE
CP
GD
PT
PQ
NH
Repetitive Use of Matrix and Exploit Partial Symmetry
Create Numerical Greens Function
WG
Use Numerical Green’s Function
GF
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5
NEC Output Features
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Comments
Structure Specifications (Wires and Patches)
Segmentation Data
Frequency
Structure Impedance Loading
Network Data
Excitation at Network Connection Points
Antenna Environment
Matrix Timing
Currents and Location
Power Budget
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6
NEC Output Features
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Charge Densities
Near Fields
Input Impedance Data
Radiation Patterns
Average Power Gain
Scattering Cross Section
Radiated Fields Near Ground
Normalized Gain
Coupling Data
Plane Wave Excitation
Receive Pattern
7
NEC2 Ground Conditions
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Perfectly conducting ground-image
Reflection coefficient approximation
(wire height > 0.1 )
Sommerfeld solution for wire over lossy earth
Wire ground screen approximation
Cliff approximations for radiated fields
Ground wave calculations
8
Space Wave and Surface
Wave
x
Wave
Surface
eR, s



Observation
Point
Lossy Earth
Direct wave follows free space attenuation
Reflected wave path slightly longer +
suffers some loss at reflection point
Surface wave hugs the interface and
decays rapidly
9
Wire Modeling
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Wire Specifications
Example:
GW
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TAG
1
No Segs
5
X1 Y1 Z1
0, 0, 0
X2 Y2 Z2
.5, 0, 0
Radius
.001
Default is equal segment lengths ( D ) and uniform radius, but
tapered radii (a) and variable segmentation is an option.
Arcs are formed as sections of polygons
10
Wire Modeling
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Tag & Segment numbers help locate loads & sources
Segment connections are described by integer arrays
“+” Current Ref.
Ex.
1
G.P.
For automatic segment connection:
Separation of segment ends
Segment length
2
End 1
Seg#
1
1
2
1
2
3
-4
3
0
-5
4
10003
2
5
< 10-3
End 2
Free e nd
Patch
0
11
Wire Modeling

Wire Modeling Guidelines

Segment Length D
relative to wavelength
is a key parameter
a
D
D < 0.1 for accuracy in most cases
D < 0.05
in critical regions
D < 0.2
on long, straight segments

Avoid extremely short segments (D < 10-4 )
12
Wire Modeling

a Must be small relative to both  and D
a < 0.5 D
a < 2D
a < ~ 0.1
with thin wire kernel
with extended T.W. kernel
since no transverse current & no
variations around the wire are
included
13
Wire Modeling
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Avoid:
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Large changes in radius (especially on short
segments)
Sharp bends in thick wires
Wires that are connected must contact at segment ends
Connection
Separation/Length
< 10-3
No
Connection
14
Wire Modeling

Use equal length segment lengths next to sources
D

*
D
~
*
D
No voltage sources or loads at a wire open end
~
15
Wire Modeling

Source Modeling Guidelines
Balanced:
Source “gap” is a
segment with E-field on it
Unbalanced:
Coax Feed
Multiple:
YIN
YIN = Y1+Y2+Y3
16
Wire Modeling

Computational Checks for RIN & Gain
Find Radiated Power by integrating the far field:
E
PRAD
Input Power:
r2
=
2
r 
1
PIN = VI
2

4p
E
h
dW
*
For a Lossless Antenna

2
PIN = PRAD
NEC prints “Average Power Gain”
GAVE =
1
P
G P d W = RA D when W = 4p
WW
PIN

17
Wire Modeling

For a loss-free antenna, average gain is a check on
solution accuracy
Source voltage
Vo
V
S
NEC solves for current
I (s)
1
Input power
PIN = Re V 0 I * (0)

o


2
PIN is sensitive to errors in I(s)
Integrate radiated power over sphere in far field
PRAD is a stationary function of I (s)
For Loss-Free Antenna
PRAD = PIN
18
Wire Modeling

Average Power Gain
G AVE =
G
Pd
W
W
W
1
G P = ( 4p  Re E x H * / PIN
2
G A V E = kPRA D / PIN
k = 1 for free space
(

= 2 for perfect ground
Corrected PIN = Computed PIN x (GAVE/k)
Corrected Input Resistance = 2 GAVE PIN
k | I (0)|
2
= Computed RIN x (GAVE/k)
Corrected Gain = Computed Gain x (k/GAVE)
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Wire Modeling
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Wires near lossy earth

Reflection coefficient approximation is reasonable for:
vertical wires at least
0.1  to 0.2  above the ground
horizontal wires at least 0.4  above earth
Sommerfeld/Norton works for:
wires as close as 10-6 
height should be several time radius
{h2 + a2} 1/2 > 10-6  , h > ~ 3a
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Surface Modeling
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Surface Specifications
Area A
Arbitrary Shape
Patch has area &
normal direction
Center
of
Patch
Input data: Coordinates of patch center, a, b, Area
Other Options:
Rectangular
Triangular
Quadrilateral
3 corners (RHR)
“
4 corners
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Surface Modeling
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Area should be less than 0.04 2
(.2  x .2  )
Since no defined shape, avoid long, thin patches
Since currents defined at center only, not good for edge
currents
Where radius of curvature is small, use smaller patches
Surface must be closed and not too thin (no plates, no
fins or wings)
Wires must connect at patch centers
Increase definition at connection points
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Surface Modeling
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Wire Grid Modeling
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Use wire grids where edge connections are needed
Wire grid = surface if mesh is “small enough”
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Problem:
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- can’t afford real fine meshes
- sparse meshes have too much
L, not enough C
Possible Solutions: - negative L distributed loading
- fat, rod-like wires
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Surface Modeling
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Wire gridding is acceptable for thin structures, plates,
wings, etc. and for far field responses / not for surface
charge or currents
Grid size not too critical
(~ 0.1  at midband)
D/a not critical
(10< D/a < 30 good for wires attaching to
surface)
Use equal radii and segmentation at junctions
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Patch vs. Wire
Grid/Resources
L
W
Patch: 2LW
Grid: 2LW + L + W
But Patch can be .2 on a side …
2
LG
(2
x
WG
2
)
LW
2
Ex: 4x2 grid
20x20 grid
Patch: 4
Grid: 22
Patch: 200
Grid: 840
Usually find patch model will save about 40% on
computational resources
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GC -- Wire Radius/Segment
Tapering
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

Set radius = 0 on the GW
card > follow with a GC card
RDEL -- Ratio of adjacent segment lengths
RAD 1, RAD 2 -- Radius of 1st segment, radius
of last segment
Make RDEL < 2 and adjacent segments radii
ratio < 2
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GE -- Geometry End
(Gound Plane Options)

Options (sets symmetry w.r.t. ground plane)
0 -- No ground plane (free space)
1 -- Ground plane present
“touch” wires connected
-1 -- Ground plane present
“touch” wires insulated
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
GE 1
GE-1
current
current
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GX -- Reflections
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Exploit symmetry for faster solutions
Tag number increment
GW1
GW2
GW3
GW4
Tag
GW5
 Increment  GW6
by 4
GW7
GW8
Reflection control
Reflect along
( 
x
y
z
Axis
(
in y-z plane
in x-z plane
in x-y plane

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GX -- Reflection Examples
3 Basic Wires
X, Y, Z Directed from (A, B, C)
Z
Z
GX 100
Right Upper
A
One Corner
Right, Upper, Front
2B
C
A
Y
B
C
Y
A
C
X
Z
GX 111
X
Z
GX 110
2A
2B
2B
2A
C
C
2A
2B
Upper
2B
2A
2C
2C
C
2C
Y
Y
2A
2C
2B
2A
X
X
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RP - Radiation Patterns
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RP 0: Space wave = direct + reflected
RP 1 : Ground wave = spacewave + surface
wave. Must specify observation point(s)
Space wave (or sky wave) dominates in
ionospheric propagation
Surface wave decays rapidly with
distance and frequency
30
NT -- Networks
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+
V1
-
Connection between 2 segments containing
admittances (impedances)
Segments do not have to be nearby
(not so in real life)
2-port Y-parameters
Example:
I1
Y11
Y12
Y22
I2
Y11V1  Y12V2 = I1
+ Y V Y V = I
12 1
22 2
2
V2
-
R
Y11 = Y22 =
1
Y12 = R
Series Resistor
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1
R
TL -- Transmission Lines
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NEC’s transmission lines are equations, not wires
If transmission line (TL), load (LD), and voltage
source (Ex) are on the same segment …
V
Segment
ZL = load on LD
ZT
ZL
ZT = load on TL
Transmission Line
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Transmission Line
Application

Transmission line equations are for balanced
conditions only!
OK!
NOT BALANCED!
33
Crossed Feeds

Turnstile radiators present a challenge at the feed
point
V
jV
Dipoles Co-Planar
Feeds Displaced
Slight
Vertical
Displacement
j V/2
V/2
V/2
j V/2
4 Feeds, Centers Connected
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Current Directions

Positive current flows from END 1 to END 2
I
X1, Y1 , Z1
X2, Y2 , Z2
35
Current Directions

Ex: VEE dipole, fed at corner
B
A
2

B
A
2
-
+
C
+
-
+
+
C
-
-
1
GW 1, 4, X C , YC , Z C , X B , YB , Z B , a
GW 2, 4, X C , YC , Z C , X A , YA , Z A , a
1
GW 1, 4, X C , YC , Z C , X B , YB , Z B , a
GW 2, 4, X A , YA , Z A , X C , YC , Z C , a
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E- and H-Fields for a
Desired Power
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NEC uses peak values for
voltage, current, and fields
We usually apply 1 volt to an unknown
Zin
E rms = E peak / 2
E rms =
Desired Power
 E NEC 1 volt
source
 NEC Power for 
2

1
volt
source


37
NEC User Notes Feeding of Arrays

Problem:
Array excitations are in terms of feed point currents
(amplitude & phase)
NEC does not allow current drives, only voltage
(amplitude & phase) at feed points
You can’t drive a feed with a specified current unless
you know the driving point impedance. But the driving
point impedance depends on the current drive and, of
course, the physical arrangement of the array elements.
You could possibly “iterate” yourself to an approximate
solution by twiddling voltage drives
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38
NEC User Notes Feeding of Arrays
Solution:
Current generators are realizable by high impedance, high voltage
series source:

~1 AMP into circuits
whose input
impedance is <104W


If you use
in NEC, the large numbers used will swamp out the
drive segment voltage and you won’t be able to use the results
Can overcome this problem by replacing the series resistor by an
appropriate network but there is an easier method…..
39
NEC User Notes Feeding of Arrays
Details:
The NT card(s) are used thusly:
I
One feed
segment
of array
Cards:
Far-Way
Segment
I1

V1
-
I2
YC
YA
YB

V2
-
~
V
“Extra” added
segment to support
the generator. Use
GW 901, 1, …, or
similar large tag
number.
Set: Y11 = YA + YC = Y22 = 0
Y12 = -YC = j  I = - I1 = - jV
NT (Tag, Seg
Seg),
), 901, 1, 0, 0 0, 1 0, 0
EX 0, 901, 1, 0, (j x FEED PT. CURRENT)
GW 901, 1, 103, 0, 0, (103 + slightly more), 0, 0, (RADIUS)
}
One
set
per
feed
Make sure these GW900’s do not interact with each other / squirt them off in all directions
(LATEST VIEWER ALLOWS YOU TO ELIMINATE A RANGE OF SEGMENTS FROM THE VIEW!)
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NEC User Notes Feeding of Arrays
Process:
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Set up enough GW900 cards for far-out feed segments, one for
each array element. Make them very short w.r.t a wavelength so
they will not radiate. Put them after any GS scaling to maximize
the distance between dummy and actual geometry.
Add an NT card for connection between each GW900 and its
companion feed point segment.
Put the correct current values on the EX0, 900 cards to match the
array design.
The input impedance at the feed points is in the Network Excitation
Table instead of under antenna input impedance.
Choose the dummies to be just one segment and set the radius so
D/a  10 or more.
41
NEC
User
Notes
-Feeding
Equivalent Radius for Nonof
Arrays
(Example)
Circular Cross-Sections
/4
/4
I1 = 1
CE
GW
GW
GW
GW
GE
GN
NT
NT
EX
EX
~
I2 = -j
~
2 Phased Verticals -- Current Source Fed
1, 5, 0, 0, 0, 0, 0, 0.25, .001
2, 5, 0.25, 0, 0, 0.25, 0, 0.25, .001
901, 1, 999, 999, 999, 999, 999.001, 999, .0001 Dummy 1
902, 1, -999, 999, 999, -999, 999.001, 999, .0001 Dummy 2
1
1
901, 1, 1, 1, 0, 0, 0, 1, 0, 0
902, 1, 1, 1, 0, 0, 0, 1, 0, 0
0, 901, 1, 0, 0, 1
0, 902, 1, 0, 0, -1
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47
47
NEC
User
Notes
-Equivalent Radius for NonUsing
NT
as
Loads
Circular Cross-Sections
R
4
1
7
1
4
Y11 = 1/R
Place load here
(50 W, 300 W)
NT
Y22 = 
1, 4,
1, 6,
0.02, 0,
0, 0,
1, 4,
1, 6,
.00333, 0,
6

NT

1e10, 0
XQ
NT
0, 0
1e10, 0
XQ
EN
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47
NEC User Notes -Equivalent
Radius for
NonMinimum Segment
Lengths
at BentCross-Sections
Wire Junctions
Circular
Wire 2 (Radius a2)
a = angle between wires
Match points from each wire at
intersection
a
Wire 1 (Radius a1)
D1/2
• Match points for both wires must lie outside the volumes
• Set a segment length limit to enforce this
THUS :
ALSO :
a 
a 
 a
 a
D1 > 2  1  2  and D 2 > 2  1  2 
 tan a sin a 
 sin a tan a 
D1
D2
> 8(or 2 and
> 8(or 2  (with EK, 0.5
a1
a2
44
Equivalent Radius for NonCircular Cross-Sections




Equivalent radius must lie between
inscribed and circumscribed circles which
bound the conductor boundary.
Best fit: Circles formed with same area
and perimeter as the conductor boundary.
Inner circle : ai = A / p
Outer circle : a0 = P / 2p
45
Equivalent Radius for NonCircular Cross-Sections
A
P
 ae 
p
2p

Choose the mean:
A
ae 
P

p 2p
2
46
Equivalent Radius for NonCircular Cross-Sections
ae = 0.2 A  .0P
S
• TRIANGLE:
S
ae = 0.425
S
S
• SQUARE:
S
S
ae = 0.65
S
• RECTANGLE OR STRIP:
T
W
W/T
1
2
3
5
10
100

ae
0.6 w
0.44 w
0.37 w
0.32 w
0.26 w
47
47
Modeling Guidelines




Estimate runtime
Accuracy checks
 Vary segmentation -- check convergence
 Check reciprocity
 Test for average gain
 Check grids vs. patches
Size problem in wavelengths
Locate functional parts before modeling
 Don’t forget the coupling to baluns, etc. by
near fields
48
Modeling Guidelines



Always exploit symmetry for large problems
Model the radiators first
 Check the literature
 Duplicate literature before approaching the full
problem
Strip out details/simplify structure
 Transmission lines and connections
 Supporting structures
 Environmental interactions
49
Modeling Guidelines

Wire grid modeling






Outline corners
Grid size approximately 0.1  nominal
Try “equal area” rule
Try two segments/side
Minimize D and a changes (< 2:1) at key
junctions (near feedpoints)
Use denser gridding (2x) at connection points
of wires and surfaces
50
Modeling Guidelines

Surface patch modeling




Make sure surface is closed
Maximum patch size: (0.2   0.2 )
Avoid long narrow patches
Use large patches on smooth surfaces:
smaller patches on curved areas
51
Modeling Guidelines


Vary segmentation, grid size, patch size
and note results -- look for convergence
Consider possible problem areas
 Sharp bends in thick wires
 Changes in wire radius
 Wires connected to lossy ground
 Wires too thick?
52
Modeling Guidelines

Determine number of segments needed
 D/ < 0.1 in most cases
 D/ too small? Low frequency limit
 D/ too small? Pencil lead vs. poker chips
“Thin Wire”
( a << D )
“Tuna Can”
(aD)
“Poker Chip”
( a >> D )
53