Re: NEC-LIST: Extracting Q factor for an Antenna

> Help, Does anyone know of a way of extracting Q factor for an
> antenna from NEC 2?
>
> Alan Johnson

Alan,

Think of an antenna as an La-Ca-Ra circuit.

It follows then that there are two ways to deduce an effective
Q-factor, depending on the antenna type --- antenna system is
electricall small or larger.

If the antenna impedance is highly inductive, j Xa>>Ra such as for a
small loop; or highly capacitive, -j Xa>>Ra such as for an
electrically small monopole, then

Q = Xa/Ra*.

For the more general antenna, determine the antenna system bandwidth
(BW), the frequency difference for the frequencies for which (plus or
minus) Xa = Ra. That is the impedance phase angle is plus and minus
45-degrees.

Following Terman, and considering the antenna near to its resonant
frequency to behave like an La-Ca-Ra circuit, where these parameters
are approximately independent of frequency over the antenna bandwidth,
then the bandwidth

 BW (theta + or - 45-degrees) = f/Q.

An alternative, frequently used by radio engineers, is to determine
the BW for VSWR < 2:1.

A final comment: why do want Qa, to determine bandwidth?

For very narrow band antennas the operational (loaded) bandwidth is
about 1.5-1.7 times the unloaded antenna bandwidth (the bandwidth
computed by NEC). This is because when conjugately matched the source
impedance loads the tuned antenna system (we are considering narrow
band antenna systems). [1].

To compute this bandwidth using NEC we have to tune the antenna (put
the reactance required to tune as a load in the antenna model). For
small loops the tuning reactance is a capacitor (no additional loss
resistance). For VLF/LF antennas the tuning reactance is an inductor
which has a loss resistance, and so if we want to use the formula
above, Ra = Ras (where Ras is the antenna system resistance which
includes the inductor loss resistance Rc).

For proper operation of transmitters you want the SWR < 1.5 to 2:1.

Jack

* This formula is an approximation and valid only if the antenna is
small and its operating frequency f is low compared to the resoant
frequency fo of the antenna system. The general formula for large
VLF/LF antennas is

BW = Ra x f x [1 - (f/fo) squared] divided by Xa

Refewrence

[1] J.S. Belrose, W. Maxwell and C.T. Rauch, "Source Impedance of HF
Tuned Power Amplifiers and the Conjugate Match", Communications
Quarterly, Fall 1997 issue, pp. 25-40.

_____________________________________________
John S. (Jack) Belrose, PhD Cantab, VE2CV
Senior Radioscientist
Radio Sciences Branch
Communications Research Centre
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>
_____________________________________________
Received on Thu Mar 04 1999 - 20:13:18 EST