Buck wrote:


Maybe I used the wrong word, 'resonance', but I was referring to the
lowest SWR match, which I would assume for the example to be less than
1.5:1 on a given frequency.


Lowest SWR is not the same thing as resonance.

This is one of those cases where the Smith chart is a good visual aid
[1]. Here's a three-step guide:

1. The Smith chart is just another kind of "map projection". Instead of
plotting latitude and longitude, we are plotting the resistive and
reactive parts of complex impedances.

Geographical map projections are chosen to make certain features easy to
see correctly, eg distance, direction, or area. The peculiar shape of
the Smith chart is also designed to make certain things easy... once
you've learned how to read the map.

2. All purely resistive impedances are on the "meridian line", the
symmetry axis passing through the center of the chart. The resistance
scale is nonlinear so that resistances from almost zero to almost
infinity can be plotted. Impedances that lie anywhere off that meridian
line have a reactive component. Anywhere inside one half-circle is
inductive; anywhere in the opposite half-circle is capacitive.

3. At the center of the chart is your chosen system reference impedance
(usually 50 ohms resistive). When you plot an impedance anywhere on the
chart, the distance from the center point indicates its SWR, and the
direction indicates the phase angle [2]. This gives the Smith chart one
of its special features: you can draw circles of constant SWR.

It would obviously have been much easier to say that with the help of a
drawing [3] but hose three points are all you need to know in order to
use the Smith chart as a visual aid.

In particular, it is enough to *show* you the difference between
resonance and lowest SWR.

When you plot the R-X impedance of your antenna against frequency across
an amateur band, it traces a short arc on the Smith chart. If the
antenna is supposed to give "a good 50-ohm match", the whole arc has to
stay close to the center of the chart.

The frequency of minimum SWR is where the impedance arc passes closest
to the exact center of the chart. The resonant frequency is where the
arc crosses the meridian line (zero reactance). Those two frequencies
are generally not the same.



[1] Reg will disagree; but Reg also has the kind of mind that can lift
the same information straight out of the transmission-line equations.
The Smith chart is for "the rest of us" who need to think in more visual
terms. Fortunately those two different viewpoints are converging: we can
now have computer programs that solve the equations exactly in the
background, and plot them on the screen as a visual aid.

[2] Strictly speaking, radius is directly proportional to the magnitude
of the reflection coefficient. One complete turn around the chart
represents 180deg of phase angle, for the same reason that impedance
along a (lossless) transmission line repeat themselves every HALF
wavelength.

[3] The ARRL Antenna Handbook (current 20th edn) has a good chapter
about understanding and using the Smith chart... with real drawings.



--
73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek