# Additional loss due to VSWR

Hams often refer to Additional loss due to VSWR, indeed some ham publications contain graphs that show the Additional loss due to VSWR. Let's take an example from the award winning article Understanding SWR by Example (Walraven 2006). The example and its analysis is quoted below for reader's convenience.

Why Ladder Line Works for High SWR Open wire line, window line or ladder line has been used since the early days of radio. There is a good reason, since the loss of this type of cable is quite low at HF frequencies — lower than all but the very best coax cable. For instance, 300 feet of 450 Ω ladder line has a loss of less than 0.5 dB at 30 MHz when matched. A good quality expensive coax might have 1 dB of loss in the same length, but most high end amateur coax cable will have more than 2 dB attenuation under those conditions. It is because of this low loss that air dielectric (or mostly air in the case of window line) line can be used effectively on antennas that have high SWR, if the matching is provided at the transmitter. The lower loss of this type of line allows most of the reflections to radiate instead of being lost within the cable. One last example shows how this works. You have just installed a full wave HF dipole. To feed it, you use 300 feet of 450 Ω ladder line with a loss of 0.5 dB at 30 MHz. You’ve modeled your antenna for 10 meters and you just happen to know that the impedance is 4500 Ω. That corresponds to a SWR of 4500/450 or 10:1 on your ladder line. Pretty bad, right? Not so fast. Consulting Figure 1 and knowing your matched loss is 0.5 dB shows an additional loss of 0.9 dB at an SWR of 10:1. The total loss of this antenna system is 1.4 dB. Not bad. Toss in a balanced line tuner and you’re ready to go! Your smart aleck buddy decides to install the same antenna but he springs for the best and most expensive coax figuring his antenna is only 40 feet away from his radio and he doesn’t like the look of ladder line. He boasts that his coax loss is specified at 0.25 dB, which is half that of your ladder line. He figures he can also use a tuner to take care of the mismatch. You quietly smile at him because you know that the 4500 Ω of the antenna will present an SWR of 90:1 on his 50 Ω cable resulting in a mismatch loss of 12 dB beyond the 0.25 dB cable loss. Sure he can tune his SWR to 1:1 with the tuner at his radio, but guess who will be working the DX?

Lets review the example. The stated matched line loss of 0.5dB for 300ft of 450Ω ladder line at 29MHz is probably optimistic, as is the assumption that Zo is 450Ω. The following analysis uses N7WS's characterisation of Wireman 551 ladder line, matched line loss 0.9dB and Zo=400Ω. Using TLLC for the ladder line case, line loss for Wireman 551 under the stated conditions is 3.5dB, more than double K5DVW's 1.4dB. K5DVW does not state the specific coax line analysed, but a practical line that has 0.25dB matched line loss for 40ft at 29MHz is LMR400, and it is used in the following analysis. Using TLLC for the coax case, line loss for LMR400 under the stated conditions is 5.9dB, less than half K5DVW's 12dB.

 K5DVW VK1OD 300' ladder line 1.4dB 3.5dB 40' coax 12.0dB 5.9dB Difference 10.6dB 2.4dB

The outcomes are quite different. There are two factors that contribute to the difference:

• K5DVW's matched line loss of nominal 450Ω ladder line is optimistic (possibly based on ARRL figures, see A review of QST article "The Lure of Ladder Line" for more information); and
• the Additional loss due to VSWR Graph is not correct in this scenario.

So, what is wrong with the Additional Loss Due to VSWR Graph? The graphs are usually based directly or indirectly on the formula LossRatio=(1+S^2)/(2*S) that depends on a set of assumptions that are rarely stated. Some of the graphs are 'adjusted' for source end VSWR, but the adjustment adds more assumptions that again, are usually not stated. Smith (Electronic Applications of the Smith Chart) states:

If a waveguide is one or more wavelengths long, the average increase in dissipative loss due to standing waves in a region extending plus or minus one-half wavelength from the point of observation may be expressed as a coefficient or factor of the one-way transmission loss per unit length.

and goes on to give the above formula. So, the graphs are often misused in ignorance of the underlying assumptions. The ongoing reference to Additional loss due to VSWR in our handbooks, tools, language etc engenders and reinforces a flawed concept that line losses where VSWR>1 are necessarily greater than the matched line loss.

# Changes

 Version Date Description 1.01 15/4/2010 Initial. 1.02 16/10/11 Updated links 1.03

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