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LTSpice speaker model from impedance measurement data

For several years now I've been wanting a usable spice model for my speakers. There're some generic models out there, but they're all far from what my speakers measure like. I have actually once tried to ''somehow'' resemble my speaker with a bunch of coil-, cap- and resistor-models, but that was really a pain in the @ss and eventually was abandoned for not being a practical approach at all.

I just lately got my feet wet with Class D amplification, so that old problem of the want for a speaker model came up again. After some more thorough thinking I came up with the following idea: What if I could create an approximate model based on a lookup table, filled with real-world measurement results?

Turns out this has already been done before. I have never encountered it thus far when searching the web for how to create a speaker spice model, but looking for the right keywords brought up a thread on the German mikrocontroller.net-forum. Fortunately the whole thing is as easy as pie, which makes me wonder even more why it is not ubiquitous with diyaudio and LTSpice already...

The Model

Without further ado, here it is:

.subckt MAXI330 1 2
B1 1 2 V=I(B1)  MAG FREQ=
+ 20.142, 20.883, -74.570
+ 50.537, 8.537, -52.902
+ 98.145, 6.676, 4.844
+ 494.019, 5.673, 19.204
+ 1017.700, 9.171, 39.194
+ 4983.032, 21.734, -10.051
+ 9965.698, 8.458, 25.251
+ 45714.109, 42.504, 65.181
.ends

I have removed most of the values to keep the example short, but since you're going to measure your own values anyway that's not much of a problem. Let me explain what each line does.

.subckt MAXI330 1 2

B1 1 2 V=I(B1) MAG FREQ=

+ 20.142, 20.883, -74.570

.ends

How to use this

Very simple. Fire up LTSpice with a new project and press the ''S'' key. This will open a small window where you can add some text as a SPICE directive to your project. Just paste the whole model code here, which you have already created before. Press ENTER and click anywhere in your project to place the text somewhere. Now hit ''F2'' and type ''xv''. This should give you a symbol called xvaristor (many others with two pins labelled 1 and 2 will do, even your own, but I find this one rather convenient). Place one of them in your project. Now Right-Click on the label ''varistor'' and change the value to the name of your model, so MAXI330 in my case here.

That's it, really! Now you have a part that almost looks like the classic load resistor and almost behaves like your loudspeaker in an .AC-simulation. I have also tried this in a transient analysis, but some of my models work OK while others don't. Maybe I'll investigate on that further someday, but for now I'm happy with a model which helps in designing output filters tailored to my speakers.

How to measure a speaker

My measurement setup. Not very sophisticated, but it does the trick.

Get yourself a copy of the ARTA suite, if you haven't already.

http://www.artalabs.hr/

Fire up LIMP and read through the help file. It isn't all too long and describes how to hook up your speaker to your soundcard with a single 100R resistor. I actually used my onboard RealTek thingie and its headphone out with no exterally added amplifier. Make sure that you use the highest possible sample rate. LIMP can sample up to 96000 (no 192000 sadly), so set this value under Sounds and Audio in the Windows Control Panel. Usually there it's set to 48000 and 16bit, but that setting will screw up your measurements above 24kHz, even when LIMP is set to 96000.

Start a stepped sine measurement from 20 Hz to 45000 Hz and watch as the measurement graph is slowly drawn on your screen. When that is done and the graph looks fine, click on File > Export as ... > CSV (Excel) file and save your data to a file.

./limp.png

Now open that file with an editor of your choice. I prefer Notepad++ here over Notepad.

https://notepad-plus-plus.org/

It should look like this:

Frequency(Hz), Magnitude(ohms), Phase(deg)
20.142, 20.883, -74.570
20.508, 20.522, -74.346
21.240, 19.844, -73.894
21.973, 19.183, -73.459
22.705, 18.588, -72.954
23.438, 18.015, -72.488
24.170, 17.489, -71.986
24.902, 16.985, -71.538
25.635, 16.516, -71.069

Remove the first line, we don't need that anymore (press shift + down-arrow, then delete). Now add a + sign at the beginning of every line. Here the column mode of Notepad++ comes in handy. Hold down shift + alt and hit page down a few times, until you've reached the end of the file. Release all keys and hit + and space. You will see those two characters added to the beginning of every line. Remove the lonely + sign in the last line, then press ctrl + A to select everything, and then ctrl + C to copy your data to the clipboard. Paste into LTSpice, add the other three lines of the model, and you're done.

./ltspice_speaker_models.png

red = S6
blue = ERGO31
green = JVC
magenta = MAXI330

In case you need something to play around with, here are some of my speaker models.

.subckt MAXI330 1 2
B1 1 2 V=I(B1)  MAG FREQ=
+ 20.142, 20.883, -74.570
+ 20.508, 20.522, -74.346
+ 21.240, 19.844, -73.894
+ 21.973, 19.183, -73.459
+ 22.705, 18.588, -72.954
+ 23.438, 18.015, -72.488
+ 24.170, 17.489, -71.986
+ 24.902, 16.985, -71.538
+ 25.635, 16.516, -71.069
+ 26.367, 16.069, -70.581
+ 27.100, 15.651, -70.092
+ 27.832, 15.252, -69.621
+ 28.564, 14.856, -69.147
+ 29.297, 14.490, -68.667
+ 30.029, 14.149, -68.205
+ 30.762, 13.814, -67.674
+ 31.494, 13.503, -67.165
+ 32.593, 13.073, -66.451
+ 33.691, 12.645, -65.716
+ 34.790, 12.259, -64.912
+ 35.889, 11.888, -64.108
+ 36.987, 11.558, -63.374
+ 38.086, 11.222, -62.645
+ 39.185, 10.916, -61.790
+ 40.283, 10.615, -60.974
+ 41.382, 10.349, -60.174
+ 42.480, 10.096, -59.328
+ 43.579, 9.850, -58.514
+ 44.678, 9.610, -57.625
+ 46.143, 9.319, -56.519
+ 47.607, 9.044, -55.314
+ 49.072, 8.793, -54.166
+ 50.537, 8.537, -52.902
+ 52.002, 8.323, -51.736
+ 53.467, 8.089, -50.500
+ 54.932, 7.892, -49.281
+ 56.396, 7.676, -47.886
+ 58.228, 7.475, -46.162
+ 60.059, 7.294, -44.433
+ 61.890, 7.104, -42.562
+ 63.721, 6.916, -40.844
+ 65.552, 6.756, -38.924
+ 67.383, 6.601, -36.959
+ 69.214, 6.467, -34.962
+ 71.411, 6.321, -32.499
+ 73.608, 6.196, -29.955
+ 75.806, 6.090, -27.111
+ 78.003, 6.015, -24.295
+ 80.200, 5.950, -21.420
+ 82.397, 5.919, -18.336
+ 84.961, 5.908, -14.708
+ 87.524, 5.947, -10.922
+ 90.088, 6.032, -7.103
+ 92.651, 6.156, -3.237
+ 95.215, 6.351, 0.649
+ 98.145, 6.676, 4.844
+ 101.074, 7.084, 8.710
+ 104.004, 7.672, 12.517
+ 106.934, 8.418, 15.517
+ 110.229, 9.552, 17.877
+ 113.525, 11.031, 18.568
+ 116.821, 12.937, 17.265
+ 120.117, 15.235, 12.902
+ 123.779, 17.818, 4.267
+ 127.441, 19.520, -7.905
+ 131.104, 19.500, -20.913
+ 134.766, 17.987, -31.801
+ 138.794, 15.763, -39.729
+ 142.822, 13.770, -44.173
+ 146.851, 12.202, -46.195
+ 151.245, 10.906, -47.032
+ 155.640, 9.903, -46.998
+ 160.034, 9.112, -46.350
+ 164.795, 8.427, -45.200
+ 169.556, 7.885, -43.754
+ 174.683, 7.423, -41.985
+ 179.810, 7.056, -40.167
+ 184.937, 6.752, -38.434
+ 190.430, 6.475, -36.439
+ 195.923, 6.250, -34.512
+ 201.782, 6.047, -32.363
+ 207.642, 5.878, -30.352
+ 213.867, 5.737, -28.208
+ 220.093, 5.617, -26.203
+ 226.685, 5.510, -24.049
+ 233.276, 5.453, -22.064
+ 240.234, 5.351, -20.367
+ 247.192, 5.278, -18.105
+ 254.517, 5.273, -15.905
+ 261.841, 5.258, -14.775
+ 269.531, 5.152, -13.710
+ 277.588, 5.234, -11.398
+ 285.645, 5.198, -10.582
+ 294.067, 5.090, -8.785
+ 302.856, 5.054, -6.722
+ 311.646, 5.040, -4.845
+ 320.801, 5.040, -3.025
+ 330.322, 5.044, -1.271
+ 339.844, 5.053, 0.433
+ 349.731, 5.073, 2.136
+ 359.985, 5.101, 3.757
+ 370.605, 5.133, 5.324
+ 381.592, 5.163, 6.863
+ 392.944, 5.200, 8.441
+ 404.297, 5.243, 9.952
+ 416.016, 5.292, 11.327
+ 428.101, 5.347, 12.756
+ 440.552, 5.408, 14.111
+ 453.369, 5.470, 15.399
+ 466.553, 5.533, 16.703
+ 480.103, 5.601, 17.968
+ 494.019, 5.673, 19.204
+ 508.667, 5.758, 20.451
+ 523.682, 5.845, 21.675
+ 539.063, 5.937, 22.798
+ 554.810, 6.031, 23.878
+ 570.923, 6.130, 24.947
+ 587.769, 6.238, 25.991
+ 604.980, 6.344, 26.988
+ 622.559, 6.459, 27.960
+ 640.869, 6.583, 28.868
+ 659.546, 6.708, 29.731
+ 678.955, 6.838, 30.560
+ 698.730, 6.972, 31.367
+ 719.238, 7.109, 32.110
+ 740.479, 7.255, 32.847
+ 762.085, 7.410, 33.470
+ 784.424, 7.554, 33.962
+ 807.495, 7.674, 34.491
+ 831.299, 7.808, 35.385
+ 855.835, 7.986, 36.156
+ 880.737, 8.160, 36.797
+ 906.372, 8.349, 37.399
+ 933.105, 8.544, 37.932
+ 960.571, 8.750, 38.382
+ 988.770, 8.960, 38.832
+ 1017.700, 9.171, 39.194
+ 1047.363, 9.390, 39.593
+ 1078.125, 9.626, 39.884
+ 1109.619, 9.865, 40.138
+ 1142.212, 10.110, 40.324
+ 1175.537, 10.361, 40.479
+ 1209.961, 10.619, 40.544
+ 1245.483, 10.874, 40.626
+ 1282.104, 11.134, 40.656
+ 1319.824, 11.405, 40.705
+ 1358.643, 11.690, 40.738
+ 1398.560, 12.000, 40.726
+ 1439.575, 12.320, 40.539
+ 1481.689, 12.640, 40.359
+ 1525.269, 12.964, 40.027
+ 1569.946, 13.297, 39.737
+ 1616.089, 13.647, 39.292
+ 1663.330, 13.994, 38.766
+ 1712.036, 14.334, 38.027
+ 1762.207, 14.632, 37.254
+ 1813.843, 14.892, 36.477
+ 1866.943, 15.125, 35.702
+ 1921.509, 15.297, 35.171
+ 1977.905, 15.457, 34.924
+ 2035.767, 15.736, 34.960
+ 2095.459, 16.139, 34.874
+ 2156.982, 16.591, 34.324
+ 2220.337, 17.014, 33.555
+ 2285.522, 17.404, 32.601
+ 2352.539, 17.766, 31.652
+ 2421.387, 18.102, 30.585
+ 2492.432, 18.404, 29.556
+ 2565.308, 18.690, 28.478
+ 2640.381, 18.949, 27.480
+ 2717.651, 19.201, 26.419
+ 2797.119, 19.442, 25.450
+ 2879.150, 19.672, 24.388
+ 2963.379, 19.894, 23.458
+ 3050.171, 20.115, 22.440
+ 3139.526, 20.338, 21.542
+ 3231.445, 20.579, 20.532
+ 3326.294, 20.823, 19.632
+ 3423.706, 21.115, 18.580
+ 3524.048, 21.425, 17.556
+ 3627.319, 21.766, 16.297
+ 3733.521, 22.115, 14.972
+ 3843.018, 22.474, 13.332
+ 3955.444, 22.818, 11.615
+ 4071.167, 23.135, 9.502
+ 4190.552, 23.389, 7.238
+ 4313.232, 23.538, 4.574
+ 4439.575, 23.543, 1.815
+ 4569.580, 23.376, -1.234
+ 4703.613, 23.015, -4.213
+ 4841.309, 22.466, -7.295
+ 4983.032, 21.734, -10.051
+ 5129.150, 20.865, -12.713
+ 5279.297, 19.904, -14.871
+ 5433.838, 18.878, -16.845
+ 5593.140, 17.821, -18.216
+ 5757.202, 16.775, -19.302
+ 5926.025, 15.766, -19.771
+ 6099.609, 14.802, -20.008
+ 6278.320, 13.904, -19.602
+ 6462.158, 13.068, -19.033
+ 6651.489, 12.296, -17.854
+ 6846.313, 11.592, -16.486
+ 7046.997, 10.958, -14.531
+ 7253.540, 10.393, -12.446
+ 7465.942, 9.899, -9.788
+ 7684.570, 9.472, -7.064
+ 7909.790, 9.112, -3.812
+ 8141.602, 8.819, -0.579
+ 8380.005, 8.590, 3.116
+ 8625.732, 8.427, 6.670
+ 8878.418, 8.322, 10.565
+ 9138.428, 8.277, 14.195
+ 9406.128, 8.287, 18.097
+ 9681.885, 8.349, 21.591
+ 9965.698, 8.458, 25.251
+ 10257.568, 8.611, 28.448
+ 10558.228, 8.803, 31.793
+ 10867.676, 9.035, 34.603
+ 11186.279, 9.294, 37.542
+ 11514.038, 9.585, 39.952
+ 11851.318, 9.903, 42.519
+ 12198.486, 10.246, 44.521
+ 12555.908, 10.608, 46.741
+ 12923.950, 10.996, 48.400
+ 13302.612, 11.395, 50.319
+ 13692.261, 11.817, 51.673
+ 14093.628, 12.251, 53.333
+ 14506.714, 12.707, 54.428
+ 14931.885, 13.167, 55.875
+ 15369.507, 13.654, 56.753
+ 15819.946, 14.142, 58.023
+ 16283.569, 14.654, 58.704
+ 16760.742, 15.167, 59.829
+ 17251.832, 15.709, 60.320
+ 17757.203, 16.230, 61.299
+ 18277.588, 16.781, 61.710
+ 18812.988, 17.332, 62.650
+ 19364.137, 17.918, 62.936
+ 19931.396, 18.491, 63.772
+ 20515.504, 19.099, 63.962
+ 21116.820, 19.687, 64.765
+ 21735.719, 20.328, 64.868
+ 22372.559, 20.941, 65.633
+ 23028.076, 21.615, 65.644
+ 23703.004, 22.249, 66.363
+ 24397.705, 22.952, 66.297
+ 25112.549, 23.606, 66.990
+ 25848.266, 24.340, 66.861
+ 26605.590, 25.016, 67.540
+ 27385.254, 25.788, 67.348
+ 28187.621, 26.487, 68.019
+ 29013.428, 27.295, 67.759
+ 29863.402, 28.008, 68.416
+ 30738.648, 28.856, 68.116
+ 31639.527, 29.597, 68.772
+ 32566.773, 30.480, 68.397
+ 33521.117, 31.236, 69.072
+ 34503.297, 32.158, 68.654
+ 35514.406, 32.930, 69.367
+ 36555.176, 33.914, 68.913
+ 37626.344, 34.711, 69.643
+ 38729.004, 35.745, 69.128
+ 39863.891, 36.595, 69.886
+ 41032.105, 37.700, 69.300
+ 42234.375, 38.527, 70.096
+ 43471.801, 39.706, 69.457
+ 44745.484, 40.889, 69.492
+ 45714.109, 42.504, 65.181
.ends

.subckt S6 1 2
B1 1 2 V=I(B1)  MAG FREQ=
+ 20.142, 7.540, 20.971
+ 20.508, 7.564, 21.387
+ 21.240, 7.666, 22.072
+ 21.973, 7.772, 22.653
+ 22.705, 7.869, 23.831
+ 23.438, 8.016, 22.457
+ 24.170, 8.265, 24.358
+ 24.902, 8.211, 24.728
+ 25.635, 8.416, 22.599
+ 26.367, 8.571, 25.396
+ 27.100, 8.707, 25.959
+ 27.832, 8.895, 26.814
+ 28.564, 9.152, 26.909
+ 29.297, 9.343, 27.048
+ 30.029, 9.612, 26.830
+ 30.762, 9.956, 26.499
+ 31.494, 10.260, 26.504
+ 32.593, 10.745, 24.986
+ 33.691, 11.197, 22.590
+ 34.790, 11.741, 18.890
+ 35.889, 11.688, 13.854
+ 36.987, 11.419, 10.143
+ 38.086, 10.832, 5.684
+ 39.185, 9.773, 5.393
+ 40.283, 9.277, 6.141
+ 41.382, 8.722, 8.292
+ 42.480, 8.337, 10.536
+ 43.579, 8.289, 13.789
+ 44.678, 8.266, 16.001
+ 46.143, 8.263, 19.290
+ 47.607, 8.524, 22.131
+ 49.072, 8.587, 23.603
+ 50.537, 8.799, 26.125
+ 52.002, 9.052, 27.514
+ 53.467, 9.304, 29.022
+ 54.932, 9.570, 30.376
+ 56.396, 9.904, 30.942
+ 58.228, 10.249, 32.646
+ 60.059, 10.687, 33.419
+ 61.890, 11.088, 34.216
+ 63.721, 11.659, 34.672
+ 65.552, 12.195, 35.299
+ 67.383, 12.806, 35.545
+ 69.214, 13.429, 35.354
+ 71.411, 14.197, 35.290
+ 73.608, 15.114, 34.832
+ 75.806, 16.106, 34.015
+ 78.003, 17.170, 32.780
+ 80.200, 18.341, 30.941
+ 82.397, 19.550, 28.882
+ 84.961, 21.062, 25.475
+ 87.524, 22.514, 21.265
+ 90.088, 23.837, 16.443
+ 92.651, 24.916, 10.750
+ 95.215, 25.525, 4.646
+ 98.145, 25.606, -2.567
+ 101.074, 25.019, -9.614
+ 104.004, 23.933, -15.831
+ 106.934, 22.512, -21.098
+ 110.229, 20.783, -25.813
+ 113.525, 19.087, -29.304
+ 116.821, 17.578, -31.737
+ 120.117, 16.219, -33.379
+ 123.779, 14.940, -34.466
+ 127.441, 13.836, -34.951
+ 131.104, 12.901, -34.886
+ 134.766, 12.103, -34.537
+ 138.794, 11.361, -33.786
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+ 207.642, 7.298, -11.355
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+ 807.495, 11.769, 38.011
+ 831.299, 11.976, 38.628
+ 855.835, 12.224, 39.295
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+ 933.105, 13.133, 41.101
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+ 1047.363, 14.630, 42.399
+ 1078.125, 15.042, 42.540
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+ 1175.537, 16.382, 42.574
+ 1209.961, 16.836, 42.489
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+ 1282.104, 17.829, 42.070
+ 1319.824, 18.349, 41.785
+ 1358.643, 18.893, 41.434
+ 1398.560, 19.437, 40.982
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+ 1481.689, 20.571, 39.854
+ 1525.269, 21.142, 39.166
+ 1569.946, 21.742, 38.463
+ 1616.089, 22.342, 37.655
+ 1663.330, 22.955, 36.720
+ 1712.036, 23.593, 35.685
+ 1762.207, 24.174, 34.544
+ 1813.843, 24.757, 33.231
+ 1866.943, 25.264, 31.860
+ 1921.509, 25.708, 30.468
+ 1977.905, 26.054, 29.181
+ 2035.767, 26.377, 28.055
+ 2095.459, 26.754, 27.103
+ 2156.982, 27.223, 26.139
+ 2220.337, 27.773, 25.019
+ 2285.522, 28.301, 23.642
+ 2352.539, 28.782, 22.138
+ 2421.387, 29.152, 20.559
+ 2492.432, 29.453, 19.016
+ 2565.308, 29.713, 17.537
+ 2640.381, 29.945, 16.097
+ 2717.651, 30.106, 14.785
+ 2797.119, 30.346, 13.680
+ 2879.150, 30.678, 12.580
+ 2963.379, 31.093, 11.448
+ 3050.171, 31.657, 10.272
+ 3139.526, 32.395, 8.912
+ 3231.445, 33.351, 7.066
+ 3326.294, 34.364, 4.634
+ 3423.706, 35.436, 1.552
+ 3524.048, 36.362, -2.510
+ 3627.319, 36.850, -7.425
+ 3733.521, 36.650, -13.017
+ 3843.018, 35.592, -18.925
+ 3955.444, 33.669, -24.636
+ 4071.167, 31.088, -29.627
+ 4190.552, 28.196, -33.481
+ 4313.232, 25.313, -36.027
+ 4439.575, 22.660, -37.307
+ 4569.580, 20.321, -37.435
+ 4703.613, 18.321, -36.563
+ 4841.309, 16.652, -34.864
+ 4983.032, 15.269, -32.496
+ 5129.150, 14.133, -29.588
+ 5279.297, 13.214, -26.242
+ 5433.838, 12.483, -22.557
+ 5593.140, 11.914, -18.609
+ 5757.202, 11.492, -14.482
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+ 6278.320, 10.992, -2.243
+ 6462.158, 11.018, 1.453
+ 6651.489, 11.108, 4.878
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+ 7046.997, 11.432, 10.980
+ 7253.540, 11.653, 13.655
+ 7465.942, 11.904, 16.093
+ 7684.570, 12.175, 18.312
+ 7909.790, 12.471, 20.345
+ 8141.602, 12.781, 22.182
+ 8380.005, 13.100, 23.855
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+ 8878.418, 13.767, 26.789
+ 9138.428, 14.112, 28.078
+ 9406.128, 14.464, 29.262
+ 9681.885, 14.823, 30.364
+ 9965.698, 15.189, 31.364
+ 10257.568, 15.553, 32.287
+ 10558.228, 15.923, 33.166
+ 10867.676, 16.304, 33.982
+ 11186.279, 16.693, 34.726
+ 11514.038, 17.083, 35.393
+ 11851.318, 17.469, 36.000
+ 12198.486, 17.851, 36.585
+ 12555.908, 18.241, 37.160
+ 12923.950, 18.644, 37.708
+ 13302.612, 19.055, 38.201
+ 13692.261, 19.470, 38.643
+ 14093.628, 19.886, 39.079
+ 14506.714, 20.324, 39.476
+ 14931.885, 20.776, 39.782
+ 15369.507, 21.213, 39.983
+ 15819.946, 21.617, 40.158
+ 16283.569, 21.995, 40.374
+ 16760.742, 22.387, 40.711
+ 17251.832, 22.832, 40.929
+ 17757.203, 23.233, 41.101
+ 18277.588, 23.630, 41.319
+ 18812.988, 24.033, 41.540
+ 19364.137, 24.436, 41.768
+ 19931.396, 24.852, 42.014
+ 20515.504, 25.276, 42.241
+ 21116.820, 25.707, 42.467
+ 21735.719, 26.148, 42.687
+ 22372.559, 26.593, 42.893
+ 23028.076, 27.044, 43.098
+ 23703.004, 27.503, 43.290
+ 24397.705, 27.964, 43.478
+ 25112.549, 28.441, 43.657
+ 25848.266, 28.908, 43.835
+ 26605.590, 29.391, 44.013
+ 27385.254, 29.885, 44.176
+ 28187.621, 30.383, 44.330
+ 29013.428, 30.881, 44.486
+ 29863.402, 31.391, 44.642
+ 30738.648, 31.909, 44.790
+ 31639.527, 32.434, 44.938
+ 32566.773, 32.972, 45.078
+ 33521.117, 33.512, 45.215
+ 34503.297, 34.062, 45.345
+ 35514.406, 34.617, 45.476
+ 36555.176, 35.181, 45.602
+ 37626.344, 35.756, 45.731
+ 38729.004, 36.343, 45.845
+ 39863.891, 36.940, 45.957
+ 41032.105, 37.548, 46.073
+ 42234.375, 38.147, 46.195
+ 43471.801, 38.782, 46.301
+ 44745.484, 39.829, 46.082
+ 45714.109, 42.081, 44.782
.ends

.subckt JVC 1 2
B1 1 2 V=I(B1)  MAG FREQ=
+ 20.142, 4.159, 10.098
+ 20.508, 4.171, 10.273
+ 21.240, 4.178, 10.696
+ 21.973, 4.189, 11.110
+ 22.705, 4.205, 11.311
+ 23.438, 4.225, 11.651
+ 24.170, 4.231, 12.040
+ 24.902, 4.250, 12.297
+ 25.635, 4.259, 12.644
+ 26.367, 4.271, 12.945
+ 27.100, 4.299, 13.258
+ 27.832, 4.315, 13.669
+ 28.564, 4.326, 13.936
+ 29.297, 4.353, 14.181
+ 30.029, 4.361, 14.554
+ 30.762, 4.393, 14.777
+ 31.494, 4.418, 15.144
+ 32.593, 4.434, 15.653
+ 33.691, 4.476, 16.083
+ 34.790, 4.516, 16.538
+ 35.889, 4.558, 16.859
+ 36.987, 4.595, 17.231
+ 38.086, 4.628, 17.559
+ 39.185, 4.683, 18.005
+ 40.283, 4.736, 18.292
+ 41.382, 4.788, 18.424
+ 42.480, 4.846, 18.564
+ 43.579, 4.888, 18.857
+ 44.678, 4.965, 18.758
+ 46.143, 5.034, 18.692
+ 47.607, 5.094, 18.483
+ 49.072, 5.158, 18.038
+ 50.537, 5.194, 17.659
+ 52.002, 5.214, 17.118
+ 53.467, 5.219, 16.746
+ 54.932, 5.190, 16.373
+ 56.396, 5.201, 16.210
+ 58.228, 5.179, 16.652
+ 60.059, 5.102, 16.772
+ 61.890, 5.116, 17.414
+ 63.721, 5.100, 18.041
+ 65.552, 5.098, 18.814
+ 67.383, 5.118, 19.680
+ 69.214, 5.128, 20.452
+ 71.411, 5.178, 21.515
+ 73.608, 5.230, 22.230
+ 75.806, 5.296, 23.312
+ 78.003, 5.384, 24.169
+ 80.200, 5.461, 25.204
+ 82.397, 5.558, 25.891
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+ 87.524, 5.803, 27.578
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+ 113.525, 8.139, 32.932
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+ 120.117, 9.378, 31.857
+ 123.779, 10.252, 30.092
+ 127.441, 11.243, 27.040
+ 131.104, 12.302, 22.267
+ 134.766, 13.231, 15.657
+ 138.794, 13.759, 6.619
+ 142.822, 13.468, -2.694
+ 146.851, 12.536, -10.389
+ 151.245, 11.276, -15.922
+ 155.640, 10.126, -19.089
+ 160.034, 9.169, -20.362
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+ 339.844, 4.639, 0.231
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+ 359.985, 4.642, 3.336
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+ 381.592, 4.699, 5.978
+ 392.944, 4.705, 7.190
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+ 416.016, 4.767, 9.570
+ 428.101, 4.806, 10.717
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+ 453.369, 4.879, 12.560
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+ 554.810, 5.232, 18.732
+ 570.923, 5.298, 19.502
+ 587.769, 5.368, 20.243
+ 604.980, 5.442, 20.904
+ 622.559, 5.516, 21.382
+ 640.869, 5.557, 21.909
+ 659.546, 5.621, 22.619
+ 678.955, 5.691, 23.279
+ 698.730, 5.765, 23.925
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+ 988.770, 6.909, 29.408
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+ 1047.363, 7.123, 30.112
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+ 1109.619, 7.374, 30.808
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+ 1245.483, 8.071, 31.283
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+ 2797.119, 13.196, 20.288
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+ 2963.379, 13.503, 17.913
+ 3050.171, 13.619, 16.631
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+ 3231.445, 13.786, 14.076
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+ 3423.706, 13.861, 11.474
+ 3524.048, 13.874, 10.147
+ 3627.319, 13.848, 8.837
+ 3733.521, 13.794, 7.539
+ 3843.018, 13.703, 6.321
+ 3955.444, 13.603, 5.242
+ 4071.167, 13.496, 4.186
+ 4190.552, 13.375, 3.173
+ 4313.232, 13.243, 2.234
+ 4439.575, 13.097, 1.318
+ 4569.580, 12.932, 0.454
+ 4703.613, 12.754, -0.316
+ 4841.309, 12.573, -0.997
+ 4983.032, 12.380, -1.608
+ 5129.150, 12.180, -2.105
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+ 5433.838, 11.789, -2.830
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+ 6278.320, 10.841, -3.152
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+ 6651.489, 10.513, -2.778
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+ 7046.997, 10.203, -2.104
+ 7253.540, 10.060, -1.651
+ 7465.942, 9.931, -1.148
+ 7684.570, 9.804, -0.606
+ 7909.790, 9.687, 0.016
+ 8141.602, 9.583, 0.675
+ 8380.005, 9.485, 1.369
+ 8625.732, 9.395, 2.112
+ 8878.418, 9.311, 2.912
+ 9138.428, 9.243, 3.747
+ 9406.128, 9.181, 4.623
+ 9681.885, 9.134, 5.507
+ 9965.698, 9.092, 6.389
+ 10257.568, 9.059, 7.307
+ 10558.228, 9.041, 8.229
+ 10867.676, 9.022, 9.117
+ 11186.279, 9.004, 9.989
+ 11514.038, 8.988, 10.954
+ 11851.318, 8.985, 11.953
+ 12198.486, 8.991, 12.971
+ 12555.908, 9.009, 13.977
+ 12923.950, 9.038, 15.021
+ 13302.612, 9.083, 16.008
+ 13692.261, 9.127, 16.945
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+ 14506.714, 9.215, 18.833
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+ 15819.946, 9.475, 21.668
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+ 19364.137, 10.112, 27.274
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+ 21116.820, 10.373, 29.316
+ 21735.719, 10.490, 30.183
+ 22372.559, 10.620, 31.007
+ 23028.076, 10.756, 31.781
+ 23703.004, 10.899, 32.550
+ 24397.705, 11.045, 33.279
+ 25112.549, 11.199, 34.008
+ 25848.266, 11.360, 34.716
+ 26605.590, 11.529, 35.408
+ 27385.254, 11.702, 36.079
+ 28187.621, 11.889, 36.677
+ 29013.428, 12.061, 37.227
+ 29863.402, 12.235, 37.871
+ 30738.648, 12.426, 38.489
+ 31639.527, 12.623, 39.079
+ 32566.773, 12.825, 39.653
+ 33521.117, 13.031, 40.224
+ 34503.297, 13.245, 40.781
+ 35514.406, 13.464, 41.310
+ 36555.176, 13.687, 41.821
+ 37626.344, 13.914, 42.337
+ 38729.004, 14.155, 42.838
+ 39863.891, 14.399, 43.319
+ 41032.105, 14.648, 43.778
+ 42234.375, 14.899, 44.256
+ 43471.801, 15.163, 44.702
+ 44745.484, 15.581, 44.788
+ 45714.109, 16.441, 43.564
.ends

.subckt ERGO31 1 2
B1 1 2 V=I(B1)  MAG FREQ=
+ 20.142, 8.862, -48.424
+ 20.508, 8.769, -48.544
+ 21.240, 8.506, -48.889
+ 21.973, 8.296, -49.128
+ 22.705, 8.085, -49.067
+ 23.438, 7.615, -49.477
+ 24.170, 7.573, -48.790
+ 24.902, 7.314, -48.252
+ 25.635, 7.104, -48.377
+ 26.367, 6.865, -47.712
+ 27.100, 6.699, -47.274
+ 27.832, 6.505, -46.861
+ 28.564, 6.339, -46.248
+ 29.297, 6.195, -45.538
+ 30.029, 6.013, -44.981
+ 30.762, 5.911, -43.875
+ 31.494, 5.736, -43.244
+ 32.593, 5.530, -42.322
+ 33.691, 5.319, -41.218
+ 34.790, 5.167, -39.804
+ 35.889, 4.994, -38.258
+ 36.987, 4.838, -36.751
+ 38.086, 4.704, -34.930
+ 39.185, 4.591, -33.689
+ 40.283, 4.456, -31.512
+ 41.382, 4.361, -29.565
+ 42.480, 4.248, -27.793
+ 43.579, 4.155, -26.081
+ 44.678, 4.064, -24.126
+ 46.143, 3.966, -20.800
+ 47.607, 3.900, -17.454
+ 49.072, 3.871, -14.663
+ 50.537, 3.809, -10.930
+ 52.002, 3.779, -7.798
+ 53.467, 3.810, -3.842
+ 54.932, 3.796, -0.506
+ 56.396, 3.863, 3.159
+ 58.228, 3.976, 8.405
+ 60.059, 4.166, 13.406
+ 61.890, 4.471, 17.617
+ 63.721, 4.639, 20.325
+ 65.552, 5.085, 24.962
+ 67.383, 6.005, 27.322
+ 69.214, 6.761, 28.126
+ 71.411, 7.957, 26.725
+ 73.608, 9.406, 22.949
+ 75.806, 10.759, 15.216
+ 78.003, 11.801, 4.060
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+ 84.961, 9.800, -22.169
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+ 164.795, 4.007, 1.827
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.ends

2018-10-24 created

2021-12-26 on gemini