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Transition analysis of magnetic recording heads using FDTD
Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
Transition analysis of magnetic recording heads using FDTD Shinji Tanabe* Mitsubishi Electric Corp., Advanced Technology R&D Center, 8-1-1 Tsukaguchi-Honmachi, Amagasaki, Hyogo 661-8661, Japan
Abstract Transition waveforms of a magnetic recording head have been analyzed using finite difference time domain (FDTD). The distributed inductance and capacitance of the head effect the rising time of the magnetic fields in the recording process. FDTD electromagnetic analysis is easy to combine with SPICE circuit analysis. Using this combined program, a transition analysis of the recording process including a write amplifier has become possible. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic recording; FDTD; Time domain analysis; Spice; Waveforms
1. Introduction
2. Time domain analysis and FDTD method
There are many reports about the magnetic field distribution analysis from a recording head in frequency domain. However, there are few reports about the transition analysis of the recording fields in time domain. The high-density recording means the increase of the data transfer rate. The analysis of the waveforms in time domain has become important in the high-frequency recording. The transient waveforms of the magnetic fields from a write head have been calculated by an finite-difference time-domain (FDTD), method. The FDTD program has been linked with a circuit simulation program, SPICE, to consider other circuits, such as a recording amplifier, effects to the transition.
2.1. Time domain analysis The numerical analysis of electromagnetic fields is separated into two types: frequency domain analysis and time domain analysis. Finite element method (FEM), and method of moments (MoM), are the analysis methods in frequency domain. FDTD is an analysis method in time domain. In frequency domain analysis, a boundary condition problem is solved using a matrix equation and the static state, that is, the energy minimum state is obtained. In order to obtain the transient state, time domain analysis is needed.
2.2. FDTD method *Fax: +81-6-6497-7288. E-mail address: [email protected] (S. Tanabe).
FDTD is an analysis method based on the two rotational equations: Faraday-Maxell’s law and
0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 3 9 4 - 8
389
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
Ampere’s law, of Maxwell’s equations @D ¼ rot H j; @t
ð1Þ
@B ¼ rot E jm ; ð2Þ @t where D, H, j, B, E, and jm are the electric flux density (c/m2), the magnetic field (A/m) the electric current density (A/m2), the magnetic flux density (Wb/m2), the electric field (V/m) and the magnetic current density (V/m2), respectively. From Eqs. (1) and (2), for example, the time differential of the xcomponent magnetic fields is calculated from the spatial differential of the electric fields and the material constants. @Hx 1 @Ey @Ez ¼ r0 Hx : ð3Þ m @z @t @y Fig. 1. Yee unit cell and the ‘‘leap frog’’ algorithm.
From the difference equation for Eq. (3), the xcomponent magnetic field at the point ði; j; kÞ in space and at ðn þ 12ÞDt time step is shown as following: 0
1 0 1 r0i;j;k Dt Dt B1 2m C B m C C i;j;k C i;j;k nþ1=2 B n1=2 B Hxj Hxji;j;k ¼ B þ C B C i;j;k r0i;j;k DtA @ r0i;j;k DtA @ 1þ 1þ 2mi;j;k 2mi;j;k n Eyji;j;kþ1=2 Eyjni;j;k1=2 Ezjni;jþ1=2;k Ezjni;j1=2;k ; Dz Dy ð4Þ where Dy and Dz is the length of the Yee unit cell (m)[1], r0 is an equivalent magnetic resistivity (O/ m) and m is the permeability (H/m). Using the Yee space lattice and the ‘‘leap frog’’ algorithm [1] (Fig. 1), magnetic fields at any point ði; j; kÞ and at any time ððn þ 12ÞDtÞ will be obtained from the past (nDt and ðn 12ÞDt) electric and magnetic field values.
3. Analysis model Fig. 2 shows the schematic cross section and Tables 1 and 2 shows the specifications of the coil and magnetic films of the write head using the FDTD calculations. The coil is one turn. In high
Fig. 2. Cross-section view of the head model.
Table 1 Coil specifications Coil Number of winding Thickness (mm) Conductivity (S/m) Dielectric constant of insulator Insulator thickness (mm)
1 1.0 5.8 107 4.8 1.0
Table 2 Magnetic film specifications Magnetic film Thickness (mm) Conductivity (S/m) Relative permeability
1.0 105 300
390
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
frequencies, not only the permeability but also the conductivity of the magnetic films becomes an important factor to decide the head efficiency. Fig. 3 shows the FDTD mesh for the calculation. The total number of the cells is 2,64,364. As the electromagnetic fields in a finite region O are solved by FDTD, the analysis region needs to be surrounded by absorbed boundaries to prevent the reflections of the radiated electromagnetic fields or the appearance of the standing waves. 2nd order Mur Finite-Difference Scheme [2] has
Fig. 3. FDTD mesh for calculation.
been used as the absorbed boundary condition. The time step for the calculation is 0.67 1015 (s).
4. Results and discussion The magnetic field response for 0.1 ns rising time write currents has been analyzed. Fig. 4 shows the magnetic field contours at 20th (1.34 1014 (s)), 80th (5.12 1014 (s)) and (5.12 1013 (s)) time steps. Fig. 5 shows the magnetic field H vectors at 80th (5.12 1014 (s)) time steps. The vectors show the magnetic fields H not the magnetic flux density B, therefore, the length of the arrow is short in the magnetic films. Fig. 6 shows an FDTD analysis result about the transition of the magnetic fields inside the head gap. Though the magneto-motive currents rise in 0.1 ns, the rising time for the magnetic field is more than double. The large head inductance and capacitance cause this slow rising. For the high-
Fig. 4. Magnetic field contours.
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
frequency recording, much smaller high efficiencyrecording head is required [3]. FDTD is using the ‘‘leap frog’’ algorithm. The algorithm does not need the matrix calculation like frequency domain methods, such as, FEM and MoM. This means that FDTD calculation will be done in reasonable small memory size. Above model is using about 2,60,000 elements, however, the required memory size was less than 100 MB. While, the disadvantage of FDTD is in the computation time, particularly at lower frequencies. FDTD method is a differential method including time. Therefore, the aspect ratio of Dx; Dy; Dz and cDt should be almost one, where c is the speed of light in free space. The size of the space lattice will be decided from the gap length in above model. 106 time steps were needed to get the
Fig. 5. Magnetic field vectors.
Fig. 6. Magnetic field response (0.1 ns rising time).
391
0.5 ns response. The CPU time was about 5 days/ case using 400 MHz CPU.
5. Linked program of FDTD and spice In order to obtain much faster rising of the recording fields, the optimum design of the head and magneto-motive circuit is needed. In order to analyze the magnetic head and the circuit simultaneously, a linked program of FDTD and SPICE is useful. The distributed inductance and capacitance of the recording head should be considered by FDTD and the lumped circuits including active non-linear elements, such as amplifier IC, should be considered by a circuit analysis program like SPICE. SPICE is a circuit analysis program developed at UC Berkeley in 1973. In the program, the ICs are broke down into transistors, diodes and other elements. For each element, each specific model has been prepared and the voltage-current characteristics are calculated in time domain. As shown in Fig. 7, the voltages obtained by SPICE and the magnetic fields obtained by FDTD are exchanged synchronously at each time step. Using this SPICE+FDTD combined program [4,5], the write field rising can be simulated with considering the recording amplifier and the transmission lines. Fig. 8 is an example of the analysis using the SPICE+FDTD program. The inductor, transmission lines and the ground planes are analyzed by FDTD and the capacitor and the FET transistor are considered by SPICE. The total recording system with the recording head, transmission lines and an amplifier can be designed optimally by this method.
Fig. 7. SPICE+FDTD program.
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S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
6. Conclusions The transition responses in recording process have been analyzed by FDTD, which is a time domain electromagnetic field analysis method. Even though the driver voltage rises in 0.1 ns, it takes more than double to rise the recording magnetic field in present specification head. In order to rise the recording field more rapidly, much smaller heads and optimized amplifier are needed. Designing the recording system, developed SPICE+FDTD program becomes a useful tool.
References [1] K.S. Yee, IEEE Trans. Antenna Propag. 14 (1966) 302. [2] G. Mur, IEEE Trans. EMC 23 (1981) 377. [3] S. Tanabe, Technical Report of IEICE, MR99-20, 1999, p. 21. [4] A. Taflove, Computation Electromagnetics, Arctech House Inc., 1995. [5] G. Kobidze, A. Nishizawa, S. Tanabe, IEEE international Symposium on EMC, 2000, p. 349. Fig. 8. Inductance analysis, using a SPICE+FDTD.
Transition analysis of magnetic recording heads using FDTD Shinji Tanabe* Mitsubishi Electric Corp., Advanced Technology R&D Center, 8-1-1 Tsukaguchi-Honmachi, Amagasaki, Hyogo 661-8661, Japan
Abstract Transition waveforms of a magnetic recording head have been analyzed using finite difference time domain (FDTD). The distributed inductance and capacitance of the head effect the rising time of the magnetic fields in the recording process. FDTD electromagnetic analysis is easy to combine with SPICE circuit analysis. Using this combined program, a transition analysis of the recording process including a write amplifier has become possible. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic recording; FDTD; Time domain analysis; Spice; Waveforms
1. Introduction
2. Time domain analysis and FDTD method
There are many reports about the magnetic field distribution analysis from a recording head in frequency domain. However, there are few reports about the transition analysis of the recording fields in time domain. The high-density recording means the increase of the data transfer rate. The analysis of the waveforms in time domain has become important in the high-frequency recording. The transient waveforms of the magnetic fields from a write head have been calculated by an finite-difference time-domain (FDTD), method. The FDTD program has been linked with a circuit simulation program, SPICE, to consider other circuits, such as a recording amplifier, effects to the transition.
2.1. Time domain analysis The numerical analysis of electromagnetic fields is separated into two types: frequency domain analysis and time domain analysis. Finite element method (FEM), and method of moments (MoM), are the analysis methods in frequency domain. FDTD is an analysis method in time domain. In frequency domain analysis, a boundary condition problem is solved using a matrix equation and the static state, that is, the energy minimum state is obtained. In order to obtain the transient state, time domain analysis is needed.
2.2. FDTD method *Fax: +81-6-6497-7288. E-mail address: [email protected] (S. Tanabe).
FDTD is an analysis method based on the two rotational equations: Faraday-Maxell’s law and
0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 3 9 4 - 8
389
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
Ampere’s law, of Maxwell’s equations @D ¼ rot H j; @t
ð1Þ
@B ¼ rot E jm ; ð2Þ @t where D, H, j, B, E, and jm are the electric flux density (c/m2), the magnetic field (A/m) the electric current density (A/m2), the magnetic flux density (Wb/m2), the electric field (V/m) and the magnetic current density (V/m2), respectively. From Eqs. (1) and (2), for example, the time differential of the xcomponent magnetic fields is calculated from the spatial differential of the electric fields and the material constants. @Hx 1 @Ey @Ez ¼ r0 Hx : ð3Þ m @z @t @y Fig. 1. Yee unit cell and the ‘‘leap frog’’ algorithm.
From the difference equation for Eq. (3), the xcomponent magnetic field at the point ði; j; kÞ in space and at ðn þ 12ÞDt time step is shown as following: 0
1 0 1 r0i;j;k Dt Dt B1 2m C B m C C i;j;k C i;j;k nþ1=2 B n1=2 B Hxj Hxji;j;k ¼ B þ C B C i;j;k r0i;j;k DtA @ r0i;j;k DtA @ 1þ 1þ 2mi;j;k 2mi;j;k n Eyji;j;kþ1=2 Eyjni;j;k1=2 Ezjni;jþ1=2;k Ezjni;j1=2;k ; Dz Dy ð4Þ where Dy and Dz is the length of the Yee unit cell (m)[1], r0 is an equivalent magnetic resistivity (O/ m) and m is the permeability (H/m). Using the Yee space lattice and the ‘‘leap frog’’ algorithm [1] (Fig. 1), magnetic fields at any point ði; j; kÞ and at any time ððn þ 12ÞDtÞ will be obtained from the past (nDt and ðn 12ÞDt) electric and magnetic field values.
3. Analysis model Fig. 2 shows the schematic cross section and Tables 1 and 2 shows the specifications of the coil and magnetic films of the write head using the FDTD calculations. The coil is one turn. In high
Fig. 2. Cross-section view of the head model.
Table 1 Coil specifications Coil Number of winding Thickness (mm) Conductivity (S/m) Dielectric constant of insulator Insulator thickness (mm)
1 1.0 5.8 107 4.8 1.0
Table 2 Magnetic film specifications Magnetic film Thickness (mm) Conductivity (S/m) Relative permeability
1.0 105 300
390
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
frequencies, not only the permeability but also the conductivity of the magnetic films becomes an important factor to decide the head efficiency. Fig. 3 shows the FDTD mesh for the calculation. The total number of the cells is 2,64,364. As the electromagnetic fields in a finite region O are solved by FDTD, the analysis region needs to be surrounded by absorbed boundaries to prevent the reflections of the radiated electromagnetic fields or the appearance of the standing waves. 2nd order Mur Finite-Difference Scheme [2] has
Fig. 3. FDTD mesh for calculation.
been used as the absorbed boundary condition. The time step for the calculation is 0.67 1015 (s).
4. Results and discussion The magnetic field response for 0.1 ns rising time write currents has been analyzed. Fig. 4 shows the magnetic field contours at 20th (1.34 1014 (s)), 80th (5.12 1014 (s)) and (5.12 1013 (s)) time steps. Fig. 5 shows the magnetic field H vectors at 80th (5.12 1014 (s)) time steps. The vectors show the magnetic fields H not the magnetic flux density B, therefore, the length of the arrow is short in the magnetic films. Fig. 6 shows an FDTD analysis result about the transition of the magnetic fields inside the head gap. Though the magneto-motive currents rise in 0.1 ns, the rising time for the magnetic field is more than double. The large head inductance and capacitance cause this slow rising. For the high-
Fig. 4. Magnetic field contours.
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
frequency recording, much smaller high efficiencyrecording head is required [3]. FDTD is using the ‘‘leap frog’’ algorithm. The algorithm does not need the matrix calculation like frequency domain methods, such as, FEM and MoM. This means that FDTD calculation will be done in reasonable small memory size. Above model is using about 2,60,000 elements, however, the required memory size was less than 100 MB. While, the disadvantage of FDTD is in the computation time, particularly at lower frequencies. FDTD method is a differential method including time. Therefore, the aspect ratio of Dx; Dy; Dz and cDt should be almost one, where c is the speed of light in free space. The size of the space lattice will be decided from the gap length in above model. 106 time steps were needed to get the
Fig. 5. Magnetic field vectors.
Fig. 6. Magnetic field response (0.1 ns rising time).
391
0.5 ns response. The CPU time was about 5 days/ case using 400 MHz CPU.
5. Linked program of FDTD and spice In order to obtain much faster rising of the recording fields, the optimum design of the head and magneto-motive circuit is needed. In order to analyze the magnetic head and the circuit simultaneously, a linked program of FDTD and SPICE is useful. The distributed inductance and capacitance of the recording head should be considered by FDTD and the lumped circuits including active non-linear elements, such as amplifier IC, should be considered by a circuit analysis program like SPICE. SPICE is a circuit analysis program developed at UC Berkeley in 1973. In the program, the ICs are broke down into transistors, diodes and other elements. For each element, each specific model has been prepared and the voltage-current characteristics are calculated in time domain. As shown in Fig. 7, the voltages obtained by SPICE and the magnetic fields obtained by FDTD are exchanged synchronously at each time step. Using this SPICE+FDTD combined program [4,5], the write field rising can be simulated with considering the recording amplifier and the transmission lines. Fig. 8 is an example of the analysis using the SPICE+FDTD program. The inductor, transmission lines and the ground planes are analyzed by FDTD and the capacitor and the FET transistor are considered by SPICE. The total recording system with the recording head, transmission lines and an amplifier can be designed optimally by this method.
Fig. 7. SPICE+FDTD program.
392
S. Tanabe / Journal of Magnetism and Magnetic Materials 235 (2001) 388–392
6. Conclusions The transition responses in recording process have been analyzed by FDTD, which is a time domain electromagnetic field analysis method. Even though the driver voltage rises in 0.1 ns, it takes more than double to rise the recording magnetic field in present specification head. In order to rise the recording field more rapidly, much smaller heads and optimized amplifier are needed. Designing the recording system, developed SPICE+FDTD program becomes a useful tool.
References [1] K.S. Yee, IEEE Trans. Antenna Propag. 14 (1966) 302. [2] G. Mur, IEEE Trans. EMC 23 (1981) 377. [3] S. Tanabe, Technical Report of IEICE, MR99-20, 1999, p. 21. [4] A. Taflove, Computation Electromagnetics, Arctech House Inc., 1995. [5] G. Kobidze, A. Nishizawa, S. Tanabe, IEEE international Symposium on EMC, 2000, p. 349. Fig. 8. Inductance analysis, using a SPICE+FDTD.