## Z and Y matrices from NEC

Quote from a NEC-LIST post by Jerry Burke:

Subject: Z-matrix
BURKE@icdc.llnl.gov
Date: Mon Aug 07 1995 - 18:31:01 METDST

> what data card do I have to add to the nec2 input file
>to get the complete Z-matrix (or something else which gets the
>strength of mutual coupling between two antennas or the ports
>of a two-port antenna)?

You probably do not need the Z matrix. It relates the amplitudes of the spline basis functions to the fields at the segment centers with the structure not there (open-circuit impedance matrix, so every segment is an open port). The matrix Y=Inverse[Z] relates the fields at points on the structure with all of the structure present to the basis function amplitudes. However, NEC uses L/U decomposition to get the solution, so you would have to compute the inverse and then apply a transformation as done in subroutine TBF to convert basis function amplitudes to currents at segment centers.

This is done for you in the currents printed in the output. Just excite the antenna ports one at a time, and the currents on the segments representing the other ports will give the mutual admittances. Remember that regular segments are short-circuited ports unless you excite them with a voltage source. However, a segment with a network or transmission line connection (NT or TL command) is open circuited unless you explicitly short it. One way to short circuit a network-segment port is to put a very small voltage source on it (like 1.e-10, but anything less than 1.e-20 will be turned into one volt by NEC). Then the current in this small voltage source (but not the segment current) will be the short-circuit current in the port. We forgot about shorting network ports in NEC-2, so the maximum coupling calculation (CP command) is not correct when networks or transmission lines are involved.

Jerry Burke
LLNL

Subject: Re: Z-matrix, S-matrix
From: Paul Elliot (pelliot@apti.com )
Date: Mon Aug 07 1995 - 21:29:32 METDST

> what data card do I have to add to the nec2 input file
>to get the complete Z-matrix (or something else which gets the
>strength of mutual coupling between two antennas or the ports
>of a two-port antenna)?

You might try computing the S-parameter coupling, because it is the easiest to measure at RF and microwaves and therefore the most widely used at those frequencies.

The S-parameters are easily calculated after running NEC by using the NEC currents on the source segments. A resistor must be included at each port in the NEC model to provide the impedance of a match terminated transmission line connected to the port. The transmission line feature of NEC is not required. The following applies to any multiport, including the two-port case.

The NEC model is run with one antenna or port excited by a voltage source Vg in series with an impedance Rg. The other antennas or ports are not excited, but they are also terminated in Rg. Rg is most commonly 50 ohms but could be any finite impedance (I have always used equal, real Rg on all ports, although in principle it should be possible to do something similar with unequal Rg on each port or a complex generator impedance).

With the excited antenna or port designated as port #i, the voltages directly across the ports or antenna inputs are:

Vi = Vg - Ii * Rg (for driven port i)

Vn = -In * Rg (for all undriven ports, i.e. n not equal to i)

Vi (i.e. the voltage across the driven port) is not equal to the NEC
excitation voltage Vg due to the voltage drop across Rg. The currents on the
undriven ports are the result of coupling. The next step is that all
voltages and currents, including those for port i, are now normalized using
the square root of Rg:

For all n including n = i:

Vn' = Vn / sqrt(Rg)

In' = In * sqrt(Rg)

The forward and scattered waves (a and b respectively) at each port (a 50
ohm transmission line if Rg = 50) are then given by:

an = (Vn' + In') / 2

bn = (Vn' - In') / 2

for all n where n is the port number.

and the resulting mutual S-parameter coupling Sn,i between port i and port n is:

Sn,i = bn / ai

Additional information on obtaining S-parameters from V and I is given in
some books including Microwave Engineering by R.E.Collin, McGraw-Hill, 1966,
p.171. A paper we presented at the 1994 ACES Conference in Monterey (pg.
504) also includes some illustrations and a comparison of measured
S-parameters with those calculated using NEC.

If NEC were perfectly accurate then the computed Sn,i would be exactly the
same as the S12 parameter measured by a perfectly accurate network analyzer.
Rg needs to be the same as the impedance of the network analyzer and the
coax used. If a balun is used in the measurement setup then if it is working
ideally it would not affect the S-parameters, but Rg does need to be
adjusted to include any impedance transformation provided by the balun.
Alternatively, when the complete S-matrix is computed between all antenna
ports, then the S-matrix can be transformed to incorporate the s-matrix of
attached baluns and matching units, which I found to be challenging for a
multiport, involving inverses and considerable matrix manipulations. It's
easier to use Touchstone or some other RF circuit simulator that can provide
a multiport device defined by it's S-matrix, and then add the other feed
components to the S-matrix of the antenna ports.

Sincerely,
Paul G. Elliot
APTI Div./ E-Systems / Raytheon

Subject: Re: Car simulation
From: Brian Austin (ee104@liverpool.ac.uk)
Date: Tue Aug 06 1996 - 16:33:32 METDST

On Tue, 30 Jul 1996 08:57:00 -0700 (PDT) Rossi Giuseppe wrote:

>
>
>
> I'm interested in simulation of antennas mounted on the car body
> in the frequency range 100 Mhz 2 Ghz.
> Does anyone have any experience or suggestion or reference in this field
> ?

>
There is quite a body of published material on antennas mounted on
a car body. For the special modelling requirements when using a wire-
grid with NEC you could refer to the following:

1. Austin, B.A. and Najm, R.K. (1991), "Wire grid modelling of vehicles with flush-mounted window antennas", Proc. IEE 7th Intl.Conf. on Antennas and Propagation, No.333, 2, pp.950-953.

2. Cox, J.W.R., (1991), "Comparison of predicted aircraft wire antenna terminal impedance (using NEC) with measurement in the HF band", ibid, pp.717-720.

3. Lee, K.S.H. et al, (1976), "Limitations of wire grid modelling of a closed surface", IEEE Trans. EMC, EMC-18, pp.123-129.

4. Ludwig, A.C., (1987), "Wire grid modeling of surfaces", IEEE Trans.on Antennas and Propagation, AP35,9, pp.1045-1048.

5. Nishikawa,L.A., (1984), "Effect of automobile body and earth on radiation patterns of antennas for FM radio", Trans. IECE of Japan, E-67, 10, PP.555-562.

6. Paknys, R.J., (1991), "The near-field of a wire-grid model", IEEE Trans. Antennas and Propagation, 39,pp.994-999.

Brian Austin

********************************************************
Dr B.A.Austin
Department of Electrical Engineering and Electronics
University of Liverpool
Brownlow Hill
Liverpool L69 3BX
U.K.

Tel.: +44151794 4520
Fax: +441517944540
email: ee104@liv.ac.uk