ARRL - QST Magazine - Measuring Cable Loss (2005)

2005·0.33 MB·English

Measuring Cable Loss
Improving measurement accuracy when
low-power analyzers are used.
By Frank Witt, AI1H
T
he matched loss of a cable Eq 29 on page 24-26 and Eq 35 on open cases. We can then find the
with a characteristic impe- page 24-27 of The ARRL Antenna cable loss (in decibels) from:
dance, Z , is the loss of the Book, 19th and 20th editions, respec-
0
cable when it is terminated in Z . A tively.
0
well-publicized way of measuring This method has two problems L =−5logρ ρ
C S O
the matched loss of a cable is to when the measuring instrument is
measure the magnitude of the reflec- a low-power analyzer like the MFJ ⎛SWR +1⎞⎛SWR +1⎞
tion coefficient, |ρ|, SWR, or return Model MFJ-259B and similar ana- =5log⎜⎜ S ⎟⎟⎜⎜ O ⎟⎟
loss, RL, at one end when the other lyzers. The first is that shorting or ⎝SWRS−1⎠⎝SWRO−1⎠
end of the cable is either shorted or opening the circuit at the far end RL +RL
= S O (Eq 2)
open. The formula for matched loss gives different answers. For electri-
4
(in decibels) for either shorted or cally short cables, these answers can
open cables is: be very different. Eq 1 assumes that
where the subscripts “S” and “O” re-
the reference impedance of the mea- fer to the short- and open-circuited
⎛SWR+1⎞ suring instrument equals the com- cases, respectively.
LC =−10logρ=10log⎜ ⎟ plex characteristic impedance of the Examination of Eq 2 reveals that
⎝SWR−1⎠ cable. However, the nominal refer- it is essentially the same as Eq 1,
RL
= ence impedance of the analyzer is except that the value of |ρ| used is
2 (Eq 1) 50 + j0 Ω, rather than the complex the geometric average of the |ρ|
characteristic impedance of the values found for the two cases. The
This is an expanded version of
cable. The second problem is that the value of return loss used is the arith-
values of |ρ|, SWR, or return loss metic average of the RL values
do not fall in favorable parts of most found for the two cases. However,
ARRL Technical Advisor analyzers’ measurement ranges. this does not solve the second prob-
41 Glenwood Rd The problem of different answers lem (that is, non-optimum measure-
Andover, MA 01810-6250 can be overcome by making a mea- ment ranges).
[email protected] surement for both the shorted and Let’s look at a specific example:
44 May/June 2005
Assume that we have 25 feet of is to use a method based on the in- When measuring cables of other
RG-58A (Belden 8259), and we want direct method for evaluating an- characteristic impedances, insert an
to measure the matched loss of the tenna tuners and baluns.3,4 A antenna tuner between the analyzer
cable at 10 MHz. The Belden catalog comparison of the two methods fol- and the cable. Terminate the cable
shows this to be 1.4 dB/100 ft, so the lows in the next section. with a load resistance, R , which
L
matched loss of our cable segment Here is a summary of how the in- equals the nominal characteristic
should measure 1.4/4 = 0.35 dB. The direct method is used for measuring impedance of the cable, and adjust
nominal characteristic impedance is the loss of an antenna tuner. Con- the tuner so that the input imped-
50 Ω, and the electrical length of this nect the analyzer to the input of the ance of the tuner is 50 + j0 Ω (|ρ| =
cable segment is 0.385 wavelength. tuner and the load resistance R to 0 and SWR = 1). Use resistors of
L
I used TLMan.mcd, the Mathcad its output. Measure the loss of the values R /2 and 2R to obtain the
L L
worksheet that is a part of Note 1, to antenna tuner by first terminating values for use in Eq 3. The loss mea-
simulate a measurement with an it in the desired load resistance, R . sured will be the loss of the tuner-
L
analyzer. TLMan.mcd is a trans- Adjust the tuner so the input imped- cable combination. Measure the loss
mission-line simulator that uses ance of the tuner is 50 + j0 Ω (|ρ| = of the tuner by terminating the
manufacturers’ data to derive trans- 0, and SWR = 1). Then terminate the tuner in R and use the indirect
L
mission-line properties. The matched tuner with R /2 and 2R , in se- method to find the tuner loss. The
L L
loss of 100 feet of cable calculates to quence. Use the analyzer readings indirect method is described in the
be 1.39 dB. This rounds to the value to compute the loss of the tuner. references of Notes 3 and 4. Subtract
given by Belden (L = 1.4 dB/100 ft). To measure 50 Ω cables, connect the tuner loss from the total loss to
C
The worksheet provides a cable model the analyzer directly to one end of obtain the matched loss of the cable.
that very accurately matches the cable as in the cases cited above.
Belden’s published matched-loss data No tuner is required. As a check, A Comparison of Methods
from 1 to 1000 MHz. The worksheet first terminate the cable in 50 Ω; the The method described in Hints
also uses the manufacturer’s velocity SWR reading should be very close and Kinks (Note 2), which we will
factor and capacitance-per-foot speci- to 1. Then terminate the cable in call the WA8VZQ method, involves
fications. To obtain an accurate simu- 25 Ω and 100 Ω and measure |ρ|, adding a 4-dB pad to move the mea-
lation, the worksheet calculates and SWR or RL for each load. Calculate sured data to a more favorable part
uses the complex characteristic im- the loss (in decibels) from: of the analyzers’ measurement
pedance. I modified the worksheet to range. We will call the method de-
use an analyzer reference impedance scribed above, which uses resistive
of 50 + j0 Ω, rather than the complex LC =−5logρ1 ρ2 −4.77dB terminations with values above and
characteristic impedance of the cable. below the nominal characteristic
⎛SWR +1⎞⎛SWR +1⎞
Now, back to the 25-foot example: =5log⎜ 1 ⎟⎜ 2 ⎟ impedance of the cable, the AI1H
For the shorted case, |ρS| = 0.937 ⎜⎝SWR1−1⎟⎠⎜⎝SWR2−1⎟⎠ method. It turns out that the two
(SWR = 30.8; RL = 0.564 dB), and methods are equivalent in concept
S S RL +RL
the calculated matched loss using −4.77dB= 1 2 −4.77dB and potential accuracy. Let’s look
Eq 1 is 0.282 dB. For the open-cir- 4 first at the formula for computing
ρ (Eq 3)
cuit case, | | = 0.909 (SWR = the loss for the WA8VZQ method:
O O
21.0, and RL = 0.829 dB) and the where the subscripts “1” and “2” re-
O
calculated matched loss is 0.414 dB. fer to the 25 Ω and 100 Ω termina-
These are clearly very different re- tion cases, respectively. L =−5logρ ρ −4dB
C S O
sults. Geometrically averaging the The nice aspect of this approach
|ρ|s and arithmetically averaging is that the analyzers are used in re- =5log⎜⎛SWRS+1⎟⎞⎜⎛SWRO+1⎟⎞
the RLs give a matched loss of 0.35 gions where they have good accu- ⎜⎝SWRS−1⎟⎠⎜⎝SWRO−1⎟⎠
dB, which is the correct value. racy, where the factory personnel
RL +RL
Although the results found from calibrate them. For a lossless cable, −4dB= S O −4dB
short- and open-circuited cables are ρ = ρ = 1/3; SWR = SWR = 2.0; 4
1 2 1 2
different, the difference is inconse- and RL = RL = 9.54 dB. For cables (Eq 4)
1 2
quential in many practical cases. with loss, the reflection-coefficient
Either case will reveal whether a magnitude, SWR and return-loss where the subscripts S and O refer to
cable is usable. My aim here is to values stay within the range where the short- and open-circuited cases,
show that the two results are differ- the analyzer has its best accuracy respectively.
ent and how we can account for and and resolution. This equation was not explicitly
correct those differences. Let’s look at our specific example: mentioned in the Hints and Kinks
The values of |ρ|, SWR, and re- 25 feet of RG-58A (Belden 8259) cable. article, but it is appropriate use for
turn loss do not lie in a favorable part Again, “measure” the cable with the WA8VZQ method. Notice that it
of the instrument’s measurement TLMan.mcd. We find that |ρ| = takes advantage of the averaging
1
range. This was recognized by Dan 0.316; SWR = 1.93; RL = 10.00 dB); technique described earlier.
1 1
Wanchic, WA8VZQ, and published in |ρ| = 0.299; (SWR = 1.85, and RL Compare Equations 3 and 4. The
2 2 2
Hints and Kinks.2 Dan suggested = 10.48 dB), which from Eq 3, gives differences are that the AI1H
“moving” the measurement to a more L = 0.35 dB. Not only is this in method involves the sequential con-
favorable range, SWR between 1 and agCreement with the actual loss, but nection of 25 Ω and 100 Ω load re-
2.3, by inserting a 4-dB 50-Ω attenu- the quantities measured are in the sistors and the WA8VZQ method
ator between the analyzer and the range where most analyzers shine. involves shorting and opening the
cable being measured. In this case, instead of SWR values circuit at the end of the cable. Also,
Another way to “move” the mea- over 20, the analyzer must measure different values are subtracted,
surement to a more favorable range SWR values just under 2. 4.77 dB for the AI1H method and
May/June 2005 45
4 dB for the WA8VZQ method. If a Accuracy and Resolution MFJ-259B for use in this applica-
4.77-dB attenuator had been used Reflection-coefficient magnitude, tion.
for the WA8VZQ method, Equations SWR and return loss are shown in The loss versus |ρ| behavior for
3 and 4 would have been identical, the above equations. This was done the AI1H method is shown in Fig 1.
except for the terminations used. because various analyzers that are The graph is based on Eq 3, where
The AI1H method uses termina- used for measuring cable loss pro- Z0/2 and 2Z0 terminations are used.
tions that are half and twice the vide best accuracy when a particu- In this case, it is assumed that ρ1 and
nominal characteristic impedance lar one of these three parameters is ρ2 are equal. The individual dots in
(25 Ω and 100 Ω, respectively, for measured. The equations are useful the graph are the only values pos-
50 Ω cables). If the terminations only if the analyzer accuracy is ad- sible because of the two-digit display
had been 1/2.323 times and 2.323 equate. For a simple check of the characteristic of the MFJ-259B,
times 50 Ω (21.5 Ω and 116.2 Ω, accuracy, test a zero length cable. which controls the resolution of the
respectively), a 4-dB term would For the AI1H method using Z /2 and instrument. To take full advantage
be used instead of the 4.77-dB term 2Z loads, a perfect analyzer0 would of the displayed result, interpret a
in Eq 3. In general, for the AI1H rea0d |ρ| = 1/3, SWR = 2.0 and RL = reading that alternates between two
method, if k is the multiplier for 9.54 dB. For the WA8VZQ method adjacent values as a value half-way
the load resistors (Z0/k and kZ0, with a 4 dB attenuator, the analyzer between the two values. For example,
where Z0 is the nominal characteris- would read |ρ| = 0.40, SWR = 2.3 interpret a reading of |ρ| that
tic impedance of the cable), the value and RL = 8.0 dB. This does not guar- “bounces” between 0.22 and 0.23 as
to be subtracted (in decibels) is antee that the intermediate read- 0.225. This leads to a resolution of
ings are accurate, but this is a good cable loss as shown in Fig 2.
⎛k+1⎞
10log ⎜ ⎟ . start. Fig 2 clearly demonstrates that
⎝ k−1⎠ Accuracy is the degree to which the resolution of loss for |ρ| mea-
The main difference between the the instrument provides the correct surements is better than that for
two methods is that for the WA8VZQ result. Resolution is the granularity SWR or Return Loss measurements
method attenuators are used, and to which the measured result can be and is better than 0.05 dB for cable
for the AI1H method resistive ter- displayed. In many cases, resolution losses up to 2 dB. Comparable
minations are used instead of a is the controlling factor in the mea- graphs to Fig 1 for SWR and Return
short and an open circuits. In most surement process. A perfect measur- Loss are not shown because the al-
cases, suitable resistors are more ing instrument is limited by the gorithms that convert measured |ρ|
available than a calibrated attenu- resolution of the displayed result. values to SWR and Return Loss in-
ators, so the AI1H method is easier As an example, let’s look at the troduce errors. The use of |ρ| for
to implement. Also, when attenua- popular MFJ-259B when used to this application of the MFJ-259B is
tors are used, they must have the measure cable loss. This instrument clearly preferred because of both
same design impedance as the nomi- measures |ρ| directly and displays accuracy and resolution consider-
nal characteristic impedance of the it on an LCD panel. It also displays ations.
cable being measured. Both methods SWR and return loss, which are com- Figs 1 and 2 apply for the AI1H
require an antenna tuner when the puted internally from the |ρ| data. method, but similar results are ob-
cable characteristic is not 50 Ω, since All three parameters are displayed tained with the WA8VZQ method. In
most analyzers have a reference re- as two decimal digits. The reference fact, if a 4.77 dB attenuator is sub-
sistance of 50 Ω. of Note 3 shows how to calibrate the stituted for the 4 dB attenuator used
Fig 1—Cable loss versus reflection coefficient magnitude for the Fig 2—Loss resolution versus cable loss for the MFJ-259B
MFJ-259B Analyzer using the AI1H method. Analyzer using the AI1H method. Solid line: Using reflection
coefficient magnitude readings. Dotted line: Using SWR readings.
Dashed line: Using return loss readings. The resolution is
controlled by the two decimal-digit display of the results.
46 May/June 2005
by WA8VZQ, the graphs would be than those of the MFJ-259B. This is for his valuable comments.
the same for the two methods. true because the higher-bit A/D con-
MFJ offers an analyzer of “im- verters eliminate the bounce re-
proved accuracy,” the MFJ-269. How ferred to above, so values between Notes
does it perform in this application? the two-digit values displayed on the 1F. Witt, AI1H, “Transmission Line Proper-
It has A/D converters with greater LCD are not available. These com- ties from Manufacturers’ Data,” The
resolution (more bits) than the A/D ments apply for this application of ARRL Antenna Compendium, Volume 6,
(Newington: ARRL, 1999), pp 179-183.
converters in the MFJ-259B. This the MFJ-269. For other applications,
TLMan.mcd is on the CD-ROM that is in-
would be very helpful if the MFJ- the improved A/D converters in the
cluded with Volume 6.
269 displayed three decimal digits MFJ-269 are useful and do result in 2Dan Wanchic, WA8VZQ, “Better Feedline-
for |ρ|, SWR and return loss, and accuracy improvement. I hope that Loss Measurements with Antenna Ana-
the SWR and return loss algorithms future versions of the MFJ-269 will lyzer,” QST, Mar 2004, “Hints & Kinks,”
were improved. Unfortunately, for provide three-digit decimal display pp 67-68.
the MFJ-269 I tested, the |ρ|, SWR for |ρ|, SWR and Return Loss and 3F. Witt, AI1H, “Evaluation of Antenna Tun-
and return loss displays show only improved algorithms to convert |ρ| ers and Baluns—An Update,” QEX, Sep/
two decimal digits. Also, the SWR data into SWR and return-loss data. Oct 2003, pp 3-15, and QEX, Nov/Dec
2003, p 62, on the Web at: www.arrl.org/
and return-loss algorithms were the
Acknowledgment tis/info/pdf/030910qex003.pdf.
same as those for the MFJ-259B. In 4F. Witt, AI1H, “Improved Accuracy in An-
fact, the displayed resolution of the I want to thank Ted Provenza, tenna Tuner Evaluation,” QST, Oct 2003,
MFJ-269 is worse by a factor of two W3OWN, for letting me borrow his “Technical Correspondence,” pp 73-74.
(twice the values displayed in Fig 2) MFJ-269 and Chris Kirk, NV1E, (cid:134)(cid:134)
May/June 2005 47