Feedpoint impedance of half-wave dipole, why is it 73?

[wannabescannist]

In free space—with the antenna remote from everything else—the theoretical impedance of a physically half-wave long antenna made of an infinitely thin conductor is 73 + j 42.5 Ω. This antenna exhibits both resistance and reactance. The positive sign in the + j 42.5-Ω reactive term indicates that the antenna exhibits an inductive reactance at its feed point. The antenna is slightly long electrically, compared to the length necessary for exact resonance, where the reactance is zero.

How was the number 73 + j 42.5 Ω calculated? Is this something I can measure with a DMM?

What I really don't understand is how they didn't specify the length of the wire...isn't that what defines the resistive component? And also why the frequency, inductance, and capacitance was not specified, as those define the reactive component.

Also, what is the last sentence talking about when it says "electrically long"? I know for resonance, the circuit is purely resistive and there is no reactance. But how do you know that the dipole is electrically long without specifying the length of the dipole and frequency it's supposed to be used at?

 

[hsdtech]

First, are you wanting to build a dipole? If so for what band? The formula for a 1/2 wave dipole is the same for any band, but I can't recall what it is off the top of my head.
Looks like they are saying the antenna is electrically long because the antenna feed point is 42 ohms and not 50 ohms.
An Antenna Analyzer is great at finding an antennas resonance.

 

[Don_Burke]

How was the number 73 + j 42.5 Ω calculated?

E/I =Z

Is this something I can measure with a DMM?

You would need something to measure the magnitude and phase of the voltage and of the current.

What I really don't understand is how they didn't specify the length of the wire...isn't that what defines the resistive component?

They did specify. One half wave physical wavelength.

And also why the frequency, inductance, and capacitance was not specified, as those define the reactive component.

That also was specified indirectly. j 42.5 Ω is the reactance, which is due to the inductance of a long antenna.

Also, what is the last sentence talking about when it says "electrically long"?

Just that. The antenna is too long electrically. That is why velocity factor is included in real-world antenna length calculations.

I know for resonance, the circuit is purely resistive and there is no reactance.

This antenna is not resonant.

But how do you know that the dipole is electrically long without specifying the length of the dipole and frequency it's supposed to be used at?

The length of the dipole was specified as one half physical wavelength. Frequency is not an issue for this discussion.

 

[N_Jay]

How was the number 73 + j 42.5 Ω calculated? Is this something I can measure with a DMM?

What I really don't understand is how they didn't specify the length of the wire...isn't that what defines the resistive component? And also why the frequency, inductance, and capacitance was not specified, as those define the reactive component.

Also, what is the last sentence talking about when it says "electrically long"? I know for resonance, the circuit is purely resistive and there is no reactance. But how do you know that the dipole is electrically long without specifying the length of the dipole and frequency it's supposed to be used at?

I don't understand how you got that far into the book without realizing you did not understand what you were reading.

Dons answers are correct, but at the same time probably no better understood than the original question.

You need to go back and read a more basic text to get the fundamentals.

 

[wannabescannist]

What I'm saying is this, and correct if and where wrong:
Impedance = Resistance +/- j * Reactance

Resistance is the real part while Reactance is the imaginary part. Resistance comes
from the resistivity of the wire multiplied by the length of the wire.
The paragraph is saying that this resistance is 73 Ohms. I forgot that half-wavelength
implies the length of the wire. But it seems like it's saying that resistivity and
wavelength (wire-length) are proportional and that they always multiply to 73.

For example, the antenna length for half-wave dipole on the 10 Meter band would be
10M/2 = 5 Meters. In order for the resistance for the full antenna to be 73 Ohms,
the resistivity of the wire would have to be 4.87 Ohm/Meter.

Compare that to a half-wave dipole for the 70cm band, whose length would be .7M/2 = 0.35 Meters.
For the resistance to be 73 Ohms the resistivity would have to be 208 Ohm/Meter.

I guess I just want to know what numbers were used to come up with 73 + 42.5j.

PS: N_Jay, this is only Chapter 2, the one after "Safety"...

 

[N_Jay]

What I'm saying is this, and correct if and where wrong:
Impedance = Resistance +/- j * Reactance..

So far so good.

Resistance is the real part while Reactance is the imaginary part...

Mathematically, yes, but reactance is as real as resistance.

Resistance comes from the resistivity of the wire multiplied by the length of the wire....

NO!
Radiation resistance does not come from the resistance of the wire. For most cases you can assume the wire has ZERO resistance.

I forgot that half-wavelength implies the length of the wire. ..

Your forgetting that half-wavelength implies the length, is like a boater saying he forgot that water is wet. It is an indication that you have not digested and understood what you think you have learned. (Sorry, not an insult, just the truth):wink:

But it seems like it's saying that resistivity and
wavelength (wire-length) are proportional and that they always multiply to 73..

No, but with your fundamental misunderstanding of the underlying science, I am not sure how to answer this one.

For example, the antenna length for half-wave dipole on the 10 Meter band would be 10M/2 = 5 Meters. In order for the resistance for the full antenna to be 73 Ohms, the resistivity of the wire would have to be 4.87 Ohm/Meter.

This is an example of how a fundamental misunderstanding makes almost all further discussion difficult, (and probably worthless).

Compare that to a half-wave dipole for the 70cm band, whose length would be .7M/2 = 0.35 Meters. For the resistance to be 73 Ohms the resistivity would have to be 208 Ohm/Meter.

And we continue.:wink:

I guess I just want to know what numbers were used to come up with 73 + 42.5j.

I think this is an empirically derived quantity, but I am sure you can get there with a smith chart and the velocity factor of a conductor in air.

PS: N_Jay, this is only Chapter 2, the one after "Safety"...

Because you understand the Safety chapter, does not imply you are ready for the rest of the text! :lol:

 

[Don_Burke]

What I'm saying is this, and correct if and where wrong:
Impedance = Resistance +/- j * Reactance

Resistance is the real part while Reactance is the imaginary part. Resistance comes
from the resistivity of the wire multiplied by the length of the wire.
The paragraph is saying that this resistance is 73 Ohms. I forgot that half-wavelength
implies the length of the wire. But it seems like it's saying that resistivity and
wavelength (wire-length) are proportional and that they always multiply to 73.

That is where you are off track. The 73 ohms of resistance accounts for the energy radiated into space. It has nothing to do with the loss due to heating of the element.

In fact, it is called "radiation resistance" and is an important figure when trying to reduce losses.

 

[wannabescannist]

Radiation resistance does not come from the resistance of the wire. For most cases you can assume the wire has ZERO resistance.

Oh....that resistance...guess I missed that implication. Is it safe to say we are always talking about radiation resistance when dealing with antennas? Guess I'll re-read this chapter assuming radiation resistance whenever I see the word resistance by itself.

Your forgetting that half-wavelength implies the length, is like a boater saying he forgot that water is wet. It is an indication that you have not digested and understood what you think you have learned. (Sorry, not an insult, just the truth):wink:

Seriously, I just wasn't thinking...it was 1 in the morning

But no insult taken...I know what you're getting at; why elaborate with correct answers on an incorrect assumption.

I think this is an empirically derived quantity, but I am sure you can get there with a smith chart and the velocity factor of a conductor in air.

Don Burke had mentioned the term velocity factor, but I felt that was opening another can of worms by asking what was meant by that. So I guess this 73 + 42.5j is just like saying the speed of light is 300 M/s....just something you have to accept. But if a half-wave dipole exhibits a 73 + 42.5j impedance in free-space (which is not resonant as Reactance is present and non-canceling), does that mean with the presence of ground, the 42.5j figure will cease and the antenna is now the right size, "electrically"? In other words, what must change in the original paragraph to make the Reactance approach 0?

Because you understand the Safety chapter, does not imply you are ready for the rest of the text! :lol:

But there's nothing in-between....

 

[N_Jay]

Oh....that resistance...guess I missed that implication. Is it safe to say we are always talking about radiation resistance when dealing with antennas? Guess I'll re-read this chapter assuming radiation resistance whenever I see the word resistance by itself.

That would be an oversimplification. It might work for a while, but be careful.

Don Burke had mentioned the term velocity factor, but I felt that was opening another can of worms by asking what was meant by that.

Nope, not a can of worms, but an important concept that you need to grasp.
The speed of light is not constant! (sort of):twisted: :lol:

So I guess this 73 + 42.5j is just like saying the speed of light is 300 M/s....just something you have to accept.

Nope, in this case it is something you measure or calculate.

But if a half-wave dipole exhibits a 73 + 42.5j impedance in free-space (which is not resonant as Reactance is present and non-canceling), does that mean with the presence of ground, the 42.5j figure will cease and the antenna is now the right size, "electrically"?

Nope

In other words, what must change in the original paragraph to make the Reactance approach 0?

The length of the antenna elements.

But there's nothing in-between....

Yes,

More basic texts.

 

[wannabescannist]

In other words, what must change in the original paragraph to make the Reactance approach 0?

The length of the antenna elements.

Why would you change the length...it's a half-wave dipole?

Or, are you saying an exactly half wavelength antenna is not resonant at the intended frequency and you always have to make adjustments?

Edit:
I found a formula that defines radiation resistance as:
R = 80*pi^2*(L/W)^2
where L=length of antenna, and W = wavelength

Using this formula, in order to get 73 Ohm calculation, L/W must be 0.304, or approximately 3/10 wavelength. Is this correct?

 

[N_Jay]

Why would you change the length...it's a half-wave dipole?

Or, are you saying an exactly half wavelength antenna is not resonant at the intended frequency and you always have to make adjustments?

Edit:
I found a formula that defines radiation resistance as:
R = 80*pi^2*(L/W)^2
where L=length of antenna, and W = wavelength

Using this formula, in order to get 73 Ohm calculation, L/W must be 0.304, or approximately 3/10 wavelength. Is this correct?

Woooo Hoooo, he is catching on!

 

[Don_Burke]

Why would you change the length...it's a half-wave dipole?

Or, are you saying an exactly half wavelength antenna is not resonant at the intended frequency and you always have to make adjustments?

The velocity factor of the conductor used to form the element must be accounted for.

That is why the formula for a halfwave (in feet) is 492/F while the formula for a halfwave antenna is 468/F (assuming a thin conductor). As the conductor is made thicker, the element will need to be even shorter.

 

[N_Jay]

The velocity factor of the conductor used to form the element must be accounted for.

That is why the formula for a halfwave (in feet) is 492/F while the formula for a halfwave antenna is 468/F (assuming a thin conductor). As the conductor is made thicker, the element will need to be even shorter.

Until the "wire" gets so short (and therefore so wide) that it looks like a disc, very much like what is on top of a disc-cone antenna.

This **** ain't magic, it's science!

 

[wannabescannist]

The velocity factor of the conductor used to form the element must be accounted for.

That is why the formula for a halfwave (in feet) is 492/F while the formula for a halfwave antenna is 468/F (assuming a thin conductor). As the conductor is made thicker, the element will need to be even shorter.

OK, it's starting to make sense now.

Based on the physical length of a half-wave dipole - at resonance - 468/F in feet would be 468*.304/F in Meters, or around 142.3/F.

142.3 is approximately 94.8% of 150 (half of 300)....so this says a resonant half-wave dipole is about 5.2% less than what it theoretically would be if the wire was exactly half-wavelength. This is verified in the Antenna Book:

However, at frequencies up to 30 MHz (the frequency range over which wire antennas are most commonly used), experience shows that the length of a practical λ/2 antenna, including the effect of diameter and end effect, is on the order of 5% less than the length of a half wave in space.

So, what about the formula that I posted above that said the antenna to wavelength factor should be about 3/10, or 0.3, in order to get a radiation resistance of 73 Ohms?

5% less of a half-wave dipole using the 468/F formula would yield a 5/10 * 0.95 or about a 0.475 factor. Where is the other 0.175?

Or, is the formula really:
R=80*pi^2*(L/W)^2 * some_factor,
where some_factor is used to account for end effect, diameter, and "something else". Solving for some_factor with R equal to 73, and L/W equal to 0.5 yields:
73 / 80 / pi^2 / 0.25 = 0.36 = some_factor

Or, do I factor in end effect & diameter into the L/W ratio (4.75/10 ), which would bring some_factor to around 0.41?

OR, is the formula not correct period?

Thanks for all the help thus far.

 

[Don_Burke]

So, what about the formula that I posted above that said the antenna to wavelength factor should be about 3/10, or 0.3, in order to get a radiation resistance of 73 Ohms?

I will have to crack some books on that one. Calculating a radiation resistance manually is not something I do on a regular basis.

 

[wannabescannist]

Don't worry about it Don, I think I'm set.

I just hate seeing something that tells you, "just use this" without an explanation or numerical backing.

 

[gcgrotz]

Radiation resistance is NOT the same as the characteristic impedance of an an antenna. 73 ohms applies to the approximate impedance at the center of a dipole radiating in free space.

I think a good antenna theory text would be a better place than here to get educated on why an impedance is what it is. Some things are better if you just accept the facts and don't worry about why.

 

[wannabescannist]

Radiation resistance is NOT the same as the characteristic impedance of an an antenna. 73 ohms applies to the approximate impedance at the center of a dipole radiating in free space.

Doesn't radiation resistance comprise the real portion of the feedpoint impedance? Radiation resistance = feedpoint impedance (only at resonance), correct?

I think a good antenna theory text would be a better place than here to get educated on why an impedance is what it is. Some things are better if you just accept the facts and don't worry about why.

I'm quoting from the ARRL Antenna Handbook, 19th edition. Are you saying more basic than that? And your second sentence, for some reason, that's hard for me...I tend to want know this stuff starting from the electron....

 

[wannabescannist]

I like to go over things I once didn't get. I think what I misunderstood the most was the definition of "electrically long". Rereading the quoted paragraph, the point it was trying make was overlooked (the fact that a resonant half-wave dipole is actually physically shorter than the calculated 1/2 wavelength at that particular frequency). Everything seems so obvious now...almost common sense. I also have to stop thinking of resistance as something you measure with an ohmmeter.

Thanks for the help you guys.

 

[N_Jay]

I like to go over things I once didn't get. I think what I misunderstood the most was the definition of "electrically long". Rereading the quoted paragraph, the point it was trying make was overlooked (the fact that a resonant half-wave dipole is actually physically shorter than the calculated 1/2 wavelength at that particular frequency). Everything seems so obvious now...almost common sense. I also have to stop thinking of resistance as something you measure with an ohmmeter.

Thanks for the help you guys.

You are catching on.

When stuff starts feeling like common sense you are 1/2 way there.

When you can take that commonsense feeling and apply what you know to a seemingly unrelated subject you have arrived.