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[TowerTalk] Line Length and SWR

 To: [TowerTalk] Line Length and SWR hwardsil@WOLFENET.com (Ward Silver) Thu, 18 Dec 1997 12:07:48 -0800 (PST)
 ```> So....If I happen to insert my Heath, Bird, or japanese SWR/Power meters > into my transimssion line at a high impedance point, , > say 200 ohms or > so, will the meter measure true SWR at the antenna, (minus the error > created by the losses in the transmisson line) or will it indicate an swr > roughly 200 divided by 50, or approximately 5:1? Can we use transmisson > line transformer theory to match the feed point impedance a the > transmitter to the transmitter output impedance? > > 73, de Pat AA6EG/N6IJ Pat - SWR is only a function of the line's characteristic impedance and the load's impedance. If you had a lossline 50-ohm line and connected it to a 200-ohm load, the SWR is 4:1 - everywhere. Assuming a 200-ohm purely resistive load - if you travel 1/8-wavelength towards the transmitter, the complex impedance at that point in the line will be about 180-ohms of pure inductive reactance. 1/8-wave further (1/4-wave from the load), the impedance will be 12.5-ohms of pure resistance. 1/8-wave further (3/8-wave from the load) and the impedance will be about 180-ohms of pure capacitive reactance. 1/8-wave further (1/2-wave from the load) and we're back to the original 200-ohms of pure resistance. Notice that the SWR is 4:1 at all points and the impedance is never 50 ohms of pure resistance. If you look at a Smith Chart, this path describes a circle, centered on a point which represents the characteristic impedance of the line. The radius of the circle is constant and represents the SWR. Notice that the path repeats around the Smith Chart once per half-wavelength. Notice also that the central point, representing the line's characteristic impedance, corresponds to an SWR of 1:1. The outer edge of the chart represents an SWR of infinity. Line losses cause the circle to spiral in towards the center point with distance, gradually reducing SWR to 1:1. Note that a lossy line has no effect on a perfectly matched load (except to reduce the power getting to it). A lossy line will cause an antenna to look "broader" by flattening its SWR curve. Imagine taking all of the SWR readings and reducing them by a constant fraction... So, to get back to your original question - the meter *should* read 4:1, or 200/50, whereever you put it in the line, no matter how long the line is, within reason. If you're only using 50-ohm line, you can't transform 200-ohms into 50-ohms through line length alone. However, you could simulate the reactances of an L-network by adding open or shorted stubs of the appropriate length, spaced an appropriate amount on the line. Or, you could use lines of other characteristic impedances (such as 75-ohms, 92-ohms, etc.) to shift the center of the circle such that a certain length brings the path of the impedance in its travels sufficiently close to 50-ohms of resistance. The latter is the technique employed to transform a loop's driving-point impedance to approx. 50-ohms by using a quarter-wave transformer of 75-ohm or 92-ohm line. A G5RV also uses this technique - a section of 300-ohm twinlead does the trick in this case. G5RV's genius was in finding a combination of antenna length and 300-ohm line length that resulted in a value of impedance at the terminals of acceptably close to 50-ohms on all the popular ham bands. Its hard enough at one frequency - but SIX?? And done by hand, too... 73, Ward N0AX -- FAQ on WWW: http://www.contesting.com/towertalkfaq.html Submissions: towertalk@contesting.com Administrative requests: towertalk-REQUEST@contesting.com Problems: owner-towertalk@contesting.com Search: http://www.contesting.com/km9p/search ```