On 25 May, 08:14, junoexpress wrote:
Hi,

I am not an "antenna person", so I have a simple question that I am
hoping someone will be so kind to answer for me.

I have data for the gain pattern of a directional antenna. The data is
given as complex numbers for both the phi and theta components. From
how I view the concept of antenna gain (as a mathematician), it seems
that you can consider the gain as a rank 2 tensor having the form:
_ _
| Gqq Gfq |
(i.a) G = | Gqf Gff |
- -

where f = phi component, q denotes the theta component

In this case, I can suppose there is no cross-polarization, so this
matrix reduces to:

_ _
| Gqq 0 |
(i.b) G = | 0 Gff |
- -

Now I have an incident E field (which happens to be RHCP), that I can
write as a plane wave:
(ii) E(t) = E0(t) [ Eq*q^hat , Ef*f^hat]
where E0(t) is the time dependence that factors out and the 2x1 vector
remaining gives the q and f components resp.

M questions is as follows:
Obviously, I am interested in the antennas response to the field. If I
want to compute the voltage induced on the antenna by the field, do I
add the two E field components or do I compute the norm of the vector
on the RHS of eqn (ii)? When I think of how a field induces a voltage,
I think of the voltage as being proportional to norm of the field. A
colleague of mine who does some work with antennas however says that
the antenna "doesn't know anything about components" and so it just
adds the two components. (also, this question is a bit of an aside
perhaps, but in the papers that I look through that deal with
polarized EM waves, only the E field and not the H field are
considered. Is there a reason why/justification for why it it can be
neglected?)

Thank you very much and you can reply to me on the ng or by my e-mail
address.

Matt Brenenman

Matt,
Gain can mean many things. If you can back up on your vector aproach a
look at Poyntings theorem would be a good start. You could then look
up past threads on Gaussian antennas as far as vectors are concerned
for radiation.
If you are looking towards a yagi design then that is a completely
different animal for radiation where the elements couple with each
other to transfer current and thus radiation which also creats a
focussing effect on the radiated lobe, where its gain is measured but
at the expense of beam width.Thus when looking at different
arrangements for radiation the Gaussian style ceases radiation when
applied energy stops where as in a coupled antenna such as a yagi
coupling and radiation occures outside the energy applied time. When
pursuing vector analysis it is a must to pursue Poyntings vector
aproach or Gaussian aproach because of the time varing factor.
That is about the limit that I can help you
Regards
Art