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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="-658.7864" x="267.6113">-</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="-646.6313" x="36 38.78 41.559999 46.559999 51 53.5 57.940004 62.940004 66.270008 69.600009 74.04001 79.04001 81.82001 84.32001 87.100009 92.100009 94.600009 99.04001 103.48001 107.92001 112.92001 115.42001 120.42001 125.42001 129.86002 133.75002 138.19002 140.69002 147.91002 150.69002 153.47002 156.25002 158.75002 166.53002 170.97002 175.97002 180.41002 182.91002 185.69002 188.47002 190.97002 195.97002 200.97002 204.86002 208.75002 211.53002 216.53002 219.31002 223.75002 226.25002 229.03002 234.03002 236.53002 244.31002 249.31002 254.31002 258.75 261.25 264.03 269.03 273.47">tive current in each phase will make it possible to move 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="-634.4762" x="36 39.33 44.33 47.11 52.11 55.440004 57.940004 60.72 65.72 68.22 72.66 77.66 82.66 85.16 87.94 92.94 95.72 100.16 103.490009 111.270008 115.71001 120.71001 123.490009 127.93001 130.71 135.15001 137.65001 142.65001 147.65001 151.54001 154.32 157.1 159.88 164.88 169.88 172.38 177.38 181.82 184.6 191.82 196.26001 200.70001 205.70001 208.20001 210.98001 215.98001 220.42002 222.92002 226.25002 231.25002 236.25002 239.58002 242.08002 247.08002 252.08002 255.97002 258.75004 261.53004 264.31004 269.31004 274.31004 278.20005 280.70005 285.70005 289.03004">rotor to any intermediate position between the four positions 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="-622.3211" x="36 41.56 44.34 49.34 54.34 57.67 62.11 64.057 71.277 76.277 78.777 81.277 88.497 93.497 96.277 100.717 105.717 108.217 113.217 117.657009 122.09701 127.09701 130.427 132.927 140.147 145.147 149.587 154.587 157.087 162.087 167.087 169.867 174.867 177.367 181.807 184.307 188.197 190.977 195.977 200.977 203.757 208.197 210.697 215.697 220.697 225.13701 229.02701 233.46701 235.96701 238.74701 242.63701 245.13701 249.57701 254.57701 259.017 262.15199 267.15199 269.93199 274.37199 278.81199 283.81199 286.31199">Figure A1, which occur when only a single phase is energized. </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="-610.166" x="36 45.440004 50.440004 54.880006 59.880006 62.380006 65.16 70.16 74.600009 77.93001 82.37001 84.87001 87.65001 91.54001 94.04001 99.04001 104.04001 108.48001 110.98001 113.76001 118.76001 121.54001 125.98001 129.31002 137.09001 141.53002 146.53002 149.31002 153.75002 156.53002 160.97002 163.47002 168.47002 173.47002 177.36002 180.14002 182.92002 185.70001 190.70001 195.70001 198.20001 200.98001 205.98001 208.76001 212.65001 215.15001 217.93001 221.82 224.32 229.32 234.32 239.32 246.54001 251.54001 254.04001 258.48 262.37004 264.87004 269.87004 274.31004 277.09004 280.42">When there is one intermediate position this is known as half </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="-598.0109" x="36 39.89 42.67 47.11 52.11 54.61 56.928 66.368007 71.368007 75.80801 80.80801 83.30801 86.088008 91.088008 95.52801 98.85801 103.29801 105.79801 110.238018 113.568019 118.00802 120.50802 123.28802 128.28803 131.61803 136.05803 140.49803 142.99803 145.77803 150.77803 153.55803 157.99803 161.32804 169.10803 173.54804 178.54804 181.32804 185.76804 188.54804 192.98804 195.48804 200.48804 205.48804 209.37804 212.15804 214.93804 217.71804 222.71804 227.71804 231.60803 234.10803 236.88803 241.88803 244.66803 248.55803 251.05803 253.83803 257.72804 260.22804 265.22804 270.22804 275.22804 282.44804 287.44804">step. When there are three intermediate positions this is known </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="-585.8558" x="36 40.440004 44.33">as </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="TSEKEM+TimesNewRomanPS-ItalicMT" font-style="italic"><tspan y="-585.8558" x="46.8301 51.8301 56.8301 61.8301 65.7201 68.5001 72.9401 76.8301 79.3301 83.2201 86.0001 90.4401">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="-585.8558" x="95.4385 97.9385 102.3785 107.3785 112.3785 114.8785 118.7685 123.7685 126.2685 131.2685 136.2685 138.7685 141.2685 148.4885 151.2685 156.2685 161.2685 165.7085 169.0385 171.5385 174.8685 179.3085 183.1985 188.1985 190.9785 195.9785 198.7585 201.5385 206.5385 211.5385 214.0385 221.8185 224.5985 229.0385 232.3685 237.3685 241.2585 244.0385 248.4785 253.4785 258.47853 261.2585 266.2585 271.2585 273.7585 276.5385 280.42854"> and so on. Higher resolution microstepping is </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="-573.7007" x="36 41 45.440004 49.33 53.770006 57.100008 59.880006 64.880008 69.32001 74.32001 76.82001 79.600009 84.600009 87.100009 94.880008 99.880008 103.21001 107.65001 110.15001 115.15001 119.59001 122.37001 126.81001 129.59001 132.37001 134.87001 139.87001 144.31002 147.09001 152.09001 158.64202">described in more detail below.</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="-551.0457" x="36.1758 43.1958 50.7658 58.3358 65.355808 72.201808 75.15581 82.72581 90.29581 97.86581 105.43581 112.45581 120.02581 125.75781 129.26381 136.28382 143.30382 151.43383 159.00383 166.02384 173.59384 181.16385 188.00986 190.96387 198.53388 201.66388 209.23389 217.36389 224.9339 232.5039 241.18392">PHASE CURRENT-SEQUENCE DIAGRAMS</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="-534.3906" x="36 41.510004 44.24 49.190004 54.140005 57.420003 61.81 63.708 70.878 75.827999 78.27799 82.118 87.06799 92.01799 99.18799 103.02799 105.47799 108.20799 113.15799 117.54799 119.997989 123.277988 128.22798 130.95798 133.68798 136.13797 139.97797 144.36797 149.31797 154.26796 158.65796 163.60796 167.99796 172.38796 174.83795 179.78795 183.06795 185.51795 188.24794 193.19794 197.58794 200.03794 202.76793 209.93793 214.88793 217.33792 222.28792 227.23792 231.62792 235.46791 239.85791 242.3079 246.6979 251.6479 254.9279 258.20793 262.59794 267.54795 270.27796 274.11796 276.56797 279.29798 282.02799 284.758 289.708">Figure A3 shows the full sequence of the two phase currents illus</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="-534.3906" x="293.5312">-</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="-522.2355" x="36 38.73 42.01 46.399999 49.129999 53.519998 58.469999 60.92 63.649999 68.6 71.049999 76.56 79.29 84.24 89.189998 92.46999 96.85999 98.75799 105.927989 110.87798 113.32798 115.59798 121.657978 126.60797 129.33797 133.17797 135.62796 139.46796 144.41796 149.36795 156.53795 160.37795 162.82794 165.55794 172.72794 177.67794 180.12793 184.51793 187.24793 191.63793 196.02793 198.75792 202.03792 204.76792 209.15792 213.54792 216.27791 218.7279 223.1179 228.0679 232.4579 235.1879 239.5779 243.4179 245.86789 248.31789 252.70789 257.6579 262.6079 265.33793 270.28794 274.67796 277.40797 281.79798 286.748 289.527">trated in Figure A2. This shows two electrical cycles, equivalent </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="-510.0804" x="36 38.73 43.68 46.13 51.08 53.530004 56.81 61.760004 64.490009 67.22001 69.670009 77.40001 81.79001 86.18001 91.130008 95.520008 100.47 103.200008 107.590007 111.98 114.71001 117.16 121.00001 123.73001 128.12001 133.07 136.91 139.36 142.64 147.59 150.04 154.98999 159.37999 162.10999 165.38999 167.83998 171.67998 174.40998 178.79998 183.74997 187.58997 190.86997 193.31996 195.58997 201.64997 206.59996 210.98996 213.43996 216.71996 221.66996 224.39995 227.12995 230.40995 234.24994 236.97994 241.36994 246.31993 248.76993 253.71993 258.66993 262.50993 265.23994 267.96995 270.69996 275.64997 280.59999 284.43998 286.88999 291.28 294.56 298.99803">to 4 full mechanical steps (8 half steps). The full-step positions are </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="-497.9253" x="36 43.73 48.12 51.399999 56.35 60.739999 65.689998">marked </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="TSEKEM+TimesNewRomanPS-ItalicMT" font-style="italic"><tspan y="-497.9253" x="68.1354">F</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="-497.9253" x="74.1938 76.6438 81.0338 85.983798 90.93379 93.38379 96.11379 101.06379 105.45379 107.903789 112.85378 117.24378 119.973789 123.253787 126.53378 130.37378 133.10378 137.49378 142.44377 144.89377 149.84377 154.79376 158.63376 161.36376 164.09375 166.82375 171.77375 176.72374 180.56374 183.01374 187.40373 190.68373 195.07373 197.52373 205.25373 209.64373 212.92372 217.87372 222.26372 227.21372"> and the half-step positions are marked </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="TSEKEM+TimesNewRomanPS-ItalicMT" font-style="italic"><tspan y="-497.9253" x="229.6449">H</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="-497.9253" x="236.8166 239.2666 241.7166 247.7766 252.1666 256.5566 261.50663 263.95664 268.90666 273.29667 276.02668 279.30668 281.75669 285.59669 288.3267 292.7167 297.7167">. Each 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="-485.7702" x="36 38.73 43.68 46.13 48.86 53.81 58.2 60.65 65.04 67.770008 72.16 76.55 79.28001 82.560009 85.29001 89.68001 94.07001 96.80001 99.25001 103.64001 108.590007 112.98 115.71001 120.100009 122.55 125.28001 129.12001 131.57 136.52 141.47 149.2 154.15 158.54 161.81999 166.20999 171.15999 173.60999 176.05998 179.33998 182.61998 187.56998 195.29998 197.74997 202.69997 205.14997 207.87996 212.82996 215.27996 220.22995 222.67995 225.12995 228.40995 233.35994 236.63994 239.08994 242.36994 246.75994 250.03993 254.42993 257.70994 262.09996 267.04997 271.43998 275.83 278.28 281.01 285.40003 288.13005 292.52006 295.24906">in the electrical cycle is numbered, from 0 to 7, for reference later.</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="-467.6151" x="36 42.11 47.11 49.89 53.78 56.28 59.61 62.39 67.39 72.39 75.72 80.16 82.66 86.55 91.55 96.55 103.770008 107.66 110.16 112.94 117.94 122.380008 125.16 127.66 130.16 137.38 142.38 146.82 151.82 154.32 159.32 162.1 165.99 170.43001 175.43001 179.32 183.21 185.99 190.99 195.99 198.49 202.38 205.16 209.6 214.6 219.6 224.04001 227.37001 229.87001 237.65001 242.65001 245.43001 250.43001 253.76001 256.26 260.7 265.7 270.7 273.48 276.81 281.81 284.59 287.09 289.59 292.37 295.15">This figure shows that, when discussing stepper motor control, it </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="-455.46" x="36 38.78 42.67 45.17 50.17 54.61 59.050004 63.490007 67.380008 71.270008 75.71001 79.04001 84.04001 86.54001 89.32001 94.32001 96.82001 101.82001 106.82001 111.82001 119.04001 121.54001 124.32001 129.32 133.76001 136.26001 139.59001 144.03002 146.81002 151.25002 154.03002 156.81002 161.81002 166.25002 168.75002 176.53002 180.97002 185.97002 190.97002 193.75002 196.53002 201.53002 206.53002 210.97002 213.47002 217.91002 222.91002 227.91002 230.41002 235.41002 238.19002 241.52002 245.96002 250.40003 253.18003 255.96002 260.96003 265.96003 268.46003 273.46003 276.79 279.29 282.07 287.07 291.51">is necessary to know the relative magnitude and direction 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="-443.3049" x="36 40.440004 45.440004 48.770006 52.100008 56.54001 61.54001 64.32001 66.82001 69.600009 74.600009 77.100009 81.54001 85.98001 90.42001 95.42001 97.92001 102.92001 107.92001 112.360019 116.250019 120.69002 123.19002 125.69002 131.25002 136.25002 138.75002 141.25002 144.58002 149.02002 151.80002 156.80002 161.24002 164.57003 167.07003 169.85002 174.85002 179.29003 184.29003 186.79003 191.79003 195.68003 200.12003 202.62003 207.62003 212.62003 217.62003 221.51003 224.29003 228.73003 233.17003 235.95003 238.45003 241.78003 246.22003 251.22003 254.55004 258.99003 262.88005 267.32005 272.32005 275.10005 279.54005 282.32005 285.10005 290.10005 295.10005 298.99006">current in each phase. So, rather than use physical representations </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="-431.1498" x="36 41 44.33 46.83 49.61 54.61 59.050004 61.550004 69.33 74.33 77.11 82.11 85.033008 87.533008 90.033008 93.923007 98.923007 103.36301 108.36301 110.86301 115.30301 119.19301 121.69301 124.47301 129.473 131.973 137.533 140.313 145.313 150.313 153.643 158.08301 161.973 163.92002 171.14002 176.14002 178.64002 183.08002 188.08002 193.08002 195.02802 202.24802 207.24802 209.74802 212.24802 217.24802 220.57802 223.07802 226.96802 229.74802 237.52802 242.52802 245.30802 249.74802 252.24802 255.02802 257.808 265.588 270.028 273.358 278.358 282.798 286.68803 291.12803 296.12803">of the motor, such as in Figures A1 and A2, or simple time-based </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="-418.9947" x="36 40.440004 45.440004 48.770006 52.100008 56.54001 61.54001 64.32001 66.82001 74.04001 78.48001 83.48001 87.92001 91.250019 96.250019 99.58002 107.360019 111.250019 113.750019 116.250019 120.140018 125.140018 129.58002 134.58002 137.08002 141.52002 145.41002 147.91002 153.47002 156.25002 161.25002 166.25002 169.58002 174.02002 175.96102 183.18102 188.18102 190.68102 193.18102 195.96102 198.74102 201.24102 204.02101 207.91101 210.41101 214.30101 217.08101 224.86101 229.86101 232.641 237.08101 240.41101 242.91101 245.69101 250.69101 253.19101 258.191 262.08103 266.52104 269.02104 273.46104 275.96104 280.96104 285.96104 290.40104 294.29106 298.73106">current waveforms, such as Figure A3, it is simpler to use a 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="-406.8396" x="36 41 43.78 48.22 53.22 56.550004 60.990007 68.770008 71.270008 73.770008 79.33 84.33 87.66 90.16 94.600009 97.100009 102.100009 105.43001 110.43001 115.43001 118.21001 122.65001 125.15001 130.15001 132.93001 137.93001 142.93001 145.71 150.15001 153.48001 155.98001 163.76001 168.76001 171.54001 176.54001 179.87001 182.37001 185.15001 190.15001 192.93001 196.82 199.32 204.32 207.1 211.54001 216.54001 219.87001 224.31002 232.09001 234.59001 237.37001 241.26001 243.76001 248.20001 251.53002 255.97002 260.41 263.19 267.63 272.63 275.13 280.13 285.13">diagram. For a 2-pole bipolar motor this diagram is created by </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="-394.6845" x="36 41 43.78 48.78 51.559999 54.339998 57.119997 62.119997 67.119998 69.619998 72.399997 77.399997 81.84 84.34 88.78 93.78 97.11 100.44 104.880008 109.880008 112.66 115.16 117.94 122.94 125.44 128.22 133.22 137.66 140.16 142.94 150.16 155.16 157.66 162.66 167.66 172.1 175.99 180.43001 184.32 186.82 191.26001 195.15001 197.65001 202.65001 205.98001 208.76001 213.76001 218.76001 223.76001 228.76001 233.76001 238.20001 240.98001 243.48001 248.48001 252.92002 257.36003 260.14 265.14 268.47 272.36003 274.86003 277.36003 280.14 285.14 289.58003 292.36003">plotting the current in the two phases as orthogonal vectors, 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="-382.5294" x="36 38.78 42.67 45.17 47.67 52.11 56 58.5 63.5 67.94 72.380008 75.16 80.16 83.490009 87.380008 89.880008 94.32001 97.100009 99.600009 104.600009 109.600009 113.600009 116.100009 118.880008 123.880008 126.380008 130.82 135.26001 139.70001 144.70001 147.20001 152.20001 154.98001 159.98001 164.42002 167.75002 170.25002 174.69002 178.58002 181.08002 184.97002 189.97002 194.97002 202.19002 207.19002 209.69002 212.47002 217.47002 219.97002 225.53002 228.31002 233.31002 238.31002 241.64002 246.08002 248.01203 255.23203 260.23204">is, as vectors at 90&#x00b0; to each other as shown in Figure A4.</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="-359.8743" x="36.1758 43.1958 50.7658 58.3358 65.355808 72.201808 75.15581 82.72581 90.29581 97.86581 105.43581 112.45581 120.02581 125.75781 129.26381 136.28382 143.85382 151.42383 158.44384 165.28984 168.24385 175.81386 178.94387 186.51387 194.64388 202.21389 209.78389 218.4639">PHASE CURRENT-PHASE DIAGRAMS</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="-343.2192" 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 99.887 103.777 106.277 109.057 114.057 118.497 120.997 125.437007 130.43701 133.76702 137.09702 141.53702 146.53702 149.31702 153.20702 155.70702 160.70702 164.03702 166.53702 172.09702 174.87702 179.87702 184.87702 188.20702 192.64702 194.59403 201.81403 206.81403 209.31403 214.31403 217.09403 222.09403 224.87403 227.65402 232.09403 237.09403 239.59403 244.59403 249.59403 252.09403 256.53404 259.03404 264.03404 269.03404 273.47404 277.36405 281.80406">Figure A4 shows the currents of Figure A3 plotted on a 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="-331.0641" x="36 41 43.78 48.22 53.22 56.550004 60.990007 68.770008 71.270008 78.490009 83.490009 87.93001 91.26001 95.70001 98.20001 100.98001 105.98001 110.42001 112.92001 117.92001 122.92001 127.360019 131.25002 135.69002 137.62602 144.29602 146.79602 151.23603 156.23603 159.56603 162.89603 167.33603 172.33603 175.11603 177.61603 180.39603 184.28603 186.78603 190.11603 194.55603 199.55603 202.88603 207.32604 211.21604 215.65604 220.65604 223.43604 227.87604 232.87604 235.37604 240.37604 245.37604 247.87604 250.65604 255.65604 260.09605 262.59605 267.59605 272.03605 275.36604 278.14604 280.92604 285.36604 289.80604 292.58604">diagram where the phase A current is represented by the vertical </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="-318.9091" x="36 38.78 41.559999 46.559999 51 53.5 57.940004 62.940004 67.94 70.44 73.22 78.22 82.66 85.16 90.16 95.16 99.600009 103.490009 107.93001 110.43001 117.100009 119.600009 124.04001 129.04001 132.37001 135.70001 140.14002 145.14002 147.92002 150.42002 155.42002 160.42002 162.92002 165.70001 170.70001 175.14002 177.64002 182.64002 187.64002 190.97002 193.75002 198.19002 203.19002 208.19002 210.97002 215.41002 218.19002 220.69002 223.47002 226.25002 231.25002 235.69002 238.19002 240.47702 246.58702 251.58702 256.027 258.527 263.527 267.967 270.747 274.077 277.40699 281.297 284.077 288.517 293.517">line and the phase B current by the horizontal line. The 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="-658.7864" x="312 317 322 329.78 334.78 339.22 342.55 346.44 348.94 353.38 358.38 361.71 365.03999 369.47999 373.37 378.37 383.37 388.37 393.37 395.87 398.65 403.65 406.15 408.93 413.93 418.37 420.87 425.87 430.87 438.65 443.65 448.09 451.41999 455.31 457.81 460.59 465.59 468.09 473.65 476.43 481.43 486.43 489.75999 494.19999 496.136 503.356 508.356 510.856 513.35598 518.91598 523.91598 527.246 529.746 534.186 539.186 543.626 551.406 556.406 559.18606 563.62606 566.12606">numbers correspond to the numbers in Figure A3. For 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="-646.1797" x="312 316.44 319.22 321.72 325.61003 328.39 332.83003">at 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="-646.1797" x="337.83003"> </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="-646.1797" x="340.33003 345.33003 347.83003 350.61003 355.61003 358.11003 363.67 366.45 371.45 376.45 379.78 384.22 386.16 393.38 398.38 400.88 403.38 406.16 411.16 415.6 418.1 423.1 428.1 432.54 436.43003 440.87004 442.81504 449.48506 451.98506 456.42506 461.42506 464.75505 468.08503 472.52503 477.52503 480.30503 482.80503 487.24504 492.24504 497.24504 499.74504 502.52503 507.52503 511.96504 514.465 519.465 524.465 528.905 532.79507 537.23507 539.73507 546.405 548.905 553.34506 558.34506">1 in Figure A3, the phase A current and the phase B 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="-646.1797" x="561.4629">-</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="-633.573" x="312 315.33 319.77 324.77 327.55 330.05 334.49 337.81999 342.25999 344.75999 349.75999 354.75999 357.53999 362.53999 365.03999 370.03999 375.03999 378.93 381.71 384.49 387.27 392.27 396.71 399.21 403.65 408.65 413.65 416.15 423.37 426.15 428.93 433.93 436.43 439.21 444.21 448.65 451.15 455.04 459.48 467.26 471.7 474.2 481.98 486.42 491.42 496.42 499.2 501.98 506.98 511.98 516.42 518.92 521.209 527.319 532.319 536.759 540.649 545.089 547.589 550.369 557.589 562.589">rent are both positive and with the same magnitude. These 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="-620.9662" x="312 316.44 321.44 324.77 328.09999 332.53999 337.53999 340.31999 344.21 346.71 351.15 354.47999 358.91999 361.41999 365.31 370.31 375.31 382.53 387.53 390.03 392.81 397.81 400.31 403.63999 406.41999 411.41999 416.41999 419.74998 424.18998 426.13099 433.35099 438.35099 440.85099 445.291 449.181 451.681 454.461 459.461 463.901 466.401 469.181 476.401 481.401 483.901 487.79103 492.79103 495.571 498.351 503.351 505.851 510.29103 513.62106 516.95108 521.95108 529.171 533.06106 535.56106 537.50808 544.728 549.728 554.728 557.50808 562.50808 567.50808">currents are shown in figure A4 as the two solid arrows. Adding </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="-608.3596" x="312 314.78 319.78 324.22 328.11003 332.55003 335.05003 337.83003 345.05003 350.05003 352.55003 356.99003 361.99003 365.32 368.65 373.09 378.09 380.87 383.37 388.37 392.81 397.25 400.03 405.03 408.36 412.25 414.75 417.53 422.53 427.53 431.97 434.75 439.75 444.19 447.52 450.02 455.02 457.8 462.8 467.24 471.13 473.63 476.41 481.41 485.85 488.35 491.68 496.12 500.01 505.01 507.79 510.57 515.01 520.01 522.79006 525.29006 533.07009 538.07009 540.8501 545.8501 549.1801 551.6801 556.1201 561.1201">these two current vectors together gives the resultant motor 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="-608.3596" x="564.2168">-</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="-595.7529" x="312 315.33 319.77 324.77 327.55 330.05 335.05 339.49 343.93 346.71 351.71 355.03999 357.53999 360.31999 365.31999 370.31999 373.09999 377.53999 381.97999 384.75999 389.19999 394.19999 396.69999 399.00199 405.11198 410.11198 414.55198 417.05198 420.38197 424.82197 428.71199 433.71199 436.49198 439.27198 443.71199 448.71199 451.49198 453.99198 456.77198 460.662 463.162 465.942 470.942 475.382 477.882 482.882 487.882 492.882 497.882 500.662 505.102 510.102 515.102 518.992 523.432 525.932 530.932 534.262 536.762 541.202 543.702 547.03207 549.8121 554.8121 559.8121 562.5921">rent vector indicated. The resultant is the hypotenuse of a right-</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="-583.1462" x="312 316.44 321.44 326.44 329.22 333.66 338.66 341.16 343.94 347.27 350.05 354.49 359.49 364.49 367.27 371.71 374.21 381.43 384.21 386.99 391.99 394.49 397.27 402.27 406.71 409.21 411.99 419.21 424.21 426.71 431.71 434.49 439.49 443.93 447.25999 449.75999 453.65 456.43 461.43 465.87 469.76 472.26 476.7 481.7 486.7 491.14 493.92 496.42 498.92 502.25 505.58 508.08 510.86 515.86 520.3 522.8 527.8 530.58 535.58 540.02 543.35006 545.85006 548.63009 555.85006 560.85006">angled triangle with the two other sides equal. If the other 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="-570.5395" x="312 315.89 318.67 323.67 328.11003 332.00004 334.50004 338.94004 342.27003 346.71003 349.21003 353.65003 357.54005 361.43006 366.43006 374.21006 378.65007 383.65007 386.15007 388.93006 393.93006 396.43006 401.43006 405.87007 408.37007 413.37007 415.87007 418.65007 423.65007 428.09007 433.09007 435.59007 438.37007 443.37007 447.81007 450.31007 458.09007 462.53007 467.53007 472.53007 475.31007 478.09007 483.09007 488.09007 492.53007 495.03007 500.03007 503.36006 505.86006 508.64006 513.64 518.08 520.58 525.58 530.58 535.58 540.58 543.36007 547.80007 552.80007 557.80007 561.69009 566.13009">sides are assumed to be 1 then the magnitude of the hypotenuse </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="-557.9327" x="312 319.22 322 324.78 327.56 330.06 335.06 339.5">will be:</tspan></text>
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<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="9.72" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-533.366" x="476.0519 476.25605 473.6219 468.7619 454.4603 428.0802 409.98158">41.1211</tspan></text>
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<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="5.67" font-family="FMJOQO+TimesNewRomanPSMT"><tspan y="-537.7198" x="432.9953 414.89668">22</tspan></text>
<text xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="9.72" font-family="ISKMGI+SymbolMT"><tspan y="-533.366" x="462.2566 440.30885 421.40345">==+</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="-528.4096" x="576"> </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="-509.8029" x="312 317.56 322.56 325.06 327.84 332.84 337.28 339.78 343.11 347.55 351.44 356.44 359.22 362 366.44 371.44 374.22 376.72 381.16 386.16 389.49 392.81999 397.25999 402.25999 405.03999 407.53999 412.53999 416.97999 421.41999 424.19999 429.19999 432.52998 435.02998 442.24998 445.02998 447.80998 450.58998 453.08998 458.08998 462.52998 465.02998 470.02998 475.02998 480.02998 488.35997 490.85997 495.85997 499.18995 501.68995 504.46995 509.46995 513.9099 516.4099 521.4099 525.8499 528.62997 533.62997 538.06997 540.56997 545.56997 548.89999 551.39999 554.18 559.18 563.62">So the resultant current vector will be 141% of the value 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="-497.1962" x="312 316.44 321.44 324.77 328.09999 332.53999 337.53999 340.31999 342.81999 345.59999 350.59999 353.09999 358.09999 363.09999 367.53999 371.43 375.87 377.811 384.48103 386.98103 391.98103 395.311 397.811 404.48103 406.98103 409.48103 414.48103 419.48103 423.37104 426.15104 428.93104 431.71104 436.71104 441.71104 446.15104 451.15104 453.65104 458.09104 460.87104 463.37104 468.37104 473.37104 477.37104">current in phase A or B, positioned at 45&#x00b0;.</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="-476.1895" x="312 318.4392 325.7712 330.4392 337.7712 345.1032 351.7752 355.1112 363.7752 367.1112 374.4432 381.7752 385.1112">Torque Ripple</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="-457.5828" x="312 319.22 324.22 330.794 333.294 335.794 338.574 343.574 348.014 350.514 353.294 358.294 361.624 366.624 371.624 376.064 378.564 383.564 388.564 391.344 396.344 401.344 404.124 406.624 411.624 414.95399 417.45399 421.89399 426.89399 431.89399 434.39399 438.83399 441.61399 446.054 450.494 453.274 456.60398 459.38398 463.82398 468.26399 471.04399 473.54399 481.32398 486.32398 489.10398 494.10398 497.43397 499.93397 502.71397 506.60398 509.10398 514.104 516.88406 520.21408 524.65408 529.09408 531.8741 534.6541 539.6541 542.1541 547.1541 550.48416 555.48416 560.48416 565.48416">Now, the torque output of any electrical motor is directly propor</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="-457.5828" x="568.5771">-</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="-444.9761" x="312 314.78 317.56 322.56 327.56 332 334.78 337.28 340.06 345.06 347.56 350.34 355.34 359.78 362.28 370.06 374.5 379.5 384.5 387.28 390.06 395.06 400.06 404.5 407 412 415.33 417.83 420.61 425.61 430.05 432.55 440.33 445.33 448.11 453.11 456.43998 458.93998 463.37998 468.37998 471.70997 475.03996 479.47996 484.47996 487.25996 489.75996 492.25996 496.69996 501.69996 506.69996 509.19996 511.97996 516.98 521.42 523.92 531.7 536.7 539.48007 544.48007 547.81008 550.31008 554.75009 559.75009">tional to the magnitude of the motor current, and the motor 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="-444.9761" x="562.8398">-</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="-432.3694" x="312 315.33 319.77 324.77 327.55 330.05 332.83 336.72 339.22 342 347 351.44 353.94 357.27 361.71 365.6 370.6 373.38 376.16 380.6 385.6 388.38 390.88 395.88 400.88 405.32 409.21003 413.65003 416.15003 420.59004 425.59004 428.92 432.25 436.69 441.69 444.47 446.97 449.47 452.8 455.58 458.08 460.86 464.75 467.25 471.69 474.47 478.91 483.35 486.68 489.18 492.50999 495.83998 500.83998 508.61997 511.11997 516.68 519.46 524.46 529.46 532.79006 537.23007 539.1481 546.36807 551.36807 553.86807 556.6481 561.6481 566.0881 568.8681">rent is the resultant phase current. It is clear from Figure A4 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="-419.7627" x="312 314.78 319.78 324.22 326.72 330.05 334.49 338.38 343.38 346.16 348.94 353.38 358.38 361.16 363.66 368.66 373.66 378.1 381.99003 386.43003 388.93003 393.37004 398.37004 401.7 405.03 409.47 414.47 417.25 419.75 424.19 426.97 429.47 432.25 437.25 441.69 444.19 449.19 453.63 456.41 459.74 463.06999 466.96 469.74 474.18 479.18 481.68 486.68 491.68 495.57 498.35 501.13 503.91 508.91 513.91006 516.41006 519.19009 523.0801 525.5801 530.5801 533.3601 538.3601 543.3601 547.8001 551.1301 553.6301 556.41018 561.41018 565.85018 570.85018">the resultant phase current at the half-step position is higher than </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="-407.156" x="312 314.78 319.78 324.22 326.72 331.16 336.16 339.49 342.81999 347.25999 352.25999 355.03999 357.53999 361.97999 364.75999 367.25999 370.03999 375.03999 379.47999 381.97999 385.30998 390.30998 393.08998 395.86997 399.19996 403.08998 405.86997 410.30998 415.30998 417.80998 422.80998 427.80998 431.69999 434.47999 437.25999 440.03999 445.03999 450.03999 452.53999 454.83699 460.94697 465.94697 468.72697 472.61698 475.11698 482.89698 487.33699 491.77699 496.77699 500.667 503.167 505.947 510.947 515.38699 518.167 520.667 523.447 528.447 532.887 535.387 543.16708 548.16708 550.9471 555.9471 559.2771">the current at the full-step position. This means that 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="-394.5493" x="312 314.78 319.78 323.11 328.11 333.11 337.55 340.05 347.27 350.05 352.83 355.61 358.11 363.11 367.55 370.05 374.49 379.49 383.93 388.93 393.93 396.71 401.71 406.71 409.21 413.65 417.54 420.04 422.82 427.82 432.26 434.76 442.54 447.54 450.32 455.32 458.65 461.15 464.47999 469.47999 472.25999 476.69999 479.47999 483.91999 487.81 490.31 492.81 496.13999 500.58 504.47 509.47 512.25 515.03 517.81008 522.81008 527.81008 530.31008 533.0901 538.0901 540.5901 547.81008 552.81008 557.25009 560.0301 562.5301 565.3101 569.20016">torque will be changing as the motor rotates, resulting in what is </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="-381.9426" x="312 317 322 327 334.22 339.22 341.72 346.16 350.05003">known as </tspan></text>
<text fill="#231f20" xml:space="preserve" transform="matrix(1 0 -0 1 0 792)" font-size="10" font-family="TSEKEM+TimesNewRomanPS-ItalicMT" font-style="italic"><tspan y="-381.9426" x="352.5518 355.3318 360.3318 363.8508 368.8508 373.8508 378.2908 380.7908 384.68083 387.46083 392.46083 397.46083 400.2408">torque ripple</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="-369.3359" x="312 316.44 320.88 325.88 329.77003 334.21003 336.71003 344.49003 348.93003 353.37004 358.37004 362.81004 367.81004 370.59004 375.03004 379.47004 382.25004 384.75004 389.75004 392.53004 397.53004 400.86003 405.30003 408.08003 410.86003 415.86003 420.86003 423.36003 427.80003 432.80003 437.80003 440.30003 447.52003 450.30003 453.08003 455.86003 458.36003 461.69 466.13 470.02003 475.02003 477.80003 480.58003 483.08003 485.86003 490.86003 493.36003 496.14 501.14 505.58003 508.91 513.35 517.79 521.68 526.12 531.12 533.62 538.06 543.06 548.06 550.84 555.84 558.62008 563.06008">cause mechanical vibration and will result in increased audible </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="-356.7292" x="312 317 322 324.78 328.67 333.11003 335.61003 340.05003 345.05003 350.05003 352.55003 357.55003 362.55003 366.44004 370.33006 373.11006 378.11006 380.89006 385.33006 387.83006 395.05006 399.49006 403.93006 407.26005 409.76005 414.76005 419.76005 422.26005 427.26005 430.04005 435.04005 439.48005 442.81004 445.31004 453.09004 457.53004 461.97004 466.97004 471.41004 476.41004 479.19004 483.63005 488.07005 490.85005 493.35005 497.79005 502.79005 510.57005 515.57009 520.57009 525.57009 530.0101 535.0101 537.7901 541.6801 544.1801 546.47317 551.8831 556.8831 560.21316 565.21316 570.21316 574.65316">noise and possible wear on other mechanical components. Torque </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="-318.9091" x="312 315.89 318.67 323.67 328.67 331.45 335.89 338.39 343.39 348.39 352.83003 356.72004 361.16004 363.66004 368.10005 370.88005 373.38005 376.16004 381.16004 385.60005 388.10005 391.43003 396.43003 399.21003 401.99003 405.32 409.21003 411.99003 416.43003 421.43003 423.93003 428.93003 433.93003 437.82005 440.60005 443.38005 446.16004 451.16004 456.16004 460.05006">single phase at the full-step positions.</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="PZDRAU+Arial-BoldMT" font-weight="bold"><tspan y="-108.1743" x="261.1689"> </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="-96.1743" x="106.0444 113.264408 119.374408 124.9344 131.0444 139.9344 146.0444 151.6044 157.7144 163.2744 168.8344 172.1644 177.7244 183.8344 186.6144 193.8344 199.3944 202.1744 205.5044 208.2844 214.95439 218.2844 223.84439">Uncompensated 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="-108.1743" x="322.7695 328.8795 331.6595 337.76948 343.87947 347.76948 353.32948 355.73347 362.95347 368.51347 371.84346 374.62345 381.29347 387.40345 392.96345 398.52345 404.08345 406.86344 414.08345 416.86344 422.42344 428.53343 432.42344 437.98344 446.87345 449.65345 452.98344 459.0934 462.98344 465.76344 472.98344 479.0934 484.6534 490.7634 499.6534 505.7634 511.3234 517.4334 522.9934 528.5534 531.8834 537.4434 543.5534 546.33346 553.5534 559.1134 561.89346 565.22348">Figure A4: Phase Diagram for Uncompensated Half </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="-96.1743" x="433.165 439.83503 443.165 448.725">Step</tspan></text>
</svg>