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The sign of reactance – a challenge posed a problem, a set of R,|X| data taken with an analyser of a quite simple network and asked readers to solve the sign of X over the range, ie to transform R,|X| to  R,X.

The sign of reactance – challenge solution gave a solution to the challenge, and The sign of reactance – challenge discussion provided some discussion about the problem and solution.

Some correspondents have asserted that the challenge (see above Smith chart) contains a response that is contrived for the purpose and not representative of real world antenna systems. Continue reading The sign of reactance – challenge reality check

The sign of reactance – a challenge posed a problem, a set of R,|X| data taken with an analyser of a quite simple network and asked readers to solve the sign of X over the range, ie to transform R,|X| to  R,X.

It is widely held that this is a trivial matter, and lots of software / firmware implement algorithms that fail on some scenarios. Though the scenario posed was designed to be a small set that provides a challenging problem, it is not purely theoretical, the characteristics of the data occur commonly in real world problems and the challenge data is derived from measurement of a real network.

Above is a Smith chart plot of the measured data that was transformed to the R,|X| for the challenge. Continue reading The sign of reactance – challenge discussion

The sign of reactance – a challenge posed a problem, a set of R,|X| data taken with an analyser of a quite simple network and asked readers to solve the sign of X over the range, ie to transform R,|X| to  R,X.

It is widely held that this is a trivial matter, and lots of software / firmware implement algorithms that fail on some scenarios. Though the scenario posed was designed to be a small set that provides a challenging problem, it is not purely theoretical, the characteristics of the data occur commonly in real world problems and the challenge data is derived from measurement of a real network.

Imported and rendered graphically in ZPlots we have:

The network measured is comprised from analyser, a 2.8m length of RG58/CU, a tee piece feeding a 50 resistor on one branch and on the other branch, another 2.8m length of RG58/CU with a 4.7Ω resistor termination.

The challenge is: what is the sign of X across the frequency range? Continue reading The sign of reactance – challenge solution

Over time, readers of The sign of reactance have suggested that determining the sign of reactance with an antenna analyser that does not directly measure the sign is not all that difficult, even for beginners. The article shoots down some of the most common algorithms as failures on simple cases.

This article gives measurements made from a simple network of two identical lengths of 50Ω coax, a 50Ω resistor and a 4.7Ω resistor. It is a network designed to offer a challenge to the simple algorithms, and it IS solvable analytically… but not with most algorithms and software,

Here is the data from measurement made with an AA-600 and then all – signs removed, so in fact the Xs column is |Xs|.

"Zplots file generated by AntScope"
"Freq(MHz)","Rs","Xs"
9.000000,78.13,53.66
9.250000,82.12,51.10
9.500000,86.10,47.83
9.750000,89.46,44.00
10.000000,92.30,39.90
10.250000,94.53,35.39
10.500000,96.21,30.71
10.750000,97.17,26.14
11.000000,97.49,21.54
11.250000,97.30,17.12
11.500000,96.54,13.04
11.750000,95.47,9.14
12.000000,93.92,5.68
12.250000,92.16,2.70
12.500000,90.25,0.17
12.750000,88.13,2.50
13.000000,85.94,4.50
13.250000,83.67,6.15
13.500000,81.45,7.36
13.750000,79.29,8.38
14.000000,77.22,9.21
14.250000,75.21,9.78
14.500000,73.23,10.16
14.750000,71.44,10.37
15.000000,69.70,10.25
15.250000,67.99,10.23
15.500000,66.50,9.99
15.750000,65.10,9.68
16.000000,63.81,9.27
16.250000,62.65,8.72
16.500000,61.59,8.15
16.750000,60.55,7.54
17.000000,59.69,6.86
17.250000,58.97,6.20
17.500000,58.20,5.43
17.750000,57.66,4.68
18.000000,57.14,3.81
18.250000,56.77,2.98
18.500000,56.47,2.16
18.750000,56.22,1.22
19.000000,56.04,0.38
19.250000,56.07,0.50
19.500000,56.02,1.38
19.750000,56.12,2.29
20.000000,56.41,3.15
20.250000,56.68,4.03
20.500000,57.11,4.86
20.750000,57.51,5.72
21.000000,58.06,6.61
21.250000,58.77,7.45
21.500000,59.54,8.22
21.750000,60.47,8.95
22.000000,61.44,9.75
22.250000,62.52,10.34
22.500000,63.77,10.97
22.750000,65.11,11.55
23.000000,66.56,12.02
23.250000,68.11,12.38
23.500000,69.82,12.64
23.750000,71.75,12.82
24.000000,73.67,12.84
24.250000,75.96,12.67
24.500000,78.12,12.27
24.750000,80.40,11.72
25.000000,83.05,10.69
25.250000,85.56,9.68
25.500000,88.29,8.09
25.750000,90.92,6.21
26.000000,93.63,3.91
26.250000,96.17,1.13
26.500000,98.61,2.16
26.750000,100.68,5.92
27.000000,102.51,10.11
27.250000,103.87,14.90
27.500000,104.65,19.98
27.750000,104.71,25.32
28.000000,103.98,30.95
28.250000,102.58,36.48
28.500000,100.14,41.97
28.750000,97.08,47.32
29.000000,93.07,51.86

Imported and rendered graphically in ZPlots we have:

The challenge is what is the sign of X across the frequency range? Continue reading The sign of reactance – a challenge