Re: NEC-LIST: Q of small antennas.

Okay Steve, to make it plain to an unsubtle person like me,
I will make your tuned reactance explicit by considering the
two possible cases.

1. At the operating frequency w0, X(w0)>0. Then the tuning
element is a capacitor and

Xs=-w0 X(w0)/w.

Then dXs/dw=w0 X(w0)/(w^2),

which, at w=w0, is X(w0)/w0.

2. X(w0)<0, the tunig element is an inductor, and
Xs=wX(s0)/w0. Then

dXs/dw=X(w0)/w0.

The value of Q which takes into account only the antenna's
impedance values is a relative measure of how difficult it
will be for a designer to incorporate the antenna into a
system. Jack's point about the actual in-use bandwidth
being a function of the connected devices is important.

Regards,
Doug

"Best Steven R Civ AFRL/SNHA" writes:

Hi Doug.

The |X|/w term is in both expressions and comes from the
fact that prior to determining the antenna Q, the antenna
must be tuned at each frequency with a lossless series
reactance, Xs.

The proper definition for Q is for the tuned antenna using
the tuned impedance:

Ztuned = R + jX + jXs

where Xs = -X and Ztuned = R

It is the derivative of Ztuned that is used to determine Q
so the |X| term is included to account for the tuning
reactance. It is for the same reason that the expression
you posted has the |X| term.

Steve

-----Original Message-----
From: D. B. Miron
To: nec-list_at_gweep.ca
Sent: 12/11/2003 9:24 PM
Subject: Re: NEC-LIST: Q of small antennas.

Hello Steven,

Now that you mention it, I have seen data sets for antennas
at anti-resonance which display the negative reactance
slope. I expect Geyi's assumptions don't fit this case.
But where does the |X|/w term in your expression come from?

Z=R+jX, dZ/dw=dR/dw+jdX/dw, so

|dZ/dw|=sqrt[(dR/dw)^2+(dX/dw)^2]

No?

Regards,
Doug

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