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Old July 16th 03, 08:12 AM
Roy Lewallen
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Dr. Slick wrote:
Roy Lewallen wrote in message ...

I disagree on this point. You can think of an antenna as a type
of tranformer, from 50 Ohms to 377 Ohms of free space. A tuned
antenna is "matching" 50 to 377 ohms, and will therefore have no
reflections, ideally.

Thinking of it doesn't make it so. All the energy applied to the antenna
is radiated, less loss, regardless of the antenna's feedpoint impedance.
How does that fit into your model.

What if the antenna was a wire shorting the transmission line?
Then there would be very little radiated power, and a lot of reflected

Yes, there would. But every watt delivered to that wire would be either
radiated or dissipated.

You can make a transformer to match 50 Ohms to, say, 200 Ohms or
so. Why not for 50 to 377? It's just another number.

That's right. You can make a transformer that converts the circuit V/I
ratio to 377 ohms. But this doesn't make a plane wave whose E to H field
ratio is 377 ohms. But you can have an antenna with a feedpoint
impedance of, say, 3 - j200 ohms, and a couple of wavelengths from the
antenna, the ratio of E to H field produced by that antenna will be 377
ohms. Another antenna, with feedpoint impedance of 950 + j700 ohms, will
also produce a fields whose E to H ratio is 377 ohms. In fact, you can
have any antenna impedance you'd like, and a few wavelengths away, the
ratio of E to H field will be 377 ohms, provided the antenna is immersed
in something resembling free space. But the fields in, on, or around a
377 ohm transmission line are unlikely to have an E to H ratio of 377 ohms.

You're trying to say that the 377 ohm E/H ratio of free space is the
same thing as a V/I ratio of 377 ohms. It isn't. Any more than 10 ft-lbs
of torque is the same as 10 ft-lbs of work or energy.

Except in the case of free space, with a given permeability and
permittivity, you have the impedance of free space, which doesn't need
a transmission line.

Sorry, I can't make any sense out of that.

ok, so perhaps the way to think of it is: when an antenna is
matched, the I and V curves

what curves?

Well, a carrier with a single frequency will be a sinewave,
correct? Feeding a real resistive impedance, the V and the I
sinewaves will be in phase (no reactance).


will be in phase (no reactance), and the

product of I*V (integrated) will be the power transmitted.

The average power radiated is always the real part of V*I(conjugate). If
V and I are in phase, this is simply equal to V*I. But what does this
have to do with the confusion between a resistor and resistance?

It doesn't really, but it does relate to this discussion. In the
sense that V and I will be in phase for either a matched antenna or an
ideal dummy load.

V and I will be in phase at the feedpoint of a purely resistive antenna.
This is true whether or not it's matched to the transmission line
feeding it, or whether the transmission line is matched to the antenna.
The relative phase of V and I at the antenna terminals has nothing to do
with whether the antenna or transmission line are matched. It also
doesn't matter what fraction of that resistance represents energy
dissipated locally and how much represents energy radiated.

I suppose what this all means is that if you have a matched
antenna, it's V and I curves

will be IN PHASE and will have the exact

same RMS values as if you had a truly resistive dummy load instead.

Yes and no. If you're feeding the antenna with a 450 ohm line, it's
matched to the line only if its impedance is 450 + j0 ohms, so it looks
like a 450 ohm dummy load, not a 50 ohm one. On the other hand, you can
feed a 50 + j0 ohm antenna with a half wavelength of 450 ohm line, and
get a perfect 50 ohm match to a transmitter at the input end of the
line, while running a 9:1 SWR on the the transmission line. Then either
the antenna or the input of the line looks like a 50 ohm dummy load.

You could make that half wavelength transmission line almost any
other characteristic impedance, like 25 or 200 Ohms, and you would
still wind up back at 50 Ohms at the input of the line (but you
couldn't change frequencies unless they were multiples of 2 of the

But the point is, you will still be at 50 Ohms at the input, so
the V and I sinewaves should be in phase.

At the input and output of the line, yes.

Therefore, you can consider the center of the Smith Chart (or the
entire real (non-reactive) impedance line) as a real resistance like
an ideal dummy load.

Do you agree with this statement Roy?


Cool. But a network analyzer looking into a black box will not
be able to tell you whether the 50 Ohms it is reading is radiated
resistance or dissipated resistance. This seems to be the crux of my

You're right. The network analyzer can't tell you what's happening to
those watts going into the antenna. Too bad. If it could, we'd have a
really cool, easy way to measure antenna efficiency, wouldn't we?

But it's worse than that. If you connect the network analyzer to two
series resistors, it can't even tell how much power is going to each
one! And it can't even tell the difference between a 50 ohm resistor, a
100 ohm resistor on the other side of a 2:1 impedance transformer, a 100
ohm resistor on the other end of a quarter wavelength of 70.7 ohm
transmission line, or a really long piece of lossy 50 ohm transmission
line. Boy, they sure are stupid.

How come nobody complains that the impedance of a light bulb, an LED, or
a loaded electric motor is resistive? It's too bad it is, too.
Otherwise, the power company wouldn't charge us for the power we're
using to run those things. Neither the power company nor the network
analyzer knows or cares how much of the power going to a light bulb or
LED is converted to light and how much to heat, or how much of the power
going to an electric motor is doing work.

If we insist on separating all resistance into "dissipative" and
"dissipationless" categories, we have to consider time. Within a small
fraction of a second, most of the energy going into an antenna is
dissipated -- mostly in the ground or (at HF) the ionosphere. So we'll
have to consider that portion of the radiation resistance as
"dissipative". The stuff that goes into space will take longer to turn
into heat, but it will eventually. So the remainder of the radiation
resistance is one that's initially dissipationless but becomes
dissipative with time. Just think, we can have a whole new branch of
circuit theory to calculate the time constants and mathematical
functions involved in the transition between dissipationless and
dissipative states! And of course it would have to be cross-disiplinary,
involving cosmology, meteorology, and geology at the very least. There
are textbooks to be written! PhD's to earn! Just think of the potential
papers on the resistance of storage batteries alone! High self-discharge
rate means a faster transition from dissipationless to dissipative. . .

Sorry, I digress. I just get so *excited* when I think of all the
possibilities this opens up for all those folks living drab and boring
lives and with so much time and so little productive to do. . .

But has this ******* creation really simplified things or enhanced

Now tell me, why can't you just make some 377 ohm transmission line
(easy to make) open circuited, and dispense with the antenna altogether?

When you figure out the answer to that one, you might begin to see the
error with your mental model.

Ok by me. I'll be waiting for your patented no-antenna 377 ohm feedline.

Roy Lewallen, W7EL

Why would you need a 377 Ohm feedline for free space, when free
space itself is the transmission line??

By golly, you're right. Design your transmitter for 377 ohm output and
do away with the transmission line, too. Just let them joules slip right
out, perfectly matched, right straight to free space. Voila!

What's wrong with thinking of an antenna as a type of series
Inductor, with a distributed shunt capacitance, that can be thought of
as a type of distributed "L" matching network that transforms from 50
Ohms to 377?

Because that's not what it does, and thinking of it that way leads you
to impossible conclusions. The antenna is converting power to E and H
fields. The ratio of E to H, or the terminal V to I are immaterial to
the conversion process. You're continuing to be suckered into thinking
that because the ratio of E to H in free space has the dimensions of
ohms that it's the same thing as the ratio of V to I in a circuit. It
isn't. A strand of spaghetti one foot long isn't the same thing as a one
foot stick of licorice, just because the unit of each is a foot.

This is related to how you need to bend the ground radials of a
1/4 WL vertical whip at 45 deg angles down, to get the input impedance
closer to 50 Ohms (as opposed to 36 Ohms or something like that if you
leave them horizontal).

There are a number of ways in which an antenna and transmission line are
similar. But don't take the analogy too far. Start with a quarter
wavelength transmission line, start splitting the conductors apart until
they're opposed like a dipole, and tell me how you've ended up with an
input impedance of 73 ohms.

There are plenty of texts you can read, on all different levels, if
you're really interested in learning about antennas, fields, and waves.

Roy Lewallen, W7EL