Read Back Signals in Magnetic Recording - Research Group Fidler

z
Analytical Calculations
Figure 3.9: a) Application of Ampere’s Law on the dashed path, b) application of Gauss’s
Law on the dashed box.
In addition we use Gauss’ Law for a box with infinitesimal small height dz over the sensing
layer:
x
a) g g
b)
−μ ⋅μ ⋅H ( z) ⋅ t+ 2 ⋅μ ⋅H ( z) ⋅ dz+μ ⋅μ ⋅ H ( z+ dz) ⋅ t = 0.
(3.25)
r 0 sig 0 g r 0 sig
Here μ r is the relative permeability of the sensing layer. The last equation is equivalent to
1 dH sig
Hg( z) =− ⋅μr ⋅t⋅ (3.26)
2 dz
Combining (3.24) and (3.26) gives a differential equation.
2
dHsig
2
1
Hsig ( z) = ⋅μr⋅g⋅t⋅ (3.27)
2 dz
Assuming the boundary conditions
ABS
H (0) = H and H ( h)
= 0
(3.28)
sig sig sig
leads to the solution
⎛h−z⎞ sinh ⎜ ⎟
λ
Hsig ( z) = Hsig⋅
⎝ ⎠
with λ=
⎛h⎞ sinh ⎜ ⎟
⎝λ⎠ ABS r
μ ⋅g⋅t . (3.29)
2
Here λ is the flux propagation length. Now the effective field can be calculated under the
terms of (3.22):
Hsig
t
Hg Hg
Hg
dz
z
x
Hsig
t
dz
g g
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