birdcage/docs/A3981-vectors/A3981-datasheet_page_41.svg
Ryan Malloy 5252d1d73c Add hardware reference docs (A3981, K60, RYS352A)
Allegro A3981 stepper motor driver: datasheet, KiCad symbols/footprint,
3D model (TSSOP-28). Two per G2 board, SPI-controlled, AUTO microstep.

NXP MK60DN512VLQ10 (Kinetis K60): datasheet and 1300-page reference
manual. Cortex-M4 96MHz MCU running the G2 firmware.

Reyax RYS352A GPS module: datasheet and PAIR command guide.
GPS receiver on the G2 board (used for auto-location/satellite lookup).

All extracted as markdown + page images + vector SVGs for LLM context.
Binary assets (PDFs, PNGs, SVGs, STEP, WRL) stored via git-lfs.
2026-02-14 18:36:42 -07:00

1547 lines
164 KiB (Stored with Git LFS)
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<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-658.7051" x="36.1758 43.7458 51.8758 60.5558 67.575809 74.59581 82.16581 89.185817 96.016819 102.476818 109.49682 116.89382 119.847827 127.41782 134.98783 141.44783 147.73284 150.68685 157.70685 164.16686 171.18686">COMPENSATED HALF STEP</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-642.2051" x="36 41.53 44.28 49.25 54.22 57.52 61.93 63.848 71.038 76.008 78.478008 82.338008 87.30801 92.27801 99.46801 103.32801 105.79801 110.208019 112.67802 117.08802 119.83802 123.13802 127.54803 130.29804 134.70804 137.17804 141.03804 146.00804 150.97805 155.38805 158.68805 161.43805 169.18805 174.15805 179.12805 182.98805 187.39806 192.36806 194.83806 199.80806 204.77806 207.24806 209.99806 214.96807 219.37807 221.84807 226.81807 231.78807 236.19808 240.05808 244.46808 246.93808 251.90808 254.65808 259.06809 264.0381 267.33808 271.74809 279.49809 281.99809">Figure A5 shows a circle superimposed on the phase diagram. </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-630.2051" x="36 42.08 47.050004 49.800004 53.660005 56.130006 60.540006 63.290006 66.590007 71.00001 73.75001 78.16001 80.63001 83.930019 88.34002 93.31002 96.61002 101.02003 104.88003 109.29003 114.26003 117.01003 120.87003 123.340038 126.090038 131.06003 135.47003 137.94004 141.24004 145.65004 150.62004 155.59004 158.34004 161.64005 166.05005 171.02005 173.49005 176.24005 181.21006 185.62006 190.59006 194.45006 196.92006 201.89006 205.19007 207.66007 210.41007 215.38007 219.79007 222.26007 225.56008 229.97008 233.83008 238.80008 241.55008 244.30008 248.71009 253.68009 256.43009 258.9001 263.8701 268.8401 273.2501 277.11009 281.52009 283.99009 288.4001 293.3701">This circle represents the required locus of the resultant phase cur</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-630.2051" x="296.4356">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-618.2051" x="36 39.3 43.71 48.68 51.43 53.9 58.870004 63.280004 67.69 70.44 75.41 78.71001 82.57001 85.04001 87.79001 92.76001 95.23001 102.98001 107.390018 110.140018 115.110019 117.860019 122.27002 125.02002 129.99002 132.46002 137.43003 142.40003 147.37003 155.67003 158.14003 162.55004 167.52004 170.82004 174.12004 178.53005 183.50005 186.25005 188.72005 196.47005 200.88005 205.85005 210.82006 213.57006 216.32006 221.29006 226.26006 230.67006 233.14006 235.05806 242.24806 244.99806 247.46807 250.21807 255.18807 259.59806 262.06806 265.36805 270.33805 273.08805 275.83805 279.13804 282.99803 285.74803 290.15803 295.15803">rent vectors to maintain 100% current magnitude. At the full-step </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-606.2051" x="36 40.97 45.940004 49.800004 52.550004 55.300004 58.050004 63.020006 67.990009 71.850009 74.32001 76.79001 81.76001 84.23001 86.70001 91.67001 94.140018 96.610019 101.58002 104.05002 106.52002 110.93002 115.900028 120.870029 123.34003 128.31003 130.78003 133.25003 138.22003 143.19004 145.94004 150.91004 153.38004 158.35004 163.32004 167.73004 170.20005 175.17005 180.14005 184.55005 188.41005 192.82006 195.29006 198.04006 201.90006 204.37006 208.78006 213.19007 215.94007 218.69007 223.66007 228.07007 230.54007 234.95008 239.92008 244.89008 247.36008 250.11008 255.08008 259.49009 261.96009 269.71009 274.1201 279.0901 284.0601">positions, 0, 2, 4, and 6, only one phase is active and the magni</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-606.2051" x="286.7844">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-594.2051" x="36 38.75 43.72 48.690004 53.100004 55.570005 60.540006 63.840005 66.310009 69.060009 74.03001 78.44001 80.91001 85.88001 90.85001 95.26002 99.12002 103.53002 106.00002 110.41003 115.38003 118.68003 121.980037 126.39004 131.36003 134.11003 136.58003 139.33003 143.19004 145.66004 150.07004 152.82004 155.29004 160.26004 165.23004 170.20005 178.50005 180.97005 182.88805 190.07805 192.82805 195.29805 198.04805 203.01805 207.42806 209.89806 214.86806 219.27806 222.02806 225.32807 228.62807 232.48807 235.23807 239.64807 244.61808 247.08808 252.05808 257.02809 260.88807 263.63807 266.38807 269.13807 274.10807 279.07807 282.93806 285.40806 287.87806 292.84806 295.34806">tude of the phase current is at 100%. At the half-step positions, 1, </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-582.2051" x="36 40.97 43.440004 45.910005 50.880006 53.350008 55.820009 60.230009 65.200008 70.170009 72.64001 77.61001 80.08001 82.55001 87.52001 92.49001 95.24001 100.210018 102.680019 107.65002 112.62002 117.03002 120.89002 125.300029 129.16002 131.63002 136.04003 139.34003 143.75003 146.22003 150.63004 155.04004 157.79004 160.54004 165.51004 169.92005 172.39005 174.68006 180.06006 185.03006 187.50006 191.91007 196.88007 200.74007 205.71007 209.01007 213.42008 215.89008 218.64008 223.61008 228.02008 230.77008 233.24008 235.99008 240.96009 245.37009 247.84009 255.59009 260.0001 264.9701 269.9401 272.6901 275.4401 280.4101 285.3801 289.8191">3, 5, and 7, both phases are active. To ensure that the magnitude </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-570.2051" x="36 40.97 44.27 46.74 49.49 54.460004 58.870004 61.340005 64.64001 69.05001 72.91001 77.88001 80.63001 83.38001 87.790019 92.76002 95.51002 97.98002 102.39002 107.36002 110.66003 113.96003 118.37003 123.340038 126.090038 128.56003 131.31003 135.17003 137.64003 142.61003 147.58003 152.55004 160.85004 163.32004 165.79004 168.54004 173.51004 177.92005 180.39005 188.14005 192.55005 197.52005 202.49005 205.24005 207.99005 212.96006 217.93006 222.34006 224.81006 229.78006 233.08007 235.55007 239.96007 244.37007 248.78008 253.75008 256.22007 261.19007 266.16007 270.57008 274.43006 278.84007 281.31007 285.72007 290.69007">of the resultant current is 100%, the magnitude of each phase cur</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-570.2051" x="293.757">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-558.2051" x="36 39.3 43.71 48.68 51.43 53.9 61.65 66.62 70.48 73.23 75.700008 80.670009 85.08001 87.55001 92.52001 97.49001 99.960018 104.930019 113.23002 115.70002 118.17002 124.81002 129.22002 131.97002 136.38002 141.35002 144.10002 148.51003 151.26003 154.01003 158.98003 163.95003 166.42003 169.17003 174.14003 178.55004 181.02004 185.99004 190.40004 193.15004 198.12004 202.53005 205.00005 209.97005 213.27005 215.74005 218.49005 223.46006 227.87006 230.34006 233.64006 238.05007 241.91007 246.88007 249.63007 252.38007 256.79008 261.76008 264.51008 266.98008 271.39009 276.36009 279.66007 282.96006 287.37007 292.34007 295.11808">rent must be 70.7%. Calculating the value of the resultant current </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-546.2051" x="36 40.41 44.27 46.74 51.710004 56.120004 59.420003 64.39 67.69 72.100009 74.57001 79.54001 82.29001 87.26001 91.67001 95.530017 98.000019 102.41002 104.88002 108.18002 112.59003 116.45003 121.42003 124.17003 126.92003 131.33003 136.30004 139.05004 141.52004 145.93004 150.90004 154.20005 157.50005 161.91005 166.88005 169.63005 172.10005 177.07006 180.37006 182.84006 187.81006 192.78006 197.75006 206.05007">as before gives a resultant current of 100%.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="ETRYCQ+ArialMT"><tspan y="-517.6222" x="145.0607">=</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="10.056242" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-520.53939" x="75.511409 80.53953 83.05358 88.0817 93.10982">0.707</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="7.5421817" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-523.0534" x="98.137859">2</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="10.056242" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-520.53939" x="101.90895 104.42301 110.094738 112.60879 117.63691 120.15096 125.179088 130.20722"> + 0.707</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="7.5421817" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-523.0534" x="135.2351">2</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="10.056242" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-520.53939" x="161.03044 166.05855 168.57262 173.60073 176.11479 181.7865 184.30057 189.32868 191.84275">0.5 + 0.5</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="ETRYCQ+ArialMT"><tspan y="-517.6222" x="203.3107">=</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="10.056242" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-520.53939" x="218.95467">1</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="ETRYCQ+ArialMT"><tspan y="-517.6222" x="227.8107">=</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1.0056242 0 -0 .99440726 0 792)" font-size="10.056242" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-520.53939" x="235.85959">1</tspan></text>
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<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-514.2051" x="291.6"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-659.0518" x="312 318.08 323.05 327.46 329.93 334.34 339.31 342.61 345.90998 350.31999 355.28999 358.03999 360.50999 365.47999 369.88999 374.3 377.05 382.02 385.31999 389.17997 391.64997 396.05998 398.80998 401.27998 406.24998 410.65998 413.40998 416.70997 420.00996 423.86994 426.61994 431.02995 435.99995 438.46995 443.43995 448.40995 452.26994 455.01994 457.76994 460.51994 465.48994 470.45994 472.92994 477.89994 480.36994 484.77995 488.07994 492.48994 494.95994 498.81993 503.78993 508.75993 515.9499 520.91989 523.38986 527.2498 532.2198 536.62979 541.03976 543.78976 547.0897 549.8397 554.2497 558.65969 561.40969 564.15969 569.15969">The current vectors at half-step position 1 are shown specifically </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-647.0518" x="312 314.75 319.72 322.19 324.94 327.69 330.44 335.41 339.27 342.02 345.31999 349.72999 352.47999 356.88999 359.36 362.11 367.08 371.49 374.24 376.71 379.46 384.43 388.84 391.31 399.06 403.47 408.44 413.41 416.16 418.91 423.88 428.85 433.26 435.73 440.7 444 446.47 449.22 454.19 458.6 461.07 464.37 468.78 472.63999 477.61 480.36 483.11 487.52 492.49 495.24 497.71 501.56999 504.31999 507.06999 510.92997 513.39999 518.36996 523.3399 525.8099 528.5599 533.52987 537.9398 540.4098 545.37979 550.34976 555.3197 563.6497">to illustrate that the magnitude of the resultant sits on the 100% </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-635.0518" x="312 316.41 319.16 322.46 326.87 329.62 334.03">circle.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-617.0518" x="312 317.56 322.56 325.88999 328.38999 332.83 335.33 339.22 342 346.44 351.44 356.44 360.88 364.21 369.21 371.71 375.6 378.38 382.82 387.82 392.82 397.26 400.59 403.09 410.87 415.87 418.65 423.65 426.97999 429.47999 432.25999 437.25999 439.75999 444.75999 449.75999 454.19999 457.52998 461.96998 464.74998 469.18998 471.68998 478.90998 481.68998 484.46998 489.46998 491.96998 499.74998 502.52998 507.52998 510.30998 518.08999 523.08999 530.87 533.37 536.15 541.15 544.48007 549.48007 554.48007 558.92007">For a standard stepper motor to operate with minimum torque </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-605.0518" x="312 315.33 318.11 323.11 328.11 330.88999 335.33 337.83 340.31999 343.09999 348.09999 352.53999 355.02998 358.35997 362.79997 366.68998 371.68998 374.46998 377.24998 381.68998 386.68998 389.46998 391.95997 396.39997 401.39997 404.72996 408.05995 412.49995 417.49995 420.27995 422.76994 430.54994 435.54994 439.43995 442.21995 444.70994 449.14994 451.92994 459.14994 463.58995 468.58995 472.47996 474.96995 477.74995 480.52995 484.96995 487.45994 492.45994 497.45994 499.94993 502.72993 507.72993 512.1699 514.6599 519.0999 524.0999 529.0999 532.9899 535.76998 540.20999 545.20999 547.99 550.48 553.26 558.26 561.59 566.59 571.59 576.03">ripple, the resultant current must always lie on the constant torque </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-593.0518" x="312 316.44 319.22 322.55 326.99 329.77 334.21 336.71 339.49 342.81999 346.14997 350.58998 354.47999 359.47999 363.91999 368.36 371.13999 373.91999 378.91999 383.36 385.86 390.86 394.18998 396.68998 399.46998 404.46998 408.90998 411.40998 416.40998 421.40998 429.18998 434.18998 438.62998 441.95997 444.45997 449.45997 452.78996 455.28996 463.06996 465.84996 470.28996 473.61994 478.61994 482.50996 485.28996 489.72996 494.72996 498.61997 501.11997 503.61997 509.17997 514.17996 517.50997 520.00997 525.00997 527.79 532.79 537.79 542.23 545.56 548.06 551.39 555.83 559.72006 564.72006 567.50009">circle irrespective of the number of microsteps. For higher resolu</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-593.0518" x="572.4687">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-581.0518" x="312 314.78 317.56 322.56 327.56 330.06 337.84 340.62 345.06 348.38999 353.38999 357.28 360.06 364.5 369.5 374.5 377.28 382.28 387.28 389.78 392.56 397.56 400.34 404.23 406.73 409.51 414.51 418.95 423.95 426.45 431.45 435.89 439.22 442 447 451.44 455.33003 457.83003 460.61003 465.61003 470.05003 472.55003 475.88 480.32 483.1 487.54 490.32 493.1 498.1 502.54 505.04 510.04 515.04006 519.48007 523.37008 527.81008 530.31008 534.75009 539.75009 543.0801 546.4101 550.8501 555.8501 558.6301 562.52017 565.02017 569.46017 572.2402">tion microstepping this then defines the relative phase currents at </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-569.0518" x="312 316.44 320.88 325.32 330.32 332.82 340.6 343.38 347.82 351.15 356.15 360.04 362.82 367.26 372.26 374.76 379.76 384.76 388.65003 391.43003 394.21003 396.99003 401.99003 406.99003">each microstep position.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-546.5518" x="312.1758 320.30583 327.87583 335.44584 343.01585 349.47584 356.49583 363.89283 366.8468 373.8668 380.32679 387.34678">QUARTER STEP</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-530.0518" x="312 317.56 322.56 325.88999 328.38999 332.83 337.83 342.27 350.05 355.05 357.83 362.27 364.77 369.21 374.21 379.21 383.1 385.88 390.88 395.32 398.65 401.15 403.93 408.93 413.37 415.87 420.87 425.31 430.31 433.09 435.59 438.91999 443.36 447.25 452.25 455.03 460.03 462.81 465.59 470.59 475.59 478.09 480.87 485.87 488.37 496.15 498.93 503.37 506.69999 511.69999 515.58999 518.37 522.81 527.81 532.81 535.59 540.59 545.59 548.37008 550.87008 555.87008 560.87008 565.31008">For example consider the next resolution in microstepping; quar</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-530.0518" x="568.4062">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-518.0518" x="312 314.78 319.22 322.55 325.05 328.94 331.72 336.16 341.16 343.66 345.975 352.085 357.085 361.525 364.025 366.805 371.805 376.245 381.245 385.135 387.635 392.635 395.965 398.465 401.245 406.245 410.685 413.185 416.51499 420.955 425.955 430.955 433.735 437.06498 441.50498 446.50498 449.00498 454.00498 459.00498 463.44499 467.335 471.775 474.275 478.715 483.715 487.04499 490.37498 494.81498 499.81498 502.59498 506.485 508.985 513.425 516.755 521.195 523.695 527.585 532.585 537.585 544.805 549.805 552.305 555.085 560.085">ter step. The locus of the required phase currents are shown in </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-506.0518" x="312 317.56 320.34 325.34 330.34 333.66999 338.11 340.05699 347.27699 352.27699 354.77699 357.098 363.20799 368.20799 372.64799 375.14799 378.47798 382.91798 387.91798 392.91798 395.69798 399.02796 403.46797 408.46797 410.96797 415.40797 420.40797 423.73796 427.06794 431.50794 436.50794 439.28794 441.78794 444.56794 449.00794 454.00794 458.44795 461.22795 463.72795 466.50794 471.50794 474.00794 478.44795 482.88795 487.32795 492.32795 494.82795 499.82795 504.82795 509.26795 513.15798 517.59799 520.09799 524.53799 528.97799 533.97799 536.47799 541.47799 545.91799 548.41799 552.858 557.298 560.078 564.518">Figure A6. The required current level in each phase can be calcu</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-506.0518" x="569.4805">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-494.0518" x="312 314.78 319.22 322 326.44 331.44 333.94 338.94 342.83003 345.61003 350.61003 355.61003 358.11003 362.00004 364.78004 372.56004 377.56004 380.34004 384.78004 387.28004 390.06004 393.39 396.17 401.17 406.17 411.17 416.17 423.95 428.39 431.17 434.5 438.831 441.331 443.831 449.391 454.391 457.72099 460.22099 464.66099 469.66099 474.10099 481.88099 486.88099 489.66099 494.10099 496.60099 499.10099 503.541 508.541 513.541 517.431 520.21109 525.21109 529.65109 532.9811 535.4811 543.2611 546.04116 550.48117 553.81118 558.81118 562.7012 565.4812 569.9212 574.9212">lated using simple trigonometry. For example, consider microstep </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-482.0518" x="312 317 322 325.89 328.67 331.45 334.23 339.23 344.23 346.73 351.73 354.23 357.01 362.01 364.51 370.07 372.85 377.85 382.85 386.18 390.62 392.56199 399.78199 404.78199 407.28199 411.722 415.612 418.112 423.112 427.552 430.332 434.772 437.552 440.332 444.772 449.772 452.272 455.052 460.052 462.552 468.112 470.892 475.892 480.892 484.222 488.662 490.599 497.819 502.819">position 7 in Figure A6 as detailed in Figure A7.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-464.0518" x="312 318.11 323.11 327.55 330.87998 335.31999 337.81999 342.25999 345.58998 350.02998 352.52998 357.52998 360.02998 365.02998 370.02998 374.46998 377.79997 380.57997 385.01997 388.34996 390.84996 394.73997 397.51997 401.95997 406.95997 410.84999 413.34999 416.67997 421.67997 425.00996 427.50996 431.94996 436.38996 440.82997 445.82997 448.32997 451.65995 456.65995 459.43995 462.21995 464.71995 468.60997 471.38996 475.82997 480.82997 483.32997 485.25697 491.92698 494.42698 497.75697 502.75697 505.53697 508.31697 510.81697 514.707 517.487 521.927 526.927 529.427 534.427 539.427 541.927 544.70706 549.70706 554.14706">There are 4 quarter steps for each full step. A full step on the </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-452.0518" x="312 317 322 326.44 330.33003 334.77003 337.27003 342.27003 345.05003 349.49003 354.49003 357.82 362.26 370.04 372.54 375.32 379.21003 381.71003 385.04 389.48 394.48 397.81 402.25 406.14 410.58003 415.58003 418.36003 422.80003 427.80003 430.30003 435.30003 440.30003 442.80003 447.80003 452.80003 456.80003 459.30003 461.80003 467.36003 472.36003 474.86003 479.30003 483.74003 488.18003 493.18003 495.68003 500.68003 505.68003 510.12004 513.45 516.23007 520.67007 524.00009 526.50009 530.3901 533.1701 537.6101 542.6101 545.1101 547.89016 552.89016 557.33016 560.66018">phase diagram is represented by 90&#x00b0;. So each quarter step incre</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-452.0518" x="565.0713">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-440.0518" x="312 319.78 324.22 329.22 332 335.89 338.39 341.17 346.17 350.61003 353.11003 358.11003 363.11003 367.55003 371.44004 375.88005 378.38005 382.82005 387.82005 392.82005 395.60005 400.04005 402.54005 407.54005 412.54005 415.04005 420.04005 425.04005">ments the phase angle by 90&#x00b0;</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-440.0518" x="429.04005"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-440.0518" x="430.28">/</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-440.0518" x="433.06"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-440.0518" x="434.31 439.31 441.81 447.45 449.95 454.95 459.95 462.45 467.45 471.45">4 = 22.5&#x00b0;.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-422.0518" x="312 315.33 320.33 322.83 328.38999 331.16999 336.16999 341.16999 344.49998 348.93998 350.88697 358.10697 363.10697 365.60697 368.38697 373.38697 377.82698 380.32698 383.65696 388.09696 391.98698 396.98698 399.76698 402.54698 406.98698 411.98698 414.76698 417.26698 425.04698 430.04698 432.82698 437.82698 441.15696 443.65696 448.09696 453.09696 456.42695 459.75694 464.19694 469.19694 471.97694 474.47694 478.91694 481.69694 484.19694 489.19694 494.19694 498.63694 501.96693 504.74693 509.18693 512.2929 515.6229 519.51296 522.29299 526.733 531.733 534.233 539.233 544.233 548.123">In Figure A7 the resultant motor current at quarter-step posi</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-422.0518" x="550.9014">-</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-410.0518" x="312 314.78 317.56 322.56">tion</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-410.0518" x="327.56"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-410.0518" x="330.06 335.06 337.56 340.34 344.23 346.73 351.73 356.73 361.17 363.67 368.67 373.67 378.11003 381.44 384.22 388.66 391.99 394.49 398.38 401.16 405.6 410.6 413.1 416.43 419.75999 424.75999 432.53999 435.03999 437.81999 442.81999 447.25999 449.75999 454.75999 459.75999 463.08998 465.86997 470.30998 475.30998 480.30998 483.08998 487.52998 490.30998 492.80998 495.30998 499.19999 504.19999 506.69999 509.47999 512.26 514.76 517.54006 521.43008 523.93008 528.37008 531.1501 533.6501 538.6501 543.6501 546.1501 551.1501 555.1501 557.6501 559.9391 566.0491 571.0491 575.4891">8 is one quarter step from the horizontal, so it is at 22.5&#x00b0;. The </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-398.0518" x="312 319.78 324.22 329.22 334.22 337 339.78 344.78 349.78 354.22 356.72 361.72 365.05 367.55 370.33 375.33 379.77 382.27 386.71 391.71 395.03999 398.36997 402.80998 407.80998 410.58998 413.08998 415.86997 420.86997 423.36997 428.36997 433.36997 437.80998 441.69999 446.13999 448.06898 454.73899 457.23899 461.679 464.45899 466.95899 471.95899 476.95899 481.399 484.72898 487.50898 491.94898 495.07096 498.40095 502.29096 505.07096 509.51097 514.511 517.011 522.011 527.011 530.901 533.681 536.46109 539.2411 544.2411">magnitude of the current in phase A at quarter-step position</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-398.0518" x="549.2411"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-398.0518" x="551.7411 556.7411 559.2411">7, </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-386.0518" x="312">I</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="7.5" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-383.5518" x="315.3301 320.74513">A7</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-386.0518" x="324.4963"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-386.0518" x="325.7463 328.2463 330.7463 333.5263 337.41633 339.91633 342.69633 347.69633 352.13633 355.4663 359.9063 363.2363 368.2363 371.56629 376.0063 378.5063 382.3963 385.1763 390.1763 392.6763 397.6763 402.6763 405.1763 410.1763 414.1763 416.6763 419.1763 426.3963 431.3963 434.1763 438.6163 443.6163 446.1163 448.8963 452.78633 455.28633 459.72633 464.72633 469.72633 474.16633 476.94633 479.44633 482.22633 487.22633 489.72633 494.72633 497.22633 502.22633 507.22633 512.2263 514.7263 519.7263 523.05636 525.55636 530.55636 535.55636 538.05636 543.05636 551.38638 553.88638 558.88638 562.2164">, is therefore sin 22.5&#x00b0;, which is equal to 0.383 or 38.3% of </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-374.0518" x="312 314.78 319.78 324.22 326.72 334.5 338.94 343.94 346.72 354.5 359.5 367.28 369.78 374.22 379.22 382.55 385.87998 390.31999 395.31999 398.09999">the maximum current.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-356.0518" x="312 317.56 320.34 328.12 330.9 333.68 338.12 341.44999 344.22999 348.572 351.072 353.572 356.352 361.352 365.792 368.292 376.072 380.512 385.512 390.512 393.292 396.072 401.072 406.072 410.512 413.012 418.012 421.34199 423.84199 426.62199 431.62199 436.06199 438.56199 443.00199 448.00199 451.33198 454.66197 459.10197 464.10197 466.88197 469.38197 472.16197 477.16197 479.66197 484.66197 489.66197 494.10197 497.99198 502.43199 504.93199 511.602 514.102 518.542 521.322 523.822 528.822 533.822 538.262 541.59207 544.3721 548.8121 551.9121 555.2421 559.13217 561.9122 566.3522 571.3522">Similarly, the magnitude of the current in phase B at quarter-step </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-344.0518" x="312 317 322 325.89 328.67 331.45 334.23 339.23">position</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-344.0518" x="344.23"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-344.0518" x="346.73 351.73 354.23 356.73">7, I</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="7.5" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-341.5518" x="360.0566 365.0591">B7</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-344.0518" x="368.8091"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-344.0518" x="370.0591 372.5591 375.0591 377.8391 381.72914 384.22914 387.00914 392.00914 396.44914 399.7791 404.21913 407.5491 412.5491 415.8791 420.3191 422.8191 427.2591 432.2591 436.1491 438.6491 443.6491 448.6491 451.1491 456.1491 460.1491 462.6491 465.1491 472.3691 477.3691 480.1491 484.5891 489.5891 492.0891 494.8691 498.75914 501.25914 505.69914 510.69914 515.6991 520.1391 522.9191 525.4191 528.19918 533.19918 535.69918 540.69918 543.19918 548.19918 553.19918 558.19918 560.69918 565.69918 569.0292">, is therefore cos 22.5&#x00b0;, which is equal to 0.924 or </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-332.0518" x="312 317 322 324.5 329.5 337.83 340.33 345.33 348.65998 351.15998 353.93998 358.93998 363.37998 365.87998 373.65998 378.09999 383.09999 385.87998 393.65998 398.65998 406.43998 408.93998 413.37998 418.37998 421.70997 425.03996 429.47996 434.47996 437.25996">92.4% of the maximum current.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-314.0518" x="312 319.22 322 324.5 327.28 332.28 336.72 339.22 344.22 349.22 353.22 355.72 360.72 365.72 369.61003 372.39 375.17 377.95 382.95 387.95 391.84004 394.34004 396.84004 401.84004 404.34004 406.84004 411.84004 414.34004 416.84004 421.84004 426.84004 429.34004 433.78004 438.78004 443.78004 446.28004 451.28004 456.28004 458.78004 461.28004 464.06004 469.06004 473.50004 476.00004 483.78004 488.22004 493.22004 498.22004 501.00004 503.78004 508.78004 513.78 518.22006 520.72006 525.72006 529.05007 531.55007 534.3301 539.3301 543.7701 546.2701 550.7101 555.7101 559.0401 562.3701 566.8101 571.8101 574.59017">At the 45&#x00b0; positions, 2, 6, 10 and 14, the magnitude of the current </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-302.0518" x="312 314.78 319.78 322.28 327.28 332.28 336.72 340.61003 345.05003 346.99504 353.66505 356.16505 360.60505 365.60505 370.60505 373.10505 378.10505 383.10505 387.54505 391.43507 395.87507 398.37507 405.04508 407.54508 414.76509 417.54508 420.32508 423.10508 425.60508 430.60508 435.04508 437.54508 441.98509 446.98509">in phase A and phase B will be cos</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-302.0518" x="450.8751"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-302.0518" x="453.3751 458.3751 463.3751 467.3751 469.8751 475.5151 478.0151 483.0151 485.5151 490.5151 495.5151 500.5151 503.0151 508.0151 511.3451 513.8451 518.8451 523.8451 526.3451 531.3451 539.6751 542.1751 544.6751 551.8951 556.8951 559.6751 564.1151 569.1151">45&#x00b0; = 0.707 or 70.7%, which </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-290.0518" x="312 314.78 318.67 321.16 323.94 328.94 333.38 335.87 339.76 344.2 351.98 356.42 358.91 366.69 371.13 376.13 381.13 383.91 386.69 391.69 396.69 401.13 403.61399 408.054 411.944 414.434 417.214 422.214 424.70399 427.48399 432.48399 436.92399 439.41398 444.41398 448.85398 451.63398 454.96397 458.29396 462.18397 464.96397 469.40397 474.40397 476.89396 481.33396 485.77397 489.66398 494.10398 496.59397 500.48399 505.48399 510.48399 517.704 522.704 525.194 527.974 532.974 535.464 538.794 541.57406 546.57406 551.57406 554.90408">is the same magnitude as in the half-step case shown in figure</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-290.0518" x="559.34408"> </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-290.0518" x="561.28 568.5 573.5 576">A5. </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-278.0518" x="312 319.22 324.22 328.66 331.16 333.94 338.94 341.44 345.33003 350.33003 358.11003 365.89 370.33003 373.11003 376.44 380.784 383.284 385.784 388.564 393.564 398.004 400.504 405.504 410.504 414.944 418.834 423.27403 425.21803 431.88804 434.38804 438.82804 443.82804 447.15803 450.488 454.928 459.928 462.708 465.208 467.988 471.87803 474.37803 477.15803 482.15803 486.59803 489.09803 492.98805 497.42805 505.20805 509.64805 512.1481 516.5881 519.3681 521.8681 526.8681 531.8681 536.3081 539.6381 542.41818 546.85818 549.9692 553.2992 557.1892 559.96926 564.40927 569.40927">Due to symmetry, the phase A current is the same at quarter-step </tspan></text>
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<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="4.86" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-124.1623" x="378.3404 381.582">B7</tspan></text>
<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="6.75" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-125.2873" x="384.0101 387.8171 390.06486 393.06187 396.43687 399.06263 402.43763 405.81263 407.50013 410.87513">=-cos22.5&#x00b0;</tspan></text>
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<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="6.75" font-family="ETRYCQ+ArialMT"><tspan y="-150.6225" x="432.0254 435.77165 439.51789 441.38764 445.13389">22.5&#x00b0;</tspan></text>
<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="6.75" font-family="UZMQSK+TimesNewRomanPSMT"><tspan y="-183.74475" x="499.79539 503.6024 506.22816 508.10466 511.47966 514.8546 518.2296 519.9171 523.2921">=sin22.5&#x00b0;</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-303.8781" x="40.3804 46.490404 49.2704 55.3804 61.490404 65.3804 70.9404 73.3444 80.5644 86.1244 89.4544 92.2344 98.904399 105.0144 110.574398 116.13439 121.69439 124.47439 131.69438 134.47438 140.03438 146.14438 150.03438 155.59438 164.48438 167.26438 170.59438 176.70438 180.59438 183.37438 190.59438 196.70438 205.59438 211.70438 217.26438 223.37438 228.93437 234.49437 237.82437 243.38437 249.49437 252.27437 259.49436 265.05436 267.83436 271.16435 273.94435 280.61436 283.94435 289.50434">Figure A5: Phase Diagram for Compensated Half Step</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-102.7197" x="66.2153 72.3253 75.1053 81.2153 87.3253 91.2153 96.7753 99.1793 106.3993 111.9593 115.2893 118.0693 124.739299 130.84929 136.40929 141.96929 147.52928 150.30928 157.52928 160.30928 165.86928 171.97928 175.86928 181.42928 190.31928 193.09928 196.42928 202.53928 206.42928 209.20928 216.98928 223.09928 228.65927 232.54927 235.87928 241.43927 245.32927 248.10927 254.77927 258.10926 263.66926">Figure A6: Phase Diagram for Quarter Step</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-102.7197" x="326.3901 332.5001 335.2801 341.39009 347.50007 351.39009 356.95008 359.35408 366.57408 372.13407 375.46406 378.24406 385.46406 391.02406 393.80406 399.36405 405.47404 408.25404 413.81404 417.144 419.924 426.034 432.14399 434.92399 441.594 447.70399 453.26399 458.82398 464.38398 467.16398 474.38398 480.49397 484.38398 488.274 493.83399 499.94398 503.27397 506.05397 514.384 519.944 526.05398 532.16397 534.944 538.274 544.384 550.49398 556.05398">Figure A7: Calculating Phase Current Magnitudes</tspan></text>
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