Correcting SWR measurement made through a long coax cable

[WA3LTJ]

Problem

My portable antenna is a very light-weight inverted V suspended by a 22 ft fiberglass pole. It uses RG-174 coax because anything heavier would bend the top of the pole. The cable is 40 ft long. I can measure the SWR at the end of the cable, but that introduces an error associated with the losses in the cable. How does one correct the SWR measurement?

 

SWR meter --------------- 40 ft coax cable ----------------------- Antenna

 

Proposed solution

Convert VSWR meter reading to return loss.

Subtract additional losses of coax cable

Convert return loss (at the antenna) to VSWR

 

Equations

This will convert measured VSWR into return loss.

RLt     total return loss

VSWRm     SWR measured by the meter (assume ratio, e.g., 2.5:1 expressed as 2.5)

RLt = -20 log10 ( (VSWRm-1)/(VSWRm+1) )                                        (1)

 

Estimated loss of the coax cable based on manufacturer’s data

RLc    Cable loss estimate

RLc = [loss per 100 ft at test frequency] * [length of cable in feet] / 100        (2)

 

We can now express all the losses. Note the signal traverses the cable twice, first the forward power, then the reflected power.

RLm    match loss (a result of the true SWR of the antenna)

RLt = RLm - 2 RLc                                                                                    (3)

 

Rearrange (3) to get the match loss of the antenna

RLm = RLt – 2 RLc                                                                                   (4)

 

Calculate the VSWR based on return loss (reverse of equation (1))

 

                                    1 + 10 ^ (-RLm/20)

VSWRa =           -----------------------------------                                   (5)

                                    1 – 10 ^ (-RLm/20)

 

Algorithm:  Given SWR reading, coax loss per 100 ft, coax length

Calculate RLt with (1)

Calculate RLc with (2)

Calculate RLm with (4)

Calculate VSWRa with (5)

I have uploaded a simple Matlab function that implements the algorithm. Note, the .txt should be changed to .m if you want to run it with Matlab.

Note: I submitted this question to Ask Dave in QST. It was answered in the February issue. Dave said I missed "the additional loss in the coax cable due to an SWR that is higher than 1:1". I am not certain he is correct. The mismatch loss is referred to the antenna. The SWR meter is correctly matched to the coax line. But, maybe there is another term I am missing.

 

Antenna_SWR.txt

Edited February 5, 2023 by K3MRI
Edited title for brevity

[K3MRI]

Hi Andy, I am probably completely off-base so please correct me, but I’m confused. Why would you want to correct the SWR? We care about the SWR at the Tuner or Radio, not at the antenna, no? The tuner ‘sees’ the coax so it has to be part of the measurement. Yes? No?

[WA3LTJ]

A mismatch at the radio might cause the radio to dissipate the excess reflected power, or to cut back power output to reduce that dissipation. A tuner can reduce those problems by making sure the combination of coax and antenna radiate or dissipate the signal. However, you would rather the antenna radiate the power.

A mismatch at the junction between the coax and the antenna implies the antenna is not 50 ohms. In the case of my 20 m dipole, the mismatch is primarily due to antenna length at the selected frequency.  I can improve the percent of power radiated by improving this match. In fact, I adjust the antenna length to minimize the SWR measured at the radio and less at the antenna is less at the SWR meter. However, when do I stop? I might be satisfied with a SWR of 1.5:1 across the whole 20 m band, knowing that at 24 feet that is the best possible performance of an inverted V. However, if the true SWR of the antenna is 2:1 when I read 1.5:1, I may stop trying to tune the antenna before the antenna is performing well. There are other reasons I might have a poor SWR. If I don't correct for the coax, I cannot tell if the antenna is working properly. Examples: the choke at the feedpoint is damaged or one leg of the dipole is longer than another. Once I know the correction for the added coax, I can make a table or graph to convert SWR readings. So, there is very little effort doing the correction. The major problem in this case is that the RG-174 has a lot of loss because of its size, so the readings can be pretty far off. Also, I cannot afford to waste too much power given the loss in the coax. Finally, the RG-174 is rated for over 100W, but that rating does not apply to the case when the antenna has a mismatch. 

 

[K3MRI]

I see what you’re trying to do. Makes sense. But you know me… doublet + windowline + transformer + tuner. Obviously, I’ll lose a little more power than you though.