I wrote a little ruby (nice interpretive language) wrapper round the C
port of the nec2 program, and began happily generating simulations. So
far so good. (When I am finished I could offer it to anyone interested)

I am new to EM stuff - so here comes what is probably a silly
misunderstanding:

Consider an array of similar aerials (antennae).

Since the situation is linear, I would expect the currents received from a
plane wave signal to be linearly related to the currents which would be
obtained at each element position if there were no aerials at the other
element positions (assuming the effect of an aerial on its surroundings is
due solely to its current, and you can linearly add a cancelling current
and thus remove it)?

The relationship can be expressed by a symmetric (reciprocity) coupling
matrix which should be independant of the incident plane wave direction?

For a regular array on a circle the matrix should be toeplitz, by
symmetry, and constitutes a cyclic FIR filter which will yield the coupled
signal observations from the (free) field values at the element positions
(to a complex scale factor). It can thus be found by division of the FFTs
(of the loaded simulation currents vs open circuit simulation currents
or vs free field plane wave calculation) and inverse FFT.

When I try this - for example with a regular 3 element circular array of
resonant dipoles - I find that the FIR coefficients derived do indeed
convert from free field pattern at the element positions to array
currents, but only for the angle from which they are derived. The
relationship seems to be signal dependant :-(. For example the plane waves
in the opposite sense (180 deg) have a quite different coupling matrix
(mostly in phase).

Can anyone point out my mistake, this is really bugging me. I have tried
increasing the number of segments to silly levels, to no avail. For 2
dipoles it works, more and it does not.

Help

There is a mutual coupling term between the elements of an array antenna.
This can be minimized by proper spacing, and by eliminating some of the
elements.
Looking back at the array - (from each angle) -- The pattern is a linear
summation of the each of the currents induced by the emitters (using complex
numbers, i.e. magnitude and angle, distance etc)
---

"stuart macgregor" wrote in message
news
I wrote a little ruby (nice interpretive language) wrapper round the C
port of the nec2 program, and began happily generating simulations. So
far so good. (When I am finished I could offer it to anyone interested)

I am new to EM stuff - so here comes what is probably a silly
misunderstanding:

Consider an array of similar aerials (antennae).

Since the situation is linear, I would expect the currents received from a
plane wave signal to be linearly related to the currents which would be
obtained at each element position if there were no aerials at the other
element positions (assuming the effect of an aerial on its surroundings is
due solely to its current, and you can linearly add a cancelling current
and thus remove it)?

The relationship can be expressed by a symmetric (reciprocity) coupling
matrix which should be independant of the incident plane wave direction?

For a regular array on a circle the matrix should be toeplitz, by
symmetry, and constitutes a cyclic FIR filter which will yield the coupled
signal observations from the (free) field values at the element positions
(to a complex scale factor). It can thus be found by division of the FFTs
(of the loaded simulation currents vs open circuit simulation currents
or vs free field plane wave calculation) and inverse FFT.

When I try this - for example with a regular 3 element circular array of
resonant dipoles - I find that the FIR coefficients derived do indeed
convert from free field pattern at the element positions to array
currents, but only for the angle from which they are derived. The
relationship seems to be signal dependant :-(. For example the plane waves
in the opposite sense (180 deg) have a quite different coupling matrix
(mostly in phase).

Can anyone point out my mistake, this is really bugging me. I have tried
increasing the number of segments to silly levels, to no avail. For 2
dipoles it works, more and it does not.

Help

I did something similar to this as part of my Master's research, except I
used a 'brute force' algorithm written in Fortran.

As the other poster suggested, you have to consider the mutual coupling.
This can really mess up the pattern if ignored, except in one special case.
That special case is when the array is completely symmetrical. That is each
dipole 'sees' the same surroundings as all other dipoles. Since you have
them in a circular arrangement, the dipoles will have to be placed radially
on the circle. That is, one end of each should point towards the center of
the circle.

What is happening is that the elements are coupling to each other. This
introduces an additional complex impedance in addition to the self impedance
of the dipoles themselves. You then have to 'dither' the phase of the
driving current (for an all driven array) to get the desired pattern. In
the case of an array with parasitic elements (that is, the driving current
is 0.0), what is typically done is to dither the self impedance of the
parasitic elements by either placing a lumped constant (inductance or
capacitance) in the parasitic element, or changing the length of the
parasitic element slightly. The more elements you have, the more
complicated the problem becomes.

Note that the pattern for receiving will be the same as for transmitting
because of reciprocity. It is usually easier to calculate the pattern for
the transmit case.


Two dipoles, as you found, are always symmetrical to each other. Get
yourself a copy of J. D. Kraus' "Antennas" and study the section on mutual
coupling and reciprocity. The newer editions also have a section on the
"Method of Moments", which is what NEC and similar programs use.

For my thesis project, I used a brute force method. Kraus gives canned
formulas for the self and mutual impedances of simple antenna
elements---dipoles, monopoles, etc. (actually, he only gives part of the
formulas and refers you to other papers). I then wrote some complex matrix
math routines in Fortran, and let it crank away. For N elements, you need
an NxN matrix of complex numbers to describe the relationship between all of
the elements. The self impedances will be on the diagonal, and the mutual
impedances for each pairing of elements will be elsewhere in the matrix.
What you do then is solve the matrix equation I=V/Z, with V being a unit
matrix (for a uniformly driven array). This will give you the currents in
the elements from which the pattern can be calculated. To 'dither' the
currents, change the complex values in the V diagonal. For a parasitic
array (I never got far enough to actually try this) all but the feed element
in V is 0.0.

Fortunately, NEC does all of this for you.

By the way, a herd of bugs have 'antennae', a herd of radios have
'antennas'. (As in Kraus' Antennas).

Jim
N8EE

The replies so far do not seem to address the issue I was trying to get
help on.

I expected a linear, signal independant symmetrical toeplitz mixing
matrix, due to aerial coupling in the symmetric layout.

As far as I can see this would be (I-K)^-1 where
K(i,j)=K(j,i)=k(i-j)=z(i,j)/(z(i,i)+zload) and K(i,i) is defined as 0.
I may be wrong, this was just from first principles.

What I got from the nec2 calculations was a linear symmetrical toeplitz
mixing matrix which *varied* with signal direction. I am probably
missing something obvious?

As to looking at the RP - I wanted to have a look at the RDF calibration
problem, and I do not see how to exploit the radiation pattern for this.

The aerial pattern I tried finally was just 3 similar thin resonant
dipoles with 0.8 wavelength spacing on a circle. No joy so far.