# ARRL

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## ARRL gain scaling definition?

Nov 30th 2014, 00:35

#### NV2K

Joined: May 20th 2014, 01:06
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I am (slowly) building an open-source tool to generate EPS, SVG, and other vector-format gain plots from NEC2 output. I would like to offer ARRL gain scaling, but am unable to locate a canonical definition.

I cannot locate a definition in either the ARRL Antenna Handbook or in the ARRL Operating Manual (2008 edition).

Anecdotal, non-canonical sources indicate that it is log dB. Clearly, this is not possible, as 0 dB often appears on plots using ARRL gain scaling, yet the logarithm of zero is undefined. Further, negative values on the decibel scale appear, yet the logarithm of a negative number is not unique (and is complex).

What is the canonical definition for this type of gain scaling? And is there a source I can cite?

TU es 73 de John/NV2K
Dec 1st 2014, 18:43

#### W1VT

Super Moderator

Joined: Apr 4th 1998, 00:00
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Jul 1980 - QST (Pg. 26)
New Look For QST's Antenna Patterns, The

Author: Hall, Jerry, K1TD
Article: QST Archive http://p1k.arrl.org/pubs_archive/73749
Dec 2nd 2014, 00:37

#### NV2K

Joined: May 20th 2014, 01:06
Total Topics: 0
Total Posts: 0
Thank you for the link to the Hall article, Zack. If I may call you Zack.

If I understand correctly, ARRL gain scaling does not use a logarithmic scaling at all, but is based on a 0.25305 power law, with -100 dB arbitrarily (and unnecessarily) placed at the origin.

(-log 0.89) ÷ 0.2 ≈ 0.2305

The results would be indistinguishable from those obtained by placing 0 gain (undefined on the decibel scale) at the center.

A logarithmic scaling (gain in dB) is replaced with a power law scaling of gain. I find this reminiscent of Stanley Smith Stevens's 1961 paper, "To honor Fechner and repeal his law," _Science_, Vol 133, 80-86. From the abstract: "Fechner's version of the psychophysical law made him famous. But a power function, not a log function, describes the operating characteristic of a sensory system."
Dec 4th 2014, 15:39

#### MATHIB

Joined: Dec 2nd 2014, 15:05
Total Topics: 0
Total Posts: 0
Hy,

To plot with a dB log scale you have to plot your radiation pattern in linear. Then, you have to change the Rho scale of the polar plot, or the Y scale, by defining the dB scale (by example [-40 -20 -10 (-6:1:0)]) that you convert in linear. Now you have to change the "Ticks" values (in linear) then, the "Ticks" label in dB.

I hope it's clear....

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