Download Cost 286 Hamburg, `Numerical Simulation of a Dipole Antenna

Numerical Simulation of a Dipole Antenna
Coupling to a Thin Wire in the Near Field
Yaping Zhang, John Paul, C Christopoulos
George Green Institute for Electromagnetics Research
University of Nottingham, Nottingham NG7 2RD, UK
www.nottingham.ac.uk/ggiemr/
Objectives of Working Group 1 within Cost 286:
Near field electromagnetic coupling of a radiating antenna
to a thin wire within a restricted space
• Phase 1: Thin wire above a ground plane in an open area;
• Phase 2: Enclosure problem, resonance;
• Phase 3: Thin wire in an enclosure,cumulative effect of
more sources.
Phase 1: Thin wire above a ground plane in an open area
Configurations of the Simulation Models
Two configurations are simulated using the Transmission Line Modelling (TLM) method.
The dipole antenna is parallel or perpendicular to the thin wire, as shown in Fig.1 (a)-(b).
(a)
(b)
100
10
0
50
half wave dipole
antenna
V
V
half wave
dipole antenna
100
0.3m
V
V
50
aligned
h1=0.1 m
h2=0.3 m
3m
h1=0.1 m
h2=0.3 m
1m
1m
3m
y
1.5 m
1.5 m
6m
6m
z
x
0
Fig.1 Configurations of the simulation models:
(a) a dipole antenna parallel to a thin wire above a ground plane;
(b) a dipole antenna perpendicular to a thin wire above a ground plane.
The problem is considered taking into account the final
configuration that needs to be tackled namely the case of
coupling inside an imperfect cavity (vehicle with windows,
non-metallic walls) and in the presence of people (very
complex EM properties).
Under these circumstances the advantages of MoM models in
describing wires are no longer decisive and differential timedomain models such as TLM and FDTD appear to be
advantageous!
However, special techniques are required to describe thin
wires (electrically small dimensions) inside cabinets
(electrically large). We describe here efficient thin-wire
formulations in connection with TLM.
TLM Formulations
Maxwell’s equations for electromagnetic wave propagation in free-space with conduction
currents are described by Eq.(1):
  H  J e    0 E 
 E  J     H 
t  0 
m

(1)
Solution of Eq.(1) is based on the 3-D TLM cell shown in Fig.2.
The fields and current densities in Eq.(1) are
normalised using the equivalences:
E  V l
H   i  l0 
,
J e   ie  l 0  ,
J m  Vm l
2
(2)
2
where l is the space step and  is the intrinsic
impedance of free-space.
0
The space and time derivative operators are
normalised using:
  ...   ...
1
l
,
 1 

t t T
(3)
Fig.2 Three dimensional TLM cell
TLM Formulations (continued)
The maximum time-step in the three-dimensional TLM algorithm is t=l/(2c), where c
is the speed of light in free-space. If the simulation is iterated at the maximum time-step, in
terms of the normalisations Eqs.(2)-(3), Maxwell’s Equations Eq.(1) in free-space could be
reduced to,
  i  i e 
 V 
(4)

2
i 

T

V

V
 

m

This set of equations is then mapped into the cell in Fig.2. For free-space modelling with
current densities, the calculation of the total fields at the centre of the cell can be expressed as,


Vx 

V 

 y
Vz  1 
  
 ix  2  

 iy 

 

 iz 


V
V
V
V
V
V
 V1i  V2i  V3i  

 iex 
i
i
i
i

i 
4  V5  V6  V7 

 ey 
i
i
i
i 

V

V

V
i 
8
9
10
11 
  1  ez 
i
i
i
i 
4 Vmx 
6  V7  V8  V9 

Vmy 
i
i
i
i 

V

V

V



10
11
0
1

Vmz 
i
i
i
i 
2  V3  V4  V5  
i
0
(5)
where the incident pulses are denoted by the superscript i. The normalised electric
conduction currents {iex,iey,iez} are used to describe currents in wires.
TLM Formulations (continued)
The reflected pulses are obtained from Eq. (6), where superscript r indicating reflection.
V

V
V

V
V

V
V

V

V
V

V
V

r
0
r
1
r
2
r
3
r
4
r
5
r
6
r
7
r
8
r
9
r
10
r
11
 Vx  i y  V1i 
 
i
 Vx  i y  V0 
  Vx  iz  V3i 
 
i 
  Vx  iz  V2 
 Vy  iz  V5i 

 
i
V

i

V


y
z
4 
  V  i  V i 
  y x 7i 
 Vy  ix  V6 
 V  i  V i 
  z x 9
  Vz  ix  V8i 
 
i 
V

i

V
z
y
11



 Vz  i y  V10i 
 

The incident voltages at the next time-step k+1 are
founf by swapping with the reflected voltages at time step k.
For example, the swap between ports 0 and 1 of the nodes
located at cell indicates Z and Z-1 is,
V  Z 1  kV0r  Z  ,
i
k 1 1
(6)
V  Z   kV1r  Z 1
i
k 1 0
(7)
At external boundaries of a mesh (for example port 6 at
Zmin), a reflection coefficient Rb is specified as,
i
k 1 6
V
 Zmin   Rb kV6r  Zmin 
(8)
where, Rb =-1: a perfect electric conductor, Rb=1: a perfect
magnetic conductor; Rb=0: a matched boundary, respectively.
For description of frequency-dependent boundaries, Rb
may be specified as a frequency-dependent function.
For a free-space simulations with current densities, equations (5)-(8) would apply to all
nodes and ports in the mesh for the software implementation.
3-D TLM Implementation
To aid the development of the model of field-wire coupling involving an x-directed
straight wire, consider the shunt node associated with Vx derided from the 3-D node. Fig.3
shows this node and Fig. 4 shows the equivalent circuit.
The voltage Vx is obtained as,
Vx  V0i  V1i  V2i  V3i  2  iex 4
Fig.3 Shunt node for evaluation of Vx
(9)
Fig.4 Equivalent circuit of a shunt
node describing Vx .
Formulations for Field-Wire Coupling
For straight wires, the telegrapher’s
equations describing an x-directed wire may
be expressed as Eqs(10)-(11), where Vw is
the wire potential, Iwx is the wire current and
Lw /l, Rw /l and Cw /l are the wire
inductance, resistance and capacitance per
unit length respectively. The field-to-wire
coupling is in the last terms of Eq.(10).
Vw  Lw  I wx  Rw 
V
 
   I wx  x
x  l  t  l 
l
I
 C  V
 wx   w  w
x  l  t

10 
11
A 3-D cell containing an x-directed wire is
shown in Fig.5, which indicates the voltage pulses
{V0, V1, V2 ,V3} interacting with the x-directed wire.
The wire inductance Lw /l=0kw and wire
capacitance Cw /l =0/kw ,where kw is a
frequency-independent dimensionless
geometrical factor.
Fig. 5 3-D TLM cell containing an x-directed wire
Formulations for Field-Wire Coupling (continued)
The velocity of propagation of charge variations along the wire is the speed of light, i.e.
LwCw . The characteristic impedance of the wire is Z w  Lw Cw  0 kw . The wire current is
normalised using I wx  iwx Z w , where iwx has the dimension of volts. The time and space
c  l
derivative operators are normalised using
  1  
 
,
x  l  X
  1  
 
t  t  T
.
Using the notations given above, Eqs.(10)-(11) may be rewritten as equations (12), where the
normalised wire resistance rw=Rw/Zw . Equations (12) may be converted to the travelling wave
format equations (13) by using the equivalences Eq.(9),
Vw
i
 2 wx  rwiwx  Vx
X
T
i
Vw
 wx  2
X
T

Vw iwx

 2Vwi 4  2Vwi 5  2iwx
X
T
i
Vw
 wx 
 2Vwi 4  2Vwi 5  2Vw
X
T

12 
13
The TLM equivalent circuit for the discrete-time solution of the equations (10)-(11) can
therefore be written as,
i
iw  Tw  2Vwi 4  2Vwi 5  2VwLx
 Vrx 2 
i
Vw   2Vwi 4  2Vwi 5  4VwC
4
where Tw   4  rw  y0 w 4 
14 
1
Equivalent Circuit for Field-Wire Coupling
Equivalent circuit for field-wire coupling for an x-directed wire is shown in Fig.6, and the
normalised equivalent circuit for field-wire coupling for an x-directed wire is shown in Fig.7.
Fig. 7 Normalised equivalent circuit for
Fig. 6 Equivalent circuit for field-wire
coupling for an x-directed wire.
field-wire coupling for an x-directed wire.
Simulation Results of a Dipole Antenna
Coupling to a Thin Wire
The configurations of the simulation models are shown in Fig.1 (a)-(b). The currents on the
thin wire at points 25 cm, 50 cm and 75 cm from the junction of the wire, and the feed current at
the gap of the dipole antenna excited by a sinusoid of 900 MHz or a Gaussian pulse with a
halfwidth of 0.8 nm are calculated in both the parallel and perpendicular cases respectively by
TLM method. The simulation results of the current transfer ratio (Iw/I_feed) for both
configurations, excited by a sinusoid or a Gaussian function, are listed in Table 1.
Table1 : Simulation Results of a Dipole Antenna Coupling to a Thin Wire
Configuration
Position to the wire
junction (cm)
Sinusoid
Iw /I_feed
Gaussian
Iw/I_feed
Parallel
25
50
75
0.050
0.056
0.056
0.052
0.056
0.056
Perpendicular
25
50
75
0.011
0.0126
0.00467
0.011
0.0128
0.00431
Table 1 shows the current transfer ratios obtained from the steady-state and pulse
excitations are in good agreement. The electromagnetic coupling is greater when a dipole is
parallel to a thin wire.
Sinusoid Dipole Coupling to a Thin Wire
(Parallel Configuration)
The currents on the thin wire at points 25 cm, 50 cm and 75 cm to the wire junction and the feed
current at the gap of the dipole antenna, excited by sinusoid source in a parallel configuration, are
calculated and the results are shown in Figs.8(a)-(d). The current transfer ratios at points 25 cm, 50 cm
and 75 cm may be obtained from these graphs and listed in Table 1.
(a)
(c)
(b)
(d)
Fig.8 Currents excited by a sinusoid dipole parallel to a thin wire:
(a) feed current at the gap of the sinusoid dipole; (b) current on the thin wire at a point 25 cm from the junction ;
(c) current on the thin wire at a point 50 cm from the junction; (d) current on the thin wire at a point 75 cm from the junction
Sinusoid Dipole Coupling to a Thin Wire
(Perpendicular Configuration)
The currents on the thin wire at points 25 cm, 50 cm and 75 cm to the wire junction and the feed
current at the gap of the dipole antenna, excited by sinusoid source in a perpendicular configuration, are
calculated and the results are shown in Figs.9(a)-(d). The current transfer ratios at points 25 cm, 50 cm
and 75 cm may be obtained from these graphs and listed in Table 1.
(a)
(c)
(b)
(d)
Fig.9 Currents excited by a sinusoid dipole perpendicular to a thin wire:
(a) feed current at the gap of the sinusoid dipole; (b) current on the thin wire at a point 25 cm from the junction ;
(c) current on the thin wire at a point 50 cm from the junction; (d) current on the thin wire at a point 75 cm from the junction.
Hz Field Distribution in the Dipole-Thin Wire Plane
Fast Fourier Transform Analyses Results
The current transfer ratios at points 25cm, 50cm and 75cm on the thin wire excited by a Gaussian
function are obtained for both the parallel and perpendicular configurations respectively. Results
obtained over the frequency range 600-1200 MHz are shown in Figs.10 (a)-(f).
(a)
(b)
(c)
(d)
(e)
(f)
Fig.10 FFT analyses of the thin wire coupling to a dipole antenna excited by a Gaussian function in both parallel and perpendicular cases:
Parallel case: (a) Current transfer ratio at 25cm; (b) Current transfer ratio at 50cm; (c) Current transfer ratio at 75cm;
Perpendicular case: (a) Current transfer ratio at 25cm; (b) Current transfer ratio at 50cm; (c) Current transfer ratio at 75cm.
The thin-wire formulation technique employed here to simulate this
problem is based on a quasi-static solution for the field around the
wire. This is a symmetrical solution and therefore can only be used
to place the wire centrally in the a computational cell. In cases
where an offset wire description is required a more complete
solution may be used which takes account of more modes (not just
the quasi-static term included by Holland and Simpson) in the wire
solution. The total field at the sampling points of the computational
cell is decomposed into its modal components, these are then
reflected by the correct modal impedance (see next slide) and then
re-combined to obtain the reflected total field for transmission to the
rest of the numerical solution.
The reason that the Holland and Simpson type of
approach is inaccurate is that there is insufficient
information contained in the quasi-static solution for a
wire. The general response of a wire to an incident
field is to generate a scattered field which in
combination with the incident field is rich in modal
information:
Ez (r , ) 

Be
n 
jn
n
Ez
H (r , ) 
j 0 r
1


J ( k0 a )
N n ( k0 r ) 
 J n ( k0 r ) 
N n ( k0 a )


“An accurate thin-wire model for 3D TLM
simulation”, P Sewell, Y K Choong, C
Christopoulos, TEMC Trans on EMC,
45(2), 2003, pp 207-217
The static solution is but the first term in this
expansion-but there is much more information
available! The impedance seen by each mode may be
obtained from the expression above E/H.
(15)
(16)
Magnitude of the electric field observed 2 and 8 nodes in front of the node containing
three dielectric coated wires when excited by a plane wave.
Conclusions
The electromagnetic coupling of a half wave
dipole antenna to a thin wire is simulated using the TLM
method. Two configurations of the dipole positions are
considered, in which the antenna is positioned either
parallel to, or perpendicular to, the thin wire. Results
obtained by using the steady-state and pulse excitations
agree closely.
Results are obtained by combining the versatility
of the TLM with the efficiency of powerful thin-wire
formulations.