Abstract:
A method and apparatus for bipolar and self DC-erase write of servo marks. The method includes providing a servo write head having first and second write gaps; and applying a varying current to the servo write head to alternately DC-erase and write sets of servo marks to regions of a servo track of a magnetic storage medium proximate the first and second write gaps, the magnetic storage medium moving with respect to the first and second write gaps. The apparatus includes a bipolar servo erase/write driver configured to generate both negative and positive polarity currents and to generate a varying bipolar current signal and a servo write head having a first write gap and second write gap spaced apart and where the servo write head is an only means for writing servo marks to the magnetic storage medium and for DC-erasing the servo tracks.

Description:
FIELD OF THE INVENTION 
     The present invention relates to the field of magnetic medium recording; more specifically, it relates to apparatuses and methods for bipolar writing servo marks to a magnetic recording medium using self DC-erase. 
     BACKGROUND 
     Magnetic recording systems (such as tape recording systems) record bits of information to a magnetic medium using a write/read head composed of write and read transducers. During both write and read operations, the write and record heads need to be positioned accurately over the data tracks of the magnetic medium. This is achieved by controlling the position of the write/read head in reference to servo-marks prewritten to servo tracks of the magnetic medium. The servo marks are written to a pre-erased medium using a servo write head. The accuracy of writing and reading data strongly depends on how well the pre-erase is performed and how well servo marks are written to the medium. Existing methods either do not produce high signal output or require complex write head structures to properly pre-erase or write the servo tracks and/or at the same time properly pre-erase the data tracks. Accordingly, there exists a need in the art to mitigate the deficiencies and limitations described hereinabove. 
     SUMMARY 
     A first aspect of the present invention is a method, comprising: providing a servo write head having first and second write gaps; and applying a varying current to the servo write head to alternately DC-erase and write sets of servo marks to regions of a servo track of a magnetic storage medium proximate to the first and second write gaps, the magnetic storage medium moving with respect to the first and second write gaps. 
     A second aspect of the present invention is a method, comprising: providing a servo write head having (a) a first write gap and second write gap spaced apart and (b) an induction coil configured to generate respective magnetic fields proximate to the first and second write gaps when a current is applied to the coil by a bipolar servo erase/write driver, the bipolar servo erase/write driver configured to generate both negative and positive polarity currents; generating a varying current signal using the bipolar servo erase/write driver; moving a magnetic storage medium past the first and second write gaps in a linear direction from the first write gap toward the second write gap; and applying the varying current to the coil of the servo write head to alternately DC-erase and write sets of servo marks to regions of a servo track of the magnetic storage medium as the magnetic storage medium moves past the first and second write gaps, the servo track DC-erased and written only by the servo write head. 
     A third aspect of the present invention is an apparatus, comprising: a bipolar servo erase/write driver configured to generate both negative and positive polarity currents and to generate a varying current signal; a servo write head having a first write gap and second write gap spaced apart and configured to generate respective magnetic fields proximate to the first and second write gaps when the varying signal is applied to servo write head by the bipolar servo erase/write driver; a component that moves a magnetic storage medium past the first and second write gaps in a direction from the first write gap toward the second write gap; and wherein the servo write head is the only means for writing servo marks to the magnetic storage medium and for DC-erasing the servo tracks. 
     These and other aspects of the invention are described below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features of the invention are set forth in the appended claims. The invention itself, however, will be best understood by reference to the following detailed description of illustrative embodiments when read in conjunction with the accompanying drawings, wherein: 
         FIG. 1A  is a cutaway cross-section view through line  1 A- 1 A of  FIG. 1B  illustrating a servo write head according to an embodiment of the present invention; 
         FIG. 1B  is a bottom view of the servo write head of  FIG. 1A ; 
         FIG. 2A  is a cutaway cross-section view through line  2 A- 2 A of  FIG. 2B  illustrating a servo write head according to an embodiment of the present invention; 
         FIG. 2B  is a bottom view of the servo write head of  FIG. 2A ; 
         FIG. 3A  is a plot of current levels versus medium position or time of a servo write signal  160  to be applied to servo write heads according to embodiments of the present invention; 
         FIG. 3B  illustrates the servo marks written to a magnetic tape medium by the left gap of the servo write head using the signal of  FIG. 3A ; 
         FIG. 3C  illustrates the servo marks written to a magnetic tape medium by the right gap of the servo write head using the signal of  FIG. 3A ; 
         FIG. 3D  illustrates the composite servo marks written to magnetic tape medium by the left and right gaps of the servo write head using the signal of  FIG. 3A ; 
         FIG. 3E  illustrates the servo signal generated by the servo marks of  FIG. 3D ; 
         FIG. 4  is a first exemplary graphical solution for conditions under which the embodiments of the present invention may be practiced with self DC-erasing and no overwrite of the servo track; 
         FIG. 5  is a second exemplary graphical solution for conditions under which the embodiments of the present invention may be practiced with self DC-erasing and no overwrite of the servo track; and 
         FIG. 6  is a flowchart of the method of writing servo marks with self DC-erase according to embodiments of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     There are two conventional methods of writing servo marks to magnetic tape. In the first method, the medium is AC-erased and then uni-polar (i.e., only positive or only negative) current pulses are applied to write the servo marks. This method produces relatively weak servo output signals. In the second method, the magnetic tape is uni-polar (e.g., negatively) DC-erased and then uni-polar (e.g., positive) current pulses are applied to write the servo marks. This method produces a relatively strong servo output signal but requires the use of a DC-erase head and DC-erase driver or permanent magnets to erase the magnetic tape prior to servo writing. An additional problem with the second method is that it is preferable that the data tracks be AC-erased rather than DC-erased for improved data recording. DC-erase methods also DC-erase the data tracks unless the DC-erase head has the same width as the servo write head and is precisely aligned with the servo write head, or unless complex hybrid DC-erase/AC-erase heads are used. 
     In addition, uni-polar writing implies that the magnetization transition that defines positive (negative) peaks and negative (positive) peaks are defined by the trailing edge and the leading edge of the write gap in the servo write head respectively. Therefore, servo signal peak amplitude and width can be slightly different if the magnetic fields at the trailing edge and at the leading edge differ due to undesired physical differences of the edges of the write gap resulting from the servo head fabrication process. 
     The present invention is a new bi-polar servo mark writing method for writing timing based servo marks to a magnetic storage medium (e.g., magnetic tape). In one embodiment, the inventive method uses a dual-gap erase/write head and a bi-polar (both positive and negative) DC-erase/write driver and does not use a separate erase head and erase driver for erasing the servo mark regions of the magnetic tape. The dual-gap erase/write head both writes and erases depending on the polarity and timing of the erase/write signal. The erase/write driver can provide positive and negative currents to the dual-gap write head and can be turned off to apply zero current, or to apply near zero current (a near zero current is defined as a positive or negative current that does not change the magnetic state of the medium) at defined times to avoid overwriting the servo marks. Moreover, the inventive method completely eliminates the need for a separate DC-erase of the magnetic medium prior to writing the servo marks, since only a dual-gap servo erase/write head is used to self-DC-erase the servo track and write servo marks as the magnetic tape passes under the dual-gap head. Prior to writing servo marks to the servo track of the magnetic tape, the entire tape (e.g., the servo track regions and data track regions) may be AC-erased. 
       FIG. 1A  is a cutaway cross-section view through line  1 A- 1 A of  FIG. 1B  illustrating a servo write head according to an embodiment of the present invention. In  FIG. 1A , a dual-gap servo write head  100  includes ferromagnetic body  105  having a left gap  110 L and a right gap  110 R spaced a center-to-center distance Sg apart and an induction coil  115 . Ferromagnetic body  105  need not be formed from iron but has the property of being ferromagnetic. Left and right gaps  110 L and  110 R have respective widths Wl and Wr. Induction coil  115  is electrically connected to a bipolar DC servo erase/write driver  120 , which generates a varying current signal that is applied to induction coil  115 . Opposite ends of coil  115  are electrically connected to respective positive and negative current terminals of bipolar servo erase/write driver  120 . A magnetic tape  125  having a thickness T and spaced a distance S (in the Z-direction) from dual-gap servo write head  100  moves at a velocity V in the X-direction. When a current i(t) is applied to coil  115 , a magnetic write bubble  130 L is induced in magnetic tape  125  under gap  110 L, thereby magnetizing a region  135 L of the magnetic tape. The same current i(t) induces a magnetic write bubble  130 R in magnetic tape  125  under gap  110 R, thereby magnetizing a region  135 R of the magnetic tape. The magnetic regions  135 L and  135 R are wider (in the X-direction) than the write bubbles because magnetic tape  125  is moving from right to left while the write current i(t) remains, in this example, at a constant positive value. 
     Regions  135 R and  135 L will be magnetized when the write field strengths in the X-direction (Hx) generated by the gaps  110 L and  110 R are greater than coercivity of the magnetic medium (Hc). Each write bubble  130 L and  130 R has two edges. The leading edge is the rightmost edge and the trailing edge is the leftmost edge. The average width (in the X-direction) of write bubbles  130 L and  130 R depends on the distance S, the amplitude of the write current, the widths Wl and Wr, and the coercivity of magnetic tape  125 . For optimum writing, the widths of write bubbles  130 L and  130 R should be about the same as the widths of gaps  110 L and  110 R, respectively. Wl and Wr may be the same or may be different. As can be seen, both regions  135 L and  135 R are written at the same time. The widths (in the X-direction) of regions  135 L and  135 R are a function of the velocity V of magnetic tape  125 , the time duration of the current i(t), and the write bubble parameters discussed supra. 
       FIG. 1B  is a bottom view of the servo write head of  FIG. 1A . In  FIG. 1B , gaps  110 L and  110 R are trapezoidal in shape and are slanted away from the Y-direction by respective angles Al and Ar. Gaps  110 L and  110 R are slanted toward each other. The magnitudes of angles Al and Ar may be the same or different. 
       FIG. 2A  is a cutaway cross-section view through line  2 A- 2 A of  FIG. 2B  illustrating a servo write head according to an embodiment of the present invention. In  FIG. 2A , a dual-gap servo write head  140  includes a first ferromagnetic body  145 L having a left gap  150 L and a first induction coil  155 L and a second ferromagnetic body  145 R having a right gap  150 R and a second induction coil  155 R. Left and right gaps  150 L and  150 R are spaced the center-to-center distance Sg apart. Left and right gaps  110 L and  110 R have respective widths Wl and Wr. Induction coils  155 L and  155 R are electrically connected in parallel (or alternatively in series) to bipolar servo erase/write driver  120  which generates a varying current signal that is applied to induction coils  155 L and  155 R. Opposite ends of coils  155 L and  155 R are electrically connected to respective positive and negative current terminals of bipolar servo erase/write driver  120 . 
       FIG. 2B  is a bottom view of the servo write head of  FIG. 2A . In  FIG. 2B , gaps  150 L and  150 R are trapezoidal and are slanted in the Y-direction by respective angles Al and Ar. Gaps  150 L and  150 R are slanted toward each other. Angles Al and Ar may be the same or different. 
     Although magnetic tape  125  is depicted as under servo erase/write heads  100  and  140 , alternatively  FIGS. 1A and 2A  may be rotated 180° about the Y-axis so the magnetic tape passes over the servo erase/write heads in which case  FIGS. 1B and 2B  would depict top surfaces of the servo erase/write heads. 
       FIG. 3A  is a plot of current levels versus medium position or time of a servo write signal  160  to be applied to servo write heads according to embodiments of the present invention. The X-scale of  FIG. 3A  may be converted from a medium position scale to a time scale by dividing the position scale by the velocity V of the magnetic tape past the servo write head. When write current is plotted versus the position of the moving magnetic tape the segments, d 1   ab , d 2   ab , d 3   ab , d 4   ab , d 1   cd , d 2   cd , d 3   cd  and d 4   cd  are used. The positions can also be thought as defining the lengths of sequential segments or distances between positions along the tape. By dividing by V, d 1   ab  becomes a time interval between a time t 0  and a time t 1 , d 2   ab  becomes an interval between time t 1  and a time t 2 , d 3   ab  becomes a time interval between time t 2  and a time t 3 , d 4   ab  becomes a time interval between time t 3  and a time t 4 , d 1   cd  becomes a time interval between time t 4  and a time t 5 , d 2   cd  becomes a time interval between time t 5  and a time t 6 , d 3   cd  becomes a time interval between time t 6  and a time t 7 , and d 4   cd  becomes a time interval between time t 7  and a time t 8  (not shown). In  FIG. 3A , the pulse width in distance d 2   ab  is b 1  and the space between pulses is s 1 . The pulse width in distance d 2   cd  is b 2  and the space between pulses is s 2 . In one example, b 1 =b 2  and s 1 =s 2 . 
     Magnetic tape passing the servo write head is magnetized when the applied current has sufficient amplitude (either positive or negative). In the present illustration, positive current writes the medium magnetization in the +X-direction and is used for writing servo marks. Negative current writes the magnetization in the −X-direction and is used for DC-erasing the servo tracks. Alternatively, positive currents may be used to erase and negative currents to write. 
     In terms of tape position, in the distance d 1   ab  the current is negative and DC-erase of the servo track is performed; in distance d 2   ab , the current alternates (in pulses of controlled time duration) from negative to positive to negative three times (in this example) to write a pair of A and B servo marks and perform DC-erase between consecutive A and B servo marks. Note that the width of the servo marks is defined by the duration of the positive pulses and is independent of the width of the write gap. Similarly, the distance between two marks is defined by the duration of the negative pulses and is independent of the width of the write gap. Moreover, the servo mark edges are defined by the trailing edge of the write gap only. In distance d 3   ab  the write current is negative and DC-erase is performed. In distance d 4   ab  the current is zero or near zero to avoid overwriting the servo marks when the left gap passes over the servo marks written by the right gap. In the distance d 1   cd  the current is negative and DC-erase of the servo track is performed. In distance d 2   cd , the current alternates (in pulses of controlled time duration) from negative to negative to positive to negative three times (in this example) to write a pair of C and D servo marks. In distance d 4   cd  the current is zero or near zero to avoid overwriting the servo marks when the left gap passes over the servo marks written by the right gap. In distance d 3   cd  the current is negative and DC-erase of the servo track is performed. The same sequence can be repeated for additional A and B servo mark pairs and additional C and D servo marks pairs. In  FIG. 3A , the distance AC is measured from the leading edge of the first pulse of the first burst of three pulses to the leading edge of the first pulse of leading edge of the second burst of three pulses. In terms of time, between t 0  and t 1  the current is negative and DC-erase of the servo track is performed; between time t 1  and t 2 , the current alternates from negative to positive to negative three times to write a pair of A and B servo marks and perform DC-erase between consecutive A and B servo marks. Between time t 2  and t 3  the write current is negative and DC-erase is performed. Between t 3  and t 4  the current is zero or near zero to avoid overwriting the servo marks when the left gap passes over the servo marks written by the right gap. Between t 4  and t 5  the current is negative and DC-erase of the servo track is performed. Between t 5  and t 6  the current alternates from positive to negative to positive to write a pair of C and D servo marks. Between t 6  and t 7  the current is negative and DC-erase of the servo track is performed. Between t 7  and t 8  (the next t 0 ) the current is zero or near zero to avoid overwriting the servo marks when the left gap passes over the servo marks written by the right gap. The same sequence can be repeated for additional A and B servo mark pairs and additional C and D servo marks pairs. 
       FIG. 3B  illustrates the servo marks written to a magnetic tape medium by the left gap of the servo write head using the signal of  FIG. 3A .  FIG. 3C  illustrates the servo marks written to a magnetic tape medium by the right gap of the servo write head using the signal of  FIG. 3A .  FIG. 3D  illustrates the composite servo marks written to magnetic tape medium by the left and right gaps of the servo write head using the signal of  FIG. 3A . In  FIGS. 3B ,  3 C and  3 D servo marks are illustrated by the solid black trapezoids. In  FIG. 3B , a servo mark track  165  illustrates the position of the A and C servo marks. Servo marks B and D are not illustrated. Distances d 1 , d 2 , d 3  and d 4  associated with the A servo marks are the same as the diab, d 2   ab  and d 3   ab  and d 4   ab  distances of  FIG. 3A , and distances d 1 , d 2 , d 3  and d 4  associated with the C servo marks are the same as the d 1   cd , d 2   cd  and d 3   cd  and d 4   cd  distances of  FIG. 3A . In  FIG. 3C , the position on track  165  of servo marks B is illustrated with the start of servo marks D. Servo marks A and C are not illustrated. In  FIG. 3D , servo marks A, B and C are illustrated and the start of servo marks D is illustrated. Also, the number of servo marks in the AB servo mark pairs may be different from the number of servo marks in the CD servo mark pairs. 
       FIG. 3E  illustrates the servo signal generated by the servo marks of  FIG. 3D . In  FIG. 3E , a servo signal  170  generated by reading servo marks A, B and C are plotted versus the corresponding position on the medium as in  FIGS. 3A through 3E . 
     Since the sequence of servo mark pairs AB-CD-AB-CD-etc. is written with two gaps, it is important to apply the correct sequence of current changes and polarities to prevent overwriting the B and D servo-marks with the left gap of the servo writer. In addition, self-DC-erase (i.e., full DC-erase between A-B, B-C, C-D, D-A etc. servo marks with the use of a single servo write head) can be achieved with the correct timing of sequence of currents but this adds restrictions on servo mark pattern achievable as discussed infra. 
     The waveform of servo write signal  160  can be designed as follows: 
     From  FIGS. 3A through 3D  the following two equations can be defined:
 
 AC=d 2 ab+d 3 ab+d 4 ab+d 1 cd   (1)
 
 CA=d 2 cd+d 3 cd+d 4 cd+d 1 ab   (2)
 
With d 1   ab , d 3   ab , d 1   cd  and d 3   cd  as unknowns, there are eight conditions for full self DC-erasing of the servo track with no overwriting of servo marks. These conditions are given by the inequalities in Table I:
 
                                               TABLE I                       In order that:   The following condition must be satisfied:                                    1   There be no overwrite of   d3ab &lt; Sg − [(Sh/2)*(tan(Al) +           B marks after d3ab   tan(Ar))] − d2ab − Wl       2   There be full DC-erase   d1ab + d3ab &gt; Sg + [(Sh/2)*(tan(Al) +           between marks A and B   tan(Ar))] − d2ab − Wl       3   There be full DC-erase   d3ab + d1cd &gt; AC − Sg − Wr +           between marks B and C   [(Sh/2)*(tan(Al) + tan(Ar))] − d2ab       4   There be no overwrite of   d1cd &lt; AC − Sg − [(Sh/2)*(tan(Al) +           B marks after d4ab   tan(Ar))] − d2ab       5   There be no overwrite of   d3cd &lt; Sg − [(Sh/2)*(tan(Al) +           D marks after d3cd:   tan(Ar))] − d2cd − Wl       6   There be full DC-erase   d1cd + d3cd &gt; Sg + [(Sh/2)*(tan(Al) +           between marks C and D   tan(Ar))] − d2cd − Wl       7   There be full DC-erase   d3cd + d1ab &gt; CA − Sg − Wr +           between marks D and A   [(Sh/2)*(tan(Al) + tan(Ar))] − d2cd       8   There be no overwrite of   d1ab &lt; CA − Sg − [(Sh/2)*(tan(Al) +           D marks after d4cd   tan(Ar))] − d2cd                    
Where:
         Sg is the center-to-center distance between the left and right gaps (see  FIGS. 1A and 2A );   Wl is the width of the left gap in an X-direction;   Wr is the width of the right gap in the X-direction;   Al is the angle of the left gap slanted away from the Y-direction;   Ar is the angle of the right gap slanted away from the Y-direction; and   d 1   ab , d 2   ab , d 3   ab , d 4   ab , d 1   cd , d 2   cd , d 3   cd  and d 4   cd  are sequential segments along the magnetic tape in the X-direction where:
           in segment d 1   ab  the current is negative;   in segment d 2   ab  the current pulses from negative to positive and back to negative N times, where N is a positive integer equal to or greater than one where:   in segment d 3   ab  the current is negative;   in segment d 4   ab  the current is zero or near zero;   in segment d 1   cd  the current is negative;   in segment d 2   cd  the current pulses from negative to positive and back to negative N times;   in segment d 3   cd  the current is negative; and   in segment d 4   cd  the current is zero or near zero;   
           Sh is the width of the servo track in the Y-direction; and       

     the X-direction is defined as the direction of movement of the magnetic storage medium (e.g., magnetic tape) from the right gap to left gap and the Y-direction is defined as a direction perpendicular to the X-direction. 
     Alternatively, in order to make the number of servo marks in the AB servo mark pairs different from the number of servo mark pairs in the CD pairs, instead of pulsing N times in each of distances d 2   ab  and d 2   cd , N 1  pulses are applied in distance d 2   ab  to write the AB marks and N 2  pulses are applied in distance d 2   cd  to write the CD servo marks. Both N 1  and N 2  are positive integers greater than one with N 1  not equal to N 2 . 
       FIG. 4  is a first exemplary graphical solution for conditions under which the embodiments of the present invention may be practiced with self DC-erasing and no overwrite of the servo track. In  FIG. 4 , the values of TABLE II have been substituted into the conditional expressions of TABLE Ito produce the plots of  FIG. 4 . 
     
       
         
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                 Parameter 
                 Symbol 
                 Value 
               
               
                   
               
             
             
               
                 Sg Distance 
                 AB or Sg 
                 50 μm  
               
               
                 Angle of left gap 
                 Al 
                 6° 
               
               
                 Angle of right gap 
                 Ar 
                 6° 
               
               
                 Left write gap 
                 Wl 
                 0.3 μm     
               
               
                 Right write gap 
                 Wr 
                 0.3 μm     
               
               
                 Servo track width 
                 Sh 
                 90 μm  
               
               
                 AC distance 
                 AC 
                 100 μm  
               
               
                 CA distance 
                 CA 
                 100 μm  
               
               
                 Servo pulse width (b of FIG. 3A) 
                 Together 
                 2 μm 
               
               
                 Number of pulses in A and B bursts 
                 these 
                 4 
               
               
                 Number of pulses in C and D bursts 
                 allow 
                 5 
               
               
                 Pulse to pulse distance for A and B bursts (s1 
                 evaluation 
                 4 μm 
               
               
                 of FIG. 3A) 
                 of d2ab 
               
               
                 Pulse to pulse distance for C and D bursts (s2 
                 and d2cd 
                 4 μm 
               
               
                 of FIG. 3A) 
               
               
                   
               
             
          
         
       
     
     In  FIG. 4 , condition ( 1 ) is plotted by line  200 , condition ( 2 ) is plotted by line  205 , condition ( 3 ) is plotted by line  210 , condition ( 4 ) is plotted by line  215 , condition ( 5 ) is plotted by line  220 , condition ( 6 ) is plotted by line  225 , condition ( 7 ) is plotted by line  230 , and condition ( 8 ) is plotted by lines  235 . Regions  240 ,  245 ,  250  and  255  are regions where trailing edge servo writing with self-DC-erase is achievable. For example, with d 1   ab =d 1   cd =22 μm, d 3   ab =25 μm and d 3   cd =20 μm all conditions are satisfied. 
       FIG. 5  is a second exemplary graphical solution for conditions under which the embodiments of the present invention may be practiced with self DC-erasing and no overwrite of the servo track. In  FIG. 5 , the values of TABLE III have been substituted into the condition expressions of TABLE Ito produce the plots of  FIG. 4 . 
     
       
         
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 Parameter 
                 Symbol 
                 Value 
               
               
                   
               
             
             
               
                 Sg Distance 
                 AB 
                 50 μm  
               
               
                 Angle of left gap 
                 Al 
                 6° 
               
               
                 Angle of right gap 
                 Ar 
                 0° 
               
               
                 Left write gap 
                 Wl 
                 0.3 μm     
               
               
                 Right write gap 
                 Wr 
                 0.3 μm     
               
               
                 Servo track width 
                 Sh 
                 180 μm  
               
               
                 AC distance 
                 AC 
                 100 μm  
               
               
                 CA distance 
                 CA 
                 100 μm  
               
               
                 Servo pulse width (b of FIG. 3A) 
                 Together 
                 1 μm 
               
               
                 Number of pulses in A and B bursts 
                 these 
                 4 
               
               
                 Number of pulses in C and D bursts 
                 allow 
                 5 
               
               
                 Pulse to pulse distance for A and B bursts (s1 
                 evaluation 
                 2 μm 
               
               
                 of FIG. 3A) 
                 of d2ab 
               
               
                 Pulse to pulse distance for C and D bursts (s2 
                 and d2cdd 
                 2 μm 
               
               
                 of FIG. 3A) 
               
               
                   
               
             
          
         
       
     
     In  FIG. 4 , condition ( 1 ) is plotted by line  300 , condition ( 2 ) is plotted by line  305 , condition ( 3 ) is plotted by line  310 , condition ( 4 ) is plotted by line  315 , condition ( 5 ) is plotted by line  320 , condition ( 6 ) is plotted by line  325 , condition ( 7 ) is plotted by line  330 , and condition ( 8 ) is plotted by line  335 . Regions  340 ,  345 ,  350  and  355  are regions where trailing edge servo writing with self-DC-erase is achievable. For example, with d 1   ab =d 1   cd =30 μm and d 3   ab =d 3   cd =30 μm all conditions are satisfied. 
       FIG. 6  is a flowchart of the method of writing servo marks with self DC-erase according to embodiments of the present invention. In the following description, except when referring to numbers of pulses, “negative” may be substituted for “positive” and “positive” substituted for “negative.” In step  400 , the servo write signal (e.g.,  160  of  FIG. 3A ) is designed using the conditions of TABLE I and equations (1) and (2). The use of a general purpose computer as an aid in the design of the servo write signal is useful. The servo write signal is supplied to the servo write head (e.g., dual-gap servo write head  100  of  FIG. 1A  or dual-gap servo write head  140  of  FIG. 2A ) by the bipolar servo erase/write driver (e.g.,  120  of  FIG. 1A ). The servo write signal is a current signal having four distinct phases. During steps  405  through  420 , the magnetic tape is moving at a constant velocity past the servo write head. Signal design techniques include graphical and numeric methods. 
     In step  405 , a negative current is applied to erase regions of the servo track across from both gaps of the servo write head for a time T 1 . 
     Alternatively, when the number of AB servo marks is to be different from the number of CD servo marks, the negative current is applied for a time T 1 ( 1 ) or T 1 ( 2 ) on alternating passes through the loop  405 ,  410 ,  415 ,  420 ,  425  and  430 . T 1 ( 1 ) may or may not be equal to T 1 ( 2 ). 
     In step  410 , the current is pulsed from negative to positive to negative N times for a time T 2 . The current is positive during each pulse for a time Tp and negative for a time Tn. T 2  is equal to N(Tp)+(N−1)Tn. During time T 2 , pairs of N servo marks are written to the servo track across from both gaps. 
     Alternatively, when the number of AB servo marks is to be different from the number of CD servo marks, in step  410 , the current is pulsed from negative to positive to negative N 1  times for a time T 2 ( 1 ) or N 2  times for a time T 2 ( 2 ). The current is positive during each pulse for a time Tp and negative for a time Tn. T 2 ( 1 ) is equal to N 1 (Tp)+(N 1 −1)Tn and T 2 ( 2 ) is equal to N 2 (Tp)+(N 2 −1)Tn. During time T 2 ( 1 ), pairs of N 1  marks are written to the servo track across from both gaps. During time T 2 ( 2 ), pairs of N 2  marks are written to the servo track across from both gaps. N 1  pulses in time T 2 ( 1 ) or N 2  pulses in time T 2 ( 2 ) are applied on alternating passes through the loop  405 ,  410 ,  415 ,  420 ,  425  and  430 . N 1  and N 2  are positive non-equal integers greater than zero. T 2 ( 1 ) may or may not be equal to T 2 ( 2 ). 
     In step  415 , a negative current is applied to erase regions of the servo track across from both gaps of the servo write head for a time T 3 . 
     Alternatively, when the number of AB servo marks is to be different from the number of CD servo marks, the negative current is applied for a time T 3 ( 1 ) or T 3 ( 2 ) on alternating passes through the loop  405 ,  410 ,  415 ,  420 ,  425  and  430 . T 3 ( 1 ) may or may not be equal to T 3 ( 2 ). 
     In step  420 , a zero or near zero current is applied to the servo write head to prevent overwriting of servo marks written in step  410  for a time T 4 . 
     Alternatively, when the number of AB servo marks is to be different from the number of CD servo marks, the zero or near zero current is applied for a time T 4 ( 1 ) or T 4 ( 2 ) on alternating passes through the loop  405 ,  410 ,  415 ,  420 ,  425  and  430 . T 4 ( 1 ) may or may not be equal to T 4 ( 2 ). 
     In step  425  it is determined if writing of servo marks is to be stopped. If not, the method loops back to step  405  otherwise writing of servo marks is terminated. 
     Whether or not T 1 ( 1 ) is or not equal to T 1 ( 2 ), T 2 ( 1 ) is or not equal to T 2 ( 2 ), T 3 ( 1 ) is or not equal to T 3 ( 2 ), and T 4 ( 1 ) is or not equal to T 4 ( 2 ) depends on satisfying the conditions of TABLE I. For example, in the second example (TABLE III) N 1 =4 and N 2 =5 and T 1 ( 1 )=T 1 ( 2 ) and T 3 ( 1 )=T 3 ( 2 ). 
     The alternative when the number of AB servo marks is to be different from the number of CD servo marks may be summarized in terms of T 1 , T 2 , T 3  and T 4  where T 1 , T 2 , T 3  and T 4  remain substantially the same, (ii) T 1 , T 2 , T 3  and T 4  alternate between two different values, or (iii) one or more of T 1 , T 2 , T 3  and T 4  remain the substantially the same and one or more of T 1 , T 2 , T 3  and T 4  alternate between two different values. 
     Thus, the embodiments of the present invention provide apparatuses and methods for bipolar writing servo marks to a magnetic storage medium using self DC-erase. It should be understood that while magnetic tape has been used in describing the embodiments of the present invention, the embodiments of the present invention are applicable to any moving magnetic storage medium. 
     The description of the embodiments of the present invention is given above for the understanding of the present invention. It will be understood that the invention is not limited to the particular embodiments described herein, but is capable of various modifications, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, it is intended that the following claims cover all such modifications and changes as fall within the true spirit and scope of the invention.