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Increased Productivity Example #4
Digitized Signal from Magnetic Recording
- Magnetic recording of transitions written onto
a computer disc drive may produce an isolated pulse as shown
below. This pulse comes from a disc drive's read/write channel. Each
transition will cause such a signal to occur.
-
-
Figure 2.5.1 An isolated Readback Pulse
from a disc drive
- The signal's shape is very important to the
electrical engineering development groups of disc drives. A readback
pulse should be symmetric and have a relatively fast rise time (i.e.
steep slope) for improved peak detection capability. A math model for
the pulse can help gain insight into what electronic
sub-system/components are causing the pulse to be asymmetric or have a
slow rise time.
- The longitudinal magnetic force was assumed
the main contributing factor in determining a readback pulse shape,
before the early 1980's. This force component was modeled by a series
of three Lorentz functions. These functions have varying independent
parameters that are dependent upon the drive's Thin-Film-Head (TFH)
composition, size and shape. The value for these parameters was helpful
in understanding a design and manufacturing flaw.
- A Lorentz function has represented/modeled an
isolated readback pulse for some time. The basic Lorentz function is
defined as y =
 . The isolated pulse model is a composite
of three Lorentz functions as stated here:
-
- where
- vi =
Amplitude of a Lorentz pulse;
pw_50i = Lorentz pulse width, measured
at 50% height of vi; and,
ti = Origin of the ith Lorentz.
- In the early 1980s, this model was found to be
inadequate when Thin Film Heads were starting to be used in disc
drives. An examination of the math model versus actual data plots
showed that the 1970s model was no longer sufficient. The longitudinal
force coupled with the increased vertical force were used to provide an
excellent model for TFH readback pulses in the mid 1980s as shown in
the following math model, signal2:
-
- where
- vi =
Amplitude of a longitudinal magnetic force;
vci = Amplitude of vertical force
component;
pw_50i = Lorentz pulse width, measured
at 50% height of vi; and,
ti = Origin of the ith Lorentz
function.
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Parameter Estimation Problem
- Find the three Lorentz parameter set (vi,
vci, pw_50i and ti)
values necessary to fit the Signal2(t) model
to a digitized isolated readback pulse. Assume a total of 512 equal
spaced points (i.e. Δt constant between points).
- Note: Our CurvFit
application will solve this curve fit problem with a Lorentz series
or a 'Modified' Lorentz series.
Increased Productivity Example #4
Source Code:
-
Problem Curvefit
common v(3), vc(3), pw_50(3), time0(3),
npoints, data(512), signal(512), error(512)
data v/ -.1, 1., .05/, vc/ .1, .1, .1/,
pw_50/ 50, 40, 50/
delta_t = .9765625 : npoints = 512
open( 11, file="pulse.dat", status=old)
do j = 1, npoints
read(11,*) data(j)
signal(j) = (j - npoints/2) * delta_t
end do
FIND v, vc, pw_50, time0; IN Pulse;
TO MATCH error
! 1. plot signal & data vs. time here
! 2. plot error vs. time here
end
Model Pulse
common v(3), vc(3), pw_50(3), time0(3),
npoints, data(512), signal(512), error(512)
do j = 1, npoints
sum = 0
do i = 1, 3
sum = sum + Lorentz( time(j), v(i), vc(i),
pw_50(i), time0(i))
end do
signal(j) = sum : error(j) = data(j) - signal(j)
end do
return
end
Function Lorentz( t, v_i, vc_i, pw_50_i, t_i)
x = (t - t_i) / pw_50_i : num = v_i + vc_i * x
den = 1 + x**2 : Lorentz = num / den
return
end
Increased Productivity Example #4
Other Information:
- Relating Model and Design Parameters
- Assuming the digitized data fits a math model with
quadratic convergence, how do the model parameters (M) relate to
the design dimensions? For example, this present TFH example has model
parameters vi, pw_50i,
and ti (for i = 1 to 3) while the
design parameters as shown in the following diagram are A, B, C, D,
E, & F.
- Figure 2.5.2 A TFH at flying height F above
a disc drive's media
- The governing equations may not be known for sure
but someone with an understanding of the magnetic effects on a TFH
could at least determine whether the parameters are proportional or
inversely proportional. This would help as one starts building an
understanding of what a math model might be in order to find the
optimum design parameters to produce a symmetric and "narrow"
(readback) pulse with no (or minimal) undershoots as represented in the
curve shown below
- Optimum pulse shape?
- Figure 2.5.3 An "ideal" Readback Pulse from a disc
drive
- Through acquisition of many digitized pulses with
varying pulse model parameters will eventually provide the necessary
design parameters for an optimum pulse. This would require many
man-hours of time. Another option would be to do Pulse Slimming
via a Matched
Filter as Memorex Corp. did in the 1980s.
- This Magnetic Recording problem is another
increased productivity example do to using Calculus (level) programming.
HTML code
for linking to this page:
- <a
href="http://www.digitalcalculus.com/example/magnetic-recording.html"><img
align="middle" width="100"
src="http://www.digitalcalculus.com/image/readrit-pic2.gif"/>
<strong>Model 4 Digitized Signal from Magnetic
Recording</strong> </a>, Isolated Readback Pulse, Modeling
& Simulation.
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