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Doug Dotson
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Default SSB Antenna theory

First you cite several instances that the ARRL treatment is
wrong. Then you say the they finally got it right. Where are
your references that substantiate either statement?

Doug, k3qt
s/v Callista

"Gary Schafer" wrote in message
I tried to give an abbreviated synopsis of the subject and dispel some
myths. I did not cover all the details.

You need look no further than the ARRL itself for references. If you
read the whole post you would see that near the bottom I credited the
ARRL 2000 edition of their handbook, antenna section. The definition
of "radiation resistance" is from there and the calculations of the
example antenna with impedance's and voltages developed are directly
from there.

If you also look in the 18th edition 1997? of the ARRL antenna
handbook chapter 16 "mobile and marine antennas", and probably later
versions, you will see where they properly discuss loaded short
antennas and what the coil does.

Also if you look at the earlier post titled "Notes on short SSB
antennas" you will find a reference to W8JI's web site where he
discusses these very items in detail. He and many other engineers will
tell you the same thing.

I don't mean to discredit the ARRL but their statements in regard to
tuning an antenna to a quarter wave in their older publications are
misleading as evidenced by all the misconceptions that fly around.

While that is a simplified explanation of what happens with the
antenna matching, I suppose it was easier to propagate that (no pun
intended) term for simplicity. But if you really want to understand
what is going on it will get you into trouble in understanding as it
is a conflict with what really happens.


On Thu, 29 Apr 2004 20:25:53 -0400, "Doug Dotson"

So, is this something you put together? How about some references?
ARRL is a pretty reputable outfit. If you are going to dispute their
writings, you should provide some some verifiable references.

Doug, k3qt
s/v Callista

"Gary Schafer" wrote in message
.. .
This tries to explain how short SSB antennas operate and why.
The discussion is concerning antennas that are shorter than a quarter


I looked through several older handbooks and antenna handbooks and
found most of them professing what Larry is saying about "tuning an
antenna to an electrical quarter wave."

No wonder so many people have it wrong! The ARRL has been preaching
this stuff for years. But in the same paragraphs they will speak to
the "electrical length being very close to the physical length". Can't
have it both ways! Even the 2000 ARRL handbook has it wrong.

They finally got it right in their antenna handbook. Not once did I
see reference to "tuning an antenna to an electrical quarter wave

It may seem like semantics but there are a lot of people that get
confused and think that when making the system resonant with a
shorter antenna that the antenna is really the same as a quarter wave
length antenna when there is a loading coil. It is far from that. Its
radiation resistance and its feed point resistance are both much

An antennas electrical length is what it is by itself. Adding a coil
to it to make it resonant will not change that.

Also a lot of people think that the antenna has to be resonant in
order to radiate well. That is also far from true. Using a coil to
cancel out the reactance of the antenna forms a resonant circuit with
the antenna which must be done in order to get power to the antenna.
This is a different thing than the antenna being resonant itself. But
the antenna itself will perform the same whether it is resonant or
not. The problem is getting power to the antenna as you will see


With a full quarter wave length antenna the current distribution on
the antenna is more like a sine wave curve. Larger at the bottom and
tapering slowly as you go up the antenna.

With an antenna shorter than a quarter wave length the current is
still maximum at the bottom feed point and smallest at the top.
However the shape of the distribution is different.

With a short base loaded antenna the current distribution is about
linear. In other words it drops in direct proportion to the length of
the antenna.

With center loading or top hat loading the current distribution is
"pushed up" the antenna. It has a higher almost constant current at
the lower part of the antenna and it drops off very fast at the top.


Current distribution on the antenna determines radiation resistance.
Radiation resistance determines efficiency of the antenna system. The
higher the radiation resistance the higher the efficiency of the

With a more constant current distribution that center loading gives
over base loading, the radiation resistance is greater on the antenna.
This allows more power to be put into the antenna to radiate.

Radiation resistance is not to be confused with feed point resistance.
"Radiation resistance is defined as the resistance that would
dissipate the same amount of power that is radiated by the antenna."

As an antenna is made shorter (less than a quarter wave length) the
radiation resistance drops. As radiation resistance drops you must
increase the current to maintain the same amount of power to radiate.


Note that the larger a capacitor is the less reactance it has.
The larger an inductor (coil) is the more reactance it has.

A short antenna looks like a capacitor and like any capacitor it has
capacitive reactance. That reactance is AC resistance. In order to get
power into that antenna you must have an equal amount of inductive
reactance in the circuit to cancel out the capacitive reactance. When
the two are equal the circuit is said to be resonant and purely

Note that when adding the inductance it changes nothing about the
antenna itself. Only the reactance / impedance seen at the feed point
which is the transmitter end of the coil.

The shorter the antenna (less capacitance presented) the higher the
capacitive reactance and thus the larger the coil required to cancel
it. This means more wire in the coil. The more wire in the coil the
more resistance the coil will have. (not to be confused with
reactance) The more resistance it has the more loss it will have.

It gets worse, because as the antenna gets shorter its radiation
resistance gets smaller as the coil resistance is getting larger. The
coil resistance can be 10 times or higher in resistance than the
radiation resistance of the antenna. Because they are in series the
same current that flows in the antenna also flows in the coil. The
coil will therefore absorb most of the power. (ohms law again)

By center loading the antenna rather than base loading it the current
distribution is shifted in the antenna and that increases the
radiation resistance of the antenna.
However it is not a free lunch. The higher up you raise the coil on
the antenna the more coil is required. This increases coil loss again.
But the radiation resistance of the antenna goes up faster in
proportion to the coil resistance so you end up with less system loss.


When a short antenna is used some think that the current requirement
is less rather than more for the antenna. This is related to the fact
that the voltage at the coil-antenna junction (output terminal on your
tuner) is much higher with a short antenna. Therefore the thought is
"if the voltage is higher the current must be lower".

Well it isn't! The reason the voltage is so high is because of the
high inductive reactance of the coil in the tuner. Because the
inductive reactance is high (lots of coil) the voltage goes high at
that point.

Here are some numbers to illustrate what happens when a coil is used
with a short antenna:
With a 10.5 foot antenna at 3.5 mhz the capacitance of the antenna is
around 30 pf.
The radiation resistance is about .55 ohms
This takes a 62.5 microhenry coil to equal the capactive reactance.
With a Q of around 200 the coil will have a resistance of about 6.88
The coil and antenna radiation resistance will provide a load of 7.43
ohms at the feed point. (6.88 + .55 = 7.43)

Additional matching will be required to get it to 50 ohms. But if you
apply 100 watts to the 7.43 ohms you will have a coil / antenna
current of 3.67 amps. (I squared R = 100W)

Now that reactance of the coil will be 1375 ohms. So 1375 times 3.67
amps = 5046 volts rms or 7137 volts peak across the coil!! (V= IR)
Who says you can't get zapped from 100 watts!

This is where your high voltage comes from with a low impedance


Note that there is a phase shift across the coil so the current
through the coil and the voltage across it are not in phase. That is
what allows the voltage to rise so high. You can't use ohms law here
to calculate power without allowing for the phase difference.
Otherwise it would look like 6900 watts was being delivered to the

As you increase the length of the antenna the capacitance it
represents becomes higher thus making its capacitive reactance lower.
That also makes the need for inductive reactance lower and reduces the
coil size and inductive reactance. By reducing inductive reactance you
also reduce the voltage seen across the coil.

Also increasing the length of the antenna increases its radiation
resistance which requires less current through it for the same amount
of power. With less current through the antenna you will have less
current through the coil. So with less coil impedance and less current
through it, the voltage developed across it will also be less for the
same amount of power applied to the circuit.


Using a capacity hat on a short antenna increases the amount of
capacitance that the antenna represents in the circuit. That decreases
the capacitive reactance which increases its radiation resistance.
Increasing its radiation resistance as above increases the efficiency
of the system. Also less inductive reactance is needed and the
associated benefits are also realized.


Some have advocated using coax between the tuner and whip antenna or
long wire antenna as a feeder rather than an open piece of wire.
That would be ok if the antenna were not short for the frequency being
used. Here is why it doesn't work with a short antenna like a whip or
long wire that is short for the frequency.

With the same antenna in the example above if we used just 1.5 feet of
RG 58 coax which has 21 pf /ft capacitance would give us about 30 pf
capacitance. The same amount as out whip. Putting that in parallel
with the antenna would drop the radiation resistance in half. This
would cut the efficiency of the antenna in half!

Examples above are from the 2000 ARRL handbook.

After we worry about all the losses above there are the ground losses
that are also in series with the antenna feed point. Those losses can
be several times greater than the antenna losses. You can begin to see
that a short antenna can be very inefficient.

After reading this if still interested, reread my other earlier post
about short SSB antennas and it may make more sense.