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#### Gary Schafer

- Jan 1, 1970

- 0

The discussion is concerning antennas that are shorter than a quarter

wavelength.

TUNING TO A QUARTER WAVE

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

length.

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

lower.

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

below.

CURRENT DISTRIBUTION

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.

RADIATION RESISTANCE

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

system.

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.

(OHMS LAW)

REACTANCE

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

resistive.

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.

CURRENT IN THE ANTENNA, VOLTAGE ON THE COIL

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

ohms.

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

antenna.

HIGH VOLTAGE NOT IN PHASE

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

antenna.

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.

CAPACITY HATS

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.

COAX AS A FEED LINE

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.

Regards

Gary