Overview of Battery Impedance Modeling Including Detailed State-of-the-Art Cylindrical 18650 Lithium-Ion Battery Cell Comparisons †
<p>Dynamic battery model with three <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics></math>-pairs.</p> "> Figure 2
<p>Dynamic battery model with a Warburg impedance element.</p> "> Figure 3
<p>Battery cell testing of a cylindrical 18650 battery cell [<a href="#B25-energies-15-03822" class="html-bibr">25</a>].</p> "> Figure 4
<p>Obtained Nyquist plot from EIS measurements for a cylindrical 18650 battery cell from LG Chem of model type HG2 with a nominal capacity of 3000 mAh.</p> "> Figure 5
<p>Model of a battery cell with respect to the effect of the model’s individual components on the Nyquist plot. (<b>a</b>) Three-<math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics></math>-pair model. (<b>b</b>) Warburg impedance model. In addition to the color highlighting, the labeled arrows represent the resistive and inductive parameters of the equivalent circuits.</p> "> Figure 6
<p>Obtained Bode plot from EIS measurements (green) in comparison to the parameterized Warburg impedance (red) and three-<math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics></math>-pair (blue) model for a cylindrical 18650 battery cell from LG Chem of model type HG2 with a nominal capacity of 3000 mAh.</p> "> Figure 7
<p>Obtained Nyquist plot from EIS measurements (green) in comparison to the parameterized Warburg impedance (red) and three-<math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics></math>-pair (blue) model for a cylindrical 18650 battery cell from LG Chem of model type HG2 with a nominal capacity of 3000 mAh.</p> "> Figure 8
<p>Measured cell voltage behavior for a current step in comparison to simulations for a cylindrical 18650 battery cell from LG Chem of model type HG2 with a nominal capacity of 3000 mAh.</p> "> Figure 9
<p>Comparisons of the different <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics></math>-pair models relative to the computational effort (red) and accuracy (green).</p> "> Figure 10
<p>Electrochemical impedance spectroscopy sweep of all selected cells.</p> "> Figure 11
<p>Radar chart: multiple-criteria evaluation of the selected state-of-the-art battery cells.</p> ">
Abstract
:1. Introduction
2. Recent Research on 18650 Lithium-Ion Battery Cells
3. Battery Modeling and Parameter Extraction Using Electrochemical Impedance Spectroscopy
3.1. Battery Modeling
3.1.1. RC-Link Models
3.1.2. Warburg Model
3.2. Electrochemical Impedance Spectroscopy
3.3. Parameter Extraction
3.4. Simulation in Time-Domain
4. Battery Cell Comparisons
Manufacturer | Model | Capacity Q [mAh] | Voltage [V] | C-Rate | Spec. Energy | Price [USD] |
---|---|---|---|---|---|---|
Keeppower | P1834J | 3400 | 3.7 | 2 | 262.08 | 11.53 |
LG Chem | HG2 | 3000 | 3.6 | 6.7 | 226.53 | 14.43 |
LG Chem | M26 | 2600 | 3.65 | 4 | 200.42 | 5.45 |
LG Chem | MJ1 | 3500 | 3.635 | 3 | 264.29 | 8.43 |
Lithium Werks | M1B | 2500 | 3.3 | 28 | 112.89 | 6.55 |
Murata | V3 | 2250 | 3.7 | 4.4 | 189.20 | 2.73 |
Murata | VTC5A | 2250 | 3.7 | 13.5 | 213.78 | 10.85 |
Murata | VTC6 | 3120 | 3.7 | 10 | 247.73 | 9.64 |
Nitecore | NL1835HP | 3500 | 3.6 | 2.3 | 239.81 | 29.04 |
Samsung | 30Q | 3000 | 3.6 | 5 | 231.25 | 12.01 |
Sanyo | ZT | 2700 | 3.7 | 2 | 207.26 | 2.61 |
Manufacturer | Model | ||||||||
---|---|---|---|---|---|---|---|---|---|
Keeppower | P1834J | 147.40 | 250.73 | 100.07 | 6.90 | 1.06 | 8.16 | 0.08 | 1.96 |
LG Chem | HG2 | 88.88 | 251.07 | 17.76 | 1.00 | 1.84 | 2.49 | 0.18 | 1.80 |
LG Chem | M26 | 409.17 | 882.39 | 40.66 | 5.91 | 0.24 | 1.64 | 3.77 | 2.00 |
LG Chem | MJ1 | 410.74 | 755.26 | 43.93 | 4.47 | 0.35 | 0.09 | 28.79 | 1.91 |
Lithium Werks | V3 | 25.78 | 145.36 | 6.63 | 0.72 | 11.22 | 1.59 | 0.27 | 1.86 |
Murata | V3 | 414.44 | 816.17 | 33.86 | 1.81 | 5.64 | 7.05 | 0.19 | 2.46 |
Murata | VTC5A | 79.91 | 208.19 | 73.56 | 3.05 | 0.16 | 1.61 | 1.26 | 1.70 |
Murata | VTC6 | 74.23 | 209.11 | 12.74 | 1.38 | 1.51 | 3.30 | 0.13 | 1.76 |
Nitecore | NL1835HP | 187.59 | 226.58 | 53.67 | 5.38 | 1.59 | 8.23 | 0.13 | 2.17 |
Samsung | 30Q | 73.97 | 178.70 | 13.24 | 2.57 | 0.16 | 0.78 | 1.81 | 1.98 |
Sanyo | ZT | 274.49 | 476.19 | 41.10 | 30.18 | 0.10 | 48.17 | 0.44 | 4.47 |
Manufacturer | Model | ||||||||
---|---|---|---|---|---|---|---|---|---|
Keeppower | P1834J | 136.71 | 99.10 | 9.53 | 67.71 | 7.85 | 1.29 | 16.93 | 1033.82 |
LG Chem | HG2 | 86.38 | 17.41 | 4.11 | 157.65 | 2.60 | 347.27 | 19.80 | 1391.13 |
LG Chem | M26 | 389.73 | 38.15 | 9.68 | 128.17 | 2.43 | 77.34 | 23.67 | 1057.06 |
LG Chem | MJ1 | 357.66 | 40.95 | 7.23 | 808.75 | 0.60 | 2.11 | 9.85 | 2428.49 |
Lithium Werks | M1B | 24.58 | 6.41 | 1.91 | 902.01 | 1.49 | 19.27 | 4.73 | 4432.25 |
Murata | V3 | 399.52 | 29.91 | 4.82 | 42.58 | 8.97 | 0.20 | 11.13 | 406.26 |
Murata | VTC5A | 72.75 | 73.36 | 5.14 | 150.13 | 1.96 | 390.15 | 19.26 | 1291.63 |
Murata | VTC6 | 67.50 | 12.51 | 5.26 | 129.85 | 2.28 | 4047.82 | 20.65 | 1344.85 |
Nitecore | NL1835HP | 143.74 | 52.41 | 9.36 | 97.67 | 6.79 | 1.60 | 17.61 | 850.42 |
Samsung | 30Q | 72.70 | 12.98 | 1.83 | 123.45 | 2.24 | 0.14 | 15.08 | 861.11 |
Sanyo | ZT | 261.80 | 39.80 | 40.58 | 828.57 | 18.32 | 499.70 | 43.43 | 0.10 |
Manufacturer | Model | ||||||
---|---|---|---|---|---|---|---|
Keeppower | P1834J | 136.55 | 99.90 | 15.55 | 128.77 | 15.13 | 884.67 |
LG Chem | HG2 | 86.37 | 17.48 | 4.53 | 175.10 | 14.74 | 985.19 |
LG Chem | M26 | 389.91 | 38.32 | 10.47 | 142.26 | 19.31 | 895.38 |
LG Chem | MJ1 | 357.66 | 40.95 | 7.83 | 434.08 | 4.94 | 1361.57 |
Lithium Werks | M1B | 25.75 | 6.36 | 2.85 | 363.34 | 11.85 | 859.94 |
Murata | V3 | 399.65 | 30.65 | 12.75 | 123.38 | 16.67 | 681.21 |
Murata | VTC5A | 78.66 | 73.11 | 5.35 | 151.62 | 15.12 | 1015.36 |
Murata | VTC6 | 73.61 | 12.14 | 5.41 | 130.77 | 15.04 | 995.59 |
Nitecore | NL1835HP | 169.14 | 52.30 | 15.86 | 154.31 | 17.04 | 813.53 |
Samsung | 30Q | 72.80 | 12.62 | 4.43 | 137.29 | 15.36 | 872.87 |
Sanyo | ZT | 235.60 | 38.02 | 87.16 | 509.41 | 22.89 | 1138.59 |
Manufacturer | Model | ||||
---|---|---|---|---|---|
Keeppower | P1834J | 136.63 | 99.49 | 3.43 | 131.24 |
LG Chem | HG2 | 86.37 | 17.44 | 4.29 | 165.40 |
LG Chem | M26 | 389.91 | 38.28 | 10.11 | 138.14 |
LG Chem | MJ1 | 384.75 | 41.46 | 7.27 | 151.23 |
Lithium Werks | M1B | 25.56 | 6.66 | 2.77 | 498.62 |
Murata | V3 | 391.38 | 31.52 | 11.49 | 121.36 |
Murata | VTC5A | 77.25 | 73.37 | 5.24 | 159.57 |
Murata | VTC6 | 72.11 | 12.53 | 5.33 | 135.56 |
Nitecore | NL1835HP | 163.25 | 52.67 | 14.68 | 147.01 |
Samsung | 30Q | 71.17 | 12.97 | 4.11 | 147.28 |
Sanyo | ZT | 255.02 | 41.93 | 76.10 | 144.48 |
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
EIS | Electrochemical impedance spectroscopy |
ECM | Equivalent circuit model |
Est | Estimated |
NMC | Nickel–manganese–cobalt–oxide |
RMS | Root mean square |
SOC | State of charge |
Appendix A
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.1248685 | 0.0791728 | 397.9953 | 0.1025465 | −0.0037484 | 1.584686 | 0.1158481 | −0.0014265 |
79,453.13 | 0.1192303 | 0.0660843 | 315.5048 | 0.103217 | −0.0039928 | 1.266892 | 0.1159938 | −0.0013244 |
63,140.62 | 0.1147977 | 0.0549908 | 252.4038 | 0.1038846 | −0.0041895 | 0.999041 | 0.1161152 | −0.001245 |
50,203.12 | 0.1113422 | 0.0456027 | 198.6229 | 0.1046293 | −0.0043773 | 0.7923428 | 0.1162334 | −0.0011867 |
39,890.62 | 0.108636 | 0.0378051 | 158.3615 | 0.1053615 | −0.0045084 | 0.633446 | 0.1163523 | −0.0011659 |
31,640.63 | 0.1064436 | 0.0313035 | 125.558 | 0.1061272 | −0.0046076 | 0.5040323 | 0.1164643 | −0.0011691 |
25,171.88 | 0.1046336 | 0.0260184 | 100.4464 | 0.1068876 | −0.0046767 | 0.400641 | 0.116578 | −0.0012005 |
20,015.62 | 0.1030744 | 0.0215612 | 79.00281 | 0.1077005 | −0.0046817 | 0.316723 | 0.1166854 | −0.0012651 |
15,890.62 | 0.101749 | 0.0177461 | 63.3446 | 0.1084316 | −0.0046515 | 0.2520161 | 0.1168034 | −0.0013556 |
12,609.37 | 0.1006624 | 0.0144373 | 50.22321 | 0.1092287 | −0.0045741 | 0.2003205 | 0.1169279 | −0.001486 |
10,078.13 | 0.0998588 | 0.0116388 | 38.42213 | 0.1100764 | −0.0044632 | 0.1588983 | 0.1170757 | −0.0016525 |
8015.625 | 0.0992723 | 0.0091599 | 31.25 | 0.1107429 | −0.0043228 | 0.1260081 | 0.1172597 | −0.0018626 |
6328.125 | 0.0989084 | 0.0069591 | 24.93351 | 0.1114179 | −0.0041403 | 0.1001603 | 0.117478 | −0.0021162 |
5015.625 | 0.0987513 | 0.0051215 | 19.86229 | 0.1121067 | −0.0039256 | 0.0794492 | 0.1177547 | −0.0024267 |
3984.375 | 0.0987152 | 0.0035754 | 15.625 | 0.1127404 | −0.0036522 | 0.0631739 | 0.1178996 | −0.0028201 |
3170.956 | 0.0988392 | 0.0022968 | 12.40079 | 0.1132926 | −0.0033823 | 0.0501337 | 0.1181734 | −0.0032702 |
2527.573 | 0.0990051 | 0.0012205 | 9.93114 | 0.1137499 | −0.0031128 | 0.0398258 | 0.1185147 | −0.0038034 |
1976.103 | 0.0993063 | 0.0002402 | 7.944915 | 0.1141792 | −0.002829 | 0.0316296 | 0.1189262 | −0.0044321 |
1577.524 | 0.0996115 | −0.0005684 | 6.317385 | 0.1145427 | −0.0025496 | 0.0251206 | 0.1194369 | −0.0051677 |
1265.625 | 0.1000291 | −0.0012188 | 5.008013 | 0.1148783 | −0.0022777 | 0.0199553 | 0.1200348 | −0.0060106 |
998.264 | 0.1004754 | −0.0018054 | 3.945707 | 0.1151497 | −0.0020308 | 0.0158522 | 0.1207429 | −0.0069609 |
796.875 | 0.1009431 | −0.0022927 | 3.158693 | 0.1153695 | −0.001831 | 0.0125907 | 0.1216125 | −0.0080523 |
627.7902 | 0.1014475 | −0.0027202 | 2.504006 | 0.1155009 | −0.0017247 | 0.0100011 | 0.122649 | −0.0092733 |
505.5147 | 0.1018677 | −0.0034748 | 1.998082 | 0.1156775 | −0.0015757 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.1092766 | 0.2248998 | 397.9953 | 0.0434193 | −0.0014255 | 1.584686 | 0.0488809 | −0.0006845 |
79,453.13 | 0.0943386 | 0.1867189 | 315.5048 | 0.0439041 | −0.0017356 | 1.266892 | 0.0489755 | −0.0007088 |
63,140.62 | 0.0823958 | 0.1547544 | 252.4038 | 0.0443739 | −0.0019448 | 0.999041 | 0.0490154 | −0.0007727 |
50,203.12 | 0.073147 | 0.1278604 | 198.6229 | 0.0448717 | −0.0020896 | 0.7923428 | 0.0490972 | −0.0008471 |
39,890.62 | 0.0659943 | 0.1053338 | 158.3615 | 0.0453303 | −0.0021585 | 0.633446 | 0.0492239 | −0.0009284 |
31,640.63 | 0.0604904 | 0.0865721 | 125.558 | 0.0457481 | −0.0021713 | 0.5040323 | 0.0493204 | −0.0010369 |
25,171.88 | 0.0562198 | 0.0713342 | 100.4464 | 0.0461982 | −0.0021252 | 0.400641 | 0.0494389 | −0.0011674 |
20,015.62 | 0.0527559 | 0.0587981 | 79.00281 | 0.0466082 | −0.0020387 | 0.316723 | 0.049575 | −0.0013207 |
15,890.62 | 0.049846 | 0.0483892 | 63.3446 | 0.0469207 | −0.0019299 | 0.2520161 | 0.0497354 | −0.0014936 |
12,609.37 | 0.0474084 | 0.0397036 | 50.22321 | 0.047284 | −0.0017848 | 0.2003205 | 0.0499196 | −0.0016845 |
10,078.13 | 0.0453698 | 0.0328248 | 38.42213 | 0.047561 | −0.0015983 | 0.1588983 | 0.0501327 | −0.0018932 |
8015.625 | 0.0437789 | 0.0265939 | 31.25 | 0.0478071 | −0.0014458 | 0.1260081 | 0.0503899 | −0.0021313 |
6328.125 | 0.0425866 | 0.0212104 | 24.93351 | 0.0479912 | −0.0012959 | 0.1001603 | 0.050707 | −0.0023756 |
5015.625 | 0.0417803 | 0.0167713 | 19.86229 | 0.0481562 | −0.0011457 | 0.0794492 | 0.0510177 | −0.0026636 |
3984.375 | 0.0412833 | 0.01311 | 15.625 | 0.04829 | −0.0010035 | 0.0631739 | 0.0512613 | −0.0029876 |
3170.956 | 0.0410333 | 0.0100967 | 12.40079 | 0.0483967 | −0.0008883 | 0.0501337 | 0.0515766 | −0.0033626 |
2527.573 | 0.040953 | 0.0076263 | 9.93114 | 0.048474 | −0.0007918 | 0.0398258 | 0.0519397 | −0.0037929 |
1976.103 | 0.0410131 | 0.0054395 | 7.944915 | 0.0485411 | −0.0007144 | 0.0316296 | 0.052345 | −0.0043061 |
1577.524 | 0.0411793 | 0.0037483 | 6.317385 | 0.0485999 | −0.0006589 | 0.0251206 | 0.0527913 | −0.0049178 |
1265.625 | 0.04145 | 0.0024435 | 5.008013 | 0.0486568 | −0.0006159 | 0.0199553 | 0.0533075 | −0.0056507 |
998.264 | 0.0417908 | 0.001316 | 3.945707 | 0.0487109 | −0.0005912 | 0.0158522 | 0.0539089 | −0.0065217 |
796.875 | 0.0421622 | 0.000435 | 3.158693 | 0.0487561 | −0.0005812 | 0.0125907 | 0.0546575 | −0.0075352 |
627.7902 | 0.0425336 | −0.0002752 | 2.504006 | 0.048785 | −0.0006282 | 0.0100011 | 0.0555698 | −0.0087004 |
505.5147 | 0.0428933 | −0.0010095 | 1.998082 | 0.0488152 | −0.0006623 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0270281 | 0.0510112 | 397.9953 | 0.0189963 | −0.001285 | 1.584686 | 0.0218075 | −0.0005034 |
79,453.13 | 0.0253884 | 0.042034 | 315.5048 | 0.0192669 | −0.0013371 | 1.266892 | 0.0218596 | −0.0005593 |
63,140.62 | 0.0238368 | 0.0346892 | 252.4038 | 0.0195218 | −0.0013597 | 0.999041 | 0.0219088 | −0.0006396 |
50,203.12 | 0.0224587 | 0.028629 | 198.6229 | 0.019788 | −0.0013571 | 0.7923428 | 0.0219786 | −0.0007277 |
39,890.62 | 0.0212544 | 0.023566 | 158.3615 | 0.0200324 | −0.001333 | 0.633446 | 0.0220645 | −0.0008304 |
31,640.63 | 0.0202256 | 0.0193001 | 125.558 | 0.0202645 | −0.0012876 | 0.5040323 | 0.0221599 | −0.0009504 |
25,171.88 | 0.0193954 | 0.0157813 | 100.4464 | 0.0204879 | −0.0012258 | 0.400641 | 0.0222764 | −0.0010836 |
20,015.62 | 0.0187324 | 0.0128464 | 79.00281 | 0.0206998 | −0.0011388 | 0.316723 | 0.0224157 | −0.0012388 |
15,890.62 | 0.0182021 | 0.0103873 | 63.3446 | 0.0208652 | −0.0010476 | 0.2520161 | 0.02257 | −0.0013979 |
12,609.37 | 0.0178079 | 0.0083153 | 50.22321 | 0.0210342 | −0.0009465 | 0.2003205 | 0.022744 | −0.0015738 |
10,078.13 | 0.0175344 | 0.0066434 | 38.42213 | 0.0211726 | −0.0008272 | 0.1588983 | 0.0229368 | −0.0017654 |
8015.625 | 0.0173523 | 0.0052113 | 31.25 | 0.0212756 | −0.0007398 | 0.1260081 | 0.0231749 | −0.0019767 |
6328.125 | 0.0172334 | 0.0039798 | 24.93351 | 0.0213598 | −0.0006515 | 0.1001603 | 0.0234327 | −0.0022149 |
5015.625 | 0.0171946 | 0.002978 | 19.86229 | 0.0214298 | −0.0005735 | 0.0794492 | 0.0237254 | −0.0024922 |
3984.375 | 0.0172042 | 0.002149 | 15.625 | 0.0214866 | −0.0005037 | 0.0631739 | 0.0238918 | −0.0028397 |
3170.956 | 0.0172634 | 0.0014738 | 12.40079 | 0.0215295 | −0.0004512 | 0.0501337 | 0.0241678 | −0.0032436 |
2527.573 | 0.0173475 | 0.0009013 | 9.93114 | 0.0215635 | −0.0004113 | 0.0398258 | 0.0245069 | −0.0037216 |
1976.103 | 0.0174792 | 0.0003768 | 7.944915 | 0.0215956 | −0.000385 | 0.0316296 | 0.0248878 | −0.0042882 |
1577.524 | 0.0176592 | −5.14252 × 10 | 6.317385 | 0.0216239 | −0.0003674 | 0.0251206 | 0.0253547 | −0.0049563 |
1265.625 | 0.0178237 | −0.0002872 | 5.008013 | 0.0216555 | −0.000361 | 0.0199553 | 0.0259261 | −0.0057248 |
998.264 | 0.0180239 | −0.0005892 | 3.945707 | 0.0216862 | −0.000365 | 0.0158522 | 0.0266212 | −0.0065922 |
796.875 | 0.0182497 | −0.0008151 | 3.158693 | 0.0217149 | −0.0003804 | 0.0125907 | 0.0274622 | −0.0075455 |
627.7902 | 0.0185441 | −0.0010204 | 2.504006 | 0.0217309 | −0.000421 | 0.0100011 | 0.02846 | −0.0085744 |
505.5147 | 0.0187146 | −0.001197 | 1.998082 | 0.0217637 | −0.000458 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0966546 | 0.2296797 | 397.9953 | 0.0403712 | −0.0020141 | 1.584686 | 0.0487848 | −0.0008954 |
79,453.13 | 0.0846547 | 0.1895272 | 315.5048 | 0.0409519 | −0.00242 | 1.266892 | 0.0489051 | −0.0008715 |
63,140.62 | 0.0747234 | 0.1564347 | 252.4038 | 0.0415329 | −0.0027181 | 0.999041 | 0.0489573 | −0.000893 |
50,203.12 | 0.0668013 | 0.1288408 | 198.6229 | 0.0421687 | −0.0029507 | 0.7923428 | 0.0490464 | −0.0009222 |
39,890.62 | 0.0606243 | 0.1058351 | 158.3615 | 0.0427831 | −0.0030902 | 0.633446 | 0.0491726 | −0.0009654 |
31,640.63 | 0.0557685 | 0.0867745 | 125.558 | 0.0433754 | −0.0031623 | 0.5040323 | 0.0492651 | −0.0010422 |
25,171.88 | 0.0519299 | 0.0713938 | 100.4464 | 0.0439915 | −0.0031717 | 0.400641 | 0.0493674 | −0.0011376 |
20,015.62 | 0.0487785 | 0.0587523 | 79.00281 | 0.0446058 | −0.0031139 | 0.316723 | 0.049484 | −0.0012605 |
15,890.62 | 0.0460777 | 0.0483253 | 63.3446 | 0.0451049 | −0.0030099 | 0.2520161 | 0.0496149 | −0.0014128 |
12,609.37 | 0.0436614 | 0.0398372 | 50.22321 | 0.0456536 | −0.0028599 | 0.2003205 | 0.0497622 | −0.0015893 |
10,078.13 | 0.0417969 | 0.0326567 | 38.42213 | 0.0461585 | −0.0026443 | 0.1588983 | 0.0499284 | −0.0017973 |
8015.625 | 0.040286 | 0.0264873 | 31.25 | 0.0465649 | −0.0024568 | 0.1260081 | 0.0501436 | −0.0020488 |
6328.125 | 0.0391497 | 0.0210795 | 24.93351 | 0.0469163 | −0.0022442 | 0.1001603 | 0.0503926 | −0.0023315 |
5015.625 | 0.0383782 | 0.0166105 | 19.86229 | 0.0472345 | −0.002043 | 0.0794492 | 0.0506666 | −0.0026804 |
3984.375 | 0.0379164 | 0.0129349 | 15.625 | 0.0475009 | −0.0018265 | 0.0631739 | 0.0508549 | −0.0031077 |
3170.956 | 0.0376951 | 0.0099074 | 12.40079 | 0.0477274 | −0.0016386 | 0.0501337 | 0.05114 | −0.0036086 |
2527.573 | 0.0376513 | 0.0074127 | 9.93114 | 0.0479105 | −0.0014772 | 0.0398258 | 0.0514869 | −0.0042026 |
1976.103 | 0.0377576 | 0.0052137 | 7.944915 | 0.048071 | −0.0013354 | 0.0316296 | 0.0518988 | −0.0049148 |
1577.524 | 0.0379564 | 0.0035503 | 6.317385 | 0.048215 | −0.0012056 | 0.0251206 | 0.052416 | −0.0057554 |
1265.625 | 0.0382099 | 0.002264 | 5.008013 | 0.0483443 | −0.0010999 | 0.0199553 | 0.0530341 | −0.006749 |
998.264 | 0.0385243 | 0.0010381 | 3.945707 | 0.0484586 | −0.0010122 | 0.0158522 | 0.053786 | −0.0079163 |
796.875 | 0.0389035 | 0.0001484 | 3.158693 | 0.0485629 | −0.000945 | 0.0125907 | 0.0547004 | −0.0092978 |
627.7902 | 0.0393823 | −0.0007584 | 2.504006 | 0.0486232 | −0.0009398 | 0.0100011 | 0.0558614 | −0.0108991 |
505.5147 | 0.0397737 | −0.0014985 | 1.998082 | 0.0486871 | −0.0009189 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0079583 | 0.015456 | 397.9953 | 0.0073792 | −0.0007232 | 1.584686 | 0.0095521 | −0.0007176 |
79,453.13 | 0.0077506 | 0.012553 | 315.5048 | 0.0075201 | −0.0007394 | 1.266892 | 0.0096394 | −0.0007658 |
63,140.62 | 0.0076456 | 0.0101667 | 252.4038 | 0.0076518 | −0.0007433 | 0.999041 | 0.009738 | −0.0008235 |
50,203.12 | 0.007478 | 0.0082821 | 198.6229 | 0.0077874 | −0.0007354 | 0.7923428 | 0.0098419 | −0.0008886 |
39,890.62 | 0.0073124 | 0.0067639 | 158.3615 | 0.0079095 | −0.0007195 | 0.633446 | 0.0099489 | −0.000963 |
31,640.63 | 0.0071356 | 0.00551 | 125.558 | 0.0080259 | −0.0006992 | 0.5040323 | 0.0100622 | −0.0010505 |
25,171.88 | 0.0069773 | 0.0045022 | 100.4464 | 0.0081304 | −0.0006747 | 0.400641 | 0.0101829 | −0.0011544 |
20,015.62 | 0.0068252 | 0.0036595 | 79.00281 | 0.0082343 | −0.0006513 | 0.316723 | 0.0103195 | −0.0012759 |
15,890.62 | 0.0067029 | 0.0029554 | 63.3446 | 0.008324 | −0.0006304 | 0.2520161 | 0.0104657 | −0.0014135 |
12,609.37 | 0.0066001 | 0.0023601 | 50.22321 | 0.0084135 | −0.0006072 | 0.2003205 | 0.0106226 | −0.0015734 |
10,078.13 | 0.0065243 | 0.0018726 | 38.42213 | 0.0085098 | −0.0005873 | 0.1588983 | 0.0107998 | −0.0017597 |
8015.625 | 0.0064723 | 0.0014576 | 31.25 | 0.0085824 | −0.000573 | 0.1260081 | 0.0110136 | −0.0019671 |
6328.125 | 0.0064459 | 0.0010936 | 24.93351 | 0.008659 | −0.0005612 | 0.1001603 | 0.0112486 | −0.0021938 |
5015.625 | 0.006417 | 0.0007872 | 19.86229 | 0.0087345 | −0.0005503 | 0.0794492 | 0.011507 | −0.0024582 |
3984.375 | 0.0064146 | 0.000527 | 15.625 | 0.0088148 | −0.0005429 | 0.0631739 | 0.0117202 | −0.002815 |
3170.956 | 0.0064829 | 0.0003013 | 12.40079 | 0.0088881 | −0.00054 | 0.0501337 | 0.0120081 | −0.0032167 |
2527.573 | 0.0065185 | 0.000102 | 9.93114 | 0.0089543 | −0.000541 | 0.0398258 | 0.0123561 | −0.0036783 |
1976.103 | 0.0065863 | −8.89512 × 10 | 7.944915 | 0.0090227 | −0.0005459 | 0.0316296 | 0.0127677 | −0.0042152 |
1577.524 | 0.0066646 | −0.0002207 | 6.317385 | 0.0090927 | −0.0005544 | 0.0251206 | 0.0132643 | −0.0048324 |
1265.625 | 0.0067543 | −0.0003524 | 5.008013 | 0.0091637 | −0.0005678 | 0.0199553 | 0.0138502 | −0.0055317 |
998.264 | 0.0068689 | −0.0004619 | 3.945707 | 0.0092389 | −0.000587 | 0.0158522 | 0.0145628 | −0.0062858 |
796.875 | 0.006972 | −0.0005543 | 3.158693 | 0.0093143 | −0.0006089 | 0.0125907 | 0.015398 | −0.0071035 |
627.7902 | 0.0071366 | −0.0006284 | 2.504006 | 0.0093843 | −0.0006417 | 0.0100011 | 0.0163756 | −0.0079552 |
505.5147 | 0.0072355 | −0.0006941 | 1.998082 | 0.0094648 | −0.0006763 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0908763 | 0.0903867 | 397.9953 | 0.0546987 | −0.0032018 | 1.584686 | 0.0680739 | −0.0013925 |
79,453.13 | 0.0843899 | 0.0771878 | 315.5048 | 0.0553186 | −0.0035739 | 1.266892 | 0.0681984 | −0.0012949 |
63,140.62 | 0.0785404 | 0.0660436 | 252.4038 | 0.0559647 | −0.0038887 | 0.999041 | 0.0683197 | −0.0012272 |
50,203.12 | 0.073268 | 0.0563074 | 198.6229 | 0.056698 | −0.004179 | 0.7923428 | 0.0684299 | −0.0011948 |
39,890.62 | 0.0687767 | 0.0477939 | 158.3615 | 0.0574403 | −0.0044111 | 0.633446 | 0.0685364 | −0.001184 |
31,640.63 | 0.0649896 | 0.0402858 | 125.558 | 0.0582268 | −0.0046007 | 0.5040323 | 0.0686342 | −0.0012102 |
25,171.88 | 0.0618655 | 0.0337827 | 100.4464 | 0.0590275 | −0.0047235 | 0.400641 | 0.0687331 | −0.0012747 |
20,015.62 | 0.0594746 | 0.0282526 | 79.00281 | 0.0599031 | −0.0047822 | 0.316723 | 0.0688458 | −0.0013789 |
15,890.62 | 0.057397 | 0.0238233 | 63.3446 | 0.0607081 | −0.0047747 | 0.2520161 | 0.0689639 | −0.0015071 |
12,609.37 | 0.0557907 | 0.0196854 | 50.22321 | 0.0615392 | −0.0047001 | 0.2003205 | 0.0691007 | −0.0016893 |
10,078.13 | 0.0545102 | 0.016216 | 38.42213 | 0.0625209 | −0.0045273 | 0.1588983 | 0.06925 | −0.0019242 |
8015.625 | 0.0534262 | 0.0131923 | 31.25 | 0.0631918 | −0.0043495 | 0.1260081 | 0.0694776 | −0.002198 |
6328.125 | 0.0526449 | 0.0104187 | 24.93351 | 0.0638697 | −0.0041137 | 0.1001603 | 0.0697321 | −0.00252 |
5015.625 | 0.0521434 | 0.0080767 | 19.86229 | 0.0645144 | −0.0038529 | 0.0794492 | 0.0700286 | −0.0029109 |
3984.375 | 0.0518367 | 0.0061121 | 15.625 | 0.065108 | −0.003563 | 0.0631739 | 0.0702699 | −0.0033734 |
3170.956 | 0.0517411 | 0.004398 | 12.40079 | 0.0656158 | −0.003282 | 0.0501337 | 0.0706129 | −0.0038999 |
2527.573 | 0.0517466 | 0.0029842 | 9.93114 | 0.0660602 | −0.0030124 | 0.0398258 | 0.0710385 | −0.0045101 |
1976.103 | 0.0519044 | 0.0017277 | 7.944915 | 0.0664529 | −0.0027421 | 0.0316296 | 0.0715282 | −0.0052147 |
1577.524 | 0.0522193 | 0.0007457 | 6.317385 | 0.0668098 | −0.0024838 | 0.0251206 | 0.0721251 | −0.0060257 |
1265.625 | 0.0524198 | −0.0001756 | 5.008013 | 0.0671138 | −0.0022242 | 0.0199553 | 0.0728206 | −0.0069552 |
998.264 | 0.0528263 | −0.0008868 | 3.945707 | 0.0673928 | −0.0019915 | 0.0158522 | 0.0736353 | −0.0080305 |
796.875 | 0.0532544 | −0.0015371 | 3.158693 | 0.0676015 | −0.0017888 | 0.0125907 | 0.0746055 | −0.0092603 |
627.7902 | 0.0536592 | −0.0021301 | 2.504006 | 0.0677484 | −0.0016754 | 0.0100011 | 0.0757566 | −0.0106687 |
505.5147 | 0.0540903 | −0.0027782 | 1.998082 | 0.0679144 | −0.0015231 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0221435 | 0.0416029 | 397.9953 | 0.0146257 | −0.0013271 | 1.584686 | 0.0172051 | −0.000594 |
79,453.13 | 0.0205168 | 0.0345462 | 315.5048 | 0.0149077 | −0.0013449 | 1.266892 | 0.0172719 | −0.0006555 |
63,140.62 | 0.0189863 | 0.0286748 | 252.4038 | 0.0151649 | −0.001327 | 0.999041 | 0.0173444 | −0.0007358 |
50,203.12 | 0.0176359 | 0.0237701 | 198.6229 | 0.0154242 | −0.0012776 | 0.7923428 | 0.0174229 | −0.0008307 |
39,890.62 | 0.0164808 | 0.0196299 | 158.3615 | 0.0156441 | −0.0012089 | 0.633446 | 0.0175209 | −0.0009351 |
31,640.63 | 0.015526 | 0.0161181 | 125.558 | 0.0158446 | −0.0011239 | 0.5040323 | 0.0176296 | −0.0010554 |
25,171.88 | 0.0147641 | 0.0132173 | 100.4464 | 0.0160126 | −0.0010335 | 0.400641 | 0.0177575 | −0.0011906 |
20,015.62 | 0.0141578 | 0.0107754 | 79.00281 | 0.0161672 | −0.0009364 | 0.316723 | 0.017904 | −0.0013497 |
15,890.62 | 0.0136905 | 0.0087176 | 63.3446 | 0.0162858 | −0.00085 | 0.2520161 | 0.018069 | −0.0015176 |
12,609.37 | 0.0133359 | 0.0069877 | 50.22321 | 0.0163956 | −0.0007666 | 0.2003205 | 0.0182546 | −0.0017024 |
10,078.13 | 0.0130984 | 0.0055851 | 38.42213 | 0.0164986 | −0.0006781 | 0.1588983 | 0.0184611 | −0.0019107 |
8015.625 | 0.0129175 | 0.004362 | 31.25 | 0.0165698 | −0.0006183 | 0.1260081 | 0.0187059 | −0.0021414 |
6328.125 | 0.0128115 | 0.0033328 | 24.93351 | 0.0166363 | −0.0005631 | 0.1001603 | 0.0189853 | −0.0023982 |
5015.625 | 0.0127634 | 0.002469 | 19.86229 | 0.0166939 | −0.0005195 | 0.0794492 | 0.0192993 | −0.0026998 |
3984.375 | 0.0127624 | 0.0017537 | 15.625 | 0.0167526 | −0.0004792 | 0.0631739 | 0.0194735 | −0.0030758 |
3170.956 | 0.0128173 | 0.0011543 | 12.40079 | 0.0168016 | −0.0004499 | 0.0501337 | 0.0197495 | −0.0035167 |
2527.573 | 0.0129039 | 0.0006444 | 9.93114 | 0.0168429 | −0.0004341 | 0.0398258 | 0.0200795 | −0.0040435 |
1976.103 | 0.0130311 | 0.0001759 | 7.944915 | 0.0168874 | −0.0004238 | 0.0316296 | 0.0204735 | −0.0046773 |
1577.524 | 0.0131993 | −0.0001646 | 6.317385 | 0.0169318 | −0.0004201 | 0.0251206 | 0.0209515 | −0.0054274 |
1265.625 | 0.0133735 | −0.0004532 | 5.008013 | 0.0169745 | −0.000426 | 0.0199553 | 0.0215309 | −0.0063131 |
998.264 | 0.0135926 | −0.0007461 | 3.945707 | 0.0170186 | −0.0004387 | 0.0158522 | 0.0222598 | −0.0073251 |
796.875 | 0.0138098 | −0.000927 | 3.158693 | 0.0170626 | −0.0004604 | 0.0125907 | 0.0231535 | −0.0084563 |
627.7902 | 0.0141171 | −0.0011235 | 2.504006 | 0.0170985 | −0.0005027 | 0.0100011 | 0.0242472 | −0.0096969 |
505.5147 | 0.0143321 | −0.0012667 | 1.998082 | 0.017148 | −0.0005427 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0879812 | 0.1481455 | 397.9953 | 0.0428469 | −0.0062364 | 1.584686 | 0.1164448 | −0.013879 |
79,453.13 | 0.07657 | 0.123725 | 315.5048 | 0.043709 | −0.0071615 | 1.266892 | 0.1180402 | −0.012307 |
63,140.62 | 0.0676103 | 0.103003 | 252.4038 | 0.0445944 | −0.0081327 | 0.999041 | 0.1194289 | −0.0108242 |
50,203.12 | 0.0606382 | 0.0853893 | 198.6229 | 0.0456372 | −0.0093081 | 0.7923428 | 0.1205813 | −0.0095485 |
39,890.62 | 0.0553028 | 0.070491 | 158.3615 | 0.046748 | −0.0105765 | 0.633446 | 0.1215468 | −0.0084807 |
31,640.63 | 0.0512146 | 0.0579771 | 125.558 | 0.0480276 | −0.0120621 | 0.5040323 | 0.1223859 | −0.0075594 |
25,171.88 | 0.0480681 | 0.0477495 | 100.4464 | 0.0495362 | −0.0136992 | 0.400641 | 0.1231264 | −0.0067841 |
20,015.62 | 0.0453814 | 0.039578 | 79.00281 | 0.0514548 | −0.015677 | 0.316723 | 0.1237845 | −0.0061443 |
15,890.62 | 0.043366 | 0.0323901 | 63.3446 | 0.0535497 | −0.0176669 | 0.2520161 | 0.1243658 | −0.0056656 |
12,609.37 | 0.041696 | 0.0263934 | 50.22321 | 0.0562943 | −0.0199185 | 0.2003205 | 0.1249248 | −0.0053085 |
10,078.13 | 0.0403855 | 0.0214538 | 38.42213 | 0.0600724 | −0.0225275 | 0.1588983 | 0.1254459 | −0.005074 |
8015.625 | 0.0393601 | 0.0171103 | 31.25 | 0.0636698 | −0.0244999 | 0.1260081 | 0.1259869 | −0.0049502 |
6328.125 | 0.0386264 | 0.0132648 | 24.93351 | 0.0680598 | −0.0263627 | 0.1001603 | 0.1265979 | −0.0049444 |
5015.625 | 0.0381998 | 0.0100543 | 19.86229 | 0.0731652 | −0.0277673 | 0.0794492 | 0.127203 | −0.0050668 |
3984.375 | 0.0380204 | 0.0073407 | 15.625 | 0.0787275 | −0.0286473 | 0.0631739 | 0.1276219 | −0.0053199 |
3170.956 | 0.0380381 | 0.0050687 | 12.40079 | 0.0842165 | −0.0287812 | 0.0501337 | 0.1281739 | −0.005688 |
2527.573 | 0.0381944 | 0.00314 | 9.93114 | 0.0894108 | −0.0282311 | 0.0398258 | 0.1287955 | −0.0062142 |
1976.103 | 0.0385069 | 0.0013511 | 7.944915 | 0.0943403 | −0.027125 | 0.0316296 | 0.1295339 | −0.0069028 |
1577.524 | 0.0389252 | −8.39468 × 10 | 6.317385 | 0.098933 | −0.0255314 | 0.0251206 | 0.1304023 | −0.0077701 |
1265.625 | 0.0394291 | −0.0012829 | 5.008013 | 0.1030899 | −0.0236223 | 0.0199553 | 0.1314791 | −0.0088435 |
998.264 | 0.0400255 | −0.0023903 | 3.945707 | 0.1068144 | −0.0214934 | 0.0158522 | 0.1327369 | −0.0101245 |
796.875 | 0.0406607 | −0.0033893 | 3.158693 | 0.109775 | −0.0194901 | 0.0125907 | 0.134222 | −0.0116194 |
627.7902 | 0.0413667 | −0.004337 | 2.504006 | 0.1123291 | −0.0175198 | 0.0100011 | 0.1361137 | −0.013299 |
505.5147 | 0.0419844 | −0.0053385 | 1.998082 | 0.1145305 | −0.0156595 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0946529 | 0.2290136 | 397.9953 | 0.0339269 | −0.0024245 | 1.584686 | 0.0434677 | −0.0011698 |
79,453.13 | 0.0819638 | 0.1894378 | 315.5048 | 0.0345953 | −0.002841 | 1.266892 | 0.0436243 | −0.0011659 |
63,140.62 | 0.0714598 | 0.1571168 | 252.4038 | 0.0352568 | −0.0031424 | 0.999041 | 0.0437223 | −0.0012025 |
50,203.12 | 0.062837 | 0.1302273 | 198.6229 | 0.0359764 | −0.0033643 | 0.7923428 | 0.0438498 | −0.0012519 |
39,890.62 | 0.0556963 | 0.1076581 | 158.3615 | 0.0366571 | −0.0034918 | 0.633446 | 0.0440113 | −0.0013178 |
31,640.63 | 0.049904 | 0.0886351 | 125.558 | 0.0373131 | −0.0035442 | 0.5040323 | 0.0441573 | −0.0014132 |
25,171.88 | 0.0453839 | 0.0729338 | 100.4464 | 0.0379921 | −0.0035301 | 0.400641 | 0.0443166 | −0.0015366 |
20,015.62 | 0.04182 | 0.0598291 | 79.00281 | 0.0386522 | −0.0034566 | 0.316723 | 0.0444921 | −0.0016931 |
15,890.62 | 0.0390227 | 0.0489216 | 63.3446 | 0.0391997 | −0.0033446 | 0.2520161 | 0.0446728 | −0.0018799 |
12,609.37 | 0.0366828 | 0.0400819 | 50.22321 | 0.0398047 | −0.0031885 | 0.2003205 | 0.0448847 | −0.002095 |
10,078.13 | 0.0349889 | 0.0327589 | 38.42213 | 0.0403597 | −0.002951 | 0.1588983 | 0.0451265 | −0.0023513 |
8015.625 | 0.0336134 | 0.0265466 | 31.25000 | 0.0408069 | −0.0027558 | 0.1260081 | 0.0454311 | −0.0026386 |
6328.125 | 0.0325147 | 0.0211865 | 24.93351 | 0.0411978 | −0.0025345 | 0.1001603 | 0.0457688 | −0.0029667 |
5015.625 | 0.031728 | 0.0167765 | 19.86229 | 0.0415558 | −0.0023069 | 0.0794492 | 0.0461697 | −0.0033393 |
3984.375 | 0.0312123 | 0.0130973 | 15.625 | 0.0418631 | −0.0020835 | 0.0631739 | 0.0464468 | −0.0037884 |
3170.956 | 0.0309261 | 0.0100438 | 12.40079 | 0.0421239 | −0.001886 | 0.0501337 | 0.0468366 | −0.0042939 |
2527.573 | 0.0308192 | 0.007502 | 9.93114 | 0.0423325 | −0.0017232 | 0.0398258 | 0.0472708 | −0.0048936 |
1976.103 | 0.0308805 | 0.0052059 | 7.944915 | 0.0425223 | −0.0015771 | 0.0316296 | 0.0477769 | −0.0055975 |
1577.524 | 0.0310815 | 0.0034198 | 6.317385 | 0.0426942 | −0.0014501 | 0.0251206 | 0.0483192 | −0.006443 |
1265.625 | 0.0313858 | 0.0020199 | 5.008013 | 0.0428534 | −0.0013462 | 0.0199553 | 0.0489668 | −0.0074593 |
998.264 | 0.031783 | 0.0007766 | 3.945707 | 0.0430018 | −0.0012622 | 0.0158522 | 0.0497471 | −0.0086739 |
796.875 | 0.0322553 | −0.0002422 | 3.158693 | 0.0431373 | −0.0012007 | 0.0125907 | 0.0506762 | −0.0101087 |
627.7902 | 0.0327596 | −0.0011034 | 2.504006 | 0.0432359 | −0.0011962 | 0.0100011 | 0.0518396 | −0.0117824 |
505.5147 | 0.0332487 | −0.0018776 | 1.998082 | 0.0433367 | −0.0011866 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0828266 | 0.0457434 | 397.9953 | 0.0749414 | −0.0017523 | 1.584686 | 0.0787976 | −0.0005471 |
79,453.13 | 0.0809362 | 0.0376686 | 315.5048 | 0.0752806 | −0.00181 | 1.266892 | 0.078868 | −0.0005583 |
63,140.62 | 0.0792872 | 0.0310407 | 252.4038 | 0.0756082 | −0.0018365 | 0.999041 | 0.078924 | −0.0005935 |
50,203.12 | 0.0779122 | 0.0255593 | 198.6229 | 0.0759639 | −0.0018352 | 0.7923428 | 0.0789693 | −0.0006462 |
39,890.62 | 0.076765 | 0.0209828 | 158.3615 | 0.0762938 | −0.0017986 | 0.633446 | 0.07905 | −0.0007101 |
31,640.63 | 0.0758132 | 0.0171386 | 125.558 | 0.0766017 | −0.0017378 | 0.5040323 | 0.0791149 | −0.0007916 |
25,171.88 | 0.0750618 | 0.0140326 | 100.4464 | 0.0769002 | −0.0016438 | 0.400641 | 0.0791943 | −0.0008968 |
20,015.62 | 0.0744389 | 0.0114443 | 79.00281 | 0.0771847 | −0.0015295 | 0.316723 | 0.079296 | −0.0010257 |
15,890.62 | 0.0739383 | 0.0092165 | 63.3446 | 0.0774023 | −0.0014051 | 0.2520161 | 0.0794045 | −0.0011681 |
12,609.37 | 0.0735982 | 0.0073407 | 50.22321 | 0.0776351 | −0.0012626 | 0.2003205 | 0.0795289 | −0.0013362 |
10,078.13 | 0.0733737 | 0.005805 | 38.42213 | 0.077801 | −0.0011237 | 0.1588983 | 0.0796797 | −0.0015245 |
8015.625 | 0.0732104 | 0.0045275 | 31.25 | 0.0779436 | −0.0010173 | 0.1260081 | 0.0798632 | −0.0017487 |
6328.125 | 0.0731225 | 0.0034439 | 24.93351 | 0.0780625 | −0.0008994 | 0.1001603 | 0.080081 | −0.0020106 |
5015.625 | 0.0731179 | 0.0025267 | 19.86229 | 0.0781594 | −0.0008123 | 0.0794492 | 0.080338 | −0.0023121 |
3984.375 | 0.0731527 | 0.0017773 | 15.62500 | 0.0782557 | −0.0007288 | 0.0631739 | 0.0804754 | −0.0026933 |
3170.956 | 0.0732276 | 0.0011627 | 12.40079 | 0.078332 | −0.0006649 | 0.0501337 | 0.0807233 | −0.0031301 |
2527.573 | 0.0733397 | 0.0006433 | 9.93114 | 0.0783949 | −0.0006051 | 0.0398258 | 0.0810342 | −0.0036578 |
1976.103 | 0.073498 | 0.000176 | 7.944915 | 0.0784661 | −0.0005625 | 0.0316296 | 0.0814081 | −0.0042783 |
1577.524 | 0.0735868 | −0.0002381 | 6.317385 | 0.0785276 | −0.000528 | 0.0251206 | 0.0818835 | −0.0050041 |
1265.625 | 0.0736945 | −0.0004144 | 5.008013 | 0.0785756 | −0.0005014 | 0.0199553 | 0.0824643 | −0.0058469 |
998.264 | 0.0738555 | −0.0007793 | 3.945707 | 0.078635 | −0.0004855 | 0.0158522 | 0.0831695 | −0.0067785 |
796.875 | 0.0739945 | −0.0009796 | 3.158693 | 0.0786838 | −0.0004743 | 0.0125907 | 0.0840358 | −0.0078132 |
627.7902 | 0.0743914 | −0.0012108 | 2.504006 | 0.0786861 | −0.0005304 | 0.0100011 | 0.0850497 | −0.0089263 |
505.5147 | 0.0745843 | −0.0016749 | 1.998082 | 0.0787401 | −0.0005386 |
f | Re{} | −Im{} | f | Re{} | −Im{} | f | Re{} | −Im{} |
---|---|---|---|---|---|---|---|---|
100,078.1 | 0.0204554 | 0.0424421 | 397.9953 | 0.0143356 | −0.0017233 | 1.584686 | 0.0180373 | −0.0005258 |
79,453.13 | 0.0191664 | 0.0351409 | 315.5048 | 0.0146914 | −0.0018033 | 1.266892 | 0.0180942 | −0.0005607 |
63,140.62 | 0.0178412 | 0.0290207 | 252.4038 | 0.0150398 | −0.0018383 | 0.999041 | 0.0181468 | −0.0006153 |
50,203.12 | 0.0166587 | 0.02395 | 198.6229 | 0.0154111 | −0.0018306 | 0.7923428 | 0.0182093 | −0.0006842 |
39,890.62 | 0.0156286 | 0.0197132 | 158.3615 | 0.015749 | −0.0017822 | 0.633446 | 0.018281 | −0.0007649 |
31,640.63 | 0.0147656 | 0.0161344 | 125.558 | 0.0160718 | −0.0016951 | 0.5040323 | 0.0183604 | −0.0008632 |
25,171.88 | 0.0140868 | 0.0131942 | 100.4464 | 0.0163535 | −0.0015841 | 0.400641 | 0.0184516 | −0.0009833 |
20,015.62 | 0.0135381 | 0.010734 | 79.00281 | 0.0166147 | −0.0014487 | 0.316723 | 0.0185619 | −0.0011228 |
15,890.62 | 0.013101 | 0.0086604 | 63.3446 | 0.0168187 | −0.0013157 | 0.2520161 | 0.0186885 | −0.0012786 |
12,609.37 | 0.0127708 | 0.0069195 | 50.22321 | 0.0170036 | −0.0011807 | 0.2003205 | 0.0188344 | −0.0014552 |
10,078.13 | 0.0125416 | 0.0055062 | 38.42213 | 0.0171731 | −0.0010285 | 0.1588983 | 0.0189985 | −0.0016562 |
8015.625 | 0.0123923 | 0.004292 | 31.25 | 0.0172851 | −0.0009256 | 0.1260081 | 0.019207 | −0.0018813 |
6328.125 | 0.0123006 | 0.0032406 | 24.93351 | 0.0173859 | −0.0008225 | 0.1001603 | 0.0194631 | −0.0021334 |
5015.625 | 0.0122703 | 0.0023859 | 19.86229 | 0.0174736 | −0.0007351 | 0.0794492 | 0.0197137 | −0.0024323 |
3984.375 | 0.0122798 | 0.0016512 | 15.625 | 0.0175527 | −0.0006575 | 0.0631739 | 0.0198955 | −0.0027912 |
3170.956 | 0.0123429 | 0.0010478 | 12.40079 | 0.0176152 | −0.0005956 | 0.0501337 | 0.020161 | −0.0032082 |
2527.573 | 0.012438 | 0.0005293 | 9.93114 | 0.017673 | −0.0005477 | 0.0398258 | 0.0204629 | −0.0037025 |
1976.103 | 0.0125761 | 4.705668 × 10 | 7.944915 | 0.0177241 | −0.0005111 | 0.0316296 | 0.0208239 | −0.0042916 |
1577.524 | 0.0127546 | −0.0003247 | 6.317385 | 0.0177719 | −0.0004829 | 0.0251206 | 0.0212594 | −0.0049911 |
1265.625 | 0.0129461 | −0.0005996 | 5.008013 | 0.0178188 | −0.0004654 | 0.0199553 | 0.0217911 | −0.0058103 |
998.264 | 0.0131688 | −0.0009203 | 3.945707 | 0.0178669 | −0.0004554 | 0.0158522 | 0.0224513 | −0.0067609 |
796.875 | 0.0134094 | −0.0011433 | 3.158693 | 0.0179102 | −0.0004566 | 0.0125907 | 0.0232629 | −0.007835 |
627.7902 | 0.0137432 | −0.0014048 | 2.504006 | 0.0179446 | −0.0004777 | 0.0100011 | 0.0242624 | −0.0090211 |
505.5147 | 0.013986 | −0.001595 | 1.998082 | 0.0179889 | −0.000497 |
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Estaller, J.; Kersten, A.; Kuder, M.; Thiringer, T.; Eckerle, R.; Weyh, T. Overview of Battery Impedance Modeling Including Detailed State-of-the-Art Cylindrical 18650 Lithium-Ion Battery Cell Comparisons. Energies 2022, 15, 3822. https://doi.org/10.3390/en15103822
Estaller J, Kersten A, Kuder M, Thiringer T, Eckerle R, Weyh T. Overview of Battery Impedance Modeling Including Detailed State-of-the-Art Cylindrical 18650 Lithium-Ion Battery Cell Comparisons. Energies. 2022; 15(10):3822. https://doi.org/10.3390/en15103822
Chicago/Turabian StyleEstaller, Julian, Anton Kersten, Manuel Kuder, Torbjörn Thiringer, Richard Eckerle, and Thomas Weyh. 2022. "Overview of Battery Impedance Modeling Including Detailed State-of-the-Art Cylindrical 18650 Lithium-Ion Battery Cell Comparisons" Energies 15, no. 10: 3822. https://doi.org/10.3390/en15103822
APA StyleEstaller, J., Kersten, A., Kuder, M., Thiringer, T., Eckerle, R., & Weyh, T. (2022). Overview of Battery Impedance Modeling Including Detailed State-of-the-Art Cylindrical 18650 Lithium-Ion Battery Cell Comparisons. Energies, 15(10), 3822. https://doi.org/10.3390/en15103822