44 May/June 2005

ARRL Technical Advisor41 Glenwood RdAndover, MA 01810-6250ai1h@arrl.net

Measuring Cable Loss

By Frank Witt, AI1H

Improving measurement accuracy whenlow-power analyzers are used.

The matched loss of a cablewith a characteristic impe-dance, Z0, is the loss of thecable when it is terminated in Z0. Awell-publicized way of measuringthe matched loss of a cable is tomeasure the magnitude of the reflec-tion coefficient, ||, SWR, or returnloss, RL, at one end when the otherend of the cable is either shorted oropen. The formula for matched loss(in decibels) for either shorted oropen cables is:

2RL

1SWR1SWR

log10log10LC

=

+==

This is an expanded version of

Eq 29 on page 24-26 and Eq 35 onpage 24-27 of The ARRL AntennaBook, 19th and 20th editions, respec-tively.

This method has two problemswhen the measuring instrument isa low-power analyzer like the MFJModel MFJ-259B and similar ana-lyzers. The first is that shorting oropening the circuit at the far endgives different answers. For electri-cally short cables, these answers canbe very different. Eq 1 assumes thatthe reference impedance of the mea-suring instrument equals the com-plex characteristic impedance of thecable. However, the nominal refer-ence impedance of the analyzer is50 + j0 , rather than the complexcharacteristic impedance of thecable. The second problem is that thevalues of ||, SWR, or return lossdo not fall in favorable parts of mostanalyzers measurement ranges.

The problem of different answerscan be overcome by making a mea-surement for both the shorted and

open cases. We can then find thecable loss (in decibels) from:

4

11

11

5

5

OS

O

O

S

S

OSC

RLRL

SWRSWR

SWRSWR

log

logL

+=

+

+=

=

(Eq 1)

(Eq 2)

where the subscripts S and O re-fer to the short- and open-circuitedcases, respectively.

Examination of Eq 2 reveals thatit is essentially the same as Eq 1,except that the value of || used isthe geometric average of the ||values found for the two cases. Thevalue of return loss used is the arith-metic average of the RL valuesfound for the two cases. However,this does not solve the second prob-lem (that is, non-optimum measure-ment ranges).

Lets look at a specific example:

May/June 2005 45

Assume that we have 25 feet ofRG-58A (Belden 8259), and we wantto measure the matched loss of thecable at 10 MHz. The Belden catalogshows this to be 1.4 dB/100 ft, so thematched loss of our cable segmentshould measure 1.4/4 = 0.35 dB. Thenominal characteristic impedance is50 , and the electrical length of thiscable segment is 0.385 wavelength.

I used TLMan.mcd, the Mathcadworksheet that is a part of Note 1, tosimulate a measurement with ananalyzer. TLMan.mcd is a trans-mission-line simulator that usesmanufacturers data to derive trans-mission-line properties. The matchedloss of 100 feet of cable calculates tobe 1.39 dB. This rounds to the valuegiven by Belden (LC = 1.4 dB/100 ft).The worksheet provides a cable modelthat very accurately matchesBeldens published matched-loss datafrom 1 to 1000 MHz. The worksheetalso uses the manufacturers velocityfactor and capacitance-per-foot speci-fications. To obtain an accurate simu-lation, the worksheet calculates anduses the complex characteristic im-pedance. I modified the worksheet touse an analyzer reference impedanceof 50 + j0 , rather than the complexcharacteristic impedance of the cable.

Now, back to the 25-foot example:For the shorted case, |S| = 0.937(SWRS = 30.8; RLS = 0.564 dB), andthe calculated matched loss usingEq 1 is 0.282 dB. For the open-cir-cuit case, |O| = 0.909 (SWRO =21.0, and RLO = 0.829 dB) and thecalculated matched loss is 0.414 dB.These are clearly very different re-sults. Geometrically averaging the||s and arithmetically averagingthe RLs give a matched loss of 0.35dB, which is the correct value.

Although the results found fromshort- and open-circuited cables aredifferent, the difference is inconse-quential in many practical cases.Either case will reveal whether acable is usable. My aim here is toshow that the two results are differ-ent and how we can account for andcorrect those differences.

The values of ||, SWR, and re-turn loss do not lie in a favorable partof the instruments measurementrange. This was recognized by DanWanchic, WA8VZQ, and published inHints and Kinks.2 Dan suggestedmoving the measurement to a morefavorable range, SWR between 1 and2.3, by inserting a 4-dB 50- attenu-ator between the analyzer and thecable being measured.

Another way to move the mea-surement to a more favorable range

is to use a method based on the in-direct method for evaluating an-tenna tuners and baluns.3,4 Acomparison of the two methods fol-lows in the next section.

Here is a summary of how the in-direct method is used for measuringthe loss of an antenna tuner. Con-nect the analyzer to the input of thetuner and the load resistance RLtoits output. Measure the loss of theantenna tuner by first terminatingit in the desired load resistance, RL.Adjust the tuner so the input imped-ance of the tuner is 50 + j0 (|| =0, and SWR = 1). Then terminate thetuner with RL/2 and 2RL, in se-quence. Use the analyzer readingsto compute the loss of the tuner.

To measure 50 cables, connectthe analyzer directly to one end ofthe cable as in the cases cited above.No tuner is required. As a check,first terminate the cable in 50 ; theSWR reading should be very closeto 1. Then terminate the cable in25 and 100 and measure ||,SWR or RL for each load. Calculatethe loss (in decibels) from:

dB4.774

RLRLdB4.77

SWRSWR

SWRSWR

5log

dB4.77log5LC

+=

+

+==

21

2

2

1

1

21

11

11

When measuring cables of othercharacteristic impedances, insert anantenna tuner between the analyzerand the cable. Terminate the cablewith a load resistance, RL, whichequals the nominal characteristicimpedance of the cable, and adjustthe tuner so that the input imped-ance of the tuner is 50 + j0 (|| =0 and SWR = 1). Use resistors ofvalues RL/2 and 2RL to obtain thevalues for use in Eq 3. The loss mea-sured will be the loss of the tuner-cable combination. Measure the lossof the tuner by terminating thetuner in RL and use the indirectmethod to find the tuner loss. Theindirect method is described in thereferences of Notes 3 and 4. Subtractthe tuner loss from the total loss toobtain the matched loss of the cable.

A Comparison of MethodsThe method described in Hints

and Kinks (Note 2), which we willcall the WA8VZQ method, involvesadding a 4-dB pad to move the mea-sured data to a more favorable partof the analyzers measurementrange. We will call the method de-scribed above, which uses resistiveterminations with values above andbelow the nominal characteristicimpedance of the cable, the AI1Hmethod. It turns out that the twomethods are equivalent in conceptand potential accuracy. Lets lookfirst at the formula for computingthe loss for the WA8VZQ method:

dB4RLRL

dB4

SWRSWR

SWRSWR

log

dBlogL

OS

O

O

S

S

OSC

+=

+

+=

=

4

11

11

5

45

(Eq 4)

where the subscripts S and O refer tothe short- and open-circuited cases,respectively.

This equation was not explicitlymentioned in the Hints and Kinksarticle, but it is appropriate use forthe WA8VZQ method. Notice that ittakes advantage of the averagingtechnique described earlier.

Compare Equations 3 and 4. Thedifferences are that the AI1Hmethod involves the sequential con-nection of 25 and 100 load re-sistors and the WA8VZQ methodinvolves shorting and opening thecircuit at the end of the cable. Also,different values are subtracted,4.77 dB for the AI1H method and

(Eq 3)

where the subscripts 1 and 2 re-fer to the 25 and 100 termina-tion cases, respectively.

The nice aspect of this approachis that the analyzers are used in re-gions where they have good accu-racy, where the factory personnelcalibrate them. For a lossless cable,1 = 2 = 1/3; SWR1 = SWR2 = 2.0;and RL1 = RL2 = 9.54 dB. For cableswith loss, the reflection-coefficientmagnitude, SWR and return-lossvalues stay within the range wherethe analyzer has its best accuracyand resolution.

Lets look at our specific example:25 feet of RG-58A (Belden 8259) cable.Again, measure the cable withTLMan.mcd. We find that |1| =0.316; SWR1 = 1.93; RL1 = 10.00 dB);|2| = 0.299; (SWR2 = 1.85, and RL2= 10.48 dB), which from Eq 3, givesLC = 0.35 dB. Not only is this inagreement with the actual loss, butthe quantities measured are in therange where most analyzers shine.In this case, instead of SWR valuesover 20, the analyzer must measureSWR values just under 2.

46 May/June 2005

Fig 1Cable loss versus reflection coefficient magnitude for theMFJ-259B Analyzer using the AI1H method.

Fig 2Loss resolution versus cable loss for the MFJ-259BAnalyzer using the AI1H method. Solid line: Using reflectioncoefficient magnitude readings. Dotted line: Using SWR readings.Dashed line: Using return loss readings. The resolution iscontrolled by the two decimal-digit display of the results.

4 dB for the WA8VZQ method. If a4.77-dB attenuator had been usedfor the WA8VZQ method, Equations3 and 4 would have been identical,except for the terminations used.

The AI1H method uses termina-tions that are half and twice thenominal characteristic impedance(25 and 100 , respectively, for50 cables). If the terminationshad been 1/2.323 times and 2.323times 50 (21.5 and 116.2 ,respectively), a 4-dB term wouldbe used instead of the 4.77-dB termin Eq 3. In general, for the AI1Hmethod, if k is the multiplier forthe load resistors (Z0/k and kZ0,where Z0 is the nominal characteris-tic impedance of the cable), the valueto be subtracted (in decibels) is

+

1110log k

k .

The main difference between thetwo methods is that for the WA8VZQmethod attenuators are used, andfor the AI1H method resistive ter-minations are used instead of ashort and an open circuits. In mostcases, suitable resistors are moreavailable than a calibrated attenu-ators, so the AI1H method is easierto implement. Also, when attenua-tors are used, they must have thesame design impedance as the nomi-nal characteristic impedance of thecable being measured. Both methodsrequire an antenna tuner when thecable characteristic is not 50 , sincemost analyzers have a reference re-sistance of 50 .

Accuracy and ResolutionReflection-coefficient magnitude,

SWR and return loss are shown inthe above equations. This was donebecause various analyzers that areused for measuring cable loss pro-vide best accuracy when a particu-lar one of these three parameters ismeasured. The equations are usefulonly if the analyzer accuracy is ad-equate. For a simple check of theaccuracy, test a zero length cable.For the AI1H method using Z0/2 and2Z0 loads, a perfect analyzer wouldread || = 1/3, SWR = 2.0 and RL =9.54 dB. For the WA8VZQ methodwith a 4 dB attenuator, the analyzerwould read || = 0.40, SWR = 2.3and RL = 8.0 dB. This does not guar-antee that the intermediate read-ings are accurate, but this is a goodstart.

Accuracy is the degree to whichthe instrument provides the correctresult. Resolution is the granularityto which the measured result can bedisplayed. In many cases, resolutionis the controlling factor in the mea-surement process. A perfect measur-ing instrument is limited by theresolution of the displayed result.

As an example, lets look at thepopular MFJ-259B when used tomeasure cable loss. This instrumentmeasures || directly and displaysit on an LCD panel. It also displaysSWR and return loss, which are com-puted internally from the || data.All three parameters are displayedas two decimal digits. The referenceof Note 3 shows how to calibrate the

MFJ-259B for use in this applica-tion.

The loss versus || behavior forthe AI1H method is shown in Fig 1.The graph is based on Eq 3, whereZ0/2 and 2Z0 terminations are used.In this case, it is assumed that 1 and2 are equal. The individual dots inthe graph are the only values pos-sible because of the two-digit displaycharacteristic of the MFJ-259B,which controls the resolution of theinstrument. To take full advantageof the displayed result, interpret areading that alternates between twoadjacent values as a value half-waybetween the two values. For example,interpret a reading of || thatbounces between 0.22 and 0.23 as0.225. This leads to a resolution ofcable loss as shown in Fig 2.

Fig 2 clearly demonstrates thatthe resolution of loss for || mea-surements is better than that forSWR or Return Loss measurementsand is better than 0.05 dB for cablelosses up to 2 dB. Comparablegraphs to Fig 1 for SWR and ReturnLoss are not shown because the al-gorithms that convert measured ||values to SWR and Return Loss in-troduce errors. The use of || forthis application of the MFJ-259B isclearly preferred because of bothaccuracy and resolution consider-ations.

Figs 1 and 2 apply for the AI1Hmethod, but similar results are ob-tained with the WA8VZQ method. Infact, if a 4.77 dB attenuator is sub-stituted for the 4 dB attenuator used

May/June 2005 47

by WA8VZQ, the graphs would bethe same for the two methods.

MFJ offers an analyzer of im-proved accuracy, the MFJ-269. Howdoes it perform in this application?It has A/D converters with greaterresolution (more bits) than the A/Dconverters in the MFJ-259B. Thiswould be very helpful if the MFJ-269 displayed three decimal digitsfor ||, SWR and return loss, andthe SWR and return loss algorithmswere improved. Unfortunately, forthe MFJ-269 I tested, the ||, SWRand return loss displays show onlytwo decimal digits. Also, the SWRand return-loss algorithms were thesame as those for the MFJ-259B. Infact, the displayed resolution of theMFJ-269 is worse by a factor of two(twice the values displayed in Fig 2)

than those of the MFJ-259B. This istrue because the higher-bit A/D con-verters eliminate the bounce re-ferred to above, so values betweenthe two-digit values displayed on theLCD are not available. These com-ments apply for this application ofthe MFJ-269. For other applications,the improved A/D converters in theMFJ-269 are useful and do result inaccuracy improvement. I hope thatfuture versions of the MFJ-269 willprovide three-digit decimal displayfor ||, SWR and Return Loss andimproved algorithms to convert ||data into SWR and return-loss data.

AcknowledgmentI want to thank Ted Provenza,

W3OWN, for letting me borrow hisMFJ-269 and Chris Kirk, NV1E,

for his valuable comments.

Notes1F. Witt, AI1H, Transmission Line Proper-

ties from Manufacturers Data, TheARRL Antenna Compendium, Volume 6,(Newington: ARRL, 1999), pp 179-183.TLMan.mcd is on the CD-ROM that is in-cluded with Volume 6.

2Dan Wanchic, WA8VZQ, Better Feedline-Loss Measurements with Antenna Ana-lyzer, QST, Mar 2004, Hints & Kinks,pp 67-68.

3F. Witt, AI1H, Evaluation of Antenna Tun-ers and BalunsAn Update, QEX, Sep/Oct 2003, pp 3-15, and QEX, Nov/Dec2003, p 62, on the Web at: www.arrl.org/tis/info/pdf/030910qex003.pdf.

4F. Witt, AI1H, Improved Accuracy in An-tenna Tuner Evaluation, QST, Oct 2003,Technical Correspondence, pp 73-74.