A correspondent wrote about the apparent conflict between Exploiting your antenna analyser #11 and Alan, K0BG’s discussion of The SWR vs. Resonance Myth. Essentially the correspondent was concerned that Alan’s VSWR curve was difficult to understand.

## K0BG’s pitch

For convenience, here is the relevant explanation.

By definition, an antenna’s resonant point will be when the reactive component (j) is equal to zero (X=Ø, or +jØ). At that point in our example shown at left, the R value reads 23 ohms, and the SWR readout will be 2.1:1 (actually 2.17:1). If we raise the analyzer’s frequency slightly, the reactive component will increase (inductively) along with an increase in the resistive component, hence the VSWR will decrease, perhaps to 1.4:1. In this case, the MFJ-259B is connected to an

unmatched, screwdriver antenna mounted on the left quarter panel, and measured through a 12 inch long piece of coax. This fact is shown graphically in the image at right (below).

Note that the graph is unscaled, and that frustrates interpretation. The text is also not very clear, a further frustration. It is easy to draw a graph… but is the graph inspired by a proposition or is it supporting evidence.

### My interpretation

The text hints that Z is measured at the antenna input at some frequency where R=23, X=0, and the indicated VSWR is 2.1. Alan correctly notes VSWR_{50} for a load of 23+j0Ω is 2.17, so there appears to be some small error in the instrument’s display of one or more of the quantities.

He goes on to state that increasing frequency a little the reactive component will increase (inductively) along with an increase in the resistive component.

This behaviour is most unlike the feed point impedance of a heavily loaded mobile whip (as indicted by the value of R at resonance). Loaded short monopoles near resonance typically show a value of R (at the feed point) that changes only very slowly as frequency increases and X that changes relatively quickly with frequency from negative below resonance to positive above resonance.

Above is the measured feed point impedance of a MobileOne M40-1 helically loaded 1.5m monopole in the roof of a vehicle. (Forget the blue curve, Rigexpert’s Antscope software does not allow it to be turned off… it is their concession to the ham market that wants to think of impedance as a scalar quantity.)

Concentrate on the red R curve and green X curve:

- R is almost constant, but it does increase by a very small amount (perhaps 1Ω) from left to right;
- X increases from around -40Ω to +40Ω from left to right, a change of perhaps 80 times that of R.

The consequence of the fact that R is changing, albeit VERY slowly about resonance is that resonance (ie X=0) does NOT coincide EXACTLY with minimum VSWR.

Above is the VSWR curve, and VSWR is reported as 2.39 at resonance (X=0), and in fact minimum VSWR occurs 1kHz higher, it is 2.38. This is based on field measurement of a real antenna, and although minimum VSWR does not occur exactly at resonance, it is so close to it with this type of antenna that you are unlikely to notice the difference in the field. (Apologies that the cursor is not visible in the graph above, one of the many defects of Rigexpert’s Antscope is that it does not show the cursor when it coincides with a grid line, 7.065MHz in this case.)

Resonance of the antenna is in this example indicated by X approximately equal to zero, and is at 7.065MHz, not one kHz higher or lower.

Alan’s point about measurement through 12″ (0.3m) of coax is not very clear.

Some simple facts of measuring through 0.3m of RG58A/U coax in the M40-1 example:

- the plot of R and X will be different because the effect of standing waves on the line; and
- the plot of VSWR will be different, but by so little that you are unlikely to notice it in this type of scenario.

Above is the VSWR curve as would be observed looking into 0.3m of RG58A/U coax. If you look really hard, you will see that it is different, and most notably is that Zin at 7.065MHz (the resonant frequency measured earlier of the antenna) is 21.2+j2.9Ω. In fact, X=0 looking into that coax occurs at approximately 7.061MHz.

Alan advises Because of this issue, the SWR readout of any antenna analyzer should be ignored while attempting to match a mobile antenna!

This example with real measurements of a real antenna demonstrates quite the opposite. Looking into the coax, the best indication of resonance of the antenna is minimum VSWR looking into the coax. Indeed it is an error to tune the antenna for X=0 at an arbitrary remote point.

Don’t take my word for it, get your antenna analyser out and conduct a careful experiment. Get familiar with the equipment you use. Make some similar measurements. Be careful that the measurements are valid, particularly that you do not disturb the thing you are measuring… that can give very confusing results (Exploiting your antenna analyser #9).

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.