Re: Z-matrix, S-matrix

> 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
Received on Mon Aug 07 1995 - 18:32:00 EDT