# Resistance of an antenna

1. Jan 5, 2012

### geoduck

Is the impedance of an antenna infinite (since an antenna is an open circuit, with the ends bent opposite to each other), or finite (radiation resistance instead of an open circuit)?

The reasoning seems to be that an antenna is a transmission line terminated in an open circuit, so you get standing-wave currents (with a node at the ends). You can integrate the standing-wave currents in the formula for the electric field to get the total power-radiated, and from the total power-radiated you get the radiation resistance by dividing by the current squared.

But how should you view this radiation resistance in relation to the open circuit resistance of infinity? The only thing that makes sense is in parallel (if it's series, then infinite+finite=infinite), but then the transmission line effectively gets terminated by a resistance equal to the radiation resistance, so there is no longer a current node at the end so your assumption was wrong.

It seems that for impedance matching, people pretend that the load is the radiation resistance of the antenna rather than an open-circuit. But isn't reflection of the current-wave essential to the operation of an antenna to get standing waves in the antenna? - hence you can't have it so that no reflection occurs: there has to be an impedance mismatch.

2. Jan 5, 2012

### vk6kro

Assuming you mean a half wave dipole antenna with negligible losses due to wire resistance, then this is not a transmission line.

Most of the power entering a dipole is radiated and the impedance of a dipole at the feedpoint in free space is about 73 ohms.

3. Jan 5, 2012

### yungman

I am just studying antenna also, I don't have the radiation resistance formula right off my head. No it is not anything parallel like what you stated.

I suggest you to buy a used "Antenna Theory" by Balanis. It is a very good book and it is not that expensive used. I buy 100% uesd book and 99% come in like new for half price. Don't be cheap.

4. Jan 5, 2012

### Averagesupernova

The feedpoint of an antenna does NOT appear to be an open circuit at the design frequency. If it were we could not deliver power into it.
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I wonder why you assume there is a completely open circuit involved at all? True, an antenna can appear as an open circuit to DC, and other designs can appear as a short circuit to DC. I guess anyone can tack on an open circuit to any device and imagine it is there.
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I don't understand why you think that since an antenna has a radiation resistance that this somehow forces an antenna to not have current nodes at the ends.
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An antenna has a feedpoint impedance based on where and how the transmission line is attached to it so this guarantees us that the voltage and current vary along the length.
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One way to think of it is this: Imagine you have a transformer with a 2:1 windings and the secondary is terminated into 50 ohms. However, the primary is special and has a moveable tap. So the source is connected to one end of the primary and the moveable tap with the remaining end is left open. Think of the secondary winding and its load as the medium which an antenna appears to be dumping power into. The moveable tap is the method which the feedline is connected to the antenna. If we have a source driving this transformer with a 50 ohms Zout the tap would be attached to the midpoint of the primary to give the best match. Pretty straight forward, I doubt I need to explain it. If we want to drive it with a different source with a lower or higher Zout we simply move the tap.
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I hope I've helped in some way.

5. Jan 5, 2012

### geoduck

By infinite resistance, I meant at the load end, not at the feedpoint. I've seen two videos that explain antennas as just bent transmission lines. For example here is one of them:

Is the feedpoint impedance the same as the radiation resistance?

Last edited by a moderator: Sep 25, 2014
6. Jan 5, 2012

### geoduck

I think my question is unclear still. In transmission line theory, a line terminated by an infinite resistance (an open-circuit) has a reflection coefficient equal to 1. This reflection coefficient of 1 is what creates standing waves of current.

If you view an antenna as a transmission line that is bent, then is it still a transmission line that is terminated by infinite resistance? Or is it a transmission line terminated by the radiation resistance? Or is it not a transmission line at all?

7. Jan 5, 2012

### vk6kro

Because the antenna radiates power, it is not the same as a transmission line.

In a transmission line, the power reflects from a mismatch at the end and all returns to the sending end. This is an almost lossless process if you ignore the slight radiation from the transmission line and the hopefully slight losses due to wire resistance and dielectric heating of the transmission line insulation.

It does affect the impedance as seen at the sending end of the transmission line.

In an antenna, power vanishes from the system as it is radiated and this corresponds to a resistance at the feedpoint where the power enters the dipole.

8. Jan 5, 2012

### Antiphon

It's usually not a transmission line. Some antennas radiate from certain places, others from the whole structure.

Your difficulty stems from the fact that you are not visualizing the currents and fields in space.

The radiation resistance isn't at the ends. It's a circuit summation of a whole-space field configuration. And it would change when you bent the leads, as would the radiation pattern etc.

9. Jan 5, 2012

### geoduck

Thanks. Quick question: is the feedpoint resistance the same as the radiation resistance? A center-fed half-wavelength dipole has zero impedance at the feedpoint, while a center-fed half-wavelength dipole has infinite impedance at the feedpoint.

Does this mean that if you drive a current j through the antenna, that the power delivered would be j^2*R, which is zero in one case and infinity in the other case?

10. Jan 5, 2012

### vk6kro

A center-fed half-wavelength dipole has zero impedance at the feedpoint, while a center-fed half-wavelength dipole has infinite impedance at the feedpoint.

I don't understand this statement. It seems to say the same antenna has infinite and zero feedpoint impedance.
We have made the point, I think, that neither of these statements is true.

The feedpoint impedance of a resonant half wave dipole fed at the centre is about 73 ohms. In this case, and assuming no losses, then the feedpoint impedance would be the same as the radiation resistance.

This is like a normal resistance except that it varies with frequency, so you can use the normal formulas based on Ohm's Law.

11. Jan 5, 2012

### yungman

Don't look at antenna as tx line!!! You should get the book, it explain very clear, I am just too sick today to go read over my notes!!!

12. Jan 5, 2012

### geoduck

You're right. I actually misspoke and meant that a full-wave dipole fed at the center has infinite feedpoint impedance, which is the reason that you can't connect it at the center. But if the radiation resistance is equal to the feedpoint resistance for this case, then that would seem to imply that the radiation resistance for a center-fed full-wave dipole is infinite, or any current through such an antenna would radiate infinite power.

Thanks, I ordered the book from the library!

13. Jan 5, 2012

### Antiphon

No antenna has infinite feed point impedance.

14. Jan 5, 2012

### vk6kro

You're right. I actually misspoke and meant that a full-wave dipole fed at the center has infinite feedpoint impedance, which is the reason that you can't connect it at the center. But if the radiation resistance is equal to the feedpoint resistance for this case, then that would seem to imply that the radiation resistance for a center-fed full-wave dipole is infinite, or any current through such an antenna would radiate infinite power.

The feedpoint impedance of a full wave antenna fed in the middle is high, but not infinite.

You certainly can feed it there, though. It is just high impedance, so the drive has to be high voltage and it will supply a small current to the high impedance feed point.