When it comes to stub matching, or really any impedance matching, their are two ways I have seen it done. One is heavily based on formulas, and the other is based on the smith chart. IMO, the smith chart method is by far the easier method to learn and use. I'm not saying that their aren't other ways, but those often involve luck, or throwing parts at the problem until you find the parts that work, which I wouldn't, personally, put in the same category.
When it comes to impedance matching, aside from the simplest forms of it, it doesn't get talked about much, even between the more knowledgeable hobbyists. Except for the simplest or most tune-able matching systems (aka antenna tuners with components designed to be adjusted over a wide range of impedances including and especially the automated tuners), building a specific matching network for a specific antenna for a specific frequency really does seem to be mostly limited to trained engineers, and very few others. This isn't to say that hobbyists haven't made their own matching systems for various antennas, however, in most cases the hobbyist making said matching network generally doesn't understand how or why it works as they just copied someone else's design or followed directions. Honestly, among the current active members of this forum, I would guess maybe five of us have the working knowledge of or direct experience designing matching networks, even a simple one such as a stub match talked about above, from scratch without the heavy use of trial and error in the process.
I'm not trying to dissuade you from attempting to learn how to match antennas, I actually encourage the attempt. You will learn a lot in the process that goes beyond matching antennas. I would recommend any of the Reflections books as a starting reference as in said books their is a very good breakdown of the smith chart and how to use them. I would also be happy to help if you had any questions, although it has been a while so I would likely have to do some research (its not that I mind, but it would take time).
Another option is to learn how to model with 4nec2. If you model an antenna in said program, it can calculate the electrical lengths of said tuning stubs for you, and give you all four possible options so you can see which would work best (or require the least amount of feed line to make). If you want to make another type of matching network, it can calculate the components needed to make several other matching networks, from the basic L network to Pi and T networks as well.
The DB
