If we go back to the 40 meter linear-loaded vertical I recently looked at you will find that is truly single band. The following SWR scan covering 40 through 10 meters makes that fact clear.The antenna is mounted 2 meters above average ground.
A matching network at the feed point adds complexity, cost and (most emphatically) loss, but it can be done. However it isn't always exceptionally difficult. The present situation is an interesting case study in that regard. The reason is that the antenna is 13 meters tall, which is ~43 feet. Many hams have heard that a vertical of this height is easy to match on multiple bands with a simple network. It is also a subject of controversy for reasons that only some hams can see.
This linear-loaded antenna isn't quite a simple 43-footer since it has already been loaded to resonate on 40 meters. Even so it does show evidence of other resonances, resonances which are not especially evident from the above SWR chart. The actual R and X values do indicate some promise, though you'd have to plot them on a Smith chart to see that.
I "eyeballed" the values and decided to, metaphorically speaking, roll the dice. In EZNEC I connected a λ/2 length (calculated at 7.1 MHz) of open-wire transmission line. This is equivalent to making a full circle around the Smith chart, bringing the impedance right back to what it is at the feed point, though only on 40 meters (but is exact only for zero-loss line). At every other frequency there will be a net reactance that will transform the impedance.
After only a few minutes of fiddling with values in EZNEC I settled on 300Ω open-wire line, and I fed the antenna near the bottom rather than at the centre. The shift downward changes the values of E and I (and phase) at the feed point, which shifts the impedance (Z = E / I). Here is the resulting SWR chart from 7 to 30 MHz.
Some of the SWR dips are useful, such as on 30, 17 and 12 meters, but not all. That isn't too bad for a roll of the dice, and it shows the matching potential of the 43-foot vertical. However, please keep in mind this is only a thought experiment not a serious antenna design.
- The feed line introduces loss, including on 40 meters. The SWR is high on that section of open-wire line. In most cases the loss is modest, but first make sure of it.
- Even without shifting the feed point the antenna is not electrically symmetrical on bands above 40 meters. That means you will have a challenge, perhaps an impossible one, keeping the open-wire line from becoming a part of the antenna (i.e. radiating).
- A λ/2 of open-wire line at 40 meters is close to 20 meters long. In most stations that is a problem since the entire run isn't that long. It also needs to be mounted carefully to avoid a variety of problems.
The pattern on a multi-band antenna is always a challenge. The pattern of any antenna with an electrical length much longer than λ/2 is never simple, and can get quirky, with lobes and nulls in various directions, as you go ever higher in frequency.
For an especially bad example, let's look at how this antenna performs on 17 meters. With our "magical" feed line addition there is an attractive resonance near 18.1 MHz that draws our interest.
Ground losses are high at -9 db, which is considerably worse than on 40 meters; the pattern is asymmetric; and, there is also substantial radiation at higher angles, which does not suit my focus on DX. These figures become clear when we have EZNEC show us the currents on this antenna. Notice the position of the current maxima and minima: the bulk of the antenna's radiation comes from the bottom loading wire. This does not help us get a decent pattern.
So, again, don't be deceived by low SWR. The pattern matters. The antenna will certainly work, but will fare worse than many others.