The visual basic code for the above graphic tabled results is written using visual basic 2019 community version. The vb code runs on both “windows 7” and “windows 10”. Just to bare in mind, the impedance matching calculation with either a capacitor or an inductor, was original achieved with the quarter wavelength matching calculation, “match ohms = Sqrt( ant load * radio o/p )”. Although this equation is in the books, I was unsure, but I found that the match to the hypotinuse angle, of a right angle triangle, the equation being thus , “match ohms = Sqrt( ant load^2 + radio o/p^2 )”, would mean the matching impedance would be thus the hypotinuse angle and length, the length being the matching impedance, or thus put such as “50ohm @ hypotinuse angle”. Perhaps may have noticed that a 50ohm dipole is some 9dBV down from a full wave long wire, that is because a 50ohm dipole is around 2/5th efficient. In previous articles on the attached blog, I have suggested a cross dipole design use. One radio ham used a cross dipole and found as he put it, “ I’m getting out like I never did before”, the ham from South America, I heard on I believe the 20m band. The 50ohm cross dipole has a 3dBV gain figure up from a full wave line, a 12dBV or so difference up from his original straight 50ohm dipole used before, relative to a full wave signal electromagnetic antenna coupling to the etha. I have written the program to work with band frequencies from 136KHz up to 5GHz, the tested range to see if the results produced weird numbers. The reason why a matched condition is 45degrees, is because an antenna loading is an inductive loading. If the stub antenna wire is cut to 50ohm match ( 9% of full wave length ), then inductive loading is XL = 50 ohms at that centre frequency. The inductance of wire is “300nH / metre of wire”. Thus the impedance matching vector is thus as “element XL = 50ohms, the stub antenna,”
invTan = ( element XL / 50 ohms ) ” , then the vector is equated to as 50 ohms @ 45 degrees.