
Curve Fitting finds defective parts.submitted by: Phil Brubakeron Wed Nov 23 14:10:33 2005 
Course: Calculus  
Topic: Lorentzian Model of Isolated Pulse from Disc Drive  
Resource type: Tool  
Catalogue entry: http://mathforum.org/mathtools/ 

Resource location: http://www.digitalcalculus.com/demo/curvfit.html 

Story:  
This is a story of how a math model located a manufacturing flaw. Modeling Digitized Signal from Magnetic RecordingMagnetic 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. 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. sharp slope) for improved peak detection capability. A math model for the pulse can help gain insight into what electronic subsystem/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 ThinFilmHead (TFH) composition, size and shape. ***Note: 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 = 1 / (1 + y^2).
The isolated pulse model is a composite of three Lorentz functions as
stated here: Realworld data fit well and when a TFH produced a bell curve with a step on its back side, it too fit well. That told us that this model was excellent and the step was real. Such a TFH had some alignment problem in manufacturing and thus was destroyed. Until this model was tested these bad TFHs were had to find and demolish. A good math model is worth its weight in gold! 
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