What is the radiation impedance for a quarter-wave antenna?

[eecook]

Hi all,

I've been struggling with this for a while. I'm working on a design, and i cannot do an impedance matching network if I dont get this straight. I started looking it up on google, and I wasn't satisfied with any information I found. So I downloaded "Antenna Theory, Design and Analysis" by Balanis and, "Practical Antenna Handbook" by Carr. There seems to be a significant mismatch in the information.
I am trying to get the radiation impedance for a quarter-wave monopole antenna, it says...

...Balanis (p. 155)

It gives a formula where I get:

Z = 49.35 - j 12.73


...Carr (p. 183)

"...the feedpoint radiation resistance is a maximum of 37 ?, with only a very small reactance component." (for the quarter-wave)

He points it out once again in p. 184 showing a plot of Resistance/Reactance vs. antenna length.


Note:
I lack the knowledge to derive this from first principles and the experience working with RF. Good reference material suggestions are welcomed!


Cheers!


Simon.

[Paul Price]

As you have already presented in your post. Approx 35-37 ohms at the resonant freq.  This figure can be raised to 50  ohms by using the antenna not cut not exactly at resonance(longer) or with 45-deg. downward pointing radials at the base.
 The closer a 1/4 wave antenna is to earth surface ground, the sloppier the exact impedance and match to the transmitter. This is one reason why a 1/4 wave antenna is called a sky-stick, it works best when elevated and surrounded by a ground plane or multiple radials at the base. if these radials are pointing downward at a 45 degrees angle, the effect will be to raise the antenna feed impedance to 50 ohms.

[eecook]

Thank you very much Paul. Is there any book you recommend?

[Paul Price]

The Radio Amateurs Handbook.


Tons of stuff posted on the web by electrical engineering professors, RF engineers, ham radio operators etc.  Some of it is actually useful.

[G0HZU]

Above a perfect ground plane it should (in theory) be half the impedance of a half wave dipole.

Therefore, the impedance of the quarter wave monopole should be about (36.5 + j21) ohms. If you trim the aerial for resonance I think it will then measure about (32 +j0) ohms.

But this is in theory, and over a perfect ground. In reality you will see something a bit different due to imperfect ground etc.

[Fank1]

FYI:
Radiation impedance is not the same thing as feed point impedance.

[G0HZU]

I'm assuming that eecook really just wants to design an impedance matching network so he really just wants to know the feedpoint impedance and work back from there...

[eecook]

Thank you all,

Ok so I'm guessing the feed-point impedance is Zfeed=Zx+Zr, where Zr is the radiation impedance and Zx is, what exactly?

This is for a quarter-wave antenna, a piece of wire prependicular to the pcb, using the pcb's ground plane. The ground plane has some cut outs and drill holes, how is that going to affect the feed-point and radiation impedance?

cheers,

Simon.

NOTE: this is for a wifi application at 2.4GHz

[jlmoon]

what ever happen to the term "Open Air or Free Air Impedance"  around 317 ohms in open air? 

[eecook]

what ever happen to the term "Open Air or Free Air Impedance"  around 317 ohms in open air?

It is a different concept, Radiation Impedance relates the Voltage and Current at the feed-point (assuming no loss), Free Air Impedance relates the E and H  far fields.