fig1 shows a direct - drive dc brushless motor of the kind used by panasonic in their above referred to ag - 6300 video cassette recorder . this kind of motor is high in reliability , accuracy and durability and accordingly is excellent for use in very large data systems employing video tape for storing digital information thereon . although the number of poles is a matter of design choice , this motor includes a 16 - pole ring magnet identified by reference numeral 10 comprising permanent magnets which are alternately poled north and south and arranged in a circular fashion . above the ring magnet 10 a plurality of apertures , or &# 34 ; windows ,&# 34 ; identified by reference numeral 12 , are arranged concentrically around the upper edge of an encircling member 14 around the ring magnet 10 . a plurality of transformer coils such as identified by reference numeral 16 are mounted on the lower end of a stator member 18 and are mounted in a circular arrangement so as to fit within the circular structure of the ring magnet 10 . three pairs of position sensing coils such as those identified by reference numerals 20 and 21 are mounted on the stator member 18 above and spaced around the transformer coils 16 . position coils 20 and 21 are situated such as to be adjacent the windows 12 in the rotor member 14 when the motor is assembled . while in the preferred embodiment , the ring magnet consists of 16 individually poled magnets cooperating with 12 main coils , and three position sensing coil arrangements are shown cooperating with eight windows , other arrangements are possible and the numbers are a matter of design choice . with the arrangement shown in the preferred embodiment , the 12 coils may be connected together into three sets of four coils each , each set being so mechanically positioned as to cause rotation of the ring magnets when the coils are sequentially energized in a manner to be explained in more detail hereinafter . also with the arrangement shown in preferred embodiment wherein the number of windows in the rotor member 14 is eight and the number of position coil pairs 20 - 21 is three , the eight windows will continually pass by the three stationary position coil pairs in a three phase manner , i . e . all three coil pairs being 120 mechanical degrees apart will be exactly adjacent a window at different points every 15 degrees of rotation . as the window passes over a coil , magnetic coupling transfers less energy into the secondary winding than is the case when the window is not present with the result that every secondary winding will have an amplitude modulated signal presented at its terminals which is 15 degrees out of phase with its neighbor , as will be more clearly seen in connection with fig3 . in practice , stator 18 is mounted with respect to rotor 14 so that the coils 16 are closely adjacent to the magnets of ring 10 , and the position coils 20 and 21 are proximate the windows 12 . the apparatus is then connected in the recording device ( not shown ) and positioned so as to rotate at an angle with respect to the tape passing proximate the surface of the rotor 14 to thereby leave a recording of digital signals thereon . such tape transport mechanisms are well known in the art and will not be further described herein . fig2 shows a top view of the ring magnet 10 and the 16 magnets alternately poled south and north arranged in circular fashion . the main coils 16 are shown to be connected in three sets of four coils each identified by reference numerals 16a , 16b , and 16c , respectively . one end of the coil set 16a is connected by a conducter 26 to an input terminal 30 to receive a positive voltage thereon . the other end of the set of coils 16a is connected by a conducter 32 to an output terminal 34 which is connected to signal ground . in similar fashion , a first end of the set of coils 16b is connected by a conductor 36 to an input terminal 40 to receive a positive voltage , and the other end of set 16b is connected by a conductor 42 to an output terminal 44 also connected to signal ground . similarly , one end of the coil set 16c is connected by a conductor 46 to an input terminal 50 to receive a positive voltage , and the other end of coil set 16c is connected by a conductor 52 to an output terminal 54 connected to signal ground . it will be appreciated that with 12 coils and 16 magnets there will be displacement between some of the coils and the center of some of the magnets in all cases . for example , in fig2 the set of coils identified as 16a are all shown closely adjacent to a dividing line between a south and north poled magnet , coil set 16b is shown to be adjacent and slightly to the right of the center line of corresponding north poled magnets , and coil set 16c is shown to be slightly to the left of center of south poled magnets . accordingly , if two of the three sets of main coils are sequentially actuated by voltages applied to two of the terminals 30 , 40 and 50 , a magnetic field will be created in a rotating direction and the ring magnet 10 will follow . as soon as the magnet moves to follow , its position will be sensed by the apparatus to be described in connection with fig3 and a different set of main coils will be activated to keep the rotation going . as the motor rotates , the position sensing transformers , such as 20 and 21 , will continually pass by the windows such as 12 to provide the signals indicative of position . in fig3 eight windows identified by reference numerals 12a - 12h are shown equally spaced around in a circle 45 degrees apart from one another . three primary transformer windings identified by reference numerals 20a , 20b , and 20c are shown connected in series between an input terminal 60 and a ground connection 62 . alternately windings 20a , 20b , & amp ; 20c may be wired in parallel . one end of a first secondary winding 21a is connected by conductor 64 to a grounded terminal 66 and the other is connected by a conductor 68 to a terminal 70 . similarly , one end of a second secondary 21b is connected by a conductor 72 and a conductor 74 to terminal 66 and the other end is connected by a conductor 76 to a terminal 80 . in like fashion , one end of a third secondary winding 21c is connected by a conductor 82 and conductor 74 to terminal 66 and the other end is connected by a conductor 84 to a terminal 90 . it will be appreciated that the primary windings are energized from a source of alternating signals such as a 65 khz sinusoidal signal from terminal 60 to signal ground 62 . signals will be sensed by secondaries 21a , 21b , and 21c so as to produce outputs between terminals 66 and terminals 70 , 80 or 90 , respectively . the magnitude of these signals will depend upon the position of the transformers with respect to the windows 12a - 12h . more particularly as the window passes over a coil the magnetic coupling of the transformers between primary coils 20a , 20b , and 20c and secondary coils 21a , 21b , and 21c will transfer less energy to the secondary windings than is the case when the window is not present with the result that every secondary winding will have an amplitude modulated 65 khz signal present at its terminal . in the preferred embodiment the motor will spin at approximately 30 hz ( 1800 rpm ) so that each coil will see eight windows per revolution and will produce a 240 hz amplitude modulated output signal . it will be noted that the coils are physically separated at 120 degree positions around the circle and accordingly the 240 hz output of the three secondaries will be 120 degrees apart from each other . every time the motor turns by 15 mechanical degrees , one of the secondaries will deliver a maximum output . the actual wave form produced by the secondaries will be 240 hz envelopes modulated on the 65 khz carrier . when such signals are am detected , the carrier will be eliminated and just the 240 hz signal remain as seen in fig4 . referring to fig4 the output of the three coils 21a , 21b and 21c is shown as three 120 degree out of phase curves 94 , 96 , and 98 , respectively . it is seen that each coil peaks eight times in the 360 degrees of mechanical rotation and that each curve peaks at a different point separated from its neighbor by 15 mechanical degrees . an enlarged set of curves 94 , 96 , and 98 is shown in fig5 over 150 mechanical degrees of motion . in fig5 three square waves are generated from the positions of coils 21a , 21b and 21c as shown by curves 100 , 102 , and 104 , respectively . square wave 100 is produced by providing a low voltage represented by the lower part of curve 100 whenever the instantaneous magnitude of curve 94 has a value less than its value would be at an electrical 30 degrees in the sine wave . accordingly , curve 100 is shown rising to a high value between the 30 and 150 degree positions of sine wave 94 and falling to a low level at other times . similarly , curve 102 rises to a high value between the 30 degree and 150 degree positions of sine wave 96 and is at a low level at other times , and curve 104 rises to a high level between the 30 degree and 150 degree portions of sine ave 98 and falls to a low level at all other times . it will be noted in fig5 that when curve 100 just rises to a high value along a dash line 110 , for example , curve 102 has just fallen to a low level and curve 104 is halfway through its low level cycle . when curve 100 falls to a low level along a dash line 112 , curve 102 is halfway through its low level portion and curve 104 has just risen to a high level . when curve 104 returns to a low level along a dash line 114 , curve 102 just rises to a high level and curve 104 is halfway through its low level position . finally , when curve 102 falls to a low level along a dash line 116 , curve 100 again rises to a high level while curve 104 is halfway through its low level position . thus , for every electrical cycle of any one of the coils a high level signal is presented for one - third of the time by each of the coils 120 electrical degrees apart . this is seen in fig5 to be every 15 mechanical degrees starting with curve 102 rising to a high level at approximately seven and a half mechanical degrees of rotation . if the signals 100 , 102 , and 104 were to be presented to the main coil winding 16a , 16b , and 16c of fig2 a rotating field would be set up which would cause the ring magnets 10 to rotate and keep rotating . in the arrangement thus far described , there is a possibility that the curves 100 , 102 , and 104 might rise to a high level at a point slightly after the 30 degree point and / or fall to a low level at a point slightly before the 150 degree point , in which event a hiatus would occur between the ending of one of the curves and the beginning of the next , and the coils would receive no signal which might cause the system to fail . to overcome this problem , a point slightly less than the 30 degree point and slightly greater than the 150 degree point on each of the curves 94 , 96 , and 98 is chosen so that there will be a slight overlap . this situation is shown in fig6 wherein the square waves generated from the outputs of coils 21a , 21b and 21c are again shown as curves 100a , 102a , and 104a , respectively . it is seen that curve 100a now rises slightly to the left of dash line 110 and that curve 102a falls to a low level at point slightly to the right of dash line 110 . similarly , curve 104a rises to a high value at a point slightly in advance of dash line 112 while curve 100a falls to a low value at a point slightly to the right of dash line 112 . likewise , curve 102a rises to a high value at a point slightly to the left of dash line 114 while curve 104a falls to a low level at a point just to the right of dash line 114 . it is thus seen that if there are errors that cause slight misalignments of the 30 degree point and 150 degree point , the overlapping will assure that there is a signal at all times to the coils 16a , 16b , and 16c of fig2 . in order to produce the curves 100 , 102 , and 104 in fig5 and more particularly curves 100a , 102a and 104a in fig6 it is necessary to know where the 30 degree and 150 degree points are on curves 94 , 96 , and 98 . however , when the characteristics of the motor are not known in advance , the magnitudes of the voltages from coils 21a , 21b and 21c are not known and with out this it is not possible to determine the 30 degree and 150 degree points . accordingly in the present invention provisions are made for measuring the voltages produced by the coils 21a , 21b and 21c at an early stage in the operation thereof . more particularly at the start of operation of the motor , predetermined fixed signals are presented to coils 16a , 16b , and 16c in a predetermined sequence which causes the ring magnets 10 to move in a step motor fashion from one position to another . as it moves , the output voltages from the sensing coils 21a , 21b , and 21c are measured so as to determine the maximum and minimum values of the curves of fig5 . when the maximum and minimum values of each curve are known , the dc level of the midpoint of the curves can be obtained from the equation : ## equ1 ## the 30 degree point on a sinusoidal curve is one - half the value from the midpoint to the maximum or one - quarter of the value between the maximum value and the minimum value . the resultant desired 30 degree trip point for the system is therefore determined by the sum of these two values or ## equ2 ## thus , the computer can calculate the 30 degree and 150 degree trip points from equation ( 2 ) and then , in order to provide the overlap described in connection with fig6 a small amount , say 2 % or a little more , is then subtracted from this value so that the square pulses are widened slightly , as in fig6 to provide the desired overlap . in the use of the above mentioned panasonic motor , the voltage v 30 is usually somewhere around 3 volts and the amount subtracted therefrom to create the overlap situation is approximately 0 . 08 volts . after the above values for the trip point at v 30 are calculated , which usually takes about one and one - half rotations of rotor 10 in order to be sure of the values , the motor can thereafter be driven by these signals generated as curves 100a , 102a , and 104a in fig6 . the operation of the circuit for producing these results will be described in connection with fig7 . in fig7 the motor to be controlled is shown by reference numeral 150 having input connections shown as arrows 152 , 154 and 156 used to provide signals to terminals 30 , 40 and 50 , respectively , in fig2 . motor 150 also has output connections 158 , 160 and 162 representing the outputs from terminals 70 , 80 and 90 , respectively , in fig3 . the carrier frequency input 60 and ground connection 66 of fig3 are shown as terminals 163 and 164 , respectively , in fig7 . the output connections 158 , 160 and 162 are presented through detectors 165 , 166 and 167 , respectively , to a microprocessor 168 through connections shown as arrows 170 , 172 and 174 , respectively . the detectors 165 , 166 and 167 remove the carrier frequency outputs 158 , 160 and 162 , respectively , so as to produce signals like those shown in fig4 to microprocessor 168 . the microprocessor 168 is shown connected to a switch 178 by a connection shown as arrow 180 which operates to energize the microprocessor when it is desired to turn the motor 150 on . microprocessor 168 has a first output shown by an arrow 184 connected to a multiplexer 186 and a signal thereon causes the multiplexer 186 to switch between first and second conditions . in the first condition , multiplexer 186 operates to connect a triad of outputs shown as arrows 190 , 192 and 194 from microprocessor 168 to multiplexer 186 to a triad of outputs shown as arrows 198 , 200 and 202 from multiplxer 186 . output 198 is connected to a first current generator 208 which is also seen receiving a signal from microprocessor 168 through a connection shown as arrow 210 , a digital - to - analog converter 212 and a connection shown as arrow 214 . the output of current generator 208 is shown connected to the input 152 of motor 150 . in operation , the output of the current generator 208 is controlled on or off by the signal on input 198 from the multiplexer 186 which receives the signal from the microprocessor ( during initial start - up ) over the connection 190 . the magnitude of the current from generator 208 is controlled from microprocessor 168 via the connections 210 , digital - to - analog converter 212 and connection 214 . accordingly , at start - up , microprocessor 168 generates a predetermined voltage signal on connection 210 which is passed through the digital - to - analog computer 212 to connection 214 so that current generator 208 supplies a current signal of predetermined magnitude to motor 150 over connection 152 when called for by the signal on line 198 . similarly , output 200 of multiplexer 186 is connected to a second current generator 220 which receives a second input from microprocessor 168 via output connection 210 , digital - to - analog converter 212 and a connection shown as arrow 222 . the output of current generator 220 provides the input to motor 150 via connection 154 . accordingly , at start - up condition , microprocessor 168 sends the predetermined voltage signal on connection 210 which is passed through digital - to - analog converter 212 to connection 222 so that current generator 220 supplies a predetermined current signal on connection 154 to motor 150 when called for by the signal on line 200 . similarly , output 202 of multiplexer 186 is connected to the input of a third current generator 230 which is shown receiving a second input from microprocessor 168 via output connection 210 , digital - to - analog converter 212 and a connection shown as arrow 232 . the output of current generator 230 is connected to motor 150 by connection 156 . accordingly , at start - up , microprocessor 168 sends the predetermined voltage signal on connection 210 through digital - to - analog converter 212 to line 232 so that current generator 230 supplies a predetermine current signal to motor 150 via connection 156 when called for by a signal on output 202 of multiplexer 186 . the outputs of microprocessor 168 on connections 190 , 192 and 194 are phased so as to provide a stepping driving force to motor 150 to cause it to turn from one position to another as has been described above . when this occurs , the signals generated by coils 21a , 21b and 21c of fig3 will appear on lines 158 , 160 and 162 from motor 150 of fig7 and after the carrier frequency is removed by detectors 165 , 166 and 167 are presented to microprocessor 168 via connections 170 , 172 and 174 . microprocessor 168 now may determine the maximum and minimum values generated by the pickup coils 21a , 21b and 21c and to determine therefrom the desired trip point v 30 as described in connection with equation ( 2 ) above less an approximate 2 % to provide the overlap of fig6 . these desired trip point voltages are generated by microprocessor 168 over output connections shown by arrows 238 , 240 and 242 which are seen connected to digital - to - analog converters 248 , 250 and 252 , respectively . the outputs of digital - to - analog converters 248 , 250 and 252 are connected to the negative inputs of three comparators 258 , 260 and 262 by connections shown as arrows 264 , 266 and 268 , respectively . comparators 258 , 260 and 252 each have a positive input connected respectively to detectors 167 , 166 and 165 by connections shown as arrows 270 , 272 and 274 , respectively . comparators 258 , 260 and 262 are also shown having outputs connected to the multplexer 186 by connections shown as arrows 276 , 278 and 280 , respectively . the purpose of comparators 258 , 260 and 262 is to produce an output on connections 276 , 278 and 280 indicative of the difference between the positive and negative inputs they receive . accordingly , when the trip point value v 30 less 2 % is determined by microprocessor 168 , a voltage representative thereof appears on the negative input terminals 264 , 266 and 268 . the positive input terminals are receiving the detected output of motor 150 from the sensing coils 21a , 21b and 21c over connections 270 , 272 and 274 , respectively . therefore , the output of comparators 258 , 260 and 262 will be zero until such time as the positive input exceeds the negative input , which corresponds to the trip point determined by microprocessor 168 . accordingly , an output will appear on each of the comparators 258 , 260 and 262 only during the time between the 30 degree point and the 150 degree point ( less the approximate 2 % needed for overlap ) on lines 276 , 278 and 280 respectively . after microprocessor 168 has determined the values of the trip points for each of the coils , a signal will be presented along output 184 to multiplexer 186 which will thereafter switch to the second condition and the outputs 276 , 278 and 280 from comparators 258 , 260 and 262 will pass through multiplexer 186 to outputs 198 , 200 and 202 . as explained above , these outputs operate through current generators 208 , 220 and 230 to drive motor 150 . a connection shown as arrow 290 is shown from motor 150 to microprocessor 168 . this connection may be used to provide a signal from motor 150 to microprocessor 168 periodically as the rotor 14 rotates . the speed of this signal is indicative of the motor speed so that microprocessor 168 can determine when the motor is operating at a full desired speed . at this time , the signals to the motor can then be recalibrated to maintain the desired speed . it is accordingly seen that i have provided a circuit which can operate a dc brushless motor even though its characteristics are unknown and to provide positive and reliable start - up procedures to make sure that the motor does not stall either during start - up or running . although the present invention has been described with reference to preferred embodiments , workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention .