The DUTs | |||||||||||||||||||||||||||||||||||
Figure 1. DUTs with SMA connectors. | |||||||||||||||||||||||||||||||
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 Rx port.The Rx port of the HP8712C network analyzer is nominally 50 ohms. Specifications say that the return loss should be 18 dB. For insertion loss measurements the Rxport (load) should be a male SMA connector while the Tx port has to be a female SMA. Figure 2 shows the measurement of the Rx port impedance. A Flexiform 401 (impedance stable) cable with male N precision connectors in both ends was held in a position as seen in the figure. Open, short and load of the calibration kit were used to calibrate with very small movements of the cable. Finally the Tx port was connected to the Rx port which produced the result in figure 3. Return loss is 20 dB which is well within specification. The SMA to N adapter does not do any harm. | |||||||||||||||||||||||||||||
Figure 2. Investigating the Rx port of the HP8712C network analyzer. Here the last step of calibration is done. The calibration kit load is in red colour. | |||||||||||||||||||||||||
Figure 3. Investigating the Rx port of the HP8712C network analyzer. The magnitude of the impedance error is about 10 ohms. For the measurement of small insertion losses a much better matching is desireable. | |||||||||||||||||||
There are many ways to make the Rx port well matched. In this study attenuators were used because that particular set of attenuators with a well known impedance will be useful as the Tx port for insertion loss measurements using a radio receiver and a signal generator. The impedance of the Rx port with and without DUTs.The setup for impedance as well as insertion loss measurements is shown in figure 4. | |||||||||||||||||
Figure 4. The Tx port on the left side is fixed. The Rx port can be moved axially, the black coaxial cable can slide axially in the "third hand." | |||||||||||||
The Rx port starts with a 3 dB attenuator followed by a 6 dB attenuator and about 1 m of Flexiform 401 cable with an extra screen on it. This cable is in a soft bend and allows the small axial movement with extremely small impedance changes. The cable is followed by a 40 dB attenuator. The impedance of the Rx port is very insensitive to the impedance of whatever is connected to the other side of the 40 dB attenuator. It does not matter if it is connected to the Network analyzer or to a signal generator. Raw data for impedances and losses.Table 1 gives results with links to VNA screen dumps | |||||||||||
Device Zre Zim Loss Equ (Ohm) (Ohm) (dB) none 52.02 0.21 -0.002 1 DUT1 50.34 0.69 0.010 2 DUT3 49.09 -2.56 -0.009 3 DUT4 50.45 0.16 0.024 4 DUT7 51.84 -2.46 0.039 5 DUT13 54.04 2.24 0.071 6 DUT43 52.97 3.10 0.079 7 DUT73 55.71 0.68 0.096 8 DUT37 46.71 -2.12 0.060 9 DUT34 49.16 -0.95 0.058 10 DUT31 49.67 -1.00 0.046 11 DUT8 71.81 0.51 0.198 12 DUT83 75.04 5.42 0.289 13 DUT81 74.35 0.20 0.313 14 DUT813 69.27 -2.47 0.281 15 DUT318 55.75 14.82 0.228 16 DUT381 44.59 -18.52 0.288 17 DUT831 74.80 2.61 0.355 18 DUT183 34.89 3.87 0.199 19 DUT138 59.53 19.49 0.311 20 DUT6 53.04 1.89 0.136 - DUT18 36.77 4.60 0.214 21 DUT38 45.70 -17.41 0.142 22 DUT48 36.75 0.00 0.207 23 DUT84 73.83 1.24 0.271 24 DUT14 51.73 -0.41 0.108 25 DUT41 51.89 -0.11 0.108 26 DUT5 51.43 -0.19 0.102 - | |||||||||
Table 1. Raw data from the HP8712C network analyzer. | |||||||
Evaluation of unknowns.The impedances in table 1 all contain the unknown calibration error from the calibration kit.The insertion loss should be the sum of the mismatch loss and the sum of the dissipative losses for the DUT. Disregarding DUT5 and DUT6 which are not measured together with other DUTs we have this set of unknowns: x(1)=The dissipative loss of DUT1 x(2)=The dissipative loss of DUT3 x(3)=The dissipative loss of DUT4 x(4)=The dissipative loss of DUT7 x(5)=The dissipative loss of DUT8 x(6)=The calibration error real part x(7)=The calibration error imaginary part x(8)=The Tx port impedance error real part x(9)=The Tx port impedance error imaginary part There are 26 equations that connect these 9 unknown variables. For each line in table 1, the loss should be the sum of the dissipative losses plus the insertion loss. The insertion loss can be computed from this formula: IL = 4 * Rt * Rr / [ (Rt + Rr)2 + (Xt + Xr)2 ] Rt is the real part of the Tx port impedance. Xt is the imaginary part of the Tx port impedance. Rr is the real part of the Rx port impedance. Xr is the imaginary part of the Rx port impedance. From the equation it is obvious that we can not determine Xt and Xr separately, only their sum. Also Rt and Rr are strongly coupled. This means that we have 26 equations and 7 independent variables. The RMS deviation produced by a least squares fit will give a good insight in the measurement errors. A simple Fortran program with a Makefile for Linux can be downloaded here: losscalc100.tbz (5536 bytes) Running it with table 1 as input produces the listing displayed in table 2. | |||||
DUT100 ( 50.340 0.690) il= 0.0100 Dissipat.= 0.0556 err= 0.0419 DUT300 ( 49.090 -2.560) il=-0.0090 Dissipat.= 0.0096 err= 0.0120 DUT400 ( 50.450 0.160) il= 0.0240 Dissipat.= 0.0509 err= 0.0227 DUT700 ( 51.840 -2.460) il= 0.0390 Dissipat.= 0.0561 err= 0.0163 DUT130 ( 54.040 2.240) il= 0.0710 Dissipat.= 0.0653 err= 0.0052 DUT430 ( 52.970 3.100) il= 0.0790 Dissipat.= 0.0605 err=-0.0093 DUT730 ( 55.710 0.680) il= 0.0960 Dissipat.= 0.0658 err=-0.0144 DUT370 ( 46.710 -2.120) il= 0.0600 Dissipat.= 0.0658 err=-0.0019 DUT340 ( 49.160 -0.950) il= 0.0580 Dissipat.= 0.0605 err=-0.0046 DUT310 ( 49.670 -1.000) il= 0.0460 Dissipat.= 0.0653 err= 0.0129 DUT800 ( 71.810 0.510) il= 0.1980 Dissipat.= 0.0771 err= 0.0267 DUT830 ( 75.040 5.420) il= 0.2890 Dissipat.= 0.0867 err=-0.0094 DUT810 ( 74.350 0.200) il= 0.3130 Dissipat.= 0.1327 err=-0.0055 DUT813 ( 69.270 -2.470) il= 0.2810 Dissipat.= 0.1424 err=-0.0175 DUT318 ( 55.750 14.820) il= 0.2280 Dissipat.= 0.1424 err= 0.0149 DUT381 ( 44.590 -18.520) il= 0.2880 Dissipat.= 0.1424 err=-0.0298 DUT831 ( 74.800 2.610) il= 0.3550 Dissipat.= 0.1424 err=-0.0297 DUT183 ( 34.890 3.870) il= 0.1990 Dissipat.= 0.1424 err= 0.0283 DUT138 ( 59.530 19.490) il= 0.3110 Dissipat.= 0.1424 err= 0.0020 DUT600 ( 53.040 1.890) il= 0.1360 Dissipat.= 0.1298 err= 0.0000 DUT180 ( 36.770 4.600) il= 0.2140 Dissipat.= 0.1327 err=-0.0175 DUT380 ( 45.700 -17.410) il= 0.1420 Dissipat.= 0.0867 err= 0.0413 DUT480 ( 36.750 0.000) il= 0.2070 Dissipat.= 0.1280 err=-0.0308 DUT840 ( 73.830 1.240) il= 0.2710 Dissipat.= 0.1280 err= 0.0271 DUT140 ( 51.730 -0.410) il= 0.1080 Dissipat.= 0.1065 err=-0.0029 DUT410 ( 51.890 -0.110) il= 0.1080 Dissipat.= 0.1065 err=-0.0022 DUT500 ( 51.430 -0.190) il= 0.1020 Dissipat.= 0.1041 err=-0.0000 RMS error= 0.02004 alfa= 0.000000 step= 0.000137 1 DUT1 Dissipative loss=0.0556 2 DUT3 Dissipative loss=0.0096 3 DUT4 Dissipative loss=0.0509 4 DUT7 Dissipative loss=0.0561 5 DUT8 Dissipative loss=0.0771 6 DUT6 Dissipative loss=0.1298 7 DUT5 Dissipative loss=0.1041 8 Source impedance real part= 57.392 9 Load impedance real part= 52.835 10 Sum of complex parts= 1.269 | |||
Table 2. Results from the evaluation of dissipative losses from insertion losses measured with the HP8712C network analyzer. | |
The RMS error in the evaluation of the equations is 0.02 dB. That is by far not good enough for a DUT with a resistive loss in the order of 0.05 dB. |