Chen Thanks for that supporting addition, and for your work on the Smith Chart showing the KAT3 matching range for 160 meters. It is all a matter of the physics of the situation.
As you mentioned, the matching range of the KAT3 becomes greater as the frequency is increased. That fact is often overlooked by many hams. It is all about the amount of L and C available in the tuner, but the inductive or capacitive reactance is really what counts in producing the match. If the feedpoint in the shack has 1000 ohms of inductive reactance, and the tuner has only 600 ohms capacitive reactance to attempt to cancel that inductance, then a match will never happen. For a given L, the reactance increases with frequency, and with a given C, the reactance decreases with frequency. That can be easily seen from the formulas for inductive and capacitive reactance - for inductance, the "f: term is a multiplier, and for capacitors, it is a divisor. The limiting factor for L-network tuners is usually the largest inductance available. The capacitive component is not normally the limiting factor because that can be made quite small (high reactance). The KAT3 (and KAT100 and KAT2, and KAT1 and KXAT1) uses an L-match tuning section. The required L and C values can easily be computed using the standard formulas for an L-matching section. If the L and C values required are greater than that available in the tuner, you have exceeded the range of the tuner. Instead of adding additional feedline, it is also possible to add parallel or series capacity or inductance at the feedline connection point to bring things into a tunable range. For those who want to pursue the "fine points", study a bit about L-networks and conjugate matching. 73, Don W3FPR On 1/2/2011 8:52 PM, Kok Chen wrote: > On Jan 2, 2011, at 4:01 PM, Don Wilhelm wrote: > >> Adding or subtracting a 1/8 wavelength of feedline >> will often bring it into range, and that is normally the easiest >> solution if the only thing you are considering is the ability of the >> tuner to produce a match. > You can see what Don means by taking a look at this figure (KAT3 at 1.8 MHz, > with Smith Chart centered at 50+i0 ohms): > > http://homepage.mac.com/chen/Technical/Tuner/tuner1.8.png > > Each point on the Smith Chart is a point that the KAT3 can be brought to an > precise SWR of 1.0:1. The blue points are for the KAT3 cap on one side of > the inductor and the green points are for the cap switch to the other end of > the inductor (the KAT3 is an L tuner, with a relay K17, that switches the > caps to one or the other side of the inductor). > > The center of the Smith Chart circle represents an antenna with an SWR of > 1.0:1. As you go out towards the circumference, you have growing circles > with the same centers, with ever increasing SWR. > > Notice (as Don mentioned) that when the SRW is large (towards the > circumference of the Smith Chart), there are huge swaths of empty spots in > the Smith Chart. These are terminations that the KAT3 can never bring to an > SWR of 1.0:1. > > However (again, as Don mentioned), there are large areas beyond the blue > region where you can rotate yourself along on a constant SWR circle and drop > yourself right into where the dense green dots are! Voila, ability to tune > to an SWR of 1.0:1 while you could not do so without rotating. > > How do you rotate yourself? A length of transmission line, of course! > > If you remember your transmission line theory, adding a transmission line > will move you along a constant radius circle centered at SWR = 1.0:1. The > 1/8 wavelength that Don mentioned will rotate you by 90 degrees. In the case > of the K3, you may have to try everything up to about 3/4 of a wavelength > since the green and blue parts are not symmetrical. (Yes, 3/4 wavelength at > 160m is no fun :-). > > By the way, if you look carefully, there are SWR values outside of the > blue-green Yin-Yang looking region, that are not occupied. I.e., there > *will* be antennas that you will never be able to tune even if you try > different transmission lines until you are blue in the face. But this plot > (again, with reference center at 50 ohms) should quickly tell you which > antenna is tunable at 1.8 MHz. > > If you want to look at the full resolution PDF of the above plot (warning: > 9.4 MB), you can use this link: > > http://homepage.mac.com/chen/Technical/Tuner/tuner1.8.pdf > > The points are computed by using the capacitor and inductor values of the > KAT3. The KAT-100 uses slightly different L and C -- if you are interested > in seeing how that tuner works, and can run Xcode on a Mac, I am more than > glad to send you the source code that you can modify to produce the PDF chart > for a KAT100. > > The interesting thing about the KAT3 is that as you go up in frequency, the > dots become sparser, but do cover the most of the Smith Chart circle out to > very high SWR circles. That means that as you go up in frequency, you might > not be able to tune to exactly SWR 1.0:1 but you can get close enough that it > should not be a problem to tune "any" load well enough practically. For > example, the KAT3 looks like this on 20m: > > http://homepage.mac.com/chen/Technical/Tuner/T14080.jpg > > Again, if you have Xcode loaded on your Mac (Xcode is on every Mac OS X > Installer DVD, but you have to ask for it to be installed), I will be glad to > send you the Xcode project so you can generate plots for any frequency that > you wish. > > Vy 73 > Chen, W7AY > ______________________________________________________________ Elecraft mailing list Home: http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/mmfaq.htm Post: mailto:Elecraft@mailman.qth.net This list hosted by: http://www.qsl.net Please help support this email list: http://www.qsl.net/donate.html
