Phase array question
 

Richard Clark wrote:
On Tue, 19 Aug 2008 09:17:01 -0700, Jim Lux
wrote:

But your search for small, broadband antennas puts you bump-up against the
principle "small - broadband - efficient, choose any two".
But actually, that's not the principle.. The actual limits have to do
with the ratio of stored energy vs radiated power in the antenna (Q, in
the energy storage sense, not in the "resonant circuit" sense).

Hi Jim,

Different meanings of Q? The measure of Q may vary according to
arbitrary usage: the choice of SWR limits to define bandwidth which
infers Q. Some choose 2:1, classic Q would go further. Either way,
and for either quantitative result, the meaning of Q remains
essentially the same.


Actually, the Q you use is not the actual definition, which is the ratio
of the energy stored in the system vs the energy lost per cycle (or
possibly per radian, so there's factor of 2pi in there)

The articles that talk about size, efficiency, and Q, use this
definition (Energy stored in near field vs energy radiated away).
(e.g. the papers by Chu, Harrington, etc.)


For a single LCR tuned circuit with reasonably high Q, it just happens
that the BW/CF works out to the same thing (because it's a quadratic
equation that determines both..)


Chu, 1948, defines Q = 2*omega*mean electric energy stored beyond input
terminals/(power dissipated in radiation) (page 1170). he goes on to
say,"We have computed the Q of an antenna from the energy stored in the
equivalent circuit and the power radiated, and *interpreted it freely*
as the reciprocal of the fractional bandwidth." (my emphasis added) " To
be more accurate, one must define the bandwidth in terms of allowable
impedance variation or the tolerable reflection coefficient over the
band. For a given antenna, the bandwidth can be increased by choosing a
proper matching network. The theoretical aspect of this problem has
been dealt with by R.M. Fano."

Harrington, 1965, considering directional antennas (Chu dealt with
omnis) defines Q as = 2*omega*W/Pin [eq 54], which is slightly different
than Chu. W is either We or Wm (the energy stored in the E or H field
respectively), and Pin is the input power to the array. He goes on to
say,"If the Q is large, it is related to the frequency bandwidth of the
array as follows. Consider the array to be resonated by a suitable
reactance network at the frequency of interest, omega/sub/r. Define the
ferquency bandwidth of the array in the usual manner to be the
fractional frequency increment between the 0.707 points on the
normalized input |Z|,
beta = deltaOmega/Omega/sub/r. [eq 56]

If the Q is high (say Q10) then we have the relationship:
Q approx= 1/beta [eq 57]"


Note well the "approximately equal" and the "resonated by a suitable
reactance network"


SWR bandwidth is something totally different of course..

But again, if you pick the right SWR value for your bandwidth
measurement, then a dipole antenna is modeled pretty well by a single
pole LCR resonant, so the math works out conveniently the same.

Once you start straying away from antennas that can be modeled as a
single LCR, the "bandwidth" vs "Q" relationship goes away.

A good example would be some forms of phased arrays with non-reciprocal
devices. Antennas with multiple resonances would be another case
(except if you are only working over a restricted range, where the
single resonance in your range is approximated well by a single LCR)

Phase array question
 

On Tue, 19 Aug 2008 12:36:30 -0700, Jim Lux
wrote:

Richard Clark wrote:
On Tue, 19 Aug 2008 09:17:01 -0700, Jim Lux
wrote:

But your search for small, broadband antennas puts you bump-up against the
principle "small - broadband - efficient, choose any two".
But actually, that's not the principle.. The actual limits have to do
with the ratio of stored energy vs radiated power in the antenna (Q, in
the energy storage sense, not in the "resonant circuit" sense).

Hi Jim,

Different meanings of Q? The measure of Q may vary according to
arbitrary usage: the choice of SWR limits to define bandwidth which
infers Q. Some choose 2:1, classic Q would go further. Either way,
and for either quantitative result, the meaning of Q remains
essentially the same.


Actually, the Q you use is not the actual definition, which is the ratio
of the energy stored in the system vs the energy lost per cycle (or
possibly per radian, so there's factor of 2pi in there)

Hi Jim,

If you will note, my example was a measure, not a definition of Q.
The half power points bandwidth compared to the center frequency is a
classic computation of Q. As I point out, the choice of 2:1 SWR, not
being half power points, is arbitrary but in no way diverges from the
sense of Q (and could be extrapolated anyway).

The articles that talk about size, efficiency, and Q, use this
definition (Energy stored in near field vs energy radiated away).
(e.g. the papers by Chu, Harrington, etc.)

Use "which" definition? You offer what appear to be two, and that is
one too many.

For a single LCR tuned circuit with reasonably high Q, it just happens
that the BW/CF works out to the same thing (because it's a quadratic
equation that determines both..)


Chu, 1948, defines Q = 2*omega*mean electric energy stored beyond input
terminals/(power dissipated in radiation) (page 1170). he goes on to
say,"We have computed the Q of an antenna from the energy stored in the
equivalent circuit and the power radiated, and *interpreted it freely*
as the reciprocal of the fractional bandwidth." (my emphasis added) " To
be more accurate, one must define the bandwidth in terms of allowable
impedance variation or the tolerable reflection coefficient over the
band. For a given antenna, the bandwidth can be increased by choosing a
proper matching network. The theoretical aspect of this problem has
been dealt with by R.M. Fano."

Harrington, 1965, considering directional antennas (Chu dealt with
omnis) defines Q as = 2*omega*W/Pin [eq 54], which is slightly different
than Chu. W is either We or Wm (the energy stored in the E or H field
respectively), and Pin is the input power to the array. He goes on to
say,"If the Q is large, it is related to the frequency bandwidth of the
array as follows. Consider the array to be resonated by a suitable
reactance network at the frequency of interest, omega/sub/r. Define the
ferquency bandwidth of the array in the usual manner to be the
fractional frequency increment between the 0.707 points on the
normalized input |Z|,
beta = deltaOmega/Omega/sub/r. [eq 56]

If the Q is high (say Q10) then we have the relationship:
Q approx= 1/beta [eq 57]"

Hence the two definitions? What I see are computational models for
different systems which arbitrarily restrain loss to inhabit their
model or exclude it. Q can deteriorate considerable if you open the
definition to include more components going back to the power supplies
to the finals.

Note well the "approximately equal" and the "resonated by a suitable
reactance network"


SWR bandwidth is something totally different of course..

But again, if you pick the right SWR value for your bandwidth
measurement, then a dipole antenna is modeled pretty well by a single
pole LCR resonant, so the math works out conveniently the same.

Once you start straying away from antennas that can be modeled as a
single LCR, the "bandwidth" vs "Q" relationship goes away.

A good example would be some forms of phased arrays with non-reciprocal
devices.

This example needs a sub-example: Non-reciprocal devices? I don't see
how this will alter the concept of Q.

Antennas with multiple resonances would be another case
(except if you are only working over a restricted range, where the
single resonance in your range is approximated well by a single LCR)

All antennas have multiple resonances and it is a classic
differentiator between themselves and LCR circuits. I see no example
here that is not already offered by my original post.

Let's simply return to the quote I responded to:
On Tue, 19 Aug 2008 09:17:01 -0700, Jim Lux
wrote:
(Q, in the energy storage sense, not in the "resonant circuit" sense)
embodies two explicit definitions of Q:
1. Q for energy storage, and
2. Q for "resonant circuit."
The measurement of Q might deviate by the result offered, but
conceptually energy storage and resonance are inextricably congruent.
If by resonance you are suggesting ONLY the peak frequency, then it
follows there is(are) some other frequency(ies) that are not resonant
(a tautology), and Q follows by exactly the same relation and degree
as it does for energy storage.

If there is any suitable distinction of Q in an antenna, then it is
that the degradation of Q is a benefit to the antenna, IFF the
substantial portion of R is radiation resistance. If the benefit of
filtering (phasing) due to resonance were not an issue, then a Q of 1
would be the Holy Grail of antenna design. Even in the design of the
finals stage in a tube amplifier, Terman teaches us that the final's
tank should NOT have an excessive working Q (beyond 10-15); hence a
high Q is NOT beneficial. Q and efficiency are a slippery topic when
you try to tie them together.

73's
Richard Clark, KB7QHC

Phase array question
 

On Aug 8, 1:13 pm, Roy Lewallen wrote:
Joel Koltner wrote:
"Roy Lewallen" wrote in message
streetonline...
Not by a long shot! Here's a simple example from the EZNEC demo program,
using example file Cardioid.EZ. It's a two element array of quarter
wavelength vertical elements spaced a quarter wavelength apart and fed with
equal currents in quadrature to produce a cardioid pattern. The impedance of
a single isolated element is 36.7 + j1.2 ohms. In the array, the impedances
are 21.0 - j18.7 and 51.6 + j20.9 ohms, and the elements require 29 and 71
percent of the applied power respectively in order to produce equal fields.
The deviation is due to mutual coupling.

That's a much, much greater difference than I would have guessed. Wow...

Isn't the input impedance of one element affected not only by the relative
position of the other element, but also how it's driven? I.e., element #1
"sees" element #2 and couples to it, but how much coupling occurs depends on
whether the input of element #2 is coming from a 50 ohm generator vs. a 1 ohm
power amplifier (close to a voltage source), etc.? (Essentially viewing the
antennas as loosely coupled transformers, where the transformer terminations
get reflected back to the "primary.")

Not directly. What counts (considering the simple case of two elements)
is the magnitude and phase of the current in the other element, and
their spacing, orientation, and lengths. A good way to look at the
effect of mutual coupling is as "mutual impedance", i.e., the amount of
impedance change caused by mutual coupling. (Johnson/Jasik covers this
concept well.) If you were to feed two elements with constant current
sources (as in the Cardioid.EZ EZNEC example), mutual coupling doesn't
change the element currents, but only the feedpoint impedances. With any
other kind of feed system, the impedance change causes the currents to
change, which in turn affects the impedances. So the feed method
certainly does have an effect on the currents you get, which affects
both mutual coupling and pattern.

There's a lot more about this, and how to design feed systems which will
effect the desired currents, in the _ARRL Antenna Book_.

Thanks for the book links. Do you happen to have a copy of "Small Antenna
Design" by Douglas Miron? And have an opinion about it? Or some other book
on electrically small antennas? (Not phased arrays, though :-) -- more like
octave bandwidth VHF or UHF antennas that are typically 1/10-1/40 lambda in
physical size.)

I just recently purchased Miron's book but haven't yet looked at it in
any depth. It appears to be most interesting to anyone wanting a better
understanding of method of moments numerical methods. If you can read
German, you might be interested in _Kurze Antennen_ by Gerd Janzen. But
your search for small, broadband antennas puts you bump-up against the
principle "small - broadband - efficient, choose any two". They'll be
inefficient, which will hurt you both receiving and transmitting at VHF
and above. The book I'd go to for researching the possibilities would be
Lo & Lee's _Antenna Handbook_. You might also get some ideas from
Bailey, _TV and Other Receiving Antennas_, since TV antennas have to be
pretty broadband.

Roy Lewallen, W7EL

Simply in an effort to provide a bit more insight, or perhaps I should
better say to suggest a math tool that may lead you to more insight,
consider what "mutual impedance" means. In a simple circuit where
there's a current through an impedance, the voltage drop across it is
given by V = Z * I. If you expand this idea to include mutual
impedances, the Z becomes a matrix, and I and V are vectors. So in an
antenna system with, say, four feedpoints, V becomes a vector of four
voltages, one for each feedpoint, and I similarly is a vector of four
currents, one for each feedpoint. Z is then a four-by-four matrix
with self-impedances along the diagonal and mutual impedances off the
diagonal. It is clear that if you know the four currents, you can
find the voltages. Further, if you can invert the Z matrix, then you
can calculate the currents if you know the voltages. That also
suggests how to find the mutual impedances: if you excite one
feedpoint with a known current and leave all the rest open, you can
measure the voltages at each (including phase) and that immediately
gives you the mutual impedance from the excited feedpoint to each of
the others: your I vector has only one non-zero component. Repeat
for each feedpoint.

You can use the same sort of analysis with other systems which have
interaction among components. For example, a system of inductors
which share magnetic fields can easily be characterized by a matrix of
self-inductances and mutual inductances. For a single inductor, V =
L*di/dt; if you have two coupled inductors, V1 = L1 * di1/dt + M12 *
di2/dt, and V2 = M21 * di1/dt + L2 * di2/dt -- or in matrix notation,
V = L * d/dt(I). That can expand to as many inductors as you care to
consider.

(If this is confusing, it's probably best to just ignore this
suggestion...)

Cheers,
Tom

Phase array question
 

"K7ITM" wrote in message
...
(If this is confusing, it's probably best to just ignore this
suggestion...)

Not at all, thanks for the additional details, Tom.

Somewhere I have copies of IEEE tutorial articles on this sort of generalized
circuit theory... they ended up as references for work I did in college. (We
spent the bulk of our time worrying about scattering parameter matrices,
however. I did write some Matlab code to do n-port conversions between S, Y,
and Z parameters, though -- but based off of formulas from papers: I question
if I could have correctly derived the conversions between, e.g., S and Y
myself in a reasonable period of time, since the port terminations for the
scattering parameters were allowed to be arbitrary at each port and the math
for this requires a decent background in linear algebra.)

---Joel

Phase array question
 

Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position. It's
just that there's no valid way to multiply by the cosine of the angle
between two scalars.

I suspect you knew if I ever found my Born and Wolf after my
move, you would be in trouble - and you are.

You previously said that Born and Wolf did not agree with
Hecht, but they do, contrary to your assertions.

Their equation for irradiance (intensity) agrees with Hecht.

Itot = I1 + I2 + J12

where J12 = 2E1*E2 = 2*SQRT(I1*I2)*cos(A)

On page 258 of "Principles of Optics", by Born and Wolf,
4th edition, they label J12 as the *interference term*,
contrary to your assertions. (Hecht labels that term I12)
--
73, Cecil http://www.w5dxp.com

Phase array question
 

Cecil Moore wrote:
Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position.
It's just that there's no valid way to multiply by the cosine of the
angle between two scalars.

I suspect you knew if I ever found my Born and Wolf after my
move, you would be in trouble - and you are.

No. I assumed you could find fig 7.1 and see it for yourself. The plot
has phase on the X-axis and intensity on the Y-axis. The caption reads
Interference of two beams of equal intensity; variation of intensity
with phase difference. " At the top of the page: "Let us consider the
distribution of intensity resulting from the superposition of two waves
which are propagated in the z-direction...."

The relation is useful for precisely the reason I indicated. That is
why Heckt also includes it in his book.

I deleted the rhetorical blithering from your post. And again, please
quote my remarks directly whenever you wish to discuss them.

73, ac6xg

Phase array question
 

Jim Kelley wrote:
The relation is useful for precisely the reason I indicated. That is
why Heckt also includes it in his book.

Your Freudian slip concerning your feelings about Hecht
is more than apparent, i.e. "To Heck with Hecht"! :-)

One wonders why you said something to the effect that
Hecht had been discredited in favor of Born and Wolf.
When I recommended the 57 page chapter on interference
in "Optics", by Hecht, you said something to the effect
that interference is unimportant, yet Born and Wolf's
chapter on interference is 113 pages long and mostly
agrees with Hecht's writings.
--
73, Cecil http://www.w5dxp.com