The DUTs
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DUT1 About 30 mm of RG 400 cable. Electrical length 0.284 wavelengths.
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DUT3 Modified connectors. Electrical length 0.129 wavelengths.
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DUT8 Modified connectors. Part with high impedance. Electrical length 0.338 wavelengths.
Combinations of the DUTs were also measured. Measurement of DUTs as well as combinations of them gives rise to an overdetermined system of equations from which unknowns can be determined.
DUT18 means DUT1 male connected to DUT8 female and so on.
The test setup.
Figure 1 shows the setup with DUT381 inserted.
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| Figure 1. The 8753E with DUT381 inserted. | |||||||||||
The 8753E was run uncalibrated with "CORRECTION OFF" and "PRESET: FACTORY" The instrument behaves in an odd way after a full 2 port calibration has been performed. When run uncalibrated it behaves as expected. The electrical length was set for the instrument to show close to the correct phase with the Calibration kit for S11 and S22 and with the direct connection for S21 and S12. There are infinite numbers of different electrical lengths that fullfill this requirement for a single frequency. The length that minimizes the frequency dependency of the phase was selected. These values were selected: S11 8.3450 ns S21 4.7700 ns S22 -2.6803 ns S21 4.6860 ns The most critical aspect of S parameter measurements is the impedance stability of the cable. The blue cable in figure 1 is 112 cm of Flexiform 401. The cable is free of mechanical strain and wants to be in the measurement position. It was carefully moved as little as possible and only axially during measurements. The small movement was well within the elastic region which means that impedance variations can be assumed to not have been not very large. Two types of measurements were performed. First all combinations of the DUTs with all the parts of the calibration kit were used to measure S11 and S22. This series of measurements should allow the determination of a calibration to apply afterwords. After that the full set of S-parameters was measured for all the DUTs. Measurements were made on 1293, 1296 and 1299 MHz. Raw data for single port measurements.Table 1 gives results with links to screen dumps. | |||||||||
1293MHz 1296MHz 1299MHz
Device Parm. Zre Zim Zre Zim Zre Zim
(Ohm) (Ohm) (Ohm) (Ohm) (Ohm) (Ohm)
noneOPEN S11 374.50 -238.75 360.14 -213.50 356.72 -191.22
noneOPEN S22 257.63 -1907.7 363.94 -1771.3 460.75 -1667.9
noneSHORT S11 3.9598 -3.2278 3.5370 -2.6919 3.1508 -1.9752
noneSHORT S22 2.3464 -1.2952 2.3236 -1.4130 2.2565 -1.5363
noneLOAD S11 52.316 -2.5977 52.615 -2.5352 52.912 -2.4199
noneLOAD S22 51.059 0.6563 51.059 0.6621 51.064 0.6680
DUT1OPEN S11 3.5317 8.4541 3.2075 9.5474 3.0093 10.805
DUT1OPEN S22 2.0464 10.266 1.9717 10.400 1.8525 10.539
DUT1SHORT S11 77.047 -165.57 79.258 -162.36 81.445 -161.12
DUT1SHORT S22 17.883 -216.80 20.055 -211.96 21.961 -207.94
DUT1LOAD S11 52.881 -2.7441 53.170 -2.6953 53.463 -2.5840
DUT1LOAD S22 51.736 0.9883 51.736 0.9941 51.736 1.0020
DUT3OPEN S11 11.410 -48.900 11.195 -49.223 10.750 -49.469
DUT3OPEN S22 4.7148 -45.117 4.9355 -45.139 5.0957 -45.229
DUT3SHORT S11 6.2344 54.730 7.1250 57.020 8.4102 59.027
DUT3SHORT S22 0.4297 49.396 0.2754 49.723 0.0859 50.031
DUT3LOAD S11 51.105 -4.5957 51.367 -4.5313 51.617 -4.4102
DUT3LOAD S22 49.766 -1.7520 49.766 -1.7520 49.771 -1.7480
DUT8OPEN S11 4.4312 -6.8726 3.9773 -6.2092 3.5500 -5.3435
DUT8OPEN S22 2.6209 -2.4066 2.5972 -2.3109 2.5236 -2.2214
DUT8SHORT S11 439.88 220.00 432.47 173.41 414.72 146.14
DUT8SHORT S22 0.4380 419.48 6.3440 436.33 13.375 452.64
DUT8LOAD S11 69.992 2.9844 70.457 2.7695 70.879 2.6641
DUT8LOAD S22 68.367 12.438 68.414 12.410 68.477 12.410
DUT13OPEN S11 16.652 96.520 20.215 100.56 24.230 103.57
DUT13OPEN S22 0.1172 84.051 -0.0313 85.688 -0.1172 87.402
DUT13SHORT S11 8.7559 -35.635 8.3301 -35.455 7.7461 -35.113
DUT13SHORT S22 4.1367 -31.157 4.2422 -30.955 4.2949 -30.792
DUT13LOAD S11 54.838 -1.2695 55.176 -1.2637 55.490 -1.1777
DUT13LOAD S22 50.053 -2.4160 50.049 -2.4043 50.049 -2.4102
DUT18OPEN S11 119.97 -196.77 118.16 -188.02 117.47 -182.77
DUT18OPEN S22 190.56 -931.34 181.41 -813.56 174.28 -726.94
DUT18SHORT S11 3.9663 2.0935 3.5715 3.1500 3.2600 4.4053
DUT18SHORT S22 2.2598 10.657 2.1714 11.083 2.0430 11.516
DUT18LOAD S11 39.031 -1.1094 39.232 -0.7500 39.443 -0.3438
DUT18LOAD S22 67.684 11.613 67.750 11.602 67.793 11.602
DUT31OPEN S11 15.188 92.652 18.492 96.754 22.242 99.828
DUT31OPEN S22 -0.1328 85.773 -0.2930 87.414 -0.4375 89.086
DUT31SHORT S11 8.3887 -34.387 7.9609 -34.215 7.3906 -33.887
DUT31SHORT S22 4.2754 -32.299 4.3848 -32.061 4.4404 -31.876
DUT31LOAD S11 50.977 -5.3066 51.248 -5.2402 51.498 -5.1270
DUT31LOAD S22 53.918 2.6738 53.939 2.6621 53.959 2.6543
DUT38OPEN S11 5.5605 46.515 6.2383 49.066 7.3027 51.459
DUT38OPEN S22 0.4082 60.639 0.2324 61.486 0.0371 62.348
DUT38SHORT S11 14.441 -58.812 14.303 -58.975 13.885 -59.143
DUT38SHORT S22 7.6094 -83.711 8.1172 -82.906 8.5469 -82.273
DUT38LOAD S11 51.770 -20.043 51.822 -20.078 51.877 -20.064
DUT38LOAD S22 68.668 16.074 68.770 16.055 68.863 16.066
DUT81OPEN S11 268.30 -244.61 254.63 -227.10 248.54 214.63
DUT81OPEN S22 26.563 -242.95 27.906 -231.59 29.016 -222.07
DUT81SHORT S11 3.9126 8.3657 3.5918 9.7842 3.4150 11.380
DUT81SHORT S22 2.4872 2.7128 2.4357 2.9526 2.3353 3.1884
DUT81LOAD S11 69.156 2.9609 69.609 2.7656 70.027 2.6797
DUT81LOAD S22 36.756 -0.4063 36.725 -0.2871 36.693 -0.1758
DUT83OPEN S11 8.9727 68.633 10.625 71.809 12.758 74.434
DUT83OPEN S22 1.0039 46.852 0.8340 47.598 0.6406 48.373
DUT83SHORT S11 22.730 -82.531 23.012 -82.641 22.918 -82.988
DUT83SHORT S22 5.8008 -58.779 6.0977 -58.438 6.3418 -58.203
DUT83LOAD S11 70.727 6.0781 71.254 5.8359 71.742 5.7188
DUT83LOAD S22 53.939 -19.146 53.854 -19.145 53.777 -19.162
DUT138OPEN S11 9.9922 -40.615 9.5371 -40.168 8.8945 -39.590
DUT138OPEN S22 5.7832 -48.139 5.9473 -47.303 6.0625 -46.521
DUT138SHORT S11 10.750 74.090 12.926 77.953 15.637 81.238
DUT138SHORT S22 0.1641 84.539 0.0117 86.469 -0.1445 88.465
DUT138LOAD S11 55.256 15.723 56.115 15.852 56.945 16.010
DUT138LOAD S22 67.844 16.727 67.949 16.707 68.051 16.723
DUT183OPEN S11 7.6387 -29.037 7.1514 -28.551 6.5371 -27.883
DUT183OPEN S22 5.0547 -43.256 5.2246 -42.818 5.3340 -42.453
DUT183SHORT S11 6.0020 48.278 6.8184 51.176 8.0508 53.916
DUT183SHORT S22 1.0508 85.352 0.9414 88.293 0.8320 91.395
DUT183LOAD S11 37.924 -2.4434 38.076 -2.0762 38.246 -1.6523
DUT183LOAD S22 53.721 -18.354 53.641 -18.369 53.580 -18.383
DUT318OPEN S11 9.5313 -38.738 9.0762 -38.320 8.4551 -37.803
DUT318OPEN S22 5.5859 -47.160 5.7500 -46.357 5.8555 -45.637
DUT318SHORT S11 9.6914 69.133 11.492 72.762 13.918 76.066
DUT318SHORT S22 0.3672 81.941 0.2070 83.852 0.0625 85.816
DUT318LOAD S11 52.301 10.443 53.039 10.613 53.729 10.797
DUT318LOAD S22 65.770 8.7148 65.766 8.7266 65.770 8.7578
DUT381OPEN S11 12.564 -51.678 12.256 -51.563 11.707 -51.379
DUT381OPEN S22 4.0908 -25.968 4.1553 -25.573 4.1631 -25.226
DUT381SHORT S11 17.406 92.809 21.422 98.156 26.074 102.54
DUT381SHORT S22 1.1719 43.873 1.0039 44.807 0.8125 45.779
DUT381LOAD S11 52.020 -19.395 52.076 -19.430 52.139 -19.418
DUT381LOAD S22 35.447 -1.7324 35.410 -1.6016 35.354 -1.4785
DUT813OPEN S11 12.930 -51.824 12.553 -51.420 11.920 -50.938
DUT813OPEN S22 4.5332 -32.676 4.6289 -32.167 4.6689 -31.730
DUT813SHORT S11 17.664 97.094 21.535 101.67 25.879 105.16
DUT813SHORT S22 0.9531 58.936 0.7754 60.291 0.5859 61.695
DUT813LOAD S11 66.984 0.6797 67.348 0.5586 67.691 0.5273
DUT813LOAD S22 47.324 14.275 47.535 14.381 47.738 14.486
DUT831OPEN S11 13.375 53.988 13.004 -53.555 12.371 -53.070
DUT831OPEN S22 4.7266 -34.002 4.8184 -33.422 4.8594 -32.902
DUT831SHORT S11 18.859 101.29 23.059 105.96 27.688 109.39
DUT831SHORT S22 0.6660 62.896 0.5000 64.277 0.3008 65.715
DUT831LOAD S11 70.715 6.9102 71.309 6.6641 71.777 6.5508
DUT831LOAD S22 49.371 20.160 49.615 20.275 49.854 20.416
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Table 1. Single port raw data from the HP8753E network analyzer. | |||||
Raw data for two port measurements.Table 2 gives results with links to screen dumps. | |||
1293MHz 1296MHz 1299MHz
Device Parm. Ampl Phase Ampl Phase Ampl Phase
(U) (Deg) (U) (Deg) (U) (Deg)
none S11 0.04126 -18.57 0.04448 -17.01 0.04740 -15.03
none S12 0.89676 -2.73 0.89260 -1.17 0.88801 -0.47
none S21 0.89551 -1.21 0.89134 0.35 0.88720 1.99
none S22 0.06634 -53.98 0.06730 -63.37 0.06760 -72.80
DUT1 S11 0.03250 -75.86 0.03179 -71.23 0.03079 -65.72
DUT1 S12 0.90215 -104.55 0.90495 -103.23 0.90750 -101.91
DUT1 S21 0.89646 -103.02 0.89797 -101.63 0.90198 -100.27
DUT1 S22 0.07514 76.87 0.08074 69.32 0.08545 61.82
DUT3 S11 0.06879 -69.84 0.06939 -68.30 0.06938 -66.59
DUT3 S12 0.89280 -48.58 0.89234 -47.01 0.89189 -45.43
DUT3 S21 0.89056 -47.21 0.88955 -45.62 0.88982 -44.02
DUT3 S22 0.07484 -144.97 0.07552 -153.43 0.07533 -162.03
DUT8 S11 0.15108 1.77 0.15352 1.33 0.15581 1.23
DUT8 S12 0.89531 -87.79 0.89591 -86.54 0.89588 -85.28
DUT8 S21 0.88299 -86.34 0.88118 -84.90 0.88075 -84.45
DUT8 S22 0.18927 47.64 0.20076 47.34 0.21216 46.39
DUT13 S11 0.04304 11.96 0.04742 11.40 0.05122 11.64
DUT13 S12 0.89828 -151.08 0.90022 -149.68 0.90160 -151.08
DUT13 S21 0.89584 -149.54 0.89734 -148.14 0.90029 -146.66
DUT13 S22 0.06994 -21.96 0.07639 -29.61 0.08211 -37.42
DUT18 S11 0.10312 -177.16 0.09974 -179.04 0.09642 178.49
DUT18 S12 0.89105 171.29 0.89355 172.74 0.89591 174.19
DUT18 S21 0.89071 173.38 0.89416 174.76 0.89858 176.11
DUT18 S22 0.17234 7.16 0.16120 6.04 0.14955 5.85
DUT31 S11 0.03119 -77.77 0.03101 -71.15 0.03073 -64.33
DUT31 S12 0.89914 -150.86 0.90153 -149.45 0.90348 -148.02
DUT31 S21 0.89478 -149.12 0.89749 -147.66 0.90156 -146.22
DUT31 S22 0.10520 12.40 0.10516 5.87 0.10381 -0.68
DUT38 S11 0.17781 -77.77 0.17752 -77.43 0.17680 -77.06
DUT38 S12 0.88013 -133.72 0.88056 -132.28 0.88071 -130.83
DUT38 S21 0.86593 -131.39 0.86743 -129.75 0.87112 -128.12
DUT38 S22 0.26897 32.78 0.27142 30.28 0.27194 27.76
DUT81 S11 0.18346 8.46 0.18668 7.61 0.18946 6.95
DUT81 S12 0.87640 170.77 0.87658 172.32 0.87552 173.91
DUT81 S21 0.87365 171.44 0.87036 173.02 0.86966 174.65
DUT81 S22 0.15631 -155.65 0.16695 -156.45 0.17799 -157.97
DUT83 S11 0.16940 19.49 0.17284 18.60 0.17629 18.03
DUT83 S12 0.87979 -134.74 0.87801 -133.39 0.87555 -132.00
DUT83 S21 0.87938 -133.35 0.87623 -131.92 0.87424 -130.42
DUT83 S22 0.18632 -49.20 0.19711 -49.49 0.20788 -50.42
DUT138 S11 0.13962 56.24 0.14204 53.70 0.14479 51.56
DUT138 S12 0.89077 124.13 0.88940 125.39 0.88753 126.56
DUT138 S21 0.88534 125.37 0.88106 126.53 0.87770 127.79
DUT138 S22 0.15274 45.68 0.15920 49.26 0.16867 51.92
DUT183 S11 0.13903 -158.30 0.13675 -159.73 0.13434 -161.55
DUT183 S12 0.87110 124.91 0.87160 126.30 0.87218 127.64
DUT183 S21 0.87926 126.76 0.88098 128.02 0.88369 129.23
DUT183 S22 0.17494 -88.21 0.16435 -89.60 0.15306 -90.08
DUT318 S11 0.08784 62.85 0.09025 59.46 0.09305 56.55
DUT318 S12 0.89399 124.68 0.89290 125.96 0.89161 127.17
DUT318 S21 0.89101 126.00 0.88779 127.21 0.88578 128.45
DUT318 S22 0.09567 34.99 0.09998 41.76 0.10819 47.08
DUT381 S11 0.20951 -73.40 0.21020 -73.48 0.21035 -73.51
DUT381 S12 0.85672 125.31 0.85611 126.85 0.85613 128.39
DUT381 S21 0.85099 126.48 0.85026 128.10 0.85175 129.73
DUT381 S22 0.23091 -171.71 0.23387 -174.82 0.23525 -177.97
DUT813 S11 0.15462 -5.98 0.15655 -6.42 0.15822 -6.55
DUT813 S12 0.88475 124.81 0.88341 126.10 0.88199 127.42
DUT813 S21 0.87295 125.72 0.86890 127.13 0.86641 128.63
DUT813 S22 0.15402 115.70 0.16527 114.40 0.17630 112.35
DUT831 S11 0.18211 8.34 0.18402 7.52 0.18634 6.99
DUT831 S12 0.88305 124.28 0.88128 125.55 0.87932 126.82
DUT831 S21 0.86951 125.13 0.86451 126.55 0.86074 128.00
DUT831 S22 0.18934 98.28 0.20089 98.05 0.21292 97.10
Table 2. Two port raw data from the HP8753E network analyzer. | |
Theory.Table 1 contains 192 measured values for each frequency and table 2 contains 128. That is 320 data points. We can set up a model for all the measurements with one S-parameter matrix for each of the three DUTs. That is 18 unknowns. (S12 = S21) The calibration kit contains 6 parts and can be described by two variables each. That is 12 more unknowns. As a theoretical model we can assume a perfectly matched port on each side followed by a matching network that produces the impedances that actually occur at the SMA connectors. That gives 12 more unknowns. Finally, there is a DC offset caused by leak-through in the directional couplers which adds 4 more unknowns. In total 46 unknowns which are required to set up a model to reproduce the experimental results. The "unknowns" are actually known, but not with high enough precision. By setting up all the equations and using a least squares fit it should be possible to find the optimum values for all the unknowns. The S-parameters for the three DUTs is of particular interest since they would give the dissipative losses.This all looked like a good idea when I started it, but as it turns out I am not smart enough to set up all the equations right. Particularly, the measurements labeled none constitute a complete set of the measurements required for a "full calibration" of the instrument. All the HP 85033C calibration kit parts, port impedances and forward as well as reverse transmission are included. This page and the data was prepared before I realized processing was not so simple (at least not for me.) Iy you have a suggestion how to proceed, pleas send a note. |