Re: NEC-LIST: Q of small antennas.

>Good day,
>
>Several times over the last few years, antenna Q has been a
>hot topic on NEC-LIST. Recently, in an effort to be less
>behind on my reading, I found several articles on the
>subject in this year's IEEE Trans. A&P, and went back to a
>referenced paper from 2000, all listed below. [1] and [3]
>give different methods of calculating Q from the numerical
>solution of the antenna's current and radiation. [1] argues
>that the traditional expressions for minimum Q give values
>that are too small, and discusses some factors that affect Q
>for small antennas. [2] and [4] are re-examina;tions of
>minimum Q and maximum gain/Q. For NEC users, [4] gives a
>circuit-based expression for Q that I like (eq. (55))
>
>Q=0.5[w dX/dw + |X|)/R, w=2 pi frequency.
>
>I've left off the sub and super scripts. Be wary of typos
>in [2-4]. I think, but I'm not certain, they are all
>obvious.
>
>Doug Miron
>
>[1] Thiele, Detweiler, and Penno, "On the Lower Bound of the
>Radiation Q for Electrically Small Antennas", IEEE Trans.
>A&P, vol. 54, no. 6, pp1263-1269, June, 2003.
>[2] W. Geyi, "Physical Limitations of Antennas", IEEE Trans.
>A&P, vol. 54, no. 8, pp2116-2123, August, 2003.
>[3] W. Geyi, "A Method for the Evaluation of Small Antenna
>Q", IEEE Trans. A&P, vol. 54, no. 8, pp2124-2129, August,
>2003.
>[4] Geyi, Jarmuszewski, and Qi, "The Foster Reactance
>Theorem for Antennas and Radiation Q", IEEE Trans. A&P, vol.
>48, no. 3, pp401-408, March, 2000.
>
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One has to be careful comparing measured Q-factor with calculated
Q-factor in the case of narrow band antennas.

NEC calculates the antenna system's unloaded Q-factor. When you
measure Q-factor by measuring SWR using a tuned RF power amplifier,
or using a SWR Bridge (which is referenced to a real 50 ohm
resistance), you are measuring the loaded Q-factor. The effective
bandwidth of a narrow band antenna is increased by a factor of 1.5-2
times the unloaded Q-factor bandwidth (typically closer to a factor
of 1.5 than to 2) --- 1.6 determined for electrically small compact
loops.

In the case of an RF power amplifier the effective output impedance
is 50-ohms, if the amplifier is tuned to deliver maximum available
design power to a 50 ohm load. .The output impedance of the tuned RF
power amplifier is a dissipationless impedance. The bandwidth of
narrow band antennas is increased, but since the output impedance is
dissipationless, the 50-ohm output impedance of the tuned RF power
amplifier does not represent a power loss. If it did when matched we
would have an efficiency of 50-percent. It is well known that the
efficiency of class B and C power amplifiers is considerably greater
than 50-ohms.

John S. (Jack) Belrose, VE2CV

-- 
_____________________________________________
John S. (Jack) Belrose, PhD Cantab, VE2CV
LIFE SENIOR MEMBER of the IEEE
Fellow Radio Club of America
Atyhlobne Fellow
Radioscientist Emeritus Researcher
Communications Research Centre Canada
PO Box 11490 Stn. H
OTTAWA   ON   K2H 8S2
CANADA
TEL  613-998-2779
FAX  613-998-4077
e-mail  <john.belrose_at_crc.ca>
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