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<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="6" font-family="WSZTMG+ArialMT"><tspan y="-37.5204" x="427.7316 431.7336 433.0656 434.3976 437.7336 441.0696 443.0676 446.4036 448.0716 453.06959 454.40159 457.40159 459.39958 462.73558 466.73759 469.73759 472.73759 474.40559 477.74159 482.73957 485.73957">Allegro MicroSystems </tspan><tspan y="-30.3204" x="428.0376 431.3736 434.7096 438.0456 439.7136 443.7156 447.0516 449.0496 450.3816 455.37959 458.71559 460.38359 463.71958 465.71757 467.38557 471.71757 475.05357 478.38957 481.72557">955 Perimeter Road </tspan><tspan y="-23.1204" x="428.1096 433.10758 436.44358 439.77958 442.77958 446.11558 449.45158 452.45158 454.11958 457.45558 459.12596 460.79396 462.46195 466.79396 471.12596 472.79396 476.12995 479.46595 482.80195 486.13795 489.47395 491.47193 494.80793 498.14393 501.47993 504.81593 506.48393 510.81593 512.48397 516.48599 518.154 522.156">Manchester, NH 03103-3353 U.S.A.</tspan></text>
<text fill="#0000ff" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="6" font-family="WSZTMG+ArialMT"><tspan y="-15.920399" x="427.99559 432.32759 436.65959 440.99159 442.65959 445.99559 447.32759 448.65959 451.99559 455.33158 457.32957 460.66557 465.66355 466.99555 469.99555 471.99354 475.32954 476.99754 479.99754 483.33354">www.allegromicro.com</tspan></text>
</g>
<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="-127.1743" x="371.3999 377.5099 380.2899 386.39988 392.50987 396.39988 401.95988 404.36387 411.58387 417.14387 420.47386 423.25386 430.47386 436.03385 438.81385 442.14384 444.92384 451.59385 454.92384 460.48384 466.5938 469.3738 477.1538 483.2638 488.8238 492.7138 498.2738 501.6038 504.3838 510.49378">Figure A2: Half Step Operation</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="-658.5064" x="36 39.27 44.21 47.48 51.86 56.24 58.68 61.4 66.340007 70.72 73.44 75.880008 83.600009 88.54001 93.48001 97.86001 101.69001 104.13001 106.85001 111.790019 116.17001 118.610019 121.88001 126.820018 129.54001 134.48001 137.75002 140.19002 143.46002 146.73003 151.67003 159.39003 161.83003 164.55004 168.93004 172.20005 174.92005 177.36005 180.08005 185.02005 187.46006 190.73006 193.45006 198.39006 203.33007 206.05007 208.49007 211.21007 216.15007 218.59008 221.31008 226.25008 230.63008 233.07009 238.01009 240.73009 245.11009 250.0501 253.3201 257.7001 265.4201 267.8601 272.8001 277.7401 280.4601 283.1801 285.95814">force that moves the rotor from left to right in the diagram until </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="-646.5064" x="36 38.72 43.66 48.04 50.48 55.42 60.359998 63.079999 67.46 71.29 73.73 78.670009 81.94 84.380008 87.100009 92.04001 96.420009 98.86001 103.80001 108.18001 111.450008 119.170009 123.55 128.49 132.87001 137.81002 140.53002 142.97002 150.69002 155.07003 160.01003 164.95003 169.33003 172.05004 175.88004 178.32004 182.70005 187.64005 192.02005 194.74005 199.68006 202.12006 206.50006 209.22006 211.94007 216.88007 221.82007 224.26007 231.42008 234.14008 236.86008 241.80008 244.24008 246.96009 251.90009 256.2801 258.7201 263.6601 268.6001 271.3201 275.7001 279.5301 281.9701 286.9101 290.24009">the poles of the permanent magnets again align with the poles 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="-634.5064" x="36 38.72 43.66 48.04 50.48 54.86 57.58 61.960004 66.340007 69.060009 72.33 77.270008 84.990009 89.37 94.310009 99.25001 103.630008 106.350009 110.18001">the electromagnets.</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="-616.5064" x="36 39.33 44.33 46.83 51.83 56.270006 61.270006 65.71001 68.490009 70.990009 74.32001 78.76001 82.09001 84.59001 87.09001 89.87001 94.87001 99.31001 101.81001 106.250019 111.250019 114.58002 117.91002 122.35002 127.35002 130.13002 132.63002 135.41002 139.30002 141.80002 145.13002 147.91002 152.91002 160.13002 162.91002 167.91002 172.91002 175.41002 180.41002 185.41002 187.91002 190.69002 195.69002 199.02002 204.02002 209.02002 214.02002 219.02002 221.52002 224.30002 229.30002 233.74002 236.24002 241.24002 246.24002 250.68003 254.57003">In panel (c), the current is flowing up through the phase</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="-616.5064" x="259.01"> </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="-616.5064" x="260.94 267.61003 270.11003 277.33003 280.11003 285.11003">A wind</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="-616.5064" x="290.1064">-</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="-604.5064" x="36 38.78 43.78 48.78 51.28 54.61 57.940004 62.940004 70.72 73.22 78.22 83.22 86 88.78 93.78 101.56 104.06 106.84 111.84 114.34 117.119998 122.119998 127.119998 129.62 134.06 139.06 144.06 146.56 149.34 154.34 158.78 162.11 166.55 169.05 171.83 175.72 178.22 183.22 188.22 190.72 195.16 200.16 203.49 206.82 211.26001 216.26001 219.04001 221.54001 224.32 229.32 231.82 236.82 241.82 246.26001 250.15001 254.59001 257.09004 263.76005 266.26005 268.55406 274.66404 279.66404 282.44404 286.33406">ing from bottom to top and there is no current in phase B. This </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="-592.5064" x="36 39.33 43.770006 48.770006 53.210008 56.54001 60.430009 64.87001 68.76001 71.26001 74.04001 79.04001 83.48001 85.98001 90.98001 95.98001 98.76001 103.20001 105.70001 110.70001 114.030017 116.81001 121.250019 126.250019 129.03002 133.47002 136.25002 139.03002 144.03002 149.03002 151.53002 154.86002 158.19002 163.19002 170.97002 173.47002 176.25002 181.25002 185.69002 188.19002 190.97002 195.97002 200.97002 203.47002 208.47002 212.91002 217.91002 222.35002 225.13002 227.63002 230.13002 234.02002 239.02002 243.46002 248.46002 250.96002 253.74002 258.74003 263.18003 265.96003 268.46003 271.24003 276.24003 280.68003 284.01 288.45">reverses the pole orientation from the top panel, such that there </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="-580.5064" x="36 38.78 42.67 45.17 49.61 54.61 57.11 62.670003 65.17 70.17 75.17 77.95 82.39 84.89 89.89 94.89 97.39 100.17 105.17 109.61 111.552 118.222 120.722 125.162 127.942 132.382 136.822 139.602 142.932 147.932 155.712 160.15201 165.15201 170.15201 174.59201 177.37201 181.26201 183.76201 188.20201 193.20201 198.20201 200.70201 205.14202 210.14202 212.64202 219.86202 222.36202 227.36202 232.36202 235.14202 239.58202 242.08202 247.08202 252.08202 254.58202 257.36204 262.36204 266.80204 268.73005 275.95005 279.28004 284.28004 288.72004 292.05003">is an S pole on the A electromagnets and an N pole on the A-bar </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="-568.5064" x="36 40.440004 43.22 47.660005 52.100008 54.880006 58.210008 63.210008 70.990009 75.43001 80.43001 85.43001 89.87001 92.65001 96.54001 99.04001 100.976009 108.19601 112.086009 114.586009 119.586009 124.02601 127.35601 132.35602 135.68602 140.12602 142.62602 145.12602 147.90602 152.90602 157.34603 161.23603 165.67603 168.17603 175.95603 180.39603 185.39603 190.39603 194.83603 197.61603 200.39603 204.83603 207.33603 212.33603 217.33603 220.11603 224.55603 228.44603 230.94603 238.16603 240.94603 243.72603 246.50603 249.00603 253.44603 256.22605 259.00605 262.33604 266.77604 271.21604 273.99604 276.49604 280.93605 285.93605 290.93605">electromagnets. As before, these magnetic poles will attract and </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="-556.5064" x="36 39.33 43.770006 48.770006 53.210008 55.990007 58.490007 61.270006 66.270008 70.71001 73.21001 78.21001 82.65001 85.98001 93.76001 98.20001 103.20001 107.640018 112.640018 115.42001 117.92001 125.70001 130.14002 135.14002 140.14002 144.58002 147.36002 151.25002 153.75002 158.75002 163.75002 166.25002 169.03002 174.03002 178.47002 180.97002 184.30002 189.30002 192.08002 197.08002 200.41002 202.91002 207.91002 211.24002 216.24002 221.24002 226.24002 230.68003 233.46002 238.46002 243.46002 245.96002 250.40003 252.90003 256.23 261.23 264.56 269 273.44 275.94 278.72 283.72 288.16 290.94">repel the permanent magnets on the rotor producing a force that </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="-544.5064" x="36 43.78 48.78 53.78 58.22 62.11 64.61 67.39 72.39 76.83 79.33 82.66 87.66 90.44 95.44 98.770008 101.270008 104.600009 107.93001 112.93001 120.71001 123.21001 125.990009 130.43001 133.76001 136.54001 139.04001 141.82 146.82 149.32 152.65001 155.43001 160.43001 165.43001 168.21 170.71 173.49 178.49 180.99 183.77 188.77 193.21 195.71 200.71 203.49 207.93001 212.93001 216.26001 220.70001 228.48001 230.98001 233.48001 238.48001 243.48001 246.26001 249.04001 251.82 254.32 259.32 264.32 267.1 271.54 275.43003 277.93003 282.93003 286.26">moves the rotor from left to right in the diagram, until poles 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="-532.5064" x="36 38.78 43.78 48.22 50.72 55.72 60.160005 63.490007 71.270008 75.71001 80.71001 85.15001 90.15001 92.93001 95.43001 103.21001 107.65001 112.65001 117.65001 122.09001 124.87001 128.76001 131.26001 135.70001 140.70001 145.14002 147.92002 152.92002 155.42002 159.86002 162.64002 165.42002 170.42002 175.42002 177.92002 185.14002 187.92002 190.70001 195.70001 198.20001 200.98001 205.98001 210.42002 212.92002 217.92002 222.92002 225.70001 230.14002 234.03002 236.53002 241.53002 244.86002 247.36002 250.14002 255.14002 259.58003 262.08003 266.52003 269.30003 273.74003 278.18003 280.96003 284.29">the permanent magnets again align with the poles of the electro</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="-532.5064" x="289.2471">-</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="-520.5064" x="36 43.78 48.22 53.22 58.22 62.660005 65.44 69.33">magnets.</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="-502.5064" x="36 42.11 47.11 51.550004 54.050004 59.050004 64.05 66.83 69.61 74.61 82.39 84.89 89.89 94.33 99.33 103.770008 106.55 109.05 111.55 116.55 120.990009 125.990009 130.43001 133.21 135.71 139.04001 144.04001 147.37001 149.87001 152.37001 156.26001 161.26001 166.26001 173.48001 177.37001 179.87001 182.65001 187.65001 192.09001 194.59001 197.92002 200.70001 205.70001 210.14002 212.92002 215.42002 219.86002 224.86002 232.64002 237.64002 240.42002 245.42002 249.86002 252.64002 255.42002 260.42 265.42 267.92 275.14 277.92 280.7 285.7">The bottom panel, panel (d), shows the final combination with </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="-490.5064" x="36 40.440004 45.440004 48.770006 52.100008 56.54001 61.54001 64.32001 66.82001 70.15001 72.93001 77.93001 85.15001 87.93001 92.93001 97.93001 100.43001 105.43001 110.43001 112.93001 115.71001 120.71001 124.04001 129.04001 134.04001 139.04001 144.04001 146.54001 149.32 154.32 158.76001 161.26001 166.26001 171.26001 175.70001 179.59001 184.03002 186.53002 193.20001 195.70001 202.92002 205.70001 210.70001 215.70001 218.48001 223.48001 228.48001 230.98001 234.31002 237.64002 242.64002 250.42002 252.92002 257.92 262.92 265.7 268.48 273.48 281.26 283.76 286.54 291.54">current flowing up through the phase B winding from bottom to </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="-478.5064" x="36 38.78 43.78 48.78 51.28 55.72 60.72 65.72 68.22 71 76 80.44 83.770008 88.21001 90.71001 93.490009 97.380008 99.880008 104.880008 109.880008 112.380008 116.82001 121.82001 125.15001 128.48001 132.92002 137.92002 140.70001 143.20001 145.98001 150.98001 153.48001 158.48001 163.48001 167.92002 171.81002 176.25002 178.18302 185.40302 187.90302 190.22402 196.33402 201.33402 204.11402 208.00402 210.50402 215.50402 218.83402 223.83402 228.83402 233.83402 238.27402 242.71402 246.60402 249.10402 253.54402 258.544 261.044 268.264 270.764 275.764 280.764 283.544 287.984">top and there is no current in phase A. This produces an N pole </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="-466.5064" x="36 41 46 48.5 51.28 56.28 60.72 63.22 69.89 72.39 76.83 79.61 84.05 88.490009 91.270008 94.600009 99.600009 107.380008 111.82001 116.82001 121.82001 126.26001 129.04001 132.93001 135.43001 139.87001 144.87001 149.87001 152.37001 156.81002 159.31002 164.87001 167.37001 172.37001 177.37001 180.15001 184.59001 187.09001 192.09001 197.09001 199.59001 202.37001 207.37001 211.81002 214.31002 220.98001 224.31002 229.31002 233.75002 237.08002 239.58002 244.02002 246.80002 251.24002 255.68003 258.46003 261.79 266.79 274.57 279.01">on the B electromagnets and a S pole on the B-bar electromag</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="-466.5064" x="283.9736">-</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="-454.5064" x="36 41 45.440004 48.22 52.11 54.61 56.557 63.777 67.667 70.167 75.167 79.607 82.937007 87.937007 91.267009 95.70701 98.20701 100.70701 103.48701 108.48701 112.92701 116.81701 121.25701 123.75701 131.53702 135.97702 140.97702 145.97702 150.41703 153.19702 155.97702 160.41703 162.91703 167.91703 172.91703 175.69702 180.13703 184.02703 186.52703 193.74703 196.52703 199.30702 202.08702 204.58702 209.02703 211.80702 214.58702 217.91703 222.35703 226.79703 229.57703 232.07703 236.51703 241.51703 246.51703 249.01703 252.34703 256.78703 261.78703 266.22703 269.00703 271.50703 274.28703 279.28703 283.72703">nets. As before, these magnetic poles will attract and repel 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="-442.5064" x="36 41 45.440004 48.770006 56.550004 60.990007 65.990009 70.43001 75.43001 78.21001 80.71001 88.490009 92.93001 97.93001 102.93001 107.37001 110.15001 114.04001 116.54001 121.54001 126.54001 129.04001 131.82 136.82 141.26001 143.76001 147.09001 152.09001 154.87001 159.87001 163.20001 165.70001 170.70001 174.03002 179.03002 184.03002 189.03002 193.47002 196.25002 201.25002 206.25002 208.75002 213.19002 215.69002 219.02002 224.02002 227.35002 231.79003 236.23003 238.73003 241.51003 246.51003 250.95003 253.73003 256.23005 264.01005 269.01005 274.01005 278.45005 282.34007 284.84007 287.62007 292.62007 297.06007">permanent magnets on the rotor producing a force that moves 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="-430.5064" x="36 39.33 44.33 47.11 52.11 55.440004 57.940004 61.270006 64.600009 69.600009 77.380008 79.880008 82.66 87.100009 90.43001 93.21001 95.71001 98.490009 103.490009 105.990009 109.32001 112.100009 117.100009 122.100009 124.880008 127.380008 132.38 137.38 140.16 142.94 145.72 148.22 153.22 158.22 161 165.44 169.33 171.83 176.83 180.16 182.66 185.44 190.44 194.88 197.38 202.38 206.82 210.15001 217.93001 222.37001 227.37001 231.81002 236.81002 239.59001 242.09001 249.87001 254.31002 259.31 264.31 268.75 271.53 275.42 277.92 282.36003 287.36003 291.80003 294.58003 299.58003">rotor from left to right until poles of the permanent magnets again </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="-418.5064" x="36 40.440004 43.22 46 51 56 58.5 65.72 68.5 71.28 76.28 78.78 81.56 86.56 91 93.5 98.5 103.5 106.28 110.72 114.61 117.11 122.11 125.44 127.94 130.72 135.72 140.16 142.66 147.1 149.88 154.32 158.76001 161.54001 164.87001 169.87001 177.65001 182.09001 187.09001 192.09001 196.53002 199.31002 203.20001">align with the poles of the electromagnets.</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="-400.5064" x="36 42.11 46.550004 50.990007 55.990007 58.490007 63.490007 66.82001 69.32001 72.100009 77.100009 81.54001 84.04001 87.37001 92.37001 97.37001 100.70001 103.20001 107.09001 109.87001 114.31001 119.31001 123.20001 125.70001 128.48001 133.48001 135.98001 141.54001 144.32 149.32 154.32 157.65001 162.09001 164.02701 171.24701 176.24701 178.74701 182.07701 186.51702 191.51702 194.84702 199.28702 203.17702 207.61702 212.61702 215.39702 219.28702 221.78702 226.22702 228.72702 232.61702 235.39702 240.39702 245.39702 248.17702 252.61702 255.11702 258.44703 263.44703 266.22703 269.00703">Each of the four steps in Figure A1 represents a single full </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="-388.5064" x="36 43.78 48.22 52.660005 57.660005 62.100008 67.100009 69.880008 74.32001 78.76001 81.54001 84.04001 87.93001 90.71001 95.15001 100.15001 102.65001 107.65001 110.98001 113.48001 116.26001 121.26001 125.70001 128.20001 132.09001 134.87001 139.31002 144.31002 149.31002 153.75002 157.08002 159.58002 167.36002 172.36002 175.14002 180.14002 182.89502 185.39502 187.71402 193.82402 198.82402 203.26403 205.76403 209.09403 214.09403 219.09403 222.42403 224.92403 228.81403 231.59403 236.03403 241.03403 244.92403 247.42403 250.20403 255.20403 260.20405 264.64405 267.42405 272.42405 276.86405 280.19404">mechanical step of the stepper motor. The four steps together </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="-376.5064" x="36 39.33 43.770006 48.770006 52.100008 56.54001 60.430009 64.87001 69.87001 72.65001 75.15001 79.59001 82.09001 85.98001 88.76001 93.76001 98.76001 101.54001 105.98001 108.48001 112.92001 115.70001 120.140018 124.58002 127.360019 130.69002 133.47002 137.91002 142.35002 145.13002 147.63002 152.07003 157.07003 161.51003 164.29003 168.73003">represent a single electrical cycle.</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="-358.5064" x="36 42.11 47.11 51.550004 54.050004 57.940004 60.72 65.16 70.16 72.66 75.990009 80.43001 84.32001 89.32001 92.100009 97.100009 99.880008 102.66 107.66 112.66 115.16 120.16 124.600009 129.6 134.04001 139.04001 144.04001 147.93001 150.43001 154.87001 159.87001 162.65001 165.43001 168.76001 173.20001 175.98001 180.98001 183.48001 188.48001 193.48001 195.98001 198.76001 203.76001 208.20001 210.70001 218.48001 222.92002 227.36002 232.36002 236.80002 241.80002 244.58002 249.02002 253.46002 256.24003 258.74003 263.18003 268.18003 273.18003 277.07005 279.85005 283.18003 288.18003">The step resolution depends entirely on the mechanical construc</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="-358.5064" x="292.582">-</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="-346.5064" x="36 38.78 41.559999 46.559999 51.559999 54.059999 59.059999 62.39 64.89 67.67 72.67 77.11 79.61 87.39 92.39 95.17 100.17 103.5 106 110.44 115.44 120.44 122.94 125.72 130.72 135.72 138.5 142.94 147.38 150.16 152.94 157.94 160.44 163.22 168.22 172.66 175.99 180.43001 182.93001 190.15001 192.93001 195.71 198.49 200.99 205.99 210.43001 212.93001 217.93001 222.93001 227.93001 230.43001 235.43001 238.76001 241.26001 249.04001 254.04001 257.37 261.81 264.31 267.63999 272.63999 275.41999 278.19999">tion of the motor and typically there will be 200 or more full </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="-334.5064" x="36 39.89 42.67 47.11 52.11 56 58.5 63.5 67.94 71.270008 73.770008 81.55 85.990009 90.43001 95.43001 99.87001 104.87001 107.65001 112.09001 116.530017 119.31001 121.81001 125.140018 129.58002 134.58002 139.58002 142.36002 147.36002 150.14002 152.92002 157.92002 162.92002 165.42002 170.42002 173.75002 176.25002 179.03002 184.03002 188.47002 190.97002 198.75002 203.75002 206.53002 211.53002 214.28102 216.78102 218.73003 225.39904 227.89904 232.89904 237.89904 242.89904 246.22904 250.11904 252.89904 257.33903 262.33903 264.83903 272.61903 277.61903 280.39903 285.39903 288.729">steps per mechanical revolution of the motor. A 200-step motor </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="-322.5064" x="36 43.22 46 48.78 51.559999 54.059999 59.059999 62.39 67.39 72.39 75.17 80.17 84.61 87.11 91.55 94.05 97.380008 101.82001 105.71001 110.71001 113.490009 118.490009 121.270008 124.05 129.05 134.05 136.55 141.55 144.88 147.38 152.38 157.38">will provide a resolution of 360</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="-322.5064" x="162.38"> </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="-322.5064" x="163.62">/</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="-322.5064" x="166.4"> </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="-322.5064" x="167.65 172.65 177.65 182.65 185.15 190.79 193.29 198.29 200.79 205.79 209.79 212.29 217.29 220.62 223.12 226.45 231.45 234.23 238.67 241.45 244.23 249.23 254.23 256.72999 261.72999 266.16999 269.49998 271.99998 275.88999 278.66999 283.11 288.11">200 = 1.8&#x00b0; of rotation per 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="-304.5064" x="36 41.56 44.34 48.78 53.78 58.78 61.559999 66.56 71.56 74.06 76.84 81.84 84.34 87.119998 92.119998 96.56 99.06 104.06 109.06 114.06 119.06 122.95 125.729999 128.51 132.95 135.45 140.45 143.23 146.56 151 155.44 158.22 161 166 171 173.5 176.28 181.28 183.78 186.56 191.56 196 198.78 201.28 206.28 210.72 214.61 219.05 222.38 225.16 230.16 234.6 239.6 242.1 246.54001 251.54001 256.54 261.54 265.98 268.48 271.26 275.15003 277.65003 281.54005 284.32005">Stepping in the opposite direction to that described above is sim</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="-304.5064" x="292.0645">-</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="-292.5064" x="36 41 43.78 48.78 51.28 55.72 58.22 62.660005 67.100009 70.990009 75.43001 77.93001 82.93001 86.26001 88.76001 93.20001 98.20001 102.640018 107.640018 112.640018 115.42001 120.42001 125.42001 127.92001 130.70001 135.70001 140.14002 142.64002 146.53002 149.31002 153.75002 158.75002 161.25002 165.14002 169.58002 174.58002 179.58002 184.02002 189.02002 193.46002 197.90003 200.40003 205.40003 208.73003 211.23003 214.01003 219.01003 224.01003 228.45003 231.78003 234.56003 237.34003 242.34003 247.34003 249.84003 254.84003 259.84004 264.28004 266.78004 271.78004 275.11003 277.61003 280.39 285.39 289.83003">ply a case of changing the step sequence or inverting one of 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="-280.5064" x="36 41 46 50.440004 54.33 58.770006 61.270006 65.71001 70.71001 74.04001 77.37001 81.81001 86.81001 89.59001 92.09001 97.09001 99.87001 103.20001 107.640018 112.08002 114.860019 117.640018 122.640018 127.640018 131.53002">phase current directions.</tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="12" font-family="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-260.1064" x="36 45.996004 49.332 56.004 60.672 68.004 74.675998 78.672 85.343997 92.675998 100.007999 103.343997 110.675998">Microstepping</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="-242.1064" x="36 39.33 44.33 46.83 54.61 59.050004 64.05 69.05 71.55 75.990009 80.990009 85.990009 88.770008 91.55 95.990009 100.43001 103.21001 105.990009 110.990009 115.990009 119.880008 122.380008 125.16 127.94 130.44 133.22 137.11 139.61 144.61 149.05 153.49 157.93001 161.82 165.71 170.15001 173.48001 178.48001 180.98001 183.76001 188.76001 191.26001 194.04001 201.82 206.82 210.15001 215.15001 220.15001 224.59001 227.09001 229.87001 234.87001 239.31002 241.81002 245.14002 249.58002 253.47002 258.47004 261.25004 266.25004 269.03004 271.81004 276.81004 281.81004 284.31004 289.31004 292.64">In many applications it is necessary to improve the resolution 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="-230.1064" x="36 38.78 43.78 48.22 50.72 54.61 57.39 61.83 66.83 71.83 76.270008 79.600009 82.100009 89.880008 94.880008 97.66 102.66 105.58 108.08 110.58 113.91 118.91 122.240009 124.740009 132.52 137.52 140.85 145.29001 147.79001 152.79001 156.12001 160.56002 165.00002 167.78002 171.67002 176.11002 178.61002 183.61002 188.61002 192.50002 195.28002 198.06002 200.84001 205.84001 210.84001 213.62001 218.62001 223.62001 226.12001 230.56002 235.56002 240.56002 243.34001 246.67002 251.67002 254.45001 256.95 259.45 264.45 267.78 270.28 274.17 276.95 284.73 289.73 292.51 297.51">the stepper motor, for more precise positioning control, or simply </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="-218.1064" x="36 38.78 43.78 46.28 49.059999 54.059999 58.5 61.83 66.270008 70.71001 74.600009 79.04001 81.54001 84.32001 89.32001 93.76001 96.26001 101.26001 106.26001 114.04001 119.04001 123.48001 126.81001 129.31002 134.31002 137.64002 140.14002 144.03002 146.81002 151.25002 156.25002 160.14002 162.64002 167.64002 172.08002 175.41002 177.91002 181.24002 185.68003 190.68003 195.68003 198.46002 203.46002 206.24002 209.02002 214.02002 219.02002 221.52002 224.30002 229.30002 231.80002 235.13002 239.57003 244.57003 249.57003 254.01003 258.45 260.95 263.73 268.73 273.17">to increase the number of steps per revolution to reduce 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="-206.1064" x="36 38.78 43.78 47.11 52.11 57.11 61.550004 64.05 67.380008 70.16 75.16 80.16 82.94 87.380008 89.880008 94.32001 99.32001 104.32001 106.82001 109.600009 114.600009 119.04001 122.37001 126.81001 130.14002 135.14002 138.47002 142.91002 145.41002 148.19002 153.19002 157.63002 160.13002 165.13002 167.91002 172.91002 176.24002 180.68003 183.46002 186.24002 191.24002 196.24002 198.74002 203.18003 208.18003 213.18003 215.68003 220.68003 225.68003 228.46002 232.35002 236.79003 239.29003 244.29003 247.62003 250.12003 252.90003 257.90003 262.34004 264.84004 272.62004 277.62004 280.40003 285.40003 288.144 290.644">torque ripple and therefore the vibration and noise of the motor. </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="-194.1064" x="36 41.56 46.56 49.89 52.67 57.67 62.67 67.11 69.89 74.33 77.11 82.11 84.61 87.39 92.39 95.17 99.06 101.56 106 110.44 115.44 117.94 122.94 127.380008 129.88 134.32 138.76001 143.76001 146.54001 150.98001 155.98001 160.42002 165.42002 167.92002 172.92002 177.92002 180.42002 185.42002 188.75002 191.53002 196.53002 199.31002 204.31002 209.31002 211.81002 216.81002 221.81002 224.59001 229.59001 232.09001 237.09001 242.09001 246.53002 250.42002 254.86002 258.75004 261.25004 265.69004 268.47004 270.97004 273.75004 278.75004 283.19004">Fortunately this can be achieved by driving both phases at 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="-182.1064" x="36 39.89 44.33 52.11 56.550004 59.050004 61.83 64.61 72.39 76.83 79.33 82.11 87.11 89.61 94.61 97.94 102.94 107.380008 110.71001 113.21001 115.990009 120.990009 123.490009 131.27 136.27 141.27 145.71 148.21 150.99 155.99 160.43001 162.93001 166.26001 171.26001 174.04001 179.04001 182.37001 184.87001 187.65001 192.65001 195.15001 199.59001 202.09001 207.09001 212.09001 215.98001 218.76001 221.54001 224.32 229.32 234.32 236.82 241.82 246.26001 249.04001 256.26 260.7 265.14 270.14 272.64 275.42 282.64 287.64">same time in order to move the rotor to a position between two </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="-170.1064" x="36 40.440004 43.22 47.660005 52.100008 54.880006 58.210008 63.210008 70.990009 75.43001 80.43001 85.43001 89.87001 92.65001 96.54001 99.04001 101.34701 107.45701 112.45701 115.23701 119.12701 121.62701 124.407009 128.29701 130.79701 135.79701 140.79701 145.79701 153.01702 158.01702 160.51702 165.51702 169.95702 174.95702 179.39702 182.72702 185.50702 189.94702 194.38703 197.16703 199.94702 204.94702 207.44702 211.88703 215.77703 218.27703 226.05702 228.83702 233.27703 236.60703 241.60703 245.49703 248.27703 252.71703 257.71705 262.71705 265.49705 270.49705 275.49705">electromagnets. This is known generically as microstepping.</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="-152.1064" x="36 41.56 44.34 49.34 54.34 57.67 62.11 64.057 71.277 76.277 78.777 82.667 87.667 92.667 99.887 103.777 106.277 109.057 114.057 118.497 120.997 125.997 130.437 134.327 137.107 141.547 144.047 149.047 152.377 155.157 160.157 164.597 167.377 172.377 175.157 179.597 182.097 187.097 190.427 192.927 200.707 203.487 207.927 211.257 216.257 220.147 222.927 227.367 232.367 237.367 240.147 245.147 250.147 252.647 255.147 260.707 265.147 270.147 274.587 277.367 281.25703 283.75703 287.087 291.527 294.857">Figure A2 shows the basic principle of microstepping. Panels (a) </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="-140.1064" x="36 40.440004 45.440004 50.440004 52.940004 56.270006 60.710008 64.04001 66.54001 71.54001 74.87001 77.37001 82.93001 85.71001 90.71001 95.71001 99.04001 103.48001 105.42401 112.64401 117.64401 120.14401 124.584018 129.58402 132.91402 136.24402 140.68402 144.57402 149.57402 154.57402 159.57402 164.57402 167.07402 169.85402 174.85402 177.35402 182.35402 186.79402 191.79402 196.23403 199.01403 202.90402 205.40402 208.73403 213.17403 216.50403 219.00403 223.44403 228.44403 233.44403 235.94403 239.27404 244.27404 247.60404 250.10404 255.10404 258.43403 260.93403 264.264 267.044 272.044 277.044 280.374 284.814">and (c) of Figure A2 correspond to panels (a) and (b) of 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="-128.1064" x="36 43.22 48.22 50.72 53.22 58.780004 63.22 68.22 72.66 75.44 77.94 81.270008 86.270008 89.600009 92.100009 95.990009 100.990009 105.990009 113.21001 117.100009 119.600009 124.04001 128.48001 132.92002 137.92002 140.42002 145.42002 150.42002 154.86002 158.75002 163.19002 165.69002 170.13002 175.13002 179.57003 182.71402 187.71402 190.49402 194.93402 199.37403 204.37403 206.87403 210.76403 215.76403 220.20403 225.20403 227.70403 230.48403 235.48403 239.92403 242.70403 245.20403 247.98403 252.98403 257.424 260.754 265.194 267.694 272.134 275.464 279.904 282.404 287.404 292.404 299.624">A1. Panel (b) shows each phase energized such that there are now </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="-116.1064" x="36 38.78 46 51 53.5 57.940004 62.940004 65.72 70.16 74.600009 79.04001 84.04001 86.82001 89.32001 96.54001 99.04001 104.04001 109.04001 111.82001 116.26001 120.15001 122.65001 127.09001 132.09001 137.09001 139.59001 142.37001 149.59001 154.59001 157.09001 161.53002 166.53002 169.31002 173.75002 178.19002 182.63002 187.63002 190.41002 192.91002 198.47002 200.97002 205.97002 210.97002 213.75002 218.19002 222.08002 224.58002 227.08002 230.41002 235.41002 237.91002 240.69002 245.69002 248.47002 252.36002 254.86002 259.30003 264.30003 268.74003 276.52003 281.52003 284.30003 288.74003">two adjacent N poles and two adjacent S poles. In this example </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="-658.5064" x="312 314.78 319.78 324.22 326.72 331.16 336.16 339.49 342.81999 347.25999 352.25999 355.03999 358.93 361.43 364.21 369.21 371.71 376.71 381.71 384.49 389.49 391.99 396.99 401.99 406.43 410.32 414.76 418.65003 421.15003 423.93003 427.82005 430.32005 433.10005 438.10005 442.54005 445.04005 448.93006 453.37007 461.15007 465.59007 468.09007 470.59007 475.03007 480.03007 485.03007 487.53007 491.42008 496.42008 498.92008 501.70008 506.70008 511.14009 513.6401 519.2001 521.7001 526.1401 531.1401 536.1401 538.6401 545.86007 548.36007 553.36007 558.36007 561.1401 565.5801 569.4701">the currents in both phases is the same, and so the S and N poles </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="-646.5064" x="312 317 320.33 322.83 325.61 330.61 335.05 337.55 340.87998 345.87998 348.65998 353.65998 356.98997 359.48997 364.48997 369.48997 376.70997 379.20997 386.98997 391.98997 396.98997 401.42997 403.92997 406.70997 411.70997 414.20997 419.20997 423.64997 426.42997 429.75996 432.25996 439.47996 443.91996 448.91996 451.41996 456.41996 460.85997 463.63996 470.85997 475.29997 479.73997 484.73997 487.23997 490.01997 495.01997 499.45997 501.95997 506.95997 511.95997 515.85 518.63 521.41006 524.19009 529.19009 534.19009 538.0801 540.5801 543.3601 548.3601">of the rotor now move to half way between the positions 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="-634.5064" x="312 317 319.78 324.22 329.22 332.55 336.99 344.77 348.66 351.16 354.49 358.93 362.25999 364.75999 369.19999 374.19999 379.19999 381.69999 385.02998 389.46998 392.79997 395.29997 397.79997 403.35997 406.13996 411.13996 416.13996 419.46995 423.90995 425.84794 433.06794 438.06794 440.56794 445.56794 450.56794 453.34794 458.34794 460.84794 464.73796 469.73796 474.73796 481.95796 485.84797 488.34797 492.78797 495.28797 499.17799 501.95799 506.95799 511.95799 514.738 519.178 521.678 529.458 533.898 538.338 543.338 547.778 552.778 555.55807 559.99807 564.43807 567.2181">diagrams (a) and (c). Figure A2 only shows a single mechanical </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="-622.5064" x="312 315.89 318.67 323.11003 328.11003 330.61003 333.39 338.39 340.89 343.67 348.67 351.45 355.89 358.67 361.17 363.67 370.89 375.89 378.67 383.11003 388.11003 390.61003 393.39 397.28004 399.78004 404.78004 409.78004 414.22004 416.72004 421.72004 426.72004 431.16004 434.49003 437.27003 441.71003 445.04 447.54 452.54 455.87 458.37 462.81 465.31 468.63999 473.63999 476.41999 479.19999 481.69999 486.13999 488.91999 493.36 497.8 500.58 503.90998 506.68998 511.12998 515.56997 518.35 520.85 525.29 530.29 534.73 537.51 541.95 544.45 546.727 552.837 557.837 560.617 564.507">step in total, which is one quarter of a full electrical cycle. This </tspan></text>
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