I've been vaguely aware that Smith charts can be used to solve transmission line and impedance matching problems. Alan, together with a program called SimSmith written by Ward AE6TY, make the how-to of this crystal clear. Since buying a nanoVNA a few months ago, I've been wanting to learn more about Smith charts and now an opportunity has presented itself, along with the Elmers necessary to make it achievable by the likes of me.
What follows is a video of me (a few bloopers included) first determining the impedance values of my 17-ft whip (collapses to two feet long) when used attached to my bike and two 1/4-wave radials. The I use SimSmith and W2AEW's tutorial to determine what components I need to be able to use this antenna on 17 and 20 meters without hauling an antenna tuner.
Yes, an ATU is more convenient and versatile but they are also bulkier and heavier - a factor when biking. With this LC solution, I'll be able to operate with one antenna on two bands, using an LC network that (with BNC connectors) will fit inside a small pill bottle.