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## Antenna impedance of a dipole

Mar 18th 2022, 18:54

#### dnult

Joined: Mar 4th 2022, 20:56
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This is an antenna theory question.

I’ve been reading at old Antenna Handbook (ARRL circa 1979) and made it through the first few chapters. I decided to buy the latest 24th edition (which has many new updates) before burning more brain cells refreshing my knowledge.

Today, something struck me that I’m hoping someone can help me wrap my head around regarding the dipole’s feed-point impedance.
In a textbook perfect ½ wave dipole that is at resonance, the load should be close to a pure 50 ohm resistance. The illustrations of current and voltage on the antenna wire made me suddenly realize something that has me stumped.

Dipole current is a maximum at the center (feed point) and near zero at the ends of the wire - the resistance on the ends is infinite and the current has nowhere to go. And, it makes sense the voltage is a maximum at the end (ohms law), so naturally the potential difference at the feed point is near zero.

The thing is, that diagram shows voltage and current are 90* out of phase on the antenna (at a point in time). If I look at the dipole current and voltage illustration, it seems current is leading the voltage (capacitive reactance). If this is true, how is it possible to have a capacitive reactance present a 50,0 load?

I have a few thoughts on this, but hoping an Elmer can help me see what I’m missing.
Mar 18th 2022, 19:09

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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Antennas by John Kraus. There are free downloads of the early editions of this textbook. There is a derivation of the impedance of a half wave dipole using calculus.
Mar 18th 2022, 21:21

#### dnult

Joined: Mar 4th 2022, 20:56
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I'll look into. that. Thanks for the tip
Apr 8th 2022, 07:55

#### dnult

Joined: Mar 4th 2022, 20:56
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I got the document and read through the derivations of feedpoint impedance. It seems those equations exclude the phase so it doesn't really answer the question. If the current and voltage in a fipole antenna are 90⁰ out of phase, how can you achieve a 50 (rather 73) ohm resistive load?
Apr 11th 2022, 08:38

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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Typically you can't, unless you do something like introducing a nearby ground to reduce the impedance.

Interestingly enough, the equations for a fat dipole are seemingly impossible to solve with current math techniques. Though it may be because it hasn't attracted as much attention as Fermat's theorem.
Apr 11th 2022, 14:47

#### dnult

Joined: Mar 4th 2022, 20:56
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I have a feeling there is a "simple" answer, although it may be hard to derive mathematically. Even in an LC circuit, the phase relationships between voltage and current are different in the capacitor and inductor. I suspect there is a similar action happening in the antenna. When we look at feed point voltage and current phase strictly from the theory of the antenna, something else is missing that defines the final load impedance. Perhaps it's the impedances interacting between halves of the antenna or the air itself. I wish JK was still alive to shed light on this.