The measurement problem.Modern low noise amplifiers can give noise temperatures down to about 10 K when the device is operated at room temperature. When such amplifiers are used together with low noise antennas very small losses cause significant degradation of S/N even though the change of the NF (referenced to 290 K) would be very small.By use of cryogenic systems one can avoid the problem completely. That is what professionals do. It is however possible to do accurate measurements at room temperature with equipment available to radio amateurs. That requires measurement of noise power ratios that are close to one and therefore such measurements are slow. We can measure changes in NF by use of S/N ratios or by use of NF meters where circulators are used to isolate from the impedance variations of the noise source. The NF measurements on this page was used with this setup: Using the HP8970A with circulators. The NF will change when something (a DUT) is inserted immediately in front of a LNA. The change depends on two factors: 1) The NF of the LNA itself depends on the feed impedance. 2) Anything inserted in front of a LNA will have dissipative losses that degrade NF by attenuating the signal and adding thermal noise. We want to measure the second effect and need to know the first effect in order to correct for it. Note that mismatch losses are accounted for by the NF vs impedance variation which has to be known at the point where the DUT is inserted. A good LNA has a far more shallow minimum for the NF than the same LNA with an attenuator in front of it. The L LNA by AD6IW has a NF a little below 0.3 dB for a source impedance near 50 ohms. For VSWR=1.5:1 the NF increases by about 0.045 dB regardless of whether the feed impedance is 33 or 75 ohms or reactive. Finding the optimum input impedance for an LNA on 1296 MHz. The NF vs impedance variation is however uncertain. It depends on the knowledge of the losses in the devices used to change the impedance. The above link assumes that the losses of the impedance tuner is 0.0807 dB. The impedance tuner losses is the sum of the losses of DUT1, DUT3 and DUT8. but the S11 method gives 0.094 dB which (if correct) would make the NF minimum about 20% more shallow. An overkill study.By measuring the NF as well as the impedance of with many combinations of DUT1, DUT3, DUT8, DUTA, DUTB and DUTC one can map many points on the NF vs impedance surface. The dissipative losses are additive while the impedance changes are not (they are periodic) so one can set up an over-determined equation system for the six losses and the two parameters that determine the NF vs impedance map. By use of so many combinations of so many DUTs it should be possible to evaluate where accuracy problems occur.Table 1 shows measured noise figures and DUT impedances. The network analyzer was calibrated with a home-made calibration kit for which the accuracy might be a little uncertain. Open and short should be fairly accurate, but the load might deviate a little from 50 ohms. The DC resistance is 49.5 ohms. Each DUT is measured on the calibrated female SMA connector with the calibration load on the female connector of the DUT. Table 1 shows all the raw data. | |||||||||||||||||
Device N Tamb Te Zre Zim
(Deg. C) (K) (Ohms) (j Ohms)
NONE 108 26.5 18.29 50.00 0.00
CBA183 166 26.4 32.89 55.29 0.60
CBA 273 26.5 26.49 36.23 -4.55
183CBA 165 26.4 38.73 27.13 -9.64
183 560 26.1 26.54 53.60 -17.42
ACB 325 25.7 27.15 67.53 10.41
ACB831 163 26.0 32.81 56.76 3.06
831 212 26.1 25.91 50.31 19.40
831ACB 244 26.3 39.43 97.10 21.69
831ABC 239 26.0 36.82 80.72 -23.35
318ABC 124 25.7 37.12 60.67 -32.02
318 120 25.9 25.81 63.82 7.78
ABC318 620 26.1 33.07 46.40 2.81
ABC 278 28.0 27.40 55.50 -17.06
NONE 238 28.3 18.39 50.00 0.00
BCA 265 27.5 26.45 40.54 13.61
BCA381 431 28.0 32.34 50.82 1.09
381 174 27.8 25.57 35.66 -1.43
381BCA 141 27.6 37.60 31.68 21.49
138BCA 1744 27.3 32.83 58.88 7.14
138 267 27.1 26.56 66.17 17.03
BCA138 470 26.5 38.93 89.93 31.27
BCA183 611 26.8 36.77 76.19 -22.25
183BCA 250 27.2 34.11 32.73 4.39
ABC381 237 27.3 37.75 25.78 -2.79
381ABC 303 27.2 32.76 50.53 -0.25
NONE 282 27.3 18.46 50.00 0.00
CBA831 203 27.2 38.55 41.44 32.31
831CBA 179 27.4 32.39 53.06 -4.17
813 202 27.2 25.34 47.63 13.07
BAC 239 27.4 26.95 41.10 13.91
CAB 170 27.3 27.37 68.45 11.11
CA 130 27.3 23.33 51.02 -0.09
C 268 26.9 20.84 50.37 1.11
CB 127 27.2 24.62 69.93 10.10
B 216 27.1 22.37 69.50 11.81
BC 406 27.6 24.51 56.95 -18.30
BA 209 27.7 24.29 36.21 -5.55
A 136 27.7 21.14 51.22 1.18
AB 200 27.5 25.20 68.83 9.55
AC 211 27.7 23.47 51.70 0.03
81 374 27.8 23.83 36.85 -0.51
8 424 27.8 22.28 67.14 11.65
83 387 28.0 24.29 53.65 -19.52
3 322 27.7 20.23 49.19 -1.82
38 241 27.5 24.32 67.20 14.25
31 440 27.8 22.68 53.98 1.71
1 298 27.8 21.05 52.38 0.28
13 200 28.0 22.59 49.18 -4.12
18 362 28.3 24.88 64.46 10.07
4 272 28.3 22.52 52.01 1.23
5 493 28.2 22.90 49.84 1.10
6 250 28.1 26.63 50.43 2.28
7 501 27.9 23.19 54.08 -0.67
D 144 27.9 23.72 50.74 0.90
8B 268 28.0 23.73 54.96 -4.52
B8A 129 28.2 25.68 50.49 4.29
B8 419 28.2 23.33 50.47 -3.16
B8C 393 28.1 25.51 47.36 0.46
3C 433 28.9 22.58 48.60 1.87
C3 193 28.7 22.74 50.24 -2.25
NONE 1280 28.6 18.57 50.00 0.00
A1 247 28.6 23.79 50.82 -0.16
1A 290 28.6 23.67 48.83 0.88
C3A 206 28.8 25.16 50.93 3.27
3CA 522 28.6 25.27 52.86 -1.04
A3C 449 28.7 25.11 47.31 0.74
AC3 506 28.5 25.27 48.87 -3.47
END
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Table 1 NF and impedances for combinations of DUTs. N is the number of averages of 64 averages. Tamb is the room temperature. Te is the averaged result from the 8970A. Zre and Zim is the impedance seen by the LNA. | |||||||||||||
Table 1 is used as the input to this computer program nfdut-1.0.tbz (17669 bytes) It is a simple fortran program that makes a guess for the S parameters of the 12 DUTs in table 1. It then computes the impedance of series connected DUTs and adjusts the parameters for an optimum fit. After 20 iterations when the S parameters have converged the program computes the NF for the fitted impedance in each case using four guessed parameters. Two for the optimum source impedance one for the shallowness of the noise minimum and one for the zero point of the NF scale. The program continues to optimize all the parameters. First with a small weight on the NF agreement, but at the end with a large weigtht on that. The raw data Te from table 1 is first corrected for the variations of the room temperature to give the value that would have been observed at a room temperature of 26 Centigrade. The Te value is then converted to NF using the actual system temperature 299 K which means that the NF degradation is equal to the dissipative loss plus the change in NF due to the impedance change. The output of the parameter fit is listed in table 2. | |||||||||||
Dev. Z(mea) Zerr Loss NF(mea) NFerr VSWR NF NFloss 0 (50.00, 0.00) 0.00 -0.0000 0.2569 0.0010 1.0000 0.2559 0.0002 CBA183(55.29, 0.60) 0.15 0.1903 0.4525 0.0039 1.1080 0.2582 0.0026 CBA (36.23, -4.55) 0.07 0.0994 0.3677 -0.0043 1.4064 0.2726 0.0169 183CBA(27.13, -9.64) 0.25 0.1903 0.5283 0.0117 1.9548 0.3262 0.0705 183 (53.60,-17.42) 0.12 0.0889 0.3691 0.0021 1.4062 0.2782 0.0225 ACB (67.53, 10.41) 0.35 0.0994 0.3780 0.0022 1.4247 0.2765 0.0208 ACB831(56.76, 3.06) 0.59 0.1903 0.4522 0.0022 1.1514 0.2597 0.0040 831 (50.31, 19.40) 0.37 0.0889 0.3607 -0.0048 1.4796 0.2766 0.0210 831ACB(97.10, 21.69) 0.07 0.1903 0.5374 0.0030 2.0724 0.3441 0.0884 831ABC(80.72,-23.35) 0.33 0.1903 0.5044 -0.0054 1.8136 0.3194 0.0637 318ABC(60.67,-32.02) 0.20 0.1903 0.5088 -0.0031 1.8232 0.3215 0.0658 318 (63.82, 7.78) 0.30 0.0889 0.3598 0.0023 1.3185 0.2686 0.0129 ABC318(46.40, 2.81) 0.06 0.1903 0.4554 0.0089 1.1002 0.2562 0.0005 ABC (55.50,-17.06) 0.09 0.0994 0.3771 -0.0001 1.4008 0.2778 0.0221 0 (50.00, 0.00) 0.00 -0.0000 0.2548 -0.0011 1.0000 0.2559 0.0002 BCA (40.54, 13.61) 0.10 0.0994 0.3653 -0.0064 1.4443 0.2724 0.0167 BCA381(50.82, 1.09) 0.21 0.1903 0.4424 -0.0040 1.0254 0.2560 0.0003 381 (35.66, -1.43) 0.08 0.0889 0.3530 -0.0071 1.4015 0.2713 0.0156 381BCA(31.68, 21.49) 0.14 0.1903 0.5115 -0.0011 1.9999 0.3223 0.0666 138BCA(58.88, 7.14) 0.40 0.1903 0.4501 -0.0031 1.2315 0.2628 0.0071 138 (66.17, 17.03) 0.34 0.0889 0.3675 -0.0023 1.4930 0.2810 0.0253 BCA138(89.93, 31.27) 0.07 0.1903 0.5307 -0.0044 2.0930 0.3448 0.0891 BCA183(76.19,-22.25) 0.12 0.1903 0.5023 0.0014 1.7332 0.3106 0.0549 183BCA(32.73, 4.39) 0.10 0.1903 0.4670 -0.0046 1.5517 0.2812 0.0255 ABC381(25.78, -2.79) 0.03 0.1903 0.5140 0.0020 1.9451 0.3217 0.0660 381ABC(50.53, -0.25) 0.12 0.1903 0.4493 0.0029 1.0095 0.2560 0.0004 0 (50.00, 0.00) 0.00 -0.0000 0.2577 0.0018 1.0000 0.2559 0.0002 CBA831(41.44, 32.31) 0.12 0.1903 0.5245 0.0039 2.0540 0.3303 0.0746 831CBA(53.06, -4.17) 0.06 0.1903 0.4441 -0.0050 1.1068 0.2588 0.0031 813 (47.63, 13.07) 0.13 0.0889 0.3510 -0.0024 1.3104 0.2645 0.0089 BAC (41.10, 13.91) 0.22 0.0994 0.3722 0.0005 1.4428 0.2723 0.0166 CAB (68.45, 11.11) 0.14 0.0994 0.3780 0.0005 1.4446 0.2781 0.0224 CA (51.02, -0.09) 0.20 0.0681 0.3238 -0.0004 1.0165 0.2561 0.0004 C (50.37, 1.11) 0.07 0.0319 0.2909 0.0031 1.0249 0.2559 0.0002 CB (69.93, 10.10) 0.20 0.0630 0.3414 -0.0005 1.4518 0.2790 0.0233 B (69.50, 11.81) 0.16 0.0308 0.3113 0.0004 1.4674 0.2800 0.0243 BC (56.95,-18.30) 0.26 0.0630 0.3392 -0.0049 1.4385 0.2811 0.0255 BA (36.21, -5.55) 0.21 0.0670 0.3360 -0.0049 1.4207 0.2739 0.0182 A (51.22, 1.18) 0.08 0.0359 0.2935 0.0015 1.0325 0.2561 0.0004 AB (68.83, 9.55) 0.09 0.0670 0.3486 0.0045 1.4298 0.2771 0.0215 AC (51.70, 0.03) 0.18 0.0681 0.3250 0.0006 1.0305 0.2563 0.0006 81 (36.85, -0.51) 0.27 0.0664 0.3296 -0.0051 1.3630 0.2683 0.0127 8 (67.14, 11.65) 0.24 0.0324 0.3087 -0.0003 1.4293 0.2767 0.0210 83 (53.65,-19.52) 0.22 0.0546 0.3354 -0.0028 1.4678 0.2836 0.0279 3 (49.19, -1.82) 0.11 0.0221 0.2811 0.0026 1.0433 0.2564 0.0007 38 (67.20, 14.25) 0.17 0.0546 0.3368 0.0025 1.4705 0.2796 0.0240 31 (53.98, 1.71) 0.08 0.0561 0.3141 0.0008 1.0855 0.2573 0.0016 1 (52.38, 0.28) 0.16 0.0338 0.2920 0.0017 1.0448 0.2565 0.0009 13 (49.18, -4.12) 0.09 0.0561 0.3125 -0.0012 1.0872 0.2576 0.0020 18 (64.46, 10.07) 0.38 0.0664 0.3428 0.0044 1.3697 0.2720 0.0163 4 (52.01, 1.23) 0.00 0.0547 0.3110 0.0000 1.0473 0.2564 0.0007 5 (49.84, 1.10) 0.00 0.0606 0.3163 0.0000 1.0225 0.2558 0.0001 6 (50.43, 2.28) 0.00 0.1107 0.3666 0.0000 1.0473 0.2559 0.0002 7 (54.08, -0.67) 0.00 0.0632 0.3208 0.0000 1.0827 0.2576 0.0020 D (50.74, 0.90) 0.00 0.0720 0.3280 0.0000 1.0234 0.2560 0.0003 8B (54.96, -4.52) 0.29 0.0634 0.3279 0.0047 1.1318 0.2598 0.0041 B8A (50.49, 4.29) 0.34 0.0998 0.3537 -0.0024 1.0847 0.2563 0.0006 B8 (50.47, -3.16) 0.19 0.0634 0.3221 0.0016 1.0633 0.2572 0.0015 B8C (47.36, 0.46) 0.15 0.0958 0.3516 -0.0000 1.0534 0.2558 0.0002 3C (48.60, 1.87) 0.19 0.0542 0.3107 0.0008 1.0516 0.2557 0.0000 C3 (50.24, -2.25) 0.12 0.0542 0.3132 0.0023 1.0487 0.2568 0.0011 0 (50.00, 0.00) 0.00 -0.0000 0.2567 0.0008 1.0000 0.2559 0.0002 A1 (50.82, -0.16) 0.18 0.0700 0.3276 0.0015 1.0144 0.2561 0.0004 1A (48.83, 0.88) 0.19 0.0700 0.3260 0.0002 1.0263 0.2557 0.0000 C3A (50.93, 3.27) 0.32 0.0905 0.3456 -0.0011 1.0731 0.2562 0.0005 3CA (52.86, -1.04) 0.19 0.0905 0.3475 -0.0001 1.0594 0.2570 0.0014 A3C (47.31, 0.74) 0.10 0.0905 0.3451 -0.0012 1.0591 0.2558 0.0001 AC3 (48.87, -3.47) 0.19 0.0905 0.3477 -0.0001 1.0734 0.2572 0.0015 | |||||||||
Table 2. Result from parameter fitting. The column Zerr shows the magnitude of the difference between the measured impedance and the impedance computed from the S parameters for the 11 DUTs. NFerr shows the difference between the measured NF and the NF computed from the losses and the NF parameters. NFloss shows the loss of NF due to the non-optimum source impedance. | |||||||
From table 2 we can conclude that the NF is within 0.01 dB from the optimum NF for VSWR below 1.3 and within 0.03 dB from optimum for VSWR below 1.5. Knowing that the errors due to the VSWR is so small is useful because it means that we can measure losses as NF degradation without much concern of the mismatch as long as it is reasonable. The nfdut program also produces a list of the 11 DUTs which is shown in table 3. | |||||
Impedance for minimum NF = (48.68, 1.45) Ohms Optimum NF = 0.2557 dB (scale offset = 0.0638) Device Loss S11 S12=S21 S22 DUT1 0.0338 (0.0218,0.0022) (0.2243,0.9703) (0.0067,-.0019) DUT3 0.0221 (-.0085,-.0194) (0.6926,-.7174) (-.0348,-.0177) DUT4 0.0547 (0.0198,0.0118) (0.6990,0.7059) (0.0247,0.0069) DUT5 0.0606 (-.0015,0.0110) (0.6961,0.7082) (0.0039,0.0134) DUT6 0.1107 (0.0048,0.0226) (0.7004,0.6956) (0.0013,0.0181) DUT7 0.0632 (0.0392,-.0062) (0.7175,0.6849) (0.0285,-.0221) DUT8 0.0324 (0.1560,0.0830) (-.1003,0.9753) (0.1293,-.0476) DUTA 0.0359 (0.0116,0.0110) (-.0125,0.9957) (0.0198,-.0365) DUTB 0.0308 (0.1713,0.0808) (-.1309,0.9695) (0.1912,-.0079) DUTC 0.0319 (0.0038,0.0117) (0.7138,-.6950) (0.0188,0.0191) DUTD 0.0720 (0.0074,0.0089) (0.6879,0.7143) (0.0016,-.0004) | |||
Table 3. Output from nfdut. | |