7/31/2023 0 Comments Single stub matching smith chart![]() ![]() We also note that R(p) is not changing too quickly at this point so that measuring the stub insertion point will not be overly critical. A good initial guess would be 85 degrees. We see that this occurs somewhere between 80 and 90 degrees. Next, scan the third Column of the OUTPUT DATA to find where the parallel equivalent resistance, R(p), approaches 50 ohms. We immediately notice that the SWR is 3.88. We wish to match a 50 ohm feedline to an antenna with Z = 61 + j80. While the theory of stub matching is beyond the scope of this article, the following example illustrates how it may be performed using the AA3RL TLCalc spreadsheet. ![]() Using tuning stubs to match an antenna and transmission line is quite popular and useful. Results may not be accurate if the electrical length is greater than 90 degrees. The spreadsheet calculates the required length of stub: open for -X, shorted for +X.Īlternatively, given a stub of any length in feet which is less than ¼ wavelength, the reactance will be calculated. Input the desired inductive reactance (+X) or capacitive reactance (-X). The spreadsheet calculates the required inductance (uH.) or capacitance (uF and pf).Īnother way to obtain a desired reactance is with the use of transmission line stubs. Conversions may be made in either direction.Īt any given frequency, input the desired inductive reactance (+X) or capacitive reactance (-X). Series and Parallel equivalent circuits are very useful for transmission line matching, as well as other circuit design applications. Alternatively, the reverse calculations may be performed. The output indicates that the length should be 13.7 feet, which is 45 degrees. In the screen shot below, we want to make a transmission line 1/8 (0.125) wavelength long, using 50 ohm line with a velocity factor of 0.78, and operating at a frequency of 7.0 MHz. Series Section Line Transformer (analytic solution) for impedance matching Impedance (Z) at any single point on a lossless transmission line (for stub matching) Stub Matching - Impedance (Z) over a 180 degree cycle along a lossless transmission line. Length Conversion: Wavelength, Degrees, FeetĬapacitance and Inductance required for given reactance (X) The program performs the following calculations: I have learned from experience to keep a backup copy of the spreadsheet for when this eventually happens. If these cells are disturbed or over-written the calculations may be cease to function properly. On the far right side of each section there are areas that are used for computational purposes, in order to break complex formulas into more manageable chunks. The input data is grouped on the left side of the page, and the output data is grouped to its immediate right. Each area performs one of the calculations listed below. ![]() The spreadsheet is divided into convenient functional areas. An excellent program to check the results for lossy lines is TLA, which is included with recent versions of the ARRL Antenna Book. with high SWR or long transmission line lengths, these approximations will diverge from the actual values. I hope you will find it equally useful.Īll formulas assume lossless transmission lines, but these results are usually within the measurement tolerance achievable by the amateur in normal situations. Since then other utility functions were added that has enabled it to replace the Smith Chart, the pocket calculator, and the many computer programs for transmission line design applications. Initially I used the spreadsheet to design Stub and Series Section Line Matches. As a result, I felt the need to create a spreadsheet style program where all input values are displayed and multiple "what-if" data changes may be implemented quickly with the click of the mouse. If another calculation is desired, all the data must be re-entered. In addition, the programs usually require the data to be entered in serial form in order to obtain the calculated output. However, I have found the routines to be inconveniently scattered among many different programs. There are a variety of programs available to the Radio Amateur that will calculate virtually every transmission line parameter that one may need. AA3RL Transmission Line Calculator AA3RL Transmission Line Calculator ![]()
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