Patent Publication Number: US-6987636-B1

Title: Adjusting track density over disk radius by changing slope of spiral tracks used to servo write a disk drive

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to disk drives for computer systems. More particularly, the present invention relates to adjusting track density over disk radius by changing slope of spiral tracks used to servo write a disk drive. 
   2. Description of the Prior Art 
   When manufacturing a disk drive, servo sectors  2   0 – 2   N  are written to a disk  4  which define a plurality of radially-spaced, concentric data tracks  6  as shown in the prior art disk format of  FIG. 1 . Each data track  6  is partitioned into a plurality of data sectors wherein the servo sectors  2   0 – 2   N  are considered “embedded” in the data sectors. Each servo sector (e.g., servo sector  2   4 ) comprises a preamble  8  for synchronizing gain control and timing recovery, a sync mark  10  for synchronizing to a data field  12  comprising coarse head positioning information such as a track number, and servo bursts  14  which provide fine head positioning information. The coarse head position information is processed to position a head over a target track during a seek operation, and the servo bursts  14  are processed to maintain the head over a centerline of the target track while writing or reading data during a tracking operation. 
   The track density as determined from the width of each track  6  is typically adjusted over the disk radius to compensate for degradation in reproduction accuracy due to various factors. For example, the track density is typically decreased toward the outer diameter tracks where servo errors (track misregistration errors) are amplified due to the increase in linear velocity, windage, and disk flutter affects. The track density may also be decreased toward the inner diameter tracks to reduce inter-track interference caused by the YAW angle of the actuator arm, particularly in disk drives employing magnetoresistive (MR) heads wherein a gap exists between the read element and the write element. 
   In the past, external servo writers have been used to write the product servo sectors  2   0 – 2   N  to the disk surface during manufacturing. External servo writers employ extremely accurate head positioning mechanics, such as a laser interferometer, to ensure the product servo sectors  2   0 – 2   N  are written at the proper radial location from the outer diameter of the disk to the inner diameter of the disk, as well as to adjust the track density over the disk radius. However, external servo writers are expensive and require a clean room environment so that a head positioning pin can be inserted into the head disk assembly (HDA) without contaminating the disk. Thus, external servo writers have become an expensive bottleneck in the disk drive manufacturing process. 
   The prior art has suggested various “self-servo” writing methods wherein the internal electronics of the disk drive are used to write the product servo sectors independent of an external servo writer. For example, U.S. Pat. No. 5,668,679 teaches a disk drive which performs a self-servo writing operation by writing a plurality of spiral tracks to the disk which are then processed to write the product servo sectors along a circular path. Each spiral track is written to the disk as a high frequency signal (with missing bits), wherein the position error signal (PES) for tracking is generated relative to time shifts in the detected location of the spiral tracks. However, the &#39;679 patent does not disclose how to adjust the track density over the disk radius when servo writing a disk drive from spiral tracks. 
   There is, therefore, a need to adjust the track density over the disk radius when servo writing a disk drive from spiral tracks. 
   SUMMARY OF THE INVENTION 
   The present invention may be regarded as a method of writing product servo sectors to a disk of a disk drive to define a plurality of data tracks. The disk drive comprises control circuitry and a head disk assembly (HDA) comprising the disk, an actuator arm, a head coupled to a distal end of the actuator arm, and a voice coil motor for rotating the actuator arm about a pivot to position the head radially over the disk. A plurality of spiral tracks are written to the disk, wherein each spiral track comprises a high frequency signal interrupted at a predetermined interval by a sync mark, and a slope of the spiral tracks over a first radial segment of the disk is substantially steeper than the slope of the spiral tracks over a second radial segment of the disk. The head internal to the disk drive is used to read the spiral tracks to generate a read signal. The read signal is processed to detect the sync marks in the spiral tracks to synchronize a servo write clock. The read signal is also processed to demodulate the high frequency signal in the spiral tracks to generate a position error signal used to maintain the head internal to the disk drive along a first target circular path. The head internal to the disk drive and the servo write clock are used to write product servo sectors to the disk, wherein the steeper slope of the spiral tracks over the first radial segment causes a track density of the data tracks to be lower over the first radial segment compared to the track density of the data tracks over the second radial segment. 
   In one embodiment, the first radial segment includes an outer diameter band of the data tracks and the second radial segment includes a middle diameter band of the data tracks. In another embodiment, the first radial segment includes an inner diameter band of data tracks and the second radial segment includes a middle diameter band of data tracks. 
   In yet another embodiment, the head internal to the disk drive is used to write the spiral tracks to the disk, and the actuator arm is rotated about a pivot to move the head radially across the disk while writing the spiral tracks. The actuator arm is moved at a first angular velocity while writing the spiral tracks over the first radial segment and moved at a second angular velocity while writing the spiral tracks over the second radial segment, wherein the first angular velocity is substantially greater than the second angular velocity. In one embodiment, an external spiral track writer is used to write the spiral tracks to the disk. 
   In still another embodiment, the step of demodulating the high frequency signal in the spiral tracks comprises the step of opening a demodulation window using the servo write clock, further comprising the step of shifting the demodulation window in time relative to the servo write clock to seek the head from the first target circular path to a second target circular path. 
   In yet another embodiment, the step of demodulating the high frequency signal in the spiral tracks comprises the step of demodulating the high frequency signal into a plurality of servo burst signals. In one embodiment, the step of generating the position error signal comprises the step of computing a difference between the servo burst signals. In another embodiment, the step of shifting the demodulation window causes the plurality of servo burst signals to shift a corresponding amount to generate a non-zero position error signal. 
   In yet another embodiment, the step of demodulating the high frequency signal in the spiral tracks comprises the step of integrating the read signal to generate a ramp signal. In one embodiment, the position error signal is generated relative to a target sync mark in a spiral track and a reference point of the ramp signal. In another embodiment, the step of shifting the demodulation window causes a corresponding shift in the target sync mark to generate a non-zero position error signal. 
   In still another embodiment, the step of demodulating the high frequency signal in the spiral tracks comprises the step of generating an envelope signal from the read signal. In one embodiment, the position error signal is generated relative to a target sync mark in a spiral track and a peak in the envelope signal. In another embodiment, the step of shifting the demodulation window causes a corresponding shift in the target sync mark to generate a non-zero position error signal. 
   The present invention may also be regarded as a disk drive comprising a disk having a plurality of spiral tracks recorded thereon, wherein each spiral track comprises a high frequency signal interrupted at a predetermined interval by a sync mark, and a slope of the spiral tracks over a first radial segment of the disk is substantially steeper than the slope of the spiral tracks over a second radial segment of the disk. The disk drive further comprises a head actuated over the disk and control circuitry for writing product servo sectors to the disk to define a plurality of data tracks. The head internal to the disk drive is used to read the spiral tracks to generate a read signal. The read signal is processed to detect the sync marks in the spiral tracks to synchronize a servo write clock. The read signal is also processed to demodulate the high frequency signal in the spiral tracks to generate a position error signal used to maintain the head internal to the disk drive along a first target circular path. The head internal to the disk drive and the servo write clock are used to write product servo sectors to the disk, wherein the steeper slope of the spiral tracks over the first radial segment causes a track density of the data tracks to be lower over the first radial segment compared to the track density of the data tracks over the second radial segment. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a prior art disk format comprising a plurality of radially spaced, concentric tracks defined by a plurality of product servo sectors. 
       FIGS. 2A and 2B  illustrate an embodiment of the present invention wherein an external spiral servo writer is used to write a plurality of spiral tracks to the disk for use in writing product servo sectors to the disk. 
       FIG. 3  illustrates an embodiment of the present invention wherein each spiral track is written over multiple revolutions of the disk. 
       FIG. 4A  shows an embodiment of the present invention wherein a servo write clock is synchronized by clocking a modulo-N counter relative to when the sync marks in the spiral tracks are detected. 
       FIG. 4B  shows an eye pattern generated by reading the spiral track, including the sync marks in the spiral track. 
       FIG. 5  illustrates writing of product servo sectors using a servo write clock generated from reading the spiral tracks. 
       FIGS. 6A–6B  illustrate how in one embodiment the control circuitry for demodulating the servo bursts in product servo sectors is also used to demodulate the high frequency signal in the spiral tracks as servo bursts to generate the PES for tracking. 
       FIGS. 7A–7B  shows an embodiment wherein the control circuitry of  FIGS. 6A–6B  is modified so that the servo write clock samples the read signal over the entire eye pattern (including the servo bursts) in order to maintain synchronization. 
       FIGS. 8A–8B  show an embodiment of the present invention for calibrating the correlation between the PES generated from reading the spiral tracks and off-track displacement. 
       FIGS. 9A–9C  illustrate a seek operation to a next servo track by shifting the demodulation window an integer number of sync mark intervals to generate a non-zero PES signal. 
       FIG. 10A  illustrates an embodiment of the present invention wherein the high frequency signal in the spiral tracks is demodulated by integrating the read signal over the demodulation window and generating the PES relative to a target sync mark and a reference point on the resulting ramp signal. 
       FIG. 10B  illustrates initiating a seek operation by shifting the demodulation window an integer number of sync marks to generate a non-zero PES. 
       FIG. 11A  illustrates an embodiment of the present invention wherein the high frequency signal in the spiral tracks is demodulated by envelope detecting the read signal over the demodulation window and generating the PES relative to a target sync mark and the peak in the envelope signal. 
       FIG. 11B  illustrates initiating a seek operation by shifting the demodulation window an integer number of sync marks to generate a non-zero PES. 
       FIG. 12A  illustrates how in an embodiment of the present invention increasing the slope of the spiral tracks results in a corresponding decrease in the track density. 
       FIG. 12B  shows an embodiment of the present invention wherein the algorithm for generating the PES may be modified if the slope of the spiral tracks increases beyond a predetermined threshold. 
       FIG. 12C  shows an embodiment of the present invention wherein the spiral tracks are written with a steeper slope at the outer and inner diameter data tracks as compared to the middle diameter data tracks in order to decrease the track density over the outer diameter and inner diameter data tracks. 
       FIG. 12D  shows an embodiment wherein the slope of the spiral tracks gradually increases toward the outer diameter data tracks and the inner diameter data tracks. 
       FIG. 13  shows an embodiment of the present invention wherein an external product servo writer is used to process the spiral tracks in order to write the product servo sectors to the disk. 
       FIG. 14  shows an embodiment of the present invention wherein an external spiral servo writer is used to write the spiral tracks, and a plurality of external product servo writers write the product servo sectors for the HDAs output by the external spiral servo writer. 
       FIG. 15  shows an embodiment of the present invention wherein an external spiral servo writer is used to write the spiral tracks, and the control circuitry within each product disk drive is used to write the product servo sectors. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIGS. 2A and 2B  show an embodiment of the present invention wherein a plurality of spiral tracks  20   0 – 20   N  are written to a disk  18  of a disk drive  16  using an external spiral servo writer  36  (in an alternative embodiment, the spiral tracks are stamped onto the disk using magnetic printing techniques). The disk drive  16  comprises control circuitry  34  and a head disk assembly (HDA)  32  comprising the disk  18 , an actuator arm  26 , a head  28  coupled to a distal end of the actuator arm  26 , and a voice coil motor  30  for rotating the actuator arm  26  about a pivot to position the head  28  radially over the disk  18 . A write clock is synchronized to the rotation of the disk  18 , and the plurality of spiral tracks  20   0 – 20   N  are written on the disk  18  at a predetermined circular location determined from the write clock. Each spiral track  20   i  comprises a high frequency signal  22  ( FIG. 4B ) interrupted at a predetermined interval by a sync mark  24 . 
   The spiral tracks  20   0 – 20   N  are written (or stamped) such that over a first radial segment of the disk  4 , a slope of the spiral tracks  20   0 – 20   N  is steeper than a second radial segment of the disk  4 . As described in greater detail below, when writing the product servo sectors the varying slope of the spiral tracks  20   0 – 20   N  causes a track density of the resulting data tracks to be lower over the first radial segment of the disk compared to the track density of the data tracks over the second radial segment of the disk. For example, the slope of the spiral tracks  20   0 – 20   N  is increased toward the outer diameter data tracks in order to decrease the track density, thereby reducing servo errors due to the increase in linear velocity, windage, and disk flutter affects. 
   The external spiral servo writer  36  comprises a head positioner  38  for actuating a head positioning pin  40  using sensitive positioning circuitry, such as a laser interferometer. While the head positioner  38  moves the head  28  at a predetermined velocity over the stroke of the actuator arm  26 , pattern circuitry  42  generates the data sequence written to the disk  18  for a spiral track  20   i . In one embodiment, the external spiral servo writer  36  increases the slope of the spiral tracks  20   0 – 20   N  over the first radial segment (e.g., near the outer diameter of the disk  4 ) by increasing the angular velocity of the actuator arm  26  while writing the spiral tracks  20   0 – 20   N  over the first radial segment. 
   The external spiral servo writer  36  inserts a clock head  46  into the HDA  32  for writing a clock track  44  ( FIG. 2B ) at an outer diameter of the disk  18 . The clock head  46  then reads the clock track  44  to generate a clock signal  48  processed by timing recovery circuitry  50  to synchronize the write clock  51  for writing the spiral tracks  20   0 – 20   N  to the disk  18 . The timing recovery circuitry  50  enables the pattern circuitry  42  at the appropriate time relative to the write clock  51  so that the spiral tracks  20   0 – 20   N  are written at the appropriate circular location. The timing recovery circuitry  50  also enables the pattern circuitry  42  relative to the write clock  51  to write the sync marks  24  ( FIG. 4B ) within the spiral tracks  20   0 – 20   N  at the same circular location from the outer diameter to the inner diameter of the disk  18 . As described below with reference to  FIG. 5 , the constant interval between sync marks  24  (independent of the radial location of the head  28 ) enables the servo write clock to maintain synchronization while writing the product servo sectors to the disk. 
   In the embodiment of  FIG. 2B , each spiral track  20   i  is written over a partial revolution of the disk  18 . In an alternative embodiment, each spiral track  20   i  is written over one or more revolutions of the disk  18 .  FIG. 3  shows an embodiment wherein each spiral track  20   i  is written over multiple revolutions of the disk  18 . In the embodiment of  FIG. 2A , the entire disk drive  16  is shown as being inserted into the external spiral servo writer  36 . In an alternative embodiment, only the HDA  32  is inserted into the external spiral servo writer  36 . In yet another embodiment, an external media writer is used to write the spiral tracks  20   0 – 20   N  to a number of disks  18 , and one or more of the disks  18  are then inserted into an HDA  32 . 
   Referring again to the embodiment of  FIG. 2A , after the external spiral servo writer  36  writes the spiral tracks  20   0 – 20   N  to the disk  18 , the head positioning pin  40  and clock head  46  are removed from the HDA  32  and the product servo sectors are written to the disk  18  during a “fill operation”. In one embodiment, the control circuitry  34  within the disk drive  16  is used to process the spiral tracks  20   0 – 20   N  in order to write the product servo sectors to the disk  18 . In an alternative embodiment described below with reference to  FIGS. 13 and 14 , an external product servo writer is used to process the spiral tracks  20   0 – 20   N  in order to write the product servo sectors to the disk  18 . 
     FIG. 4B  illustrates an “eye” pattern in the read signal that is generated when the head  28  passes over a spiral track  20 . The read signal representing the spiral track comprises high frequency transitions  22  interrupted by sync marks  24 . When the head  28  moves in the radial direction, the eye pattern will shift (left or right) while the sync marks  24  remain fixed. The shift in the eye pattern (detected from the high frequency signal  22 ) relative to the sync marks  24  provides the off-track information (position error signal or PES) for servoing the head  28 . 
     FIG. 4A  shows an embodiment of the present invention wherein a saw-tooth waveform  52  is generated by clocking a modulo-N counter with the servo write clock, wherein the frequency of the servo write clock is adjusted until the sync marks  24  in the spiral tracks  20   0 – 20   N  are detected at a target modulo-N count value. The servo write clock may be generated using any suitable circuitry, such as a phase locked loop (PLL). As each sync mark  24  in the spiral tracks  20   0 – 20   N  is detected, the value of the modulo-N counter represents the phase error for adjusting the PLL. In one embodiment, the PLL is updated when any one of the sync marks  24  within the eye pattern is detected. In this manner the multiple sync marks  24  in each eye pattern (each spiral track crossing) provides redundancy so that the PLL is still updated if one or more of the sync marks  24  are missed due to noise in the read signal. Once the sync marks  24  are detected at the target modulo-N counter values, the servo write clock is coarsely locked to the desired frequency for writing the product servo sectors to the disk  18 . 
   The sync marks  24  in the spiral tracks  20   0 – 20   N  may comprise any suitable pattern, and in one embodiment, a pattern that is substantially shorter than the sync mark  10  in the conventional product servo sectors  2  of  FIG. 1 . A shorter sync mark  24  allows the spiral tracks  20   0 – 20   N  to be written to the disk  18  using a steeper slope (by moving the head faster from the outer diameter to the inner diameter of the disk  18 ), which reduces the time required to write each spiral track  20   0 – 20   N . 
   In one embodiment, the servo write clock is further synchronized by generating a timing recovery measurement from the high frequency signal  22  between the sync marks  24  in the spiral tracks  20   0 – 20   N . Synchronizing the servo write clock to the high frequency signal  22  helps maintain proper radial alignment (phase coherency) of the Gray coded track addresses in the product servo sectors. The timing recovery measurement may be generated in any suitable manner. In one embodiment, the servo write clock is used to sample the high frequency signal  22  and the signal sample values are processed to generate the timing recovery measurement. The timing recovery measurement adjusts the phase of the servo write clock (PLL) so that the high frequency signal  22  is sampled synchronously. In this manner, the sync marks  24  provide a coarse timing recovery measurement and the high frequency signal  22  provides a fine timing recovery measurement for maintaining synchronization of the servo write clock. 
     FIG. 5  illustrates how the product servo sectors  56   0 – 56   N  are written to the disk  18  after synchronizing the servo write clock in response to the high frequency signal  22  and the sync marks  24  in the spiral tracks  20   0 – 20   N . In the embodiment of  FIG. 5 , the dashed lines represent the centerlines of the data tracks. The sync marks in the spiral tracks  20   0 – 20   N  are written so that there is a shift of two sync marks  24  in the eye pattern ( FIG. 4B ) between data tracks. In an alternative embodiment, the sync marks  24  in the spiral tracks  20   0 – 20   N  are written so that there is a shift of N sync marks in the eye pattern between data tracks. In the embodiment of  FIG. 5 , the data tracks are narrower than the spiral tracks  20 , however, in an alternative embodiment the data tracks are wider than or proximate the width of the spiral tracks  20 . 
   The PES for maintaining the head  28  along a servo track (tracking) may be generated from the spiral tracks  20   0 – 20   N  in any suitable manner. Once the head  28  is tracking on a servo track, the product servo sectors  56   0 – 56   N  are written to the disk using the servo write clock. Write circuitry is enabled when the modulo-N counter reaches a predetermined value, wherein the servo write clock clocks the write circuitry to write the product servo sector  56  to the disk. The spiral tracks  20   0 – 20   N  on the disk are processed in an interleaved manner to account for the product servo sectors  56   0 – 56   N  overwriting a spiral track. For example, when writing the product servo sectors  56   1  to the disk, spiral track  20   2  is processed initially to generate the PES tracking error and the timing recovery measurement. When the product servo sectors  56   1  begin to overwrite spiral track  20   2 , spiral track  20   3  is processed to generate the PES tracking error and the timing recovery measurement. In the embodiment of  FIG. 5 , the spiral tracks  20  are written as pairs to facilitate the interleave processing; however, the spiral tracks may be written using any suitable spacing (e.g., equal spacing) while still implementing the interleaving aspect. 
     FIGS. 6A–6B  illustrate an embodiment of the present invention wherein control circuitry for demodulating the servo bursts in prior art product servo sectors is also used to demodulate the high frequency signal in the spiral tracks  20  as servo bursts to generate the PES for tracking.  FIG. 6A  shows the eye pattern of  FIG. 4B , which is processed, similar to the prior art product servo sector shown in  FIG. 1 . The servo write clock is used to open a demodulation window as the head approaches a spiral track. The first segment  22 A of the high frequency signal in the eye pattern of  FIG. 6A  is processed as a preamble similar to the preamble  8  in  FIG. 1  for synchronizing to the read signal. The first sync mark  24 A in the eye pattern is processed similar to the sync mark  10  in  FIG. 1 . The following segments  22 B– 22 E of the high frequency signal in the eye pattern are demodulated as servo bursts used to generate the PES for tracking. 
     FIG. 6B  shows example control circuitry for demodulating the prior art product servo sector of  FIG. 1  as well as the eye pattern ( FIG. 6A ) of the spiral tracks  20 . The embodiment employs a read oscillator  60  and a write oscillator  62 . The read oscillator  60  generates a read clock  58  for sampling the read signal  64  during normal operation when demodulating the product servo sectors  56  and user data recorded on the disk. The write oscillator  62  generates the servo write clock  66  used to write the product servo sectors  56  to the disk during the fill operation. The write oscillator  62  is also used to sample the read signal  64  when demodulating the servo bursts from the high frequency signal  22  in the spiral tracks  20 . When the head  28  approaches a spiral track  20  as determined from the servo write clock  66 , a demodulation window is opened for demodulating the high frequency signal  22  in the spiral track  20  to generate the position error signal used for tracking. 
   In one embodiment, after opening the demodulation window the read clock  58  samples the read signal  64  when reading the first segment  22 A of the high frequency signal representing the preamble as well as the first sync mark  24 A in the eye pattern ( FIG. 6A ) of the spiral tracks  20 . The read clock  58  is selected by multiplexer  68  as the sampling clock  70  for sampling  72  the read signal  64 . A first timing recovery circuit  76  opens the demodulation window at the appropriate time as determined from the servo write clock  66 , and then processes the read signal sample values  74  to generate a timing recovery signal used to adjust the read oscillator  60  until the read clock  58  is sampling the preamble  22 A synchronously. Once locked onto the preamble  22 A, a sync detector  78  is enabled for detecting the sync mark  24 A in the eye pattern. When the sync detector  78  detects the sync mark  24 A, it activates a sync detect signal  80 . The first timing recovery circuit  76  responds to the sync detect signal  80  by configuring the multiplexer  68  over line  82  to select the servo write clock  66  as the sampling clock  70 . The first timing recovery circuit  76  enables a timer for timing an interval between the sync mark  24 A and the start of the A servo burst  22 B in the eye pattern. When the timer expires, the first timing recovery circuit  76  enables a burst demodulator  84  over line  86  for demodulating the A, B, C and D servo bursts in the eye pattern from the read signal sample values  74 . In one embodiment, the demodulation window comprises a plurality of servo burst windows (square waves) corresponding to the intervals for demodulating the A, B, C and D servo bursts. 
   In one embodiment, the burst demodulator  84  rectifies and integrates the rectified read signal sample values  74  representing the respective A, B, C and D servo bursts to generate respective servo burst signals  88  which correspond to integrating the A, B, C and D servo bursts  14  in the prior art product servo sector of  FIG. 1 . A PES generator  90  processes the servo burst signals  88  to generate a PES signal  92  used for tracking. The PES generator  90  may compare the servo burst signals  88  to generate the PES signal  92  using any suitable algorithm when demodulating the servo bursts in either the prior art product servo sectors of  FIG. 1  or the eye pattern of  FIG. 6A . In one embodiment, the PES signal  92  when reading the eye pattern of  FIG. 6A  is generated according to (A−D)/(A+D). In this embodiment, evaluating the servo bursts near the edges of the eye pattern increases the sensitivity of the PES measurement. This is because deviations in the radial location of the head  28  cause a more precipitous change in the servo burst values at the edges of the eye pattern as compared to the servo burst values near the center of the eye pattern. 
   In the embodiment of  FIG. 6B , a control signal C/S  94  configures the first timing recovery circuit  76 , the sync detector  78 , and the PES generator  90  depending on whether the control circuitry is configured for demodulating the product servo sector (prior art product servo sector of  FIG. 1 ) or the spiral tracks. The first timing recovery circuit  76  adjusts the timing between the detection of the sync mark ( 10  in  FIG. 1 and 24A  in  FIG. 6A ) and the start of the A servo burst ( 14  in  FIG. 1 and 22B  in  FIG. 6A ). The sync detector  78  adjusts the target sync pattern depending on whether the sync mark  10  in the product servo sector is being detected or the sync mark  24 A in the eye pattern of the spiral track. The PES generator  90  adjusts the algorithm for comparing the servo burst signals  88  depending on whether the servo bursts  14  in the product servo sectors are being demodulated or the servo bursts  22 B– 22 E in the eye pattern of the spiral track are being demodulated. 
   The control circuitry in the embodiment of  FIG. 6B  further comprises a second timing recovery circuit  96  for generating a timing recovery measurement that controls the write oscillator  62  for generating the servo write clock  66 . The second timing recovery circuit  96  comprises the modulo-N counter, which is synchronized to the sync marks  24  in the spiral tracks  20 . When servoing on the spiral tracks  20 , the second timing recovery circuit  96  enables a sync mark detection window over line  98  commensurate with the modulo-N counter approaching a value corresponding to the expected occurrence of a sync mark  24  in a spiral track. When a sync mark  24  is actually detected over line  80 , the second timing recovery circuit  96  generates a coarse timing recovery measurement as the difference between the expected value of the module-N counter and the actual value. When reading the high frequency signal  22  in the spiral tracks, the second timing recovery circuit  96  generates a fine timing recovery measurement using any suitable timing recovery algorithm. For example, the fine timing recovery measurement can be generated using a suitable timing gradient, a suitable trigonometric identity, or a suitable digital signal processing algorithm such as the Discrete Fourier Transform (DFT). The coarse and fine timing recovery measurements are combined and used to adjust the write oscillator  62  in order to maintain synchronization of the servo write clock  66 . 
   The servo write clock  66  is applied to write circuitry  100  used to write the product servo sectors  56  to the disk during the fill operation. The second timing recovery circuit  96  generates a control signal  102  for enabling the write circuitry  100  at the appropriate time so that the product servo sectors  56  are written at the appropriate circumferential location from the outer diameter of the disk to the inner diameter of the disk. In one embodiment, the control signal  102  enables the write circuitry  100  each time the module-N counter reaches a predetermined value so that the product servo sectors  56  form servo wedges as illustrated in  FIG. 1  and  FIG. 5 . 
   Although the first timing recovery circuit  76  and second timing recovery circuit  96  in  FIG. 6B  adjust the frequency of sampling clock  70  until the read signal  64  is sampled  72  synchronously, any suitable timing recovery technique may be employed. In an alternative embodiment, interpolated timing recovery is employed. With interpolated timing recovery the read signal  64  is sampled asynchronously and interpolated to generate the synchronous sample values  74 . 
   In an alternative embodiment shown in  FIGS. 7A and 7B , the servo write clock  66  is used to sample the read signal over the entire eye pattern (spiral track crossing). The timing recovery circuitry  96  in  FIG. 7B  opens the demodulation window at the start of the A servo burst  22 B and closes the demodulation window at the end of the D servo burst  22 E as determined from the servo write clock  66 . In one embodiment, the timing recovery circuitry  96  generates servo burst windows within the demodulation window corresponding to the intervals for demodulating the A, B, C and D servo bursts. 
     FIGS. 8A and 8B  illustrate an embodiment of the present invention for calibrating the correlation between the PES generated from demodulating the spiral tracks  20  and the off-track displacement of the head  28 . The segments  22 B– 22 E of the high frequency signal in the spiral tracks  20  are demodulated as servo bursts to generate corresponding servo burst signals A, B, C and D. A PES is generated by comparing the servo burst signals according to any suitable algorithm, such as (A−D)/(A+D). As shown in  FIG. 8A , when the head  28  is on track a predetermined relationship between the servo burst signals (e.g., A=D) generates a predetermined value for the PES (e.g., zero). The head  28  is then moved away from the center of the track until the servo burst signals reach a second predetermined relationship (e.g., B=D) as shown in  FIG. 8B . When the servo burst signals reach the second predetermined relationship, the shift in the eye pattern relative to the sync marks  24 A– 24 D is known and therefore the amount of off-track displacement is known. Measuring the PES when the servo burst signals reach the second predetermined relationship provides the correlation (assuming a linear relationship) between the PES and the amount of off-track displacement. 
     FIGS. 9A–9B  illustrate a seek operation from a current servo track to a next servo track by shifting the demodulation window an integer number of sync mark intervals to generate a non-zero PES signal for moving the head toward the next servo track. In the embodiment of  FIG. 9A , the demodulation window and corresponding intervals (windows) for the preamble  22 A and servo bursts  22 B– 22 E are shifted by one sync mark interval relative to  FIG. 8A  (i.e., there is a shift of one sync mark per servo track). After synchronizing to the preamble  22 A, sync mark  24 B is detected to enable the timer for timing the interval between the sync mark  24 B and the start of the A servo burst  22 B. The servo bursts  22 B– 22 E are then demodulated to generate a non-zero PES which causes the servo control circuitry to move the head  28  toward the next servo track.  FIG. 9B  illustrates the head  28  moving toward the next servo track and the corresponding shift in the eye pattern and change in the PES.  FIG. 9C  illustrates the end of the seek operation after the head  28  reaches the next servo track and the eye pattern has shifted such that the A servo burst  22 B equals the D servo burst  22 E resulting in a zero PES. 
   Defining the servo track width as a shift in an integer number of sync marks (one sync mark in the example of  FIGS. 9A–9C ) simplifies implementation of the seek operation. The servo demodulation window as determined from the servo write clock  66  is simply shifted by an integer number of sync mark intervals to initiate the seek operation. The demodulation window may be shifted any suitable number of sync mark intervals depending on the frequency of the sync marks  24  in the spiral tracks  20  and the desired servo track density. 
   The high frequency signal  22  in the spiral tracks  20  may be demodulated using any suitable technique to generate the PES for tracking.  FIG. 10A  shows an embodiment of the present invention wherein the high frequency signal  22  in a spiral track  20  is demodulated by integrating the read signal to generate a ramp signal  101 . The PES is generated relative to a target sync mark  24  in the spiral track  20  and a reference point of the ramp signal  101 . In the embodiment of  FIG. 10A , there are three sync marks  24 A– 24 C in each spiral track crossing (each eye pattern) and the PES is generated as the deviation of the middle sync mark  24 B from the center of the ramp signal  101 . This deviation can be computed as the difference in the amplitude of the ramp signal  101  when the middle sync mark  24 B is detected, or the difference in time between when the middle sync mark  24 B is detected and the middle of the ramp signal  101 . Also in this embodiment, the demodulation window is opened a number of sync mark intervals preceding the expected spiral track crossing (one sync mark interval in this example) and closed a number of sync mark intervals after the expected spiral track crossing (one sync mark interval in this example). In one embodiment, the ramp signal  101  is generated by integrating the high frequency signal  22  between the sync marks  24 ; that is, integration windows within the demodulation window are generated corresponding to the segments of high frequency signal  22  between each sync mark  24  (as determined from servo write clock  66 ).  FIG. 10B  illustrates a seek operation by shifting the demodulation window one sync mark interval to generate a non-zero PES which causes the head  28  to move toward the next servo track. The head  28  is moved radially so that the eye pattern shifts until sync mark  24 C is detected in the middle of the eye pattern corresponding to the middle of the ramp signal  101 . 
     FIG. 11A  illustrates yet another embodiment of the present invention wherein the high frequency signal  22  in the spiral tracks  20  is demodulated by generating an envelope signal  103  from the read signal. The PES is generated relative to a target sync mark  24  in the spiral track  20  and a peak in the envelope signal  103 . In the embodiment of  FIG. 11A , there are three sync marks  24 A– 24 C in each spiral track crossing (each eye pattern) and the PES is generated as the deviation of the middle sync mark  24 B from the peak of the envelope signal  103 . This deviation can be computed as the difference in the amplitude of the envelope signal  103  when the middle sync mark  24 B is detected, or the difference in time between when the middle sync mark  24 B is detected and the peak of the envelope signal  103 . Also in this embodiment, the demodulation window is opened a number of sync mark intervals preceding the expected spiral track crossing (one sync mark interval in this example) and closed a number of sync mark intervals after the expected spiral track crossing (one sync mark interval in this example).  FIG. 11B  illustrates a seek operation by shifting the demodulation window one sync mark interval to generate a non-zero PES which causes the head  28  to seek toward the next servo track. The head  28  is moved radially so that the eye pattern shifts until sync mark  24 C is detected in the middle of the eye pattern corresponding to the peak of the envelope signal  103 . 
     FIG. 12A  illustrates how increasing the slope of the spiral tracks  20   0 – 20   N  decreases the track density of the data tracks (dashed lines) as compared to the slope of the spiral tracks  20   0 – 20   N  and track density of the data tracks shown in  FIG. 5 . In one embodiment, the same algorithm for generating the PES (e.g., using servo burst windows as in  FIG. 6A ) is used over the length of the spiral tracks  20   0 – 20   N  even though the slope is changing over different radial segments (e.g., over the outer and/or inner radial segments). In another embodiment, if the slope of the spiral tracks  20   0 – 20   N  exceeds a predetermined threshold, the PES algorithm is adjusted to compensate for the changing characteristics of the high frequency signal  22  relative to the sync marks  24 .  FIG. 12B  shows an embodiment wherein the slope of the spiral tracks  20   0 – 20   N  has increased to the extent that adjusting the PES algorithm, for example by adjusting the servo burst windows of  FIG. 5 , may improve servo tracking performance. 
     FIG. 12C  illustrates how in one embodiment the slope of the spiral tracks  20   0 – 20   N  is increased near the outer diameter (OD) and inner diameter (ID) compared to the middle diameter (MD). This results in a lower density for the data tracks (dashed lines) at the OD and ID as compared to the density for the data tracks at the MD. In the embodiment of  FIG. 12C , the slope of the spiral tracks  20   0 – 20   N  is shown as comprising discrete segments having respective slopes over the OD, MD and ID. In an alternative embodiment shown in  FIG. 12D , the slope of the spiral tracks  20   0 – 20   N  changes gradually over the disk radius such that the track density decreases gradually toward the OD and ID. 
     FIG. 13  shows an embodiment of the present invention wherein after writing the spiral tracks  20   0 – 20   N  to the disk  18  ( FIGS. 2A–2B ), the HDA  32  is inserted into an external product servo writer  104  comprising suitable circuitry for reading and processing the spiral tracks  20   0 – 20   N  in order to write the product servo sectors  56   0 – 56   N  to the disk  18 . The external product servo writer  104  comprises a read/write channel  106  for interfacing with a preamp  108  in the HDA  32 . The preamp  108  amplifies a read signal emanating from the head  28  over line  110  to generate an amplified read signal applied to the read/write channel  106  over line  112 . The read/write channel  106  comprises circuitry for generating servo burst signals  88  applied to a servo controller  114 . The servo controller  114  processes the servo burst signals  88  to generate the PES. The PES is processed to generate a VCM control signal applied to the VCM  30  over line  116  in order to maintain the head  28  along a circular path while writing the product servo sectors  56   0 – 56   N . The servo controller  114  also generates a spindle motor control signal applied to a spindle motor  118  over line  120  to maintain the disk  18  at a desired angular velocity. Control circuitry  122  processes information received from the read/write channel  106  over line  124  associated with the spiral tracks  20   0 – 20   N  (e.g., timing information) and provides the product servo sector data to the read/write channel  106  at the appropriate time. The product servo sector data is provided to the preamp  108 , which modulates a current in the head  28  in order to write the product servo sectors  56   0 – 56   N  to the disk  18 . The control circuitry  122  also transmits control information over line  126  to the servo controller  114  such as the target servo track to be written. After writing the product servo sectors  56   0 – 56   N  to the disk  18 , the HDA  32  is removed from the external product servo writer  104  and a printed circuit board assembly (PCBA) comprising the control circuitry  34  ( FIG. 2A ) is mounted to the HDA  32 . 
   In one embodiment, the external product servo writer  104  of  FIG. 13  interfaces with the HDA  32  over the same connections as the control circuitry  34  to minimize the modifications needed to facilitate the external product servo writer  104 . The external product servo writer  104  is less expensive than a conventional servo writer because it does not require a clean room or sophisticated head positioning mechanics. In an embodiment shown in  FIG. 14 , a plurality of external product servo writers  104   0 – 104   N  process the HDAs  32   i – 32   i+N  output by an external spiral servo writer  36  in order to write the product servo sectors less expensively and more efficiently than a conventional servo writer. In an alternative embodiment shown in  FIG. 15 , an external spiral servo writer  36  is used to write the spiral tracks, and the control circuitry  34  within each product disk drive  16   i – 16   i+N  is used to write the product servo sectors.