David:

[snip]
"David" nospam@nospam wrote in message
...
The impedance of free space / air is said to be 377 ohms. Impedance is
ratio
of E/H. The feedpoint impedance of an antenna is usually 50 or 75 ohms.
Can an antenna ever be regarded as a transducer that transforms a radio
wave
from 50 ohms to 377 ohms i.e. provides an impedance transformation? With a
[snip]

The answer is a "considered" yes!

Although the [so-called] term "characteristic impedance", often labelled as
Zo, and units of Ohms are often used to describe a certain characteristic of
a propagation media in field theory, that governs the ratio of the E to H
fields propagating in the media. This "characteristic impedance Zo" is not
the same thing as "driving point or feed point impedance Z" in circuit
theory. Although closely related, circuit theoretic concepts and field
theoretic concepts are different views of electromagnetic phenomena.

Characteristic impedance Zo and the units of Ohms are often used as the
"name" for the square root of the ratio of mu the magnetic permeability is
[u = 1.257E-7 for free space] to epsilon the electric permittivity of a
propagating media [e = 8.85E-12 for free space]

Maxwell's celebrated equations then result in the fact that...

Zo = E/H = sqrt[u/e] = sqrt[(1.257E-7)/(8.85E-12)] = 376.7 Ohms ~ 120pi Ohms

This Zo is not the same as a "feedpoint impedance" Z which is the ratio of
voltage V to current I.

Z = V/I Ohms.

That said it should be recognized that any radiating antenna is "immersed"
in a propagating media, usually free space, and the u and e of that media do
have an important affect on the "characteristic impedance, or surge
impedance" of the antenna which will in turn affect the driving point or
feedpoint impedance of the antenna.

For instance it is well known that the resonant feedpoint impedance (Ratio
of V to I) at the center of a half wave dipole in free space is 73 Ohms. If
that dipole were placed in another medium other than free space with
correspondingly different u and e, the driving point impedance of the dipole
would definitely be affected. So would it's resonant frequency, etc...

And so in that sense, an antenna may be considered to be a transducer and
not a transformer. Antennas may then be viewed as transducers that
transduce the circuit theoretic variables of electric currents and voltages
flowing in and between conductors into field theoretic variables of electric
and magnetic fields flowing through a propagation media. And... indeed
there is a "reaction" between the u and e of the media in which the antenna
is immersed and the currents and voltages flowing in and on the antenna.

The 73 Ohm driving point impedance of a free space half wave resonant dipole
[in the ideal case this is the radiation resistance] is a direct result of
the u and e of the free space in which the antenna is immersed.

If all other things were held constant and the values of u and e of the
medial were changed [i.e. move the antenna from free space where u/e=377 to
be under water where u/e=x??? the driving point impedance of the antenna
would most certainly change!

[snip]
long tapered antenna, the feedpoint is at 50 ohms. Is the end of the
antenna
at 377 ohms to launch the wave easily into free space? In this case,
antenna
is a travelling wave antenna e.g. broad bandwidth biconical. Does the
impedance gradually change from 50 ohms to 377 ohms over the length of the
antenna?
[snip]

No! Not really.

Surprisingly, the actual surge or characteristic impedance Zo of a single
wire antenna in free space, considered as a one wire transmission line
placed high over a ground plane [the earth] is actually in the neighbourhood
of several hundred Ohms... say 600Ohms or so.

The exact value of Zo is easily calculated by well known transmission line
formulas, that assume TEM mode propagation on the line, and this Zo
basically depends upon the height over ground and the diameter of the wire.
This is not a driving point impedance but is a "surge impedance". The
driving point impedance of the single wire transmission line depends upon
where and at what frequency it is "driven" by a source.

Of course because this single wire is quite distant from it's return path
[ground] this single wire transmission line is "leaky". That is it radiates
and loses, or dissipates, power to some extent, as opposed to what it might
do if it were placed very close to the ground where there was a nearby field
"cancelling" current flow. [a microstrip transmission line for instance].

We know that if this single wire transmission line high above the earth is
driven by a source it will exhibit a driving point impedance that depends
upon its length relative to the wavelength of the driving voltage or
current. [73 Ohms resistive if it is a 1/2 wave, some other in general
complex Z if it is not 1/2 wave.

[snip]
The impedance of the end of an antenna (open circuit), where it is a high
voltage point, is usually 5K or 10K ohms.
[snip]

I believe that you are referring to the driving point impedance of an end
fed half wave dipole which is certainly high and in that neighbourhood.
This is not a characteristic or a surge impedance.

And so in summary...

An antenna may be thought of as a transducer between a circuit theoretic
electro-magnetic venue and wave propagation in a propagating media, but the
relationship between the circuit driving point impedance and the
characteristic impedance of the media is quite complex and is certainly not
a simple linear relationship such as found in a transformer or other device.

As far as I understand there is no practical application that has ever
required anyone to quantitatively determine the exact relationship between
the Zo of a propagating media and the driving point impedance Z of an
antenna that is immersed in that media.

In my opinion such a determination would be a very difficult
experimental/engineering exercise. The experimenal problem is one of how
does one vary the Zo of a media while measuring the effect on the Z at the
driving point? Here's a thought experiment...

Immerse an antenna in a liquid media with a given u and e in an anechoic
tank then drive the antenna with a generator while measuring the driving
point impedance (V and I) and then pour or mix in some other liquid with
different u and e and observe the change in Z.

Would that work?

It could also be accomplished numerically on a computer by using a program
[like the NEC programs] based on solving Maxwell's partial differential
equations iteratively.

As far as I know no one has ever attempted to do this... and notwithstanding
the possibility for "invention" or "discovery" I might ask, why would one
want to do this?

Hey it might make a good Ph.D. or M.Sc. thesis... but what is the practical
application?

For all practical purposes, the characteristic impedance of the media in
which antennas are immersed never changes!

Who cares how Z varies when Zo varies?

Thoughts, comments?

--
Pete k1po

Peter O. Brackett wrote:
. . .
In my opinion such a determination would be a very difficult
experimental/engineering exercise. The experimenal problem is one of how
does one vary the Zo of a media while measuring the effect on the Z at the
driving point? Here's a thought experiment...

Immerse an antenna in a liquid media with a given u and e in an anechoic
tank then drive the antenna with a generator while measuring the driving
point impedance (V and I) and then pour or mix in some other liquid with
different u and e and observe the change in Z.

Would that work?

It could also be accomplished numerically on a computer by using a program
[like the NEC programs] based on solving Maxwell's partial differential
equations iteratively.

As far as I know no one has ever attempted to do this... and notwithstanding
the possibility for "invention" or "discovery" I might ask, why would one
want to do this?

Hey it might make a good Ph.D. or M.Sc. thesis... but what is the practical
application?
. .

It would be one of the easiest degrees ever attained. NEC-4 allows
setting the primary medium to any (reasonable) value of conductivity and
permittivity, so you can have the answer in seconds with a free space
analysis. Alternatively, you can bury the antenna deep in NEC-4's ground
medium and define the ground characteristics for your test.

I did a short consulting job a while back for some people interested in
transmitting RF for short distances under water. Immersing the antenna
eliminates the substantial signal loss incurred by reflection at the
air-water interface when the antenna is out of the water. And antenna
system design requires knowledge of the antenna feedpoint Z. I've seen
numerous papers in the IEEE publications about antennas immersed in
other media such as a plasma, and know that antennas buried in the
ground are used. So it's of considerable practical interest.

Roy Lewallen, W7EL

Roy, David:

[snip]
It could also be accomplished numerically on a computer by using a
program [like the NEC programs] based on solving Maxwell's partial
differential equations iteratively.

As far as I know no one has ever attempted to do this... and
notwithstanding the possibility for "invention" or "discovery" I might
ask, why would one want to do this?

Hey it might make a good Ph.D. or M.Sc. thesis... but what is the
practical application?

It would be one of the easiest degrees ever attained. NEC-4 allows setting
the primary medium to any (reasonable) value of conductivity and
permittivity, so you can have the answer in seconds with a free space
analysis. Alternatively, you can bury the antenna deep in NEC-4's ground
medium and define the ground characteristics for your test.

I did a short consulting job a while back for some people interested in
transmitting RF for short distances under water. Immersing the antenna
eliminates the substantial signal loss incurred by reflection at the
air-water interface when the antenna is out of the water. And antenna
system design requires knowledge of the antenna feedpoint Z. I've seen
numerous papers in the IEEE publications about antennas immersed in other
media such as a plasma, and know that antennas buried in the ground are
used. So it's of considerable practical interest.

Roy Lewallen, W7EL
[snip]

Well thanks for that input Roy, that's very interesting and of course a
useful application.

But for the "thesis" idea I was thinking of something a little more
"challenging", e.g.

Clearly the antenna "driving point impedance" Z = R +jX is a complex
function f (Zo) of the "characteristic impedance" Zo, where in general Zo =
Ro +j Xo = sqrt[u/e] of the medium in which the antenna is immersed.

Clearly this function f(Zo) is the "transducer" function that David [The OP]
was seeking.

It's clear of course that f(zo) will also be a function of complex frequency
p = s + jw.

Now expressing this functionality as:

Z(p, Zo) = f (p, Zo)

One might ask [the thesis candidate, (grin)] to derive/discover and tell
us...

What. precisely, is the functional form of this complex "transducer"
function f that takes Zo to Z [377 Ohms to 73 Ohms! (grin)]

Is f(Zo) a simple linear function? [e.g. like a transformer turns ratio as
the OP David had asked] or perhaps... A non-linear function? or maybe... A
differential or integral relationship?

What?

Except for a few isolated niche applications, such as those you mentioned
having consulted on, I can't really think of any practical applications that
demand knowledge of the functional form of "f".

Which is likely why this subject is not mentioned in antenna textbooks or
widely discussed. i.e. No one ever needed to know it and so no one worked
out this relationship or even investigated it... Simply a matter of supply
and demand (grin)! We have Ohm's Law and other such well known
relationships such as V = IR because there was a demand by "scienticulists"
(grin) to know these relationships to do real Engineering, i.e. build stuff
they needed out of stuff they could get.

The discovery of the functional form "f" of this relationship might perhaps
be at least suitably hard for a Master's Thesis, a good challenge, and I
believe that it is suitably "academic", since there is very little use for
it (grin).

What exactly is "f (Zo)"?

Thoughts, comments.

--
Pete k1po
Indialantic By-the-Sea, FL

Peter O. Brackett wrote:
What? ... What exactly is "f (Zo)"?
Thoughts, comments.

Peter, I for one, have missed your style.

Consider the following:

I(s)
+--------------------------------------------open
|
V(s) 1/4 wavelength, Z0=600 ohms
|
+--------------------------------------------open

Given: The ratio of V(s)/I(s) is 50+j0 ohms. Can you
solve for f(Z0)?
--
73, Cecil http://www.w5dxp.com

Cecil:

[snip]
"Cecil Moore" wrote in message
om...
Peter O. Brackett wrote:
What? ... What exactly is "f (Zo)"?
Thoughts, comments.

Peter, I for one, have missed your style.

Consider the following:

I(s)
+--------------------------------------------open
|
V(s) 1/4 wavelength, Z0=600 ohms
|
+--------------------------------------------open

Given: The ratio of V(s)/I(s) is 50+j0 ohms. Can you
solve for f(Z0)?
--
73, Cecil http://www.w5dxp.com
[snip]

Heh, heh...

No of course not, you would need more than just this one
experiment/measurement to determine Zo.

The case you depict is at a "singularity" so to speak and is a "pathalogical
case", because with the 1/4 wave line open at the far end, one sees only a
short circuit with Z = V/I = 0.0 [zero] as the driving point impedance and
one needs more equations than just this one singular situation to solve for
Zo of the line.

In fact though if you "vary" the Zo of the line, you would then see a change
in the driving point impendance Z of the line from zero to another value.

From such a thought experiment one should be able to formulate an expression
for Z(Zo).

Thoughts comments...

--
Pete k1po
Indialantic By-the-Sea, FL.

Peter O. Brackett wrote:

"Cecil Moore" wrote:

I(s)
+--------------------------------------------open
|
V(s) 1/4 wavelength, Z0=600 ohms
|
+--------------------------------------------open

Given: The ratio of V(s)/I(s) is 50+j0 ohms. Can you
solve for f(Z0)?

The case you depict is at a "singularity" so to speak and is a "pathalogical
case", because with the 1/4 wave line open at the far end, one sees only a
short circuit with Z = V/I = 0.0 [zero] as the driving point impedance and
one needs more equations than just this one singular situation to solve for
Zo of the line.

Sorry I wasn't clear. One sees 50 ohms, not a short circuit,
and the Z0 of the line is given at 600 ohms. The line is not
lossless and not even low loss. There is enough resistance
in the stub wire to cause a 50+j0 ohm impedance looking into
the stub. I was just wondering what is the nature of your
f(Z0) function.
--
73, Cecil http://www.w5dxp.com

Cecil et al:

[snip]
the stub. I was just wondering what is the nature of your
f(Z0) function.
--
73, Cecil http://www.w5dxp.com
[snip]

I like working with Cecil!

Like a Zen Master's rehtorical approach to facilitating understanding,
Cecil's approach
to this seemingly paradoxical "circuit-to-wave transducer" question is quite
illuminating.

Cecil has neatly sidestepped the fact that, even for the simplest practical
antennas, elementary analytic
formulae for antenna driving point impedances have never been discovered.
Let alone formulae that explicitly
show Zo as an independent variable.

This [obscure?] fact [of delinquint formulae] often comes as a surprise to
most electromagnetic novitiates, I know it did to me.

[Aside: As far as I know, the fact that no one has ever worked out an exact
analytic formula for the driving point
impedance of a simple practical half wave dipole, is not a problem in
practices since other
approximate and/or "sledge hammer" style numerical methods provide
appropriately accurate answers to all
practical Engineering questions about such matters.]

However, as a "seeker of truth", Cecil has noted an easier path as an
approach to the apparently paradoxical
question of the relationship of driving point impedance to the wave or
characteristic impedance of free space
or any other propagating media.

Cecil has zeroed in on an alternative that might give us some insight!

Namely the relatively simple "exact" formula, first revealed by Heaviside
and Kelvin approximately two hundred years ago, the celebrated formula for
the driving point impedance Z = V/I of a lossless transmission line of
characteristic [surge] impedance Zo
terminated in a load impedance ZL. This driving point impedance is given by
the surprising simple relation...

Z(Zo) = Zo[(ZL*cos(theta) + jZo*sin(theta))/(Zo*cos(theta) +
jZL*sin(theta))] (1)

Where theta = 2*pi*(d/lambda) is the relative fractional length of the
transmission line, where d is
the line length and lambda is the wavelength of a sinusoidal signal
supported on the line at the particualr
frequency of interest. Zo of course is the characteristic [surge or wave]
impedance of the line.

It is also well known [Again Kelvin and Heaviside] that Zo can be simply
expressed in terms of the fundamental
transmission line parametric constants [R, L, C, G] by the [equally]
celebrated formula for the characteristic
[surge or wave] impedance of the transmission line as

Zo = sqrt[(R + jwL)/(G + jwC)]; Where, in the lossless case R=G=0.0, Zo -
sqrt(L/C).

[Aside: The terms Impedance, and Reactance were first defined by (Reg
Edward's hero) Oliver Heaviside. I wonder
if an equally simple formula for the driving point impedance in terms of the
Zo of free space for some simple
antenna is lying out there somewhere waiting to be discovered (grin). ]

As can readily be seen, the driving point impedance Z is a function of the
dependent variable Zo and...

although the effect of this relationship is often referred to as an
trasmission line impedance "transformer", the analogy
between the so-called "transmission line transformer" (or should we say
"transducer") described by (1) falls short of
the simple turns ratio relationship where Z = ZL*N^2.

To gain insight here, Cecil has obliquely suggested that, instead of
searching for an antenna formula, that we invert
the celebrated formula (1) and use it to determine unknown characteristic
impedance Zo by assuming ZL known, and
measuring Z.

Inverting formula (1) we obtain the following relationship.

Zo(Z) = ZL[(cos(theta) - jZ*sin(theta))/(Zcos(theta) - jsin(theta))] (2)

[Aside: Apart from the fact that line parameters L,C are also implicit in
the wavelength, Cecil is this right?]

Thus we see that the relationship between Zo and Z is not a simple linear
relationship as for the common transformer,
but instead is, what mathematicians often refer to as, a so-called "bilinear
relationship.

I wonder, is it possible that such a simple relationship exists for some
antennas as well as transmission lines?

An interesting invention... now it will be public domain (smile).

One could clearly construct a sensor to measure unknown Zo's by constructing
a small piece of rigid air dielectric
terminated transmission line and then "immersing" the sensor in substances
of unknown Zo and then determine those unknown
Zo's by measuring the driving point impedance Z. The calibration curve for
this Zo sensor would be the inverse
relationship (2).

Sigh, it's too bad there is not a simple analytical relationship like (1)
for antennas, for perhaps this would
address the OP's question of the relationship between 377 Ohms free space
wave impedance and 73 Ohms driving point
impedance more directly.

On the other hand we now can see that, contrary to Roy's recent assertion up
the thread (grin), that certainly an exact
analytic solution to this problem is likely a challenging Ph.D. thesis
topic.

For... after two hundred or more years [As far as I know...] no one has yet
worked out an exact simple
analytical expression [similar to (1)] for the driving point impedance of
any simple practical antenna.

A Ph.D. thesis indeed!

Thanks Cecil!

Thoughts comments...

--
Pete K1PO
Indialantic By-the-Sea, FL