Radiation resistance of a short dipole antenna - do you have experimental results?

Has anyone verified formulas for radiation resistance of a short dipole? I have seen two formulas - according to one Rrad=800*(l^2/lambda^2) Ohms,
according to the second Rrad=200*(l^2/lambda^2) Ohms.
Which is approximately correct, if any of these?

The correct one is, I think, the second.

The 800*(l^2/lambda^2) comes from Cheng's formula Rr ~ 80*(pi)^2*(l/lambda)^2 I think its wrong.

We also get Rr = 20*(pi)^2*(l/lambda)^2
which tries to make (pi/6)*Zo ~ 20*pi^2 where pi^2 is taken to be approximately 10

The Free Space impedance (only part of the dipole formula!), also sometimes uses 120*pi, which comes from assuming the speed of light is 3*10^8 m/S, which it is not! The true value of Free Space Impedance is 376.73031 ohms, a constant in the formula.

Move on the dipole radiation resistance R_dipole = (pi/6)*376.73031*(l/lambda)^2 provided l<<lambda (a short one!)

pi*376.73031/6 = 197.255 for which 200 is supposedly an approximation.

Is there anyone who has MEASURED Rrad of a short dipole? In particular I am interested
in the case of length between 0.1 and 0.2 λ.

tomasz1000 said:

Is there anyone who has MEASURED Rrad of a short dipole? In particular I am interested
in the case of length between 0.1 and 0.2 λ.

Click to expand...

I do it all the time, but you don't need an instrument to know what happens with a short antenna. It gets a bit like feeding terminals with only a bit of capacitance across them. The impedance is (very) high, with phase near -90 degrees.

For a 1m antenna set more than 3 or 4 metres above ground..

At 30 MHz (λ = 10m) Z_real is about 2 ohms, and Z_imag is about -1340 ohms.
At 60 MHz, where the dipole is the bigger fraction of λ, Z_real ~= 9 ohms and Z_imag ~= -590 ohms.

The Rrad predicted by NEC2 simulation is the same as measured with MFJ269, on 2m antennas, but I never thought to drive it at a low frequency. In about a week, however, I will have the opportunity to try, though most around me will wonder why.

Darktrax said:

I do it all the time, but you don't need an instrument to know what happens with a short antenna. It gets a bit like feeding terminals with only a bit of capacitance across them. The impedance is (very) high, with phase near -90 degrees.

For a 1m antenna set more than 3 or 4 metres above ground..

At 30 MHz (λ = 10m) Z_real is about 2 ohms, and Z_imag is about -1340 ohms.
At 60 MHz, where the dipole is the bigger fraction of λ, Z_real ~= 9 ohms and Z_imag ~= -590 ohms.

The Rrad predicted by NEC2 simulation is the same as measured with MFJ269, on 2m antennas, but I never thought to drive it at a low frequency. In about a week, however, I will have the opportunity to try, though most around me will wonder why.

Click to expand...

Why don't you compensate the capacitive reactance?
Thanks for the data.

We do, we do.
The basic short dipole impedance is known, but kind of hard to feed. The one thing you do know is that the currents at the ends are zero, and that the structure is so far off resonance, it will take a gamma match, or some other contrivance to feed some power into it.

Darktrax said:

We do, we do.
The basic short dipole impedance is known, but kind of hard to feed. The one thing you do know is that the currents at the ends are zero, and that the structure is so far off resonance, it will take a gamma match, or some other contrivance to feed some power into it.

Click to expand...

If you compensate the capacitive reactance, then the structure must be in resonance

- - - Updated - - -

Darktrax said:

...assuming the speed of light is 3*10^8 m/S, which it is not! The true value of Free Space Impedance is 376.73031 ohms, a constant in the formula....

Click to expand...

How can Z0 be known to 8 significant decimal digits? I find it quite suspicious.

tomasz1000 said:

How can Z0 be known to 8 significant decimal digits?

Click to expand...

https://en.wikipedia.org/wiki/Impedance_of_free_space

If you compensate the capacitive reactance, then the structure must be in resonance

Click to expand...

As long as the compensation element is not part of the structure, the structure can't be in resonance, it's keeping the mainly reactive input impedance. The complete circuit however can be in resonance.

You don't say a capacitor is in resonance, you say the LC circuit is.

tomasz1000 said:

If you compensate the capacitive reactance, then the structure must be in resonance

Click to expand...

Yes - you are right, but I make the distinction between the parts of the structure that can radiate, and have the radiation resistance as a characteristic property, and those parts that do not. The original question was about the radiation resistance of a short dipole, and this we know. We can reasonably calculate it, and we can confirm our models by measuring it.

This value is hopelessly capacitive to efficiently match any practical transmission lines we might connect to it, so we can do what you suggest, and .. compensate. This is OK so long as the matching arrangement itself does not significantly radiate. The radiation resistance component remains the property of the the short bits. The matched impedance we then see is not the radiation resistance.

Getting practical..
The first thing that comes to mind is to use a loading coil between the feed points of the dipole, tapped to provide a convenient drive impedance.

We could just force it, by connecting a low loss balanced transmission line contrived to be an electrical half-wavelength at the drive frequency, and using a generator capable of delivering the high voltage-low current waveform. Instead, we choose some other length of resonant feed-line transformer, and use it with a more reasonable (say 50 ohms) generator.

The way I see it, whatever matching tricks we use, the important feature is that the short dipole, driven at the low frequency, looks like the tip-ends of of a 5x or 10x longer dipole, brought together. It does not take much current to raise the voltage of these ends, so the variation in the near field is predominantly electric, with most of the magnetic component energy storage (of the whole resonant structure) being provided by the matching arrangement.

While we are motivated to cobble up a resonant total arrangement, the short dipole parts are being operated as a non-resonant radiator. It is short! It is by definition a non-resonant radiator. The (mostly electric) near field it is permitted to have at the low drive frequency will still radiate (a bit).