Towertalk
[Top] [All Lists]

## [TowerTalk] Best vs. Maxwell -- Again??( LONG !!)

 To: [TowerTalk] Best vs. Maxwell -- Again??( LONG !!) n7cl@mmsi.com (Eric Gustafson) Fri, 19 Mar 1999 14:39:17 -0700
 ``` Hi Jeff, OK. Here is the procedure to find the additional line loss caused by operating a transmission line into a load which does not perfectly match the line impedance. I have spread it out within some explanatory text. So it appears much longer and more complicated than it really is. Nothing more than a scientific calculator is required. First, determine what the loss would be if the load _was_ properly matched to the line. If you have the ability and instrumentation, measure the matched loss. Or look up the published value for the cable and scale it to the length of line you plan to use. This value will be the matched loss (LOSS) in dB. Convert this value into nepers (a) as follows: a = (LOSS/-8.6859) units are nepers Next, determine the level of mismatch (SWR at load end of cable). Convert this value into "reflection coefficient" (p) as follows: p = ((SWR-1)/(SWR+1)) dimensionless quantity Next, calculate the total loss in the transmission line (Lt) as follows: Lt = 10*log[ ((1-p^2)*e^(-2a)) / (1-(p^2*e^(-4a))) ] where e = base of natural logarithms, units for Lt are dB Finally, subtract the matched loss from the total loss to get the additional cable loss (d) due to operating the line in a mismatched condition. d = Lt - LOSS units are dB Remember that losses expressed as power ratios in dB are negative numbers. You can use the following two examples to verify that you have done the procedure correctly. 1. 200 ft of RG213, 8:1 SWR, 20 MHz This set of parameters should produce the following results. Matched loss (LOSS) = 2.0 dB (from Fig 23 on page 16-14 of '91 ARRL handbook) Total Loss (Lt) = -4.837 dB Additional loss due to mismatch (d) = -2.837 dB 2. 200 ft. of 450 ohm open wire, 20:1 SWR, 20 MHz This set of parameters should produce the following results. Matched loss (LOSS) = 0.04 dB (Extrapolated from Fig 23 on page 16-14 of '91 ARRL handbook. Probably a bit on the high side.) Total Loss (Lt) = -0.737 dB Additional loss due to mismatch (d) = -0.657 dB 3. 200 ft of RG213, 3:1 SWR, 20 MHz This set of parameters should produce the following results. Matched loss (LOSS) = 2.0 dB (from Fig 23 on page 16-14 of '91 ARRL handbook) Total Loss (Lt) = -2.794 dB Additional loss due to mismatch (d) = -0.794 dB Now you can calculate your antenna system losses to however many decimal places you wish! 73, Eric N7CL >From: "Jeffrey R Davis" To: >Date: Fri, 19 Mar 1999 08:38:42 -0600 > >Even if no one else is interested in the equations, I would be! > >Thanks, > >Jeff N0DY -- 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.htm ```
 Current Thread [TowerTalk] Best vs. Maxwell -- Again??( LONG !!), Eric Gustafson <=