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

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

Matt Brenenman wrote:
"When I think of how a field induces a voltage, I think of voltage as
being proportional to norm of the field."

OK. Terman wrote on page 2 of his 1955 opus:
"The strength of the wave measures in terms of microvolts per meter of
stress in space is also exactly the same voltage that the magnetic flux
of the wave induces in a conductor 1 m long when sweeping across this
conductor with the velocity of light."

Since Matt mentions circular polarization, one of the problems on page
50 in Kraus` 3rd edition of "Antennas" is notable. It states:
"1-16-2 More power in C.P. Show that the average Poynting vector of a
circularly polarized wave is twice that of a linearly polarized wave if
the maximum electric field E is the same for both waves. This means that
the medium can handle twice as much power before breakdown with circular
polarization (CP) than with linear polarization (LP)."

Best regards, Richard Harrison, KB5WZI

On 29 May, 19:47, (Richard Harrison) wrote:
Matt Brenenman wrote:

"When I think of how a field induces a voltage, I think of voltage as
being proportional to norm of the field."

OK. Terman wrote on page 2 of his 1955 opus:
"The strength of the wave measures in terms of microvolts per meter of
stress in space is also exactly the same voltage that the magnetic flux
of the wave induces in a conductor 1 m long when sweeping across this
conductor with the velocity of light."

Since Matt mentions circular polarization, one of the problems on page
50 in Kraus` 3rd edition of "Antennas" is notable. It states:
"1-16-2 More power in C.P. Show that the average Poynting vector of a
circularly polarized wave is twice that of a linearly polarized wave if
the maximum electric field E is the same for both waves. This means that
the medium can handle twice as much power before breakdown with circular
polarization (CP) than with linear polarization (LP)."

Best regards, Richard Harrison, KB5WZI
Richard,
I am trying to decipher the above so my comments may well not be
relavent to what you are actually saying.
It is a given that far field circular polarisation
results in a 3 db loss with respect to radiation compared to other
polarisations. But one cannot from this assume that radiation
from a radiator changes with respect to the designed polarization.
When current is applied to a radiator in a time varient condition
the vectors involved cannot change.
The three phases of radiation are current application and electron
emmission,formation of the near field and finally formation of the
far field.
I fail to see how vectors formed in the initial stage which can
be seen as a Poyntings explanation changes or depends upon
future formations of the ensueing radiation waves.
Since the poster is interested in mathematicalanalysis of radiation
he must obviously realise that the Laws of Conservation must be held
and it woulkd appear that some confusion has been injected into his
problem.
Art

Art wrote:
"The three phases of radiation are the current application and the
electron emission, formation of the near field and finally formation of
the far field."

The questioner asked: "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) ?"

Art replied:
"Gain can mean many things."

Terman defines on page 870 of his 1955 opus:
"The extent of such concentration relative to that of some standard
antenna, termed the directive gain, is defined quantitatively as the
ratio of power that must be radiated by the comparison antenna to
develop a particular field strength in the direction of maximum
radiation to the power that must be radiated by the directional antenna
system to obtain the same field strength in the same direction."

Kraus shows how to handle arrays of point sources. All the math is
included.

Kraus wrote on page 12 of the 3rd edition of "Antennas":
"Antennas convert electrons to photons or vice versa."

If the questioner draws his information from Terman and Kraus, he won`t
err.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
If the questioner draws his information from Terman and Kraus, he won`t
err.

Don't forget Balanis who said: "Standing wave antennas,
such as the dipole, can be analyzed as traveling wave
antennas with waves propagating in opposite directions
(forward and backward) ..."

To answer the original questioner: Consider the forward
and backward traveling waves separately and phasor add
the two voltages or two currents to obtain the net
voltage or net current. For an ordinary dipole, the
forward voltage and forward current amplitudes decline
by ~5% during the forward trip from the feedpoint to the
tip of the antenna. There they are reflected and suffer
another ~5% decline on their way back to the feedpoint.
The feedpoint impedance is a result of the superposition
of the forward and reflected waves on the standing-wave
antenna.
--
73, Cecil http://www.w5dxp.com

On 30 May, 10:21, (Richard Harrison) wrote:
Art wrote:

"The three phases of radiation are the current application and the
electron emission, formation of the near field and finally formation of
the far field."

The questioner asked: "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) ?"

Art replied:
"Gain can mean many things."

Terman defines on page 870 of his 1955 opus:
"The extent of such concentration relative to that of some standard
antenna, termed the directive gain, is defined quantitatively as the
ratio of power that must be radiated by the comparison antenna to
develop a particular field strength in the direction of maximum
radiation to the power that must be radiated by the directional antenna
system to obtain the same field strength in the same direction."

Kraus shows how to handle arrays of point sources. All the math is
included.

Kraus wrote on page 12 of the 3rd edition of "Antennas":
"Antennas convert electrons to photons or vice versa."

If the questioner draws his information from Terman and Kraus, he won`t
err.

Best regards, Richard Harrison, KB5WZI

Richard, you evoked the phrase Poyntings vector which is an excellent
point to start
with respect to the formation of radiation especially with respect to
mathematical analysis
I iknow that you mentioned a couple of books to add weight to your
response
but a circular polarised wave has no place what so ever in a
mathematical analysis
of Poyntings vector. Yes we all know that there is a 3db difference
when looking
at the gain of a circular polarised antenna as well as many other
facts with
respect to antennas but you invoked "poyntings vector" where flux
movement
is used as a mathematical beginning. I am not disputing anything that
is
in the books that you often refer to but only how you interprete the
written word
to add authority to your analysis where it has no place.
I say again, since you evoked the term Poyntings vector in response to
mathematical
question that is no place to insert polarisation differences that may
take place
not in the Poynting areana but at a much later stage in radiation.
However, since you muddled things up by introducing Pointings vector
and coupled it
to circular polarisation maybe you can enlarge how this vector changes
with respect
to the choice of polarisation. Don't waffle by reciting books and
facts written
in books that don't relate to the subject at hand but give an
explanation to
the poster who acknoweledges that he is new to antennas but not to the
mathematical
aspects of same.
He is asking for assistance and not a measure of your personal
knoweledge or the books that you have or what you believe the
intent of the author is in what he states.
Regards
Art

On 30 May, 11:15, Cecil Moore wrote:
Richard Harrison wrote:
If the questioner draws his information from Terman and Kraus, he won`t
err.

Don't forget Balanis who said: "Standing wave antennas,
such as the dipole, can be analyzed as traveling wave
antennas with waves propagating in opposite directions
(forward and backward) ..."

To answer the original questioner: Consider the forward
and backward traveling waves separately and phasor add
the two voltages or two currents to obtain the net
voltage or net current. For an ordinary dipole, the
forward voltage and forward current amplitudes decline
by ~5% during the forward trip from the feedpoint to the
tip of the antenna. There they are reflected and suffer
another ~5% decline on their way back to the feedpoint.
The feedpoint impedance is a result of the superposition
of the forward and reflected waves on the standing-wave
antenna.
--
73, Cecil http://www.w5dxp.com

Cecil,
I am questioning the bundling of radiation with respect to
Poyntings vector and the polarization of the far fields.
Ofcourse any mathematical analysis must start with the
application of current and resulting movement of flux ala
Pointings vector. However I have yet to see an explanation
how this mathematical function is impacted upon by the
polarisation desired. Even if this is a misinterpretation
of what is in the books the poster is at least entitled
to a explanation of the effect of circular polarization
and how this impinges on Poyntings vector in a mathematical
sense. How else can we attract newbies to the hobby?
Ofcourse Cecil you also have muddled up things by introducing
your favorite subject but I suspect you did that because of
that rebel approach as opposed to confusing the poster(grin)
Regards
Art

art wrote:

Cecil,
I am questioning the bundling of radiation with respect to
Poyntings vector and the polarization of the far fields.
Ofcourse any mathematical analysis must start with the
application of current and resulting movement of flux ala
Pointings vector. However I have yet to see an explanation
how this mathematical function is impacted upon by the
polarisation desired. Even if this is a misinterpretation
of what is in the books the poster is at least entitled
to a explanation of the effect of circular polarization
and how this impinges on Poyntings vector in a mathematical
sense. How else can we attract newbies to the hobby?

I wouldn't worry about it, Art. The poster wanted to know how to
properly combine e-fields in order to calculate the induced voltage on
an antenna. I'm sure by now he's figured out that asking a
mathematics question on a ham radio newsgroup is a waste of time. I
expect the answer would be found in Jackson.

73, ac6xg

art wrote:
...
Cecil,
I am questioning the bundling of radiation with respect to
Poyntings vector and the polarization of the far fields.
Ofcourse any mathematical analysis must start with the
application of current and resulting movement of flux ala
Pointings vector. However I have yet to see an explanation
how this mathematical function is impacted upon by the
polarisation desired. Even if this is a misinterpretation
of what is in the books the poster is at least entitled
to a explanation of the effect of circular polarization
and how this impinges on Poyntings vector in a mathematical
sense. How else can we attract newbies to the hobby?
Ofcourse Cecil you also have muddled up things by introducing
your favorite subject but I suspect you did that because of
that rebel approach as opposed to confusing the poster(grin)
Regards
Art
Translation: "Holy Polarized Photons!" grin

Regards,
JS