Grounded verticals are rarely more than one band. A rare exception to this rule is described below. Folded grounded vertical can operate on the 14 and 18 MHz bands without switching. The antenna and matching circuit shown in the following figure.
The antenna model is shown in the file 18_14_20mm.maa. This is a file in the MMANA-GAL modeling program format.
The frequency dependence of VSWR by band is shown in the following two figures.
Both bands are covered with a large VSWR margin, so tuning the matching circuit is easy.
The tuner consists of only two elements. The L1 coil is frameless made of 2 mm copper wire. At TX 100 Wt the current in it does not exceed 2.5 A.
Capacitor C1 is made as a short piece 50 Ohm coax cable ~40 cm long open at the end. For the tuning time it makes sense to replace C1 with a tuning capacitor.
Of course, each of the tuner elements affects both bands. But L1 adjustment (stretch-compression) affects 18 MHz more, and C1 adjustment affects 14 MHz more.
You may not be able to keep all the dimensions shown in the first figure. This is especially true for the diameters of the mast tubes and the side wire.
In this case, you will have to modify the dimensions of the antenna slightly so that the described matching is still possible. The height of the antenna and the distance between the mast and the side wire will change.
To make this procedure easier, here are two model files. The first file 18_14_30mm.maa is made for a 30 mm diameter mast (antenna height 4.40 m, distance 19 cm). The second file 18_14._taper.maa describes a telescopic mast made of 25 to 16 mm tubes (antenna height 4.56 cm, distance 20 cm).