LeCroy DDM, PRML User manual

''0350/

2SHUDWRU·VDQG3URJUDPPLQJ
0DQXDO

/H&UR\
'LJLWDO2VFLOORVFRSHV

5HYLVLRQ&³)HEUXDU\ 

/H&UR\&RUSRUDWLRQ

700 Chestnut Ridge Road

Chestnut Ridge, NY 10977–6499
Tel: [phone], Fax: [phone]

/H&UR\6$

2, rue du Pré-de-la-Fontaine
1217 Meyrin 1/Geneva, Switzerland
Tel: [phone], Fax: [phone]

,QWHUQHWwww.lecroy.com

Copyright © February 1997, LeCroy. All rights reserved. Information in this publication supersedes all
earlier versions. Specifications subject to change.

LeCroy, ProBus and SMART Trigger are registered trademarks of LeCroy Corporation. Centronics is
a registered trademark of Data Computer Corp. Epson is a registered trademark of Epson America

2

C is a trademark of Philips. MathCad is a registered trademark of MATHSOFT Inc. MATLAB is

Inc. I
a registered trademark of The MathWorks, Inc. Microsoft, MS and Microsoft Access are registered
trademarks, and Windows and NT trademarks, of Microsoft Corporation. PowerPC is a registered
trademark of IBM Microelectronics. DeskJet, ThinkJet, QuietJet, LaserJet, PaintJet, HP 7470 and
HP 7550 are registered trademarks of Hewlett-Packard Company.

LCXXX-DDM/PRML-OM-E Rev C 0297

&KDSWHU³,QWURGXFWLRQ''0350/

:KDWWKH2SWLRQV2IIHU.....................................................................1–1

DDM...............................................................................................................1–1

PRML.............................................................................................................1–2

Parameter Measurements............................................................................1–2

&KDSWHU³''0+LVWRJUDPV

+LVWRJUDPV7KHRU\RI2SHUDWLRQ ..........................................2–1

LeCroy DSO Process...................................................................................2–2

Parameter Buffer...........................................................................................2–3

Parameter Events Capture...........................................................................2–4

Histogram Parameters .................................................................................2–5

Zoom Traces and Segmented Waveforms.................................................2–6

Histogram Peaks ..........................................................................................2–6

Binning and Measurement Accuracy...........................................................2–7

2SHUDWLQJWKH6FRSHWR0DNH+LVWRJUDPV ........................2–10

Selecting the Histogram Function.............................................................. 2–10

Histogram Trace Setup Menu.................................................................... 2–12

Setting Binning and Histogram Scale........................................................ 2–17

Histogram Parameters ............................................................................... 2–20

Using Measurement Cursors.....................................................................2–22

Zoom Traces and Segmented Waveforms............................................... 2–23

&RQWHQWV

&KDSWHU³''0+LVWRJUDP3DUDPHWHUV

Average (avg)................................................................................................3–1

Full Width at Half Maximum (fwhm).............................................................3–2

Full Width at xx% Maximum (fwxx )..............................................................3–3

Histogram Amplitude (hampl) ......................................................................3–4

Histogram Base (hbase)...............................................................................3–5

High (high).....................................................................................................3–6

Histogram median (hmedian).......................................................................3–7

Histogram Root Mean Square (hrms)..........................................................3–8

LLL

Histogram Top (htop)....................................................................................3–9

Low (low)..................................................................................................... 3–10

Maximum Population (maxp).....................................................................3–11

Mode (mode)............................................................................................... 3–12

Pecentile (pctl) ............................................................................................ 3–13

Peaks (pks)................................................................................................. 3–14

Range (range)............................................................................................. 3–16

Sigma (sigma)............................................................................................. 3–17

Total Population.......................................................................................... 3–18

X Coordinate of xx’th Peak (x apk).............................................................. 3–19

&KDSWHU³''0'LVN²/RFDO

/RFDO)HDWXUHV ......................................................................................4–1

Peak–Trough Identification...........................................................................4–2

Local Baselines.............................................................................................4–3

&RQWHQWV

Setting Hyteresis...........................................................................................4–5

Local Parameters..........................................................................................4–6

&KDSWHU³''0'LVN²/RFDO3DUDPHWHUV

Local Base (lbase)........................................................................................5–1

Local Baseline Separation (lbsep)...............................................................5–2

Local Maximum (lmax).................................................................................5–3

Local Minimum (lmin) ...................................................................................5–4

Local Number (lnum)....................................................................................5–5

Local Peak–to–Peak (lpp)............................................................................5–6

Local Time Between Events (ltbe)...............................................................5–7

Local Time Between Peaks (ltbp)................................................................5–8

Local Time Between Troughs (ltbt)..............................................................5–9

Local Time at Minimum (ltmn).................................................................... 5–10

Local Time at Maximum (ltmx )................................................................... 5–11

Local Time Peak–to–Trough (ltpt)..............................................................5–12

LY

Local Time Over Threshold (ltot)................................................................ 5–13

Local Time Trough–to–Peak (lttp)..............................................................5–14

Local Time Under Threshold (ltut) ............................................................. 5–15

&KDSWHU³''0'LVN²67'

6WDQGDUG'LVN'ULYH3DUDPHWHUV'LVN²67'..................... 6–1

&KDSWHU³''0'LVN²67'3DUDPHWHUV

Narrow Band Phase (nbph)..........................................................................7–1

Narrow Band Power (nbpw).........................................................................7–2

Overwrite (owrt).............................................................................................7–4

Pulse Width 50 (pw50) .................................................................................7–6

Pulse Width 50– (pw50–).............................................................................7–7

Pulse Width 50+ (pw50+).............................................................................7–8

Resolution (res).............................................................................................7–9

Track Average Amplitude (taa).................................................................. 7–11

Track Average Amplitude– (taa–).............................................................. 7–12

Track Average Amplitude+ (taa+).............................................................. 7–13

&KDSWHU³350/&RUUHODWLRQ

7KH350/2SWLRQ......................................................................... 8–1

&RUUHODWLRQ7KHRU\RI2SHUDWLRQ...................................................8–2

2SHUDWLQJWKH6FRSHIRU&RUUHODWL RQ............................................8–4

Y

&KDSWHU³350/3DUDPHWHUV

Auto-Correlation Signal–to–Noise (acsn)....................................................9–1

Non-linear Transition Shift (nlts)...................................................................9–3

&KDSWHU³''0350/5HPRWH&RQWURO&RPPDQGV

:KHQ2SHUDWLQJWKH6FRSH5HPRWHO\ .................................10–1

DEFINE, DEF.............................................................................................. 10–2

PARAMETER_CUSTOM, PACU...............................................................10–9

PARAMETER_VALUE?, PAVA?..............................................................10–13

&RQWHQWV

YL

1

Introduction: DDM & PRML

What the Options Offer

The DDM and PRML waveform processing options for
LeCroy’s color digital oscilloscopes provide:

Ø Waveform parameter measurements, allowing disk-drive

measurements to be performed over selected waveform
sections or an entire waveform

Ø Related mathematical functions for performing disk

drive waveform analysis.

DDM Option This option offers a variety of waveform parameters.

The Disk Drive (Disk–STD) parameters — see Chapter 5 —
provide standard disk drive measurements such as overwrite,
pw50 and track average amplitude (TAA).

The Local (Disk–Local) parameters — see Chapter 4 — offer
amplitude, time, baseline and other measurements for disk drive
waveform peak–trough pairs, allowing useful analysis beyond
many standard disk drive measurements.

The option also offers a Histogram Math function and
histogram parameters (see Chapter 3).

The value of histograms for use in data analysis, and in the
interpretation of measurement results, is well known. The DDM
option added to your oscilloscope provides this capability for
waveform parameter analysis. Histograms of waveform
parameter measurements can be created, statistical parameters
determined, and histogram features quantified and analyzed.

Statistical parameters alone — such as mean, standard
deviation and median — are usually insufficient for determining
whether the distribution of measured data is as expected.
Histograms provide an enhanced understanding of the
distribution of measured parameters by enabling visual
assessment of the distribution. Observations based on the
histogram of a parameter can indicate:

1–1

Introduction

1. Distribution type: normal, non-normal, etc. This is helpful in
determining whether the signal behaves as expected.

2. Distribution tails and extreme values, which can be
observed and may be related to noise or other infrequent
and non-repetitive sources.

3. Multiple modes, which can be observed and could indicate
multiple frequencies or amplitudes. These can be used to
differentiate from other sources such as jitter and noise.

PRML Option This enables correlation-based measurements. It includes a

correlation-math function and two correlation-based parameters:
auto-correlation signal–to–noise and non-linear transition shift.
The non-linear transition shift parameter can be used to
measure other correlation-based disk drive measurements such
as overwrite. The correlation math function is capable of
performing auto-correlation and cross-correlation calculations.
As with histograms, the correlation-math function is assigned to
a trace, and the correlation waveform can be displayed.

Parameter Measurements Histograms of user-selected waveform parameters are created

using the scope’s Histogram Math function. This is done by
defining a trace (A, B, C, or D) as a math function, and selecting
“Histogram” as the function to be applied to the trace. As with
other traces, histograms can be positioned and expanded using
the POSITION and ZOOM knobs on the instrument’s front
panel.

Histograms are displayed based on a set of user settings,
including bin width and number of parameter events. Special
parameters are provided for determining histogram
characteristics such as mean, median, standard deviation,
number of peaks and most-populated bin.

This broad range of histogram options and controls provides a
quick and easy method of analyzing and understanding
measurement results.

1–2

DDM & PRML

1

2

The “MEASURE” “Parameters” menu — and with it, disk drive
and histogram parameters — is accessed by pressing the
CURSORS/MEASURE button, then selecting “Parameters”
from the top menu appearing, as shown in Figure 1.1.

Figure 1.1

Parameters are used to perform waveform measurements for
the section of waveform that lies between the parameter cursors
(Annotation Ê in this figure). The position of the parameter
cursors is set using the “from” and “to” menus and controlled by
the associated ‘menu’ knobs.

The top trace shows a disk drive test waveform. A pw50
parameter measurement is being performed on the waveform
(Annotation Ë) with a value of 20.7 ns as the calculated result.
The bottom trace shows a histogram of the pw50 parameter.
Now, up to five parameters can be selected, with each displayed
on its own line below the waveform display grid. Parameter
measurements can then also be selected from the “Category”
and “measure” menus using the corresponding menu buttons.

1–3

Introduction

Categories are provided for related groups of parameter
measurements. The “Statistics” category is provided for Histogram
Parameters. After selection of a category, a parameter can be
selected from the “measure” menu. Selection of parameters is
done using the menu buttons or knobs. The parameter display
line is selected from the “On line” menu.

Figure 1.2 shows the “Disk–Std” from “Category” and “pw50 ” from
“measure” selected. The disk drive parameter categories available
are “Disk–Std”, “Disk–Local” and “Disk–PRML”, corresponding to
the Disk Drive, Local and PRML parameter groups. The pw50
parameter is selected for Line 1 and the “mode” parameter for
Line 2. The mode parameter provides the value of the histogram
bin with the most events. No parameters are selected for Lines
3–5.

1–4

Figure 1.2

DDM & PRML

not

If a parameter has additional settings that must be supplied in
order to perform measurements, the “MORE ‘xxxx’ SETUP”
menu appears. The figure above shows how the “pw50 ” parameter
requires the user to provide additional settings. But if no additional
settings are required the “DELETE ALL PARAMETERS” menu
will appear, and pressing the corresponding menu button results
in all five lines of parameters being cleared.

The “of” menu determines which input channel (“1”, “2”, “3” or “4”) or
which trace (“A”, “B”, “C” or “D”) a parameter measurement will be
performed on.

Parameter Value
Calculation and Display

When Persistence is
channels shows the captured waveform of a single sweep.

For non-segmented waveforms, the display is the same as a single
acquisition. For segmented waveforms the display shows the result
of a single acquisition for all segments.

The value displayed for a chosen parameter depends on
whether “statistics” is “On”. And on whether the waveform is
segmented. These two factors and the parameter chosen
determine whether results are provided for a single acquisition
(trigger) or multiple acquisitions. In any case, only the waveform
section between the parameter cursors is used.

If the waveform source is a memory (“M1”, “M2”, “M3” or “M4”)
then loading a new waveform into memory acts as a trigger and
sweep. This is also the case when the waveform source is a
zoom of an input channel, and when a new segment or the “All
Segments” menu is selected.

When “statistics” is “Off”, the parameter results for the last
acquisition are displayed. This corresponds to results for the last
segment for segmented waveforms with all segments displayed.
For zoom traces of segmented waveforms, selection of an
individual segment gives the parameter value for the displayed
portion of the segment between the parameter cursors.
Selection of “All Segments” provides the parameter results
from the last segment in the trace.

When “On”, and where the parameter does not use two
waveforms in calculating a result (∆dly, ∆t@lv, owrt and res),
results are shown for all acquisitions since the CLEAR SWEEPS
button was last pressed. If the parameter uses two waveforms,

being used, the display for input

1–5

Introduction

the result of comparing only the last segment per sweep for
each waveform contributes to the statistics.

The statistics for the selected segment are displayed for zoom
traces of segmented waveforms. Selection of a new segment or
“All Segments” acts as a new sweep and the parameter
calculations for the new segment(s) contribute to the statistics.

Depending on the parameter, single or multiple calculations can
be performed for each acquisition. For example, the auto­correlation signal–to–noise (acsn) parameter performs 25 or more
auto-correlation signal–to–noise calculations in producing a
parameter value for a single acquisition. And the period parameter
calculates a period value for each of up to the first 50 cycles.

When multiple calculations are performed, with “statistics” “Off”
the parameter result shows the average value of these
calculations. Whereas “On” displays the average, low, high
and sigma values of all the calculations.

In the following chapters, a description of each of the various
types of parameters is given. Also described are any
mathematical operations performed in calculating values, the
values returned by each parameter, and parameter setup
details.

1–6

2

Theory of Operation

A statistical understanding of variations in parameter
values is of great interest for many waveform parameter
measurements. Knowledge of the average, minimum,
maximum and standard deviation of the parameter may
often be enough for the user, but in many other instances a
more detailed understanding of the distribution of a
parameter’s values is desired.

Histograms provide the ability to see how a parameter’s values
are distributed over many measurements, enabling this detailed
analysis. They divide a range of parameter values into sub­ranges called bins. Maintained for each bin is a count of the
number of parameter values calculated — events — that fall
within its sub-range.

While the range can be infinite, for practical purposes it need
only be defined as large enough to include any realistically
possible parameter value. For example, in measuring TTL high­voltage values a range of ± 50 V is unnecessarily large, whereas
one of 4 V ± 2.5 V is more reasonable. It is this 5 V range that is
subdivided into bins. And if the number of bins used were 50,
each would have a sub-range of 5 V/50 bins or 0.1 V/bin. Events
falling into the first bin would then be between 1.5 V and 1.6 V.
While the next bin would capture all events between 1.6 V and

1.7 V. And so on.

After a process of several thousand events, the graph of the
count for each bin — its histogram — provides a good
understanding of the distribution of values. Histograms generally
use the ‘x’ axis to show a bin’s sub-range value, and the ‘y’ axis
for the count of parameter values within each bin. The leftmost
bin with a non-zero count shows the lowest parameter value
measurement(s). The vertically highest bin shows the greatest
number of events falling within its sub-range.

The number of events in a bin, peak or a histogram is referred to
its population. Figure 2.1 shows a histogram’s highest population
bin as the one with a sub-range of 4.3–4.4 V — to be expected
of a TTL signal. The lowest value bin with events is that with a

DDM: Histograms

2–1

DDM

Volts

Count

sub-range of 3.0–3.1 V. As TTL high voltages need to be greater
than 2.5 V, the lowest bin is within the allowable tolerance.
However, because of its proximity to this tolerance and the
degree of the bin’s separation from all other values, additional
investigation may be desirable.

LeCroy DSO Process LeCroy digital oscilloscopes generate histograms of the

parameter values of input waveforms. But first, the following
must be defined:

Ø The parameter to be histogrammed.
Ø The trace on which the histogram will be displayed.
Ø The maximum number of parameter measurement values to

be used in creating the histogram.

Ø The measurement range of the histogram.
Ø The number of bins to be used.

Once these are defined, the oscilloscope is ready to make the
histogram.

40

30

20

10

1.5
2

3

3.15

Range

4.35

4

5

6

Figure 2.1

2–2

Histograms

The sequence for acquiring histogram data is:

1. trigger

2. waveform acquisition

3. parameter calculation(s)

4. histogram update

5. trigger re-arm.
If the timebase is set in non-segmented mode, a single

acquisition occurs prior to parameter calculations. However, in
Sequence mode an acquisition for each segment occurs prior to
parameter calculations. If the source of histogram data is a
memory, storing new data to memory effectively acts as a
trigger and acquisition. Because updating the screen can take
significant processing time, it occurs only once a second,
minimizing trigger dead-time (under remote control the display
can be turned off to maximize measurement speed).

Parameter Buffer The oscilloscope maintains a circular parameter buffer of the

last
20 000 measurements made, including values that fall outside
the set histogram range. If the maximum number of events to be
used in a histogram is a number ‘N’ less than 20 000, the
histogram will be continuously updated with the last ‘N’ events
as new acquisitions occur. If the maximum number is greater
than 20 000, the histogram will be updated until the number of
events is equal to ‘N’. Then, if the number of bins or the
histogram range is modified, the scope will use the parameter
buffer values to redraw the histogram with either the last ‘N’ or
20 000 values acquired — whichever is the lesser. The
parameter buffer thereby allows histograms to be redisplayed
using an acquired set of values and settings that produce a
distribution shape with the most useful information.

2–3

DDM

In many cases the optimal range is not readily apparent. So the
scope has a powerful range-finding function. If required it will
examine the values in the parameter buffer to calculate an
optimal range and redisplay the histogram using it. The
instrument will also give a running count of the number of
parameter values that fall within, below and above the range. If
any fall below or above the range, the range-finder can then
recalculate to include these parameter values, as long as they
are still within the buffer.

Parameter Events Capture The number of events captured per waveform acquisition or

display sweep depends on the parameter type. Acquisitions are
initiated by the occurrence of a trigger event. Sweeps are
equivalent to the waveform captured and displayed on an input
channel (1, 2, 3 or 4). For non-segmented waveforms an
acquisition is identical to a sweep. Whereas for segmented
waveforms an acquisition occurs for each segment and a sweep
is equivalent to acquisitions for all segments. Only the section of
a waveform between the parameter cursors is used in the
calculation of parameter values and corresponding histogram
events.

The following table provides, for each parameter and for a
waveform section between the parameter cursors, a summary of
the number of histogram events captured per acquisition or
sweep.

2–4

Histograms

Parameters

(plus others, depending on options)

data All data values in the region analyzed.

duty, freq, period, width, Up to 49 events per acquisition.

ampl, area, base, cmean, cmedian, crms,
csdev, cycles, delay, dur, first, last, maximum,
mean, median, minimum, nbph, nbpw, over+,
over–, phase, pkpk, points, rms, sdev, ∆dly,
∆t@lv

f@level, f80–20%, fall, r@level, r20–80%, rise Up to 49 events per acquisition.

Histogram Parameters Once a histogram is defined and generated, measurements can

be performed on the histogram itself. Typical of these are the
histogram’s:

Ø Average value, standard deviation
Ø Most common value (parameter value of highest count bin)
Ø Leftmost bin position (representing the lowest measured

waveform parameter value)

Ø Rightmost bin (representing the highest measured waveform

parameter value).

Histogram parameters are provided to enable these
measurements. Available through selecting “Statistics” from the
“Category” menu, they are calculated for the selected section
between the parameter cursors (for a full description of each
parameter, see Chapter 3):

Number of Events Captured

One event per acquisition.

2–5

DDM

All Segments

avg average of data values in histogram
fwhm full width (of largest peak) at half the maximum bin
fwxx full width (of largest peak) at xx% the maximum bin
hampl histogram amplitude between two largest peaks
hbase histogram base or leftmost of two largest peaks
high highest data value in histogram
hmedian median data value of histogram
hrms rms value of data in histogram
htop histogram top or rightmost of two largest peaks
low lowest data value in histogram
maxp population of most populated bin in histogram
mode data value of most populated bin in histogram
pctl data value in histogram for which specified ‘x’% of

population is smaller

pks number of peaks in histogram
range difference between highest and lowest data values
sigma standard deviation of the data values in histogram
totp total population in histogram
xapk x-axis position of specified largest peak.

Zoom Traces and
Segmented Waveforms

Histogram Peaks Because the shape of histogram distributions is particularly

Example In Figure 2.2, a histogram of the voltage value of a five-volt

Histograms of zoom traces display all events for the displayed
portion of a waveform between the parameter cursors. When
dealing with segmented waveforms, and when a single
segment is selected, the histogram will be recalculated for all
events in the displayed portion of this segment between the
parameter cursors. But if “
histogram for all segments will be displayed.

interesting, additional parameter measurements are available
for analyzing these distributions. They are generally centered
around one of several peak value bins, known — together with
its associated bins — as a histogram peak.

amplitude square wave is centered around two peak value bins:
0 V and 5 V. The adjacent bins signify variation due to noise.
The graph of the centered bins shows both as peaks.

2–6

” is selected, the

Histograms

0

5

Volts

Figure 2.2

Determining such peaks is very useful, as they indicate
dominant values of a signal.

However, signal noise and the use of a high number of bins
relative to the number of parameter values acquired, can give a
jagged and spiky histogram, making meaningful peaks hard to
distinguish. The scope analyzes histogram data to identify peaks
from background noise and histogram definition artifacts such as
small gaps, which are due to very narrow bins.

Binning and
Measurement
Accuracy

For a detailed description on how the scope determines peaks see
the pks parameter description, Chapter 3.

Histogram bins represent a sub-range of waveform parameter
values, or events. The events represented by a bin may have a
value anywhere within its sub-range. However, parameter
measurements of the histogram itself, such as average, assume
that all events in a bin have a single value. The scope uses the
center value of each bin’s sub-range in all its calculations. The
greater the number of bins used to subdivide a histogram’s
range, the less the potential deviation between actual event
values and those values assumed in histogram parameter
calculations.

Nevertheless, using more bins may require performance of a
greater number of waveform parameter measurements, in order
to populate the bins sufficiently for the identification of a

2–7

DDM

characteristic histogram distribution.
In addition, very fine-grained binning will result in gaps between

populated bins that may make determination of peaks difficult.

Figure 2.3 shows a histogram display of 3672 parameter
measurements divided into 2000 bins. The standard deviation of
the histogram sigma (Annotation Ê) is 81.17 mV. Note the

histogram’s jagged appearance.

1

Figure 2.3

The oscilloscope’s 20 000-parameter buffer is very effective for
determining the optimal number of bins to be used. An optimal
bin number is one where the change in parameter values is
insignificant, and the histogram distribution does not have a
jagged appearance. With this buffer, a histogram can be
dynamically redisplayed as the number of bins is modified by
the user. In addition, depending on the number of bins selected,
the change in waveform parameter values can be seen.

2–8

Histograms

In Figure 2.4 the histogram shown in the previous figure has
been recalculated with 100 bins. Note how it has become far
less jagged, while the real peaks are more apparent. Also, the
change in sigma is minimal (81.17 mV vs 81 mV).

2–9

Figure 2.4

Creating and Analyzing Histograms

Function

Figure 2.5

Annotation

1

The following provides a description of the oscilloscope’s
operational features for defining, using and analyzing
histograms. The sequence of steps is typical of this
process.

DDM

Selecting the Histogram

Histograms are created by graphing a series of waveform
parameter measurements. The first step is to define the
waveform parameter to be histogrammed.
screen display accompanying the selection of a frequency (freq)
parameter measurement (
Channel 1.

Ê) for a sine waveform on

shows a

Figure 2.5

2–10

Histograms

The preceding figure shows four waveform cycles, which will
provide four freq parameter values for each histogram, each
sweep. With a freq parameter selected, a histogram based on it
can be specified.

But first the waveform trace must be defined as a histogram.
This is done by pressing the MATH SETUP button. Figure 2.6
shows the resulting display. To place the histogram on Trace A,
the menu button corresponding to the “REDEFINE A” menu is
pressed.

2–11

Figure 2.6

DDM

Once a trace is selected, the screen shown in Figure 2.7
appears. Selecting “Yes” from the “use Math?” menu enables
mathematical functions, including histograms.

Figure 2.7

Histogram Trace Setup MenuFigure 2.8 (next page) shows the display when “Histogram” is

selected from the “Math Type” menu. Here, the freq parameter
only has been defined. However, if additional parameters were
to be defined, the individual parameter would need to be
selected — by pressing the corresponding menu button or
turning the associated knob until the desired parameter
appeared in the “Histogram custom line” menu.

2–12

Figure 2.8

Histograms

Each time a waveform parameter value is calculated it can be
placed in a histogram bin. The maximum number of such values
is selected from the “using up to” menu. Pressing the
associated menu button or turning the knob allows the user to
select a range from 20 to 2 billion parameter value calculations
for histogram display.

To see the histogram, turn the trace display on by pressing the
appropriate TRACE ON/OFF button, for a display similar that
shown in Figure 2.9.

2–13

DDM

1

2

Figure 2.9

Each histogram is set by the user to capture parameter values
falling within a specified range. As the scope captures the
values in this range the bin counts increase. Values not falling
within the range are not used in creating the histogram.

Information on the histogram is provided in the Displayed
Trace Field (Annotation Ê) for the selected trace. This shows:

Ø The current horizontal per division setting for the histogram

(“1 Hz” in this example). The unit type used is determined by
the waveform parameter type on which the histogram is
based.

Ø The vertical scale in #bin counts per division (here, “200

m”).

Ø The number of parameter values that fall within the range

(“inside 0”)

Ø The percentage that fall below (“←0%”)

2–14

Histograms

Ø The percentage of values above the range (“100%→”).
This figure shows that 100% of the captured events are above

the range of bin values set for the histogram. As a result, the
baseline of the histogram graph (Annotation Ë) is displayed, but
no values appear.

Selecting the “FIND CENTER AND WIDTH” menu allows
calculation of the optimal center and bin-width values, based on
the up to the most recent parameter values calculated. The
number of parameter calculations is chosen with the “using up
to” menu (or 20 000 values if this is greater than 20 000).
Figure 2.10 shows a typical result.

2–15

1

Figure 2.10

DDM

If the trace on which the histogram is made is not a zoom, then
all bins with events will be displayed. Otherwise, press RESET
to reset the trace and display all histogram events.

The Information Window (Annotation Ê) at the bottom of the
previous screen shows a histogram of the freq parameter for
Channel 1 (designated as “A:Hfreq(1)”) for Trace A. The “1000
→ 100 pts” in the window indicates that the signal on Channel 1
has 1000 waveform acquisition samples per sweep and is being
mapped into 100 histogram bins.

Selecting “MORE HIST SETUP” allows additional histogram
settings to be specified, resulting in a display similar to that of
Figure 2.11, below.

2–16

Figure 2.11

Histograms

Setup

Binning

Scale

Binning

Setting Binning &
Histogram Scale

The “
the histogram “
“classify into” menu appears, as shown in the figure above.

The number of bins used can be set from a range of 20–2000 in
a 1–2–5 sequence, by pressing the corresponding menu button
or turning the associated knob.

If “Scale” is selected from the “Setup” menu, a screen similar
that of Figure 2.12 will be displayed.

” menu allows modifcation of either the “

” settings. If “

” is selected, the

” or

2–17

Figure 2.12

DDM

Three options are offered by the “vertical” menu for setting the
vertical scale:

1. “Linear” sets the vertical scale as linear (see previous
figure). The baseline of the histogram designates a bin value
of 0. As the bin counts increase beyond that which can be
displayed on screen using the current vertical scale, this
scale is automatically increased in a 1–2–5 sequence.

2. “Log” sets the vertical scale as logarithmic (Fig. 2.13).
Because a value of ‘0’ cannot be specified logarithmically,
no baseline is provided.

2–18

Figure 2.13

Histograms

3. “LinConstMax” sets the vertical scaling to a linear value
that uses close to the full vertical display capability of the
scope (Fig. 2.14). The height of the histogram will remain
almost constant.

3

2

1

Figure 2.14

For any of these options, the scope automatically increases the
vertical scale setting as required, ensuring the highest histogram
bin does not exceed the vertical screen display limit.

The “Center” and “Width” menus allow specification of the
histogram center value and width per division. The width per
division times the number of horizontal display divisions (10)
determines the range of parameter values centered on the
number in the “Center” menu, used to create the histogram.

2–19

DDM

In the previous figure, the width per division is 2.000 × 10
(Annotation Ê). As the histogram is of a frequency parameter,
the measurement parameter is hertz.

The range of parameter values contained in the histogram is
therefore:

( 2 k Hz/division) x (10 divisions) = 20 k Hz
with a center of 2.02 E+05 Hz (Ë).
In this example, all freq parameter values within 202 k Hz ± 10

k Hz — from 192 k Hz to 212 k Hz — are used in creating the
histogram. The range is subdivided by the number of bins set by
the user. Here, the range is 20 k Hz, as calculated above, and
the number of bins 100. Therefore, the range of each bin is:

20 k Hz / 100 bins, or

.2 k Hz per bin.
The “Center” menu allows the user to modify the center value’s

mantissa (here, 2.02), exponent (E+05) or the number of digits
used in specifying the mantissa (three). The display scale of
1 k Hz/division, shown in the Trace Display Field, is indicated by
Annotation Ì. This scale has been set using the horizontal zoom
control and can be used to expand the scale for visual
examination of the histogram trace.

The use of zoom in this way does not modify the range of data
acquisition for the histogram, only the display scale. The range
of measurement acquisition for the histogram remains based on
the center and width scale, resulting in a range of 202 k Hz ±
10 k Hz for data acquisition.

Any of these can be changed using the associated knob. And
the width/division can be incremented in a 1–2–5 sequence by
selecting “Width”, using button or knob.

3

Histogram Parameters Once the histogram settings are defined, selecting additional

parameter values is often useful for measuring particular
attributes of the histogram.

2–20

Histograms

1

Selecting “PARAMETER SETUP”, as shown in the previous
figure, accesses the “CHANGE PARAM” menus, shown in

Figure 2.15.

Figure 2.15

New parameters can now be selected or previous ones modified. In
this figure, the histogram parameters maxp and mode (Annotation
Ê) have been selected. These determine the count for the bin with
the highest peak, and the corresponding horizontal axis value of that
bin’s center.

Note that both “maxp” and “mode” are followed by “(A)” on the
display. This designates the measurements as being made on
the signal on Trace A, in this case the histogram. Note:

Ø The value of “maxp(A)” is “110 #”, indicating the highest bin

has a count of 110 events.

Ø The value of mode(A) is “203.90 k Hz”, indicating that this

bin is at 203.90 k Hz.

2–21

DDM

Ø The icon to the left of “mode” and “maxp” parameters

indicates that the parameter is being made on a trace
defined as a histogram.

However, if these parameters were inadvertently set for a trace
with no histogram they would show ‘---’.

Using Measurement Cursors The parameter cursors can be used to select a section of a

histogram for which a histogram parameter is to be calculated.
Figure 2.16 shows the average, “avg(A)” (Annotation Ê) of the

distribution between the parameter cursors for a histogram of
the frequency (“freq”) parameter of a waveform. The parameter
cursors (Ë) are set “from” 4.70 divisions (Ì) “to” 9.20 divisions
(Í) of the display.

2–22

2

3

1

4

Figure 2.16

Histograms

It is recommended that this capability be used only after the
input waveform acquisition has been completed. Otherwise, the
parameter cursors will also select the portion of the input
waveform used to calculate the parameter during acquisition.
This will create a histogram with only the local parameter values
for the selected waveform portion.

Zoom Traces and
Segmented Waveforms

Histograms can also be displayed for traces that are zooms of
segmented waveforms. When a segment from a zoomed trace
is selected, the histogram for that segment will appear. Only the
portion of the segment displayed and between the parameter
cursors will be used in creating the histogram. The
corresponding Displayed Trace Field will show the number of
events captured for the segment.

Figure 2.17 shows “Selected” a histogram of the frequency
(“freq”) parameter for “Segment 1” (Annotation Ê) of Trace “A”,
which is a zoom of a 10-segment waveform on Channel 1.

2

1

Figure 2.17

The Displayed Trace Field shows that 24 parameter events
(Annotation Ë) have been captured into the histogram. The

2–23

DDM

average value for the freq parameter is displayed as the
histogram parameter, “avg(B)”.

Figure 2.18 shows the result of selecting “All Segments”.

Figure 2.18

Note that the Displayed Trace Field indicates 30 events in the
histogram for all segments, and the change in “avg(B)”.

Histogram events can be cleared at any time by pushing the
CLEAR SWEEPS button. All events in the 20-k parameter
buffer are cleared at the same time. The vertical and horizontal
POSITION and ZOOM control knobs can be used to expand and
position the histogram for zooming-in on a particular feature of
it. The resulting vertical and horizontal scale settings are shown
in the Displayed Trace Field. However, the values in the
“Center” and “Width” menus do not change, since they

2–24

Histograms

determine the range of the histogram and cannot be used to
determine the parameter value range of a particular bin. If the
histogram is repositioned using the horizontal POSITION knob
the histogram’s center will be moved from the center of the
screen. Horizontal measurements will then require the use of
CURSORS/MEASURE.

The scope’s measurement cursors are useful for determining the
value and population of selected bins. Figure 2.19 shows the
“Time” cursor (Ê) positioned on a selected histogram bin. The
value of the bin (Ë) and the population of the bin (Ì) are also
shown.

3

1

4

2

Figure 2.19

A histogram’s range is represented by the horizontal width of the
histogram baseline. As the histogram is repositioned vertically
the left and right sides of the baseline can be seen. In this final
figure of the chapter, the left edge of the range is visible (Í).

2–25



/RFDO)HDWXUHV

''0'LVN²/RFDO

The term
computed on a waveform is determined only by information in
the immediate vicinity of a specified feature of that w aveform.
The DDM option defines a local feature as

followed by a trough

However, it is

diagram below shows a single local feature: the first peak and the
trough that follows it.

local feature computation

, like this:

not

the opposite — a trough followed by a peak. The

indicates that a parameter

a waveform peak

²

''0

3HDN²7URXJK,GHQWLILFDWLRQ The key to identifying peak–trough pairs is the ability to discrim inate

between real pairs and false ones. For exam ple, noise in a signal
can be mistaken for a local feature, as here:

Similarly, ‘bumps’ in a waveform may also be mistaken for peak–
trough pairs.

In order to avoid such misidentif ication, a hysteresis argument is
provided for many local feature parameters . T his ess entially enables
the user to set a voltage band, which a peak–trough pair must
exceed in order not be considered noise or a “bump”:

The hysteresis setting is also essential to the way peaks and troughs
are identified by the oscilloscope.

The search for local features extends from the left to the right
parameter cursor. But first a peak m ust be found. And a waveform
must rise to at least the value of the hysteresis setting in or der to be
positively identified as a peak.

²

'LVN²/RFDO

This peak search starts with the first waveform sample, whose
voltage value is used as an initial reference value for locating the
peak. If a following waveform sample is f ound to be higher than the
first by an amount greater than the hysteresis setting, a peak is said
to exist. Any sample lower than the reference value, made prior to
determination of a peak’s existence, is used as a new reference

point.
When a waveform rises by an amount that is more than the

hysteresis, compared to the lowest prior waveform sample, the
criterion for the existence of a peak is met. T hen the search for its
exact location and voltage value is initiated. Success ive s amples are
compared to find the highest sample. Next, two points are found, one
on either side of this highest sam ple and down from it by at least
25 % of the distance to the previous trough amplitude. A quadr atic
interpolation is then performed on these three samples to find the
new peak location and amplitude. The same approach, using a
sample lower than the highest sample by more than the hysteresis
setting, is used to locate the trough.

/RFDO%DVHOLQHV Many parameter measurem ents require that the baseline of a local

feature be identified. In order to account for asymm etr ies due to MR
heads, baselines are identified between the peak and trough, and
between the trough and the following peak .

²

''0

The baselines are found by locating a point at which the waveform

‘rests’ between the peak and trough and peak. T hese resting points
are identified by statistically measuring the area of least change in
voltage value between the peak and trough or trough and peak, with
internal tolerance levels set to ensure against false baseline
identification.

Another condition for identification is that the resting points m ust fall
within a band, centered around the midpoint of the peak and trough
extremes, whose height is the hysteresis setting.

If one of the baselines cannot be identified, the local baseline is set to
the found value. If neither baseline can be identified, then the loc al
baseline is set halfway between the extremes of the loc al feature’s
peak and trough.

Otherwise, the local-feature baseline is an average of the two
baselines.

If the local feature is the last to be identified before ar riving at the
right parameter cursor , it will not be possible to identify the

to–peak
to–trough

assumed to be separated by the same distance as the baselines f or
the previous local feature. And if this baseline c annot be identified,
then the local baseline becomes the midpoint of the local peak and
trough.

The separation between the baselines (local baseline separation)
can also be of interest in determining the validity of certain
measurements.

The following table summarizes the determination of the local
baseline and its separation when the local featur e
last identified before the right parameter cursor:

baseline of the following local feature. But when the

baseline is identified, then these two baselines are

is

and is

trough–

peak–

not

the

²

'LVN²/RFDO

Local baseline and local baseline separation if last local feature

Baseline identified

peak–to–trough

(PTBase)

yes (PTBase + (PTBase +

no midpoint of local peak

Local baseline and local baseline separation if not last local feature

Baseline

identified

peak–to–trough

(PTBase)

yes yes average of

yes no PTBase 0

no yes PTBase 0
no no midpoint of

Local Baseline Baseline

previous local
previous
separation))/2

and trough

Baseline

identified

trough–to–peak

(TPBase)

PTBase +
TPBase

local peak
and trough

feature’s baseline

separation

Local

Baseline

Separation

0

Baseline

Separation

PTBase –
TPBase

0

6HWWLQJ+\VWHUHVLV Hysteresis must be set for all local parameters. The determining

factors for a hysteresis value are:

1. The maximum peak–to–peak noise in the waveform

2. The minimum local feature amplitude

3. The maximum of the voltage difference between the mid-point of
any local feature and the peak–to–trough baseline or trough–to–
next peak baseline.

The value should be somewhere between the first and second
factors, above, in order to ensure that noise is not mistaken for a
local feature and that all local features are recognized. And for

²

''0

parameters that require a local bas eline to be found, the value m ust

also be twice as large as factor “3.”.

/RFDO3DUDPHWHUV The local parameters group off ers measurements of c ommon disk

drive waveform param eters. T hey are available by selecting “DISK–
Local” from the “Category” menu (

parameter, see Chapter 5

lbase baseline of local feature
lbsep separation between peak–to–trough and trough–to–

peak baselines

lmax maximum value of local feature
lmin minimum value of local feature
lnum number of local features displayed
lpp local feature peak–to–trough amplitude
ltbe time between peak–to–trough or rough–to–peak
ltbp local feature’s time between peaks
ltbt local feature’s time between troughs
ltmn time of local feature’s minimum value
ltmx time of local feature’s maximum value
ltot local feature’s time over a % threshold
ltpt time between local feature peak–to–trough
lttp time between trough–to–following peak
ltut local feature’s time under a % threshold

):

for a full description of each

All make their m easurements on identified local featur e peaks and
troughs.

Note: The scope’s variable hysteresis setting is essential to
identifying peak–trough pairs and setting tolerances on the
baseline calculation.

²



''0'LVN²/RFDO3DUDPHWHUV

OEDVH /RFDO%DVH

'HILQLWLRQ The value of the baseline for a local feature.
'HVFULSWLRQ The average value of the local baselines for all local features between the

parameter cursor s is displayed as lbase. For histogr ams, each individual
baseline value for all local features between the parameter cursors is
provided.

3DUDPHWHU6HWWLQJV Selection of the lbase parameter in the “CHANGE PARAM” menus

causes a “MORE lbase SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes how to identify local baselines.

The previous chapter describes

²

''0

OEVHS /RFDO%DVHOLQH6HSDUDWLRQ

'HILQLWLRQ The value of the baseline separation for a local feature.
'HVFULSWLRQ The average value of the separation of the two baselines used to

calculate a local baseline is displayed for all local f eatures between the
parameter cursors. For histograms, each individual baseline separation
value for all local features between the parameter cursors is provided.

The previous chapter describes how to identify local baselines.

3DUDPHWHU6HWWLQJV Selection of the lbsep parameter in the “ CHANGE PARAM” menu group

causes a “MORE lbsep SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OPD[ /RFDO0D[LPXP

'HILQLWLRQ The maximum value of a local feature.
'HVFULSWLRQ The maxim um value of all local features between the parameter cursors

is determined and the average value is displayed as lmax. For
histograms, the maximum value of each local feature between the
parameter cursors is provided.

3DUDPHWHU6HWWLQJV Selection of the Imax parameter in the “CHANGE PARAM” menu group

causes a “MORE lmax SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

''0

OPLQ /RFDO0LQLPXP

'HILQLWLRQ The minimum value of a local feature.
'HVFULSWLRQ The minimum value of all the local features between the parameter

cursors is determ ined and the average value is displayed as lmin. For
histograms, the minimum value of each local feature between the
parameter cursors is provided.

3DUDPHWHU6HWWLQJV Selection of the Imin parameter in the “CHANGE PARAM” menu group

causes a “MORE lmin SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OQXP /RFDO1XPEHU

'HILQLWLRQ The number of local features in the input waveform.
'HVFULSWLRQ The number of local features between the parameter cursors is

determined and displayed as lnum. One value of lnum each sweep is
provided for histograms.

3DUDPHWHU6HWWLQJV Selection of the Inum parameter in the “CHANGE PARAM” menu group

causes a “MORE lnum SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

''0

OSS /RFDO3HDN²WR²3HDN

'HILQLWLRQ The vertical difference between the peak and trough for a local feature.
'HVFULSWLRQ The peak–to–trough voltage diff er enc e is determined for all loc al features

in a waveform and the average is displayed as lpp. Provided for
histograms is the peak –to–peak value of each local f eature between the
parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Ipp parameter in the “CHANGE PARAM” menu group

causes a “MORE lpp SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OWEH /RFDO7LPH%HWZHHQ(YHQWV

'HILQLWLRQ The time between a local feature peak and trough or a local feature

trough and the next local feature peak.

'HVFULSWLRQ Events are defined as either peaks or troughs. The average time

between successive events in a waveform is dis played as ltbe. Provided
for histograms is the time between each successive event between the
parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itbe parameter in the “CHANGE PARAM” menu group

causes a “MORE ltbe SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

''0

OWES /RFDO7LPH%HWZHHQ3HDNV

'HILQLWLRQ The time between a local feature peak and the next local feature peak.
'HVFULSWLRQ The average of the time between successive local feature peaks is

determined and its value displayed as ltbp. Provided for histogram s are
the times between successive peaks for all peaks between the parameter
cursors.

3DUDPHWHU6HWWLQJV Selection of the Itbp param eter in the “CHANGE PARAM” menu group

causes a “MORE ltbp SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OWEW /RFDO7LPH%HWZHHQ7URXJKV

'HILQLWLRQ The time between a local trough and the next local trough.
'HVFULSWLRQ The average of the time between suc cessive troughs is deter mined and

its value displayed as ltbt. Provided for histograms are the times between
successive troughs for all troughs between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itbt parameter in the “CHANGE PARAM” menu group

causes a “MORE ltbt SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

''0

OWPQ /RFDO7LPHDW0LQLPXP

'HILQLWLRQ The time of the minimum value of a local feature.
'HVFULSWLRQ The time of the m inimum value of the first local feature in a waveform

after the left parameter cursor is determined. The time is returned as
ltmn. Provided for histograms are all times for local feature minimums
between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itmn parameter in the “CHANGE PARAM” menu group

causes a “MORE ltmn SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OWP[ /RFDO7LPHDW0D[LPXP

'HILQLWLRQ The time of the maximum value of a local feature.
'HVFULSWLRQ The time of the m aximum value of the firs t local feature in a waveform,

after the left parameter cursor, is determined and returned as ltmx.
Provided for histograms are all times for local feature maximums
between the cursors.

3DUDPHWHU6HWWLQJV Selection of the Itmx parameter in the “CHANGE PARAM” menu group

causes a “MORE ltmx SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

''0

OWSW /RFDO7LPH3HDN²WR²7URXJK

'HILQLWLRQ The time between a local feature peak and trough.
'HVFULSWLRQ The average of the time between all local feature peaks and troughs is

displayed as ltpt. Provided for histograms are the times between peak–
trough pairs for all local features between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itpt parameter in the “CHANGE PARAM” menu group

causes a “MORE ltpt SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OWRW /RFDO7LPH2YHU7KUHVKROG

'HILQLWLRQ The time a local feature spends over a user-pecified percentage of its

peak–to–trough amplitude.

'HVFULSWLRQ The peak–to–trough height of a local feature is m easured. The time the

local feature spends over a user s pecified percent of the peak-to-trough
height is then determined. The average for all local features in a
waveform is displayed as ltot. Provided for histograms is the time spent
over the threshold by each local feature between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itot parameter in the “CHANGE PARAM” menu group

causes a “MORE ltot SETUP” menu to appear. Pressing the
corresponding menu button displays hysteresis and threshold menus,
whose menu buttons or associated knobs allow the setting, r espectively,
of the values in those menus to a s pecified number of ver tical divisions,
or a percentage of the peak–to–peak height of the local feature.

previous chapter describes hysteresis.

([DPSOH

The

²

''0

OWWS /RFDO7LPH7URXJK²WR²3HDN

'HILQLWLRQ The time between a local-feature trough and the next local-feature peak.
'HVFULSWLRQ The average of the time between all local feature troughs and the

following local feature peak is displayed as lttp. Provided for histogram s
are the times between trough and following peak for all local features
between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Ittp parameter in the “CHANGE PARAM” menu group

causes a “MORE lttp SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis setting menu, whose
menu button or associated k nob allows setting of the hysteresis value to
a specified number of vertical divisions.

hysteresis.

([DPSOH

The previous chapter describes

²

'LVN²/RFDO3DUDPHWHUV

OWXW /RFDO7LPH8QGHU7KUHVKROG

'HILQLWLRQ The time a local featur e spends under a user-spec ified percentage of its

peak–to–trough amplitude.

'HVFULSWLRQ The peak–to–trough height of a local feature is m easured. The time the

local feature spends under a user-specif ied percentage of this height is
determined, and the average for all the waveform’s local features is
displayed as ltut. Provided for histograms is the time spent under the
threshold by each local feature between the parameter cursors.

3DUDPHWHU6HWWLQJV Selection of the Itut parameter in the “CHANGE PARAM” menu group

causes a “MORE ltut SETUP” menu to appear. Pressing the
corresponding menu button displays hysteresis and threshold menus,
whose menu buttons or associated knobs allow the setting, r espectively,
of the values in those menus to a s pecified number of ver tical divisions,
or a percentage of the peak-to-peak height of the local feature.

previous chapter describes hysteresis.

([DPSOH

The

²



''0'LVN²6WG

6WDQGDUG'LVN'ULYH3DUDPHWHUV'LVN²6WG

The Disk Drive parameters enable standard disk drive
waveform parameter measurements. The parameters, accessed

by selecting “',6.²6WG” from the “Category” menu, are:
nbph narrow band phase of waveform DFT

nbpw narrow band power of waveform DFT
owrt overwrite
pw50 pulse width of peaks at 50% amplitude from

baseline

pw50+ pulse width of positive peaks at 50% amplitude from

baseline

pw50– pulse width of negative peaks at 50% amplitude

from baseline

res resolution
taa track average amplitude
taa+ track average amplitude of positive peaks from

baseline

taa– track average amplitude of negative peaks from

baseline

All except nbph, nbpw and owrt make their measurements on

waveform peak–trough pairs . In addition, several of the par ameters
determine the baseline of peak–trough pairs in order to perf orm their
calculations.

Note: The scope’s variable hysteresis setting is essential for
identifying peak–trough pairs and setting tolerances on the

see

baseline calculation (

²

Chapter 4).

7

DDM: Disk–Std Parameters

nbph Narrow Band Phase

Definition Provides a measurement of the phase at a specific frequency for a

waveform.

Description nbph is the phase of the Discrete Fourier Transform (DFT) computed on

a waveform at a specific frequency. The result is the phase of the
corresponding frequency sine wave component of the waveform at the
first data point between the parameter cursors. The nbph paramter
calculates one bin of a DFT centered at the frequency provided. The bin
width is 1.05% of the frequency selected if the waveform trace displayed
by the oscilloscope is 96 * (1/frequency) or more in length (i.e. the trace
is equal to or longer than 96 cycles of a waveform at the selected
frequency). Otherwise, the bin width is:

100 / integer[(oscilloscope trace length)/(1/frequency)] %,

where integer [ ] designates discarding any fractional portions in the
result. Thus, if the waveform trace is 48.5 times longer than 1/frequency,
the bin width will be:

100/48 = 2.1% of the selected frequency.

nbph is very sensitive to frequency and it is important that the
frequency value provided be as accurate as possible if accurate results
are to be obtained.

Parameter SettingsSelection of the nbph parameter in the “CHANGE PARAM” menus

causes the “MORE nbph SETUP” menu to appear. Pressing the
corresponding menu button accesses a frequency setting menu. The
user can adjust the mantissa, exponent or number of mantissa digits by
pressing this menu’s corresponding button. And the associated ‘menu’
knob can be used to adjust these. However, if a large number of digits is
used, selection of the exact frequency may be difficult. In this case, a
number with fewer digits and less precision should be chosen for the
approximate frequency, then the precision increased as desired and the
exact value chosen.

7–1

DDM

nbpw Narrow Band Power

Definition Provides a measurement of the power at a specific frequency for a

waveform.

Description nbpw is the magnitude of the Discrete Fourier Transform (DFT)

computed on a waveform at a specific frequency. nbpw calculates one
bin of a DFT centered at the frequency provided. The bin width is 1.05%
of the frequency selected if the waveform trace on the scope is 96*
(1/frequency) or more in length (i.e. the trace is equal to or longer than
96 cycles of a waveform at the selected frequency). Otherwise, the bin
width is:

100 / integer[trace length/(1/frequency)] %,

where integer [ ] designates discarding any fractional portions in the
result. Thus, if the waveform trace is 48.5 times longer than 1/frequency
then the bin width will be:

100/48 = 2.1% of the selected frequency.

A Blackman–Harris window is applied to the input data to minimize
leakage effects. The net result is that nbpw will provide excellent results
even if frequency changes occur due to spindle speed variations. If the
actual frequency differs from the specified frequency, and the bin width
is +/– 1.05%, the resulting power will be reduced from the actual as in
this table:

Frequency Difference dB Reduction

.3% .3 dB
.6% 1.1 dB
1% 3 dB

If the bin width is greater than 1.05%, the frequency difference for which
a specified dB reduction will occur will scale proportionally to the bin
width/1.05.

nbpw results are presented in dB. All averaging, including statististics
and trend average, is performed on linear units. Average results are
converted to dB.

7–2

DDM: Disk–Std Parameters

Parameter SettingsSelection of the nbpw parameter in the “CHANGE PARAM” menus

causes the “MORE nbpw SETUP” menu to appear. Pressing the
corresponding menu button accesses a frequency setting menu. The
user can adjust the mantissa, exponent or number of mantissa digits by
pressing this menu’s corresponding button. And the associated ‘menu’
knob can be used to adjust these. However, if a large number of digits is
used, selection of the exact frequency may be difficult. In this case, a
number with fewer digits and less precision should be chosen for the
approximate frequency, then the precision increased as desired and the
exact value chosen.

7–3

DDM

owrt Overwrite

Definition The ratio of residual to original power of a low-frequency disk waveform

overwritten by a higher frequency waveform.

Description owrt measures the residual power of a low-frequency LF waveform after it has

been overwritten by a high-frequency HF waveform. The LF waveform should be
stored to memory (M1–M4) and the memory assigned to a trace (A, B, C or D).
The HF waveform can then be input to the scope, and overwrite calculated
where:

owrt = 20 log (Vr/ Vo),

where Vr is the residual Vrms of the sine wave component of the HF waveform
at the LF base frequency after the HF waveform write, and Vo is the Vrms of the
sine wave component of the LF waveform at the LF base frequency. The
calculation is performed by the scope making a narrow-band power
measurement (see nbpw parameter description) at LF, for both the HF and LF
waveforms, and subtracting the second result from the first. A menu (see
example) enables the choice of which waveform, HF or LF, is assigned to which
scope channel or trace (1, 2, 3, 4, A, B, C or D). The menu button is used to set
the input for HF or LF, while the input for the selected waveform is set with the
associated knob. The owrt results are presented in dB. All averaging, including
statistics and trend average, is performed on linear units. Average results are
converted to dB.

Note: In typical use it is preferable to use nbpw to measure the LF waveform,
and then the residual LF in the HF separately, instead of the owrt parameter.
Overwrite is the difference between the nbpw readings in dB. There are two
reasons why this is preferable: 1) nbpw, with statistics on, provides average
power readings. With owrt the low frequency signal is typically a stored single­shot acquisition due to the difficulty finding a suitable trigger for time domain
averaging of a head signal. 2) owrt computes both nbpw results each time. If
the LF is stored this is not necessary. So nbpw will take twice as many
acquisitions as owrt and achieve a more stable average result in the same
amount of time.

Parameter Settings Selection of the owrt parameter in the “CHANGE PARAM” menus causes the

“MORE owrt SETUP ” menu to appear. Pressing the corresponding menu button
accesses a frequency setting menu. This frequency is used to calculate nbpw for
both the HF and LF waveforms. The user can adjust the mantissa, exponent or
number of mantissa digits by pressing this menu’s corresponding button. And the
associated ‘menu’ knob can be used to adjust these. However, if a large number

7–4

DDM: Disk–Std Parameters

of digits is used, selection of the exact frequency may be difficult. In this case, a
number with fewer digits and less precision should be chosen for the approximate
frequency, then the precision increased as desired and the exact value chosen.

7–5

DDM

Example In the screen display below, the LF waveform is assigned to Trace A and

the HF waveform to Trace B. The LF waveform is a 1 V peak–to– peak
1 MHz sine wave, and the HF waveform a 1 V peak–to–peak 5 MHz sine
wave. Using the freq parameter to determine the frequency of the LF
waveform, the 1 MHz frequency value is confirmed (see “freq(A)” in
figure). The HF waveform has a residual 1 MHz component. Zooming
Trace B, the amplitude of the residual waveform is .1 V peak–to–peak.
Therefore, the value for overwrite should be, approximately:

20 log (.1 volt/1 volt),

or –20 dB. The scope’s parameter display shows that owrt is in fact
–19.87dB. Comparing this number to the difference of the nbpw
parameter measurements at 1 MHz, shown for both the HF and LF
waveforms, we arrive at the same result.

7–6

DDM: Disk–Std Parameters

pw50 Pulse Width 50

Definition The average pulse width at the 50% point between a local baseline and

the local-feature peak, and between the local baseline and the local
feature-trough.

Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The local baseline is identified for each
feature, and the height between the local baseline and the peak is
determined. The pulse width is measured at 50% of the peak. The same
measurement is then performed for the trough. The average of all width
measurements is displayed as pw50. Provided for histograms is the
average pw50 value for each local feature between the parameter
cursors.

Parameter SettingsSelection of the pw50 parameter in the “CHANGE PARAM” menus

causes a “MORE pw50 SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis-setting menu, whose
menu button or associated knob allows setting of the hysteresis value to
a specified number of vertical divisions. Chapter 4 describes hysteresis.

7–7

DDM

pw50– Pulse Width 50–

Definition The average pulse width measured at the 50% point between the local

feature baseline and the local feature trough.

Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The local baseline is identified for each
feature, and the height between the local baseline and trough is
determined. The pulse width is measured at 50% of the trough
amplitude. The average of all width measurements is displayed as
pw50–. Provided for histograms is the average pw50– value for each
local feature between the parameter cursors.

Parameter SettingsSelection of the pw50– parameter in the “CHANGE PARAM” menus

causes a “MORE pw50– SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis-setting menu, whose
menu button or associated knob allows setting of the hysteresis value to
a specified number of vertical divisions. Chapter 4 describes hysteresis.

7–8

DDM: Disk–Std Parameters

Pw50+ Pulse Width 50+

Definition The average pulse width at the 50% point between the local feature

baseline and the local feature peak.

Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The local baseline is identified for each
feature, and the height between the local baseline and peak is
determined. The pulse width is measured at 50% of the peak amplitude.
The average of all width measurements is displayed as pw50+.
Provided for histograms is the average pw50+ value for each local
feature between the parameter cursors.

Parameter SettingsSelection of the pw50+ parameter in the “CHANGE PARAM” menus

causes a “MORE pw50+ SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis-setting menu, whose
menu button or associated knob allows setting of the hysteresis value to
a specified number of vertical divisions. Chapter 4 describes hysteresis.

7–9

DDM

res Resolution

Definition The ratio of the track average amplitude for a high and low frequency

waveform.

Description res returns, as a percentage, the ratio of track average amplitude (see

taa parameter description) for a low frequency LF and high frequency

HF waveform:

res = (taa(LF) / taa(HF)) * 100%.

A menu (see example) is used to select the waveform — HF or LF —
and the scope channel or trace to which it will be assigned. The first
waveform read should be stored to a memory (M1–M4), and the
memory to a trace (A, B, C, or D). The user selects whether to set the
input for HF or LF by pushing the corresponding menu button. The
source of the selected waveform — 1, 2, 3, 4, A, B ,C or D — is then set
using the associated knob.

Parameter SettingsSelection of the res parameter in the “CHANGE PARAM” menus causes

a “MORE res SETUP” menu to appear. Pressing the corresponding
menu button displays a hysteresis-setting menu, whose menu button or
associated knob allows setting of the hysteresis value to a specified
number of vertical divisions. Chapter 4 describes hysteresis.

7–10

DDM: Disk–Std Parameters

Example In the figure below the LF waveform is assigned to Trace A and the HF

waveform to input Channel 1. The LF waveform is at 1 MHz and the HF
at 2 MHz. Resolution is calculated as 77.8 %.

7–11

DDM

taa Track Average Amplitude

Definition The average peak–to–trough amplitude for all local features.
Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The peak–to–trough amplitude is
determined for each feature and the average is returned as taa.
Provided for histograms is the peak–to–trough amplitude for each local
feature between the parameter cursors.

Parameter SettingsSelection of the taa parameter in the “CHANGE PARAM” menus causes

a “MORE taa SETUP” menu to appear. Pressing the corresponding
menu button displays a hysteresis-setting menu, whose menu button or
associated knob allows setting of the hysteresis value to a specified
number of vertical divisions. Chapter 4 describes hysteresis.

7–12

DDM: Disk–Std Parameters

taa– Track Average Amplitude–

Definition The average local baseline–to–trough amplitude for all local features.
Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The local baseline–to–trough amplitude is
determined for each feature and the average is returned as taa–.
Provided for histograms is the local baseline–to–trough amplitude for
each local feature between the parameter cursors.

Parameter SettingsSelection of the taa– parameter in the “CHANGE PARAM” menus

causes a “MORE taa– SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis-setting menu, whose
menu button or associated knob allows setting of the hysteresis value to
a specified number of vertical divisions. Chapter 4 describes hysteresis.

7–13

DDM

taa+ Track Average Amplitude+

Definition The average local baseline–to–peak amplitude for all local features.
Description All local features (see Chapter 4) between the parameter cursors for an

input waveform are identified. The local baseline–to–peak amplitude is
determined for each feature and the average is returned as taa+.
Provided for histograms is the local baseline–to–peak amplitude for
each local feature between the parameter cursors.

Parameter SettingsSelection of the taa+ parameter in the “CHANGE PARAM” menus

causes a “MORE taa+ SETUP” menu to appear. Pressing the
corresponding menu button displays a hysteresis-setting menu, whose
menu button or associated knob allows setting of the hysteresis value to
a specified number of vertical divisions. Chapter 4 describes hysteresis.

7–14



7KH350/2SWLRQ

The PRML option enables parameter measurements of auto-

correlation signal–to–noise (ACSN) and non-linear transition
shift (NLTS). The calculation of both these parameters is
based on a correlation math function, which is also included
in the option.

350/&RUUHODWLRQ

The acsn parameter (
periodic waveform. Since these waveforms are by definition
identical in every period, any deviation is due to uncorrelated
noise sources. By performing an auto-correlation calculation of
the waveform over successive periods, the level of less-than­perfect correlation can be measured. And with this
measurement, the noise level can be derived by ACSN.

The nlts param eter (
echoes in the auto-correlation calculation of a disk waveform.
This includes the NLTS (adjacent location), second adjacent
location, and overwrite (initial magnetization) echoes. The
parameter performs NLTS averaging, pattern-length searching,
and limit checking to reduce the effects of noise and ensure
accurate measurements.

see Chapter 9

Chapter 9

) offers the ability to measur e all

) can be applied to any

²

&RUUHODWLRQ7KHRU\RI2SHUDWLRQ

The oscilloscope’s correlation function measures the
correlation between one section of a waveform and other
sections of the same waveform having the same length, or
between a section and sections of equal length belonging to
another waveform.

When the correlation is performed on the same waveform it is
called an auto-correlation. If the shape of two waveform
sections are identical, the correlation value will be maximized.

The oscilloscope normalizes correlation values to ±1, with 1

indicating that the waveform sections are identical, –1 that the
sections are inverted from each other, and 0 no correlation.

Noiseless periodic waveforms will have perfect correlation (a
correlation value of 1) when performing auto-correlation, and
when the start of the second section is an integer number of
periods later than the start of the first section.

Correlation values can be calculated as a function of various
amounts of time shift between two waveform sections used in
calculating a correlation. This calculation, as a function of the
starting point of the second section being the i’th waveform
sample, is determined as:

350/

mean() =

variance(

Corr

=

i

N

(

∑

j=0

j

wave1 * wave2 (N+1) - mean(wave1 ) *mean(wave2 )

wave b a

∑

xab=

b

wave

) =

a

i+j

/)

variance(wave1 variance(wave1

− ,

()

x

b

(wave )

∑

x=a

b-a

N

)* )

0

2

x

- mean(wave

b
a

N
0

N+i
i

²

2

)

,

N+i
i

,

&RUUHODWLRQ

where Corri is the i’th sample point (starting from 0) of the

correlation waveform,
waveform, wave2 is the second input waveform (wave1 in an
auto-correlation), and

sample ‘a’ to sample ‘b’. The upper bound ‘N’ in the s umm ations
determines the length (length is N+1 sample points, since the
first sample is point 0) of the waveform sections on which the
correlation calculation is perf orm ed. The divisor in the cor relation
function:

wave1j is the j’th sample of the first

b

wave

is a section of a waveform from

a

variance(wave1 variance(wave1

N

)* )

0

N
0

normalizes the correlation calculation to +/– 1, while the

mean(wave1 ) *mean(wave2 )

N
0

N+i
i

term in the dividend removes any effect due to DC offset of the
input waveforms in the correlation function.

Essentially, the correlation waveform f unction takes a section of
the first waveform and calculates how it correlates with an equal­length section of a second waveform using different starting
points in the second waveform . This can be visualized as taking
a section of waveform 1, sliding it over waveform 2, and
calculating the correlation value for the area that overlaps. The
bounds of the starting point are from the beginning of the sec ond
waveform to its length, minus the section length. At the upper
bound, the end of the first waveform section lies at the last
sample point of the second waveform. Owing to the length of
waveforms in the osc illoscope being limited to 10 divisions, the
upper bound of the correlation function is 10 divisions m inus the
section length in divisions.

²

2SHUDWLQJWKH6FRSHIRU&RUUHODWLRQ

This section describes the scope’s operational f eatures for
defining and using the correlation math function.

In order to specify a correlation waveform, a waveform trace
must first be defined as a correlation math function. This is
initiated by pressing the MATH SETUP button, displaying the
menus shown in

Figure 8.1

.

350/

²

Figure 8.1

&RUUHODWLRQ

Assuming the user wishes to place the correlation waveform on
Trace A, he or she will press the m enu button corresponding to

the “REDEFINE $” menu. The “SETUP OF A” menus will
appear, as shown in

Figure 8.2.

²

Figure 8.2

350/

As the correlation function is a m ath function, “Yes” is selected
from the “use M ath? ” menu, and the m enus shown in
are accessed.

1

2 3 4

Figure 8.3

Figure 8.3

Selecting “Correlate” from the “Math Type” menu mak es Trace
A the correlation waveform. From the menu below it, the
waveform from which the section for corr elation will be taken —
here, “%”— is selected. The “ with” menu then enables selection
of the waveform with which the section is to be correlated —
here, “&”. While the “length” menu is used for setting the
section’s length — one division in this example.

²

&RUUHODWLRQ

The annotated boxes in the above figure show the sections.
Annotation ➊ indicates the section of Trace B selected for

correlation by the setting of “length”. This section is correlated
with equal-length sections of the Trace C waveform. The
correlation waveform is shown in Trace A.

Annotations ➋, ➌ and ➍ indicate the selected waveform section
overlaid on different sections of the waveform in Trace C.

With the waveform section delayed by zero (➋), it is clear that
there is little correlation with the corresponding section of
Trace C. The arrow from the box to the correlation waveform
indicates the proximity of the waveform to zero at this point.

With the se lected waveform sec tion delayed by 1.8 divisions (➌),
the corresponding section of Trace C appears almost an
inversion of the selected waveform section. The correlation
waveform is nearly –1 at this point, indicating inverse correlation.

Finally, at a delay of five divisions (➍), the sections are identical
and the correlation waveform is at 1. With a waveform section
length of one division, the last point at which the correlation
waveform can be calculated is a nine-division delay. For any
longer delay, a portion of the selected waveform section would
extend further than the last sam ple point in Trace C — which is
why the correlation waveform display stops at nine divisions.

Figure 8.4

“start” m enu to one division. This menu is used f or determining
at what point in the “with”-selected waveform the selected
section will begin the correlation. In this figure the selected
waveform section from Trace B is initially correlated with the
waveform in Trace C, starting at one division. The resulting
correlation waveform is identical to the correlation waveform in
the preceding figure
correlation starts one division fr om the start of the waveform in
Trace C, it is reduced in length by one, to eight divisions.

on the following page shows the result of setting the

8.3

, from one division on. Since the

²

350/

Figure 8.4

Figure 8.5

waveform section is selected from Trace C, “with” Trace B. A
correlation waveform very different from that of the preceding
figures
Trace C waveform section (➊) overlaid on different sections of
the Trace B waveform (➋, ➌, ➍).

, below, shows the resulting correlation waveform: the

appears. Again, the annotated boxes show the selected

²

1

2 3 4

Figure 8.5

&RUUHODWLRQ

The correlation function can be very useful in determining the
length of a periodic complex disk waveform. As s uch waveforms
have a correlation value of close to 1 (although normally not
precisely 1, due to noise), with every cycle, the period can be
determined by measuring the relative times when the correlation
waveform is this value.

²

350/

Figure 8.6

PRML waveform using the measurement cur s ors ( Annotation ➊).
The period is 980 ns (➋).

shows an example of determining the period for a

1

2

²

Figure 8.6

9

PRML Parameters

acsn Auto-Correlation Signal–to–Noise

Definition Provides a signal–to–noise ratio for periodic waveforms.
Description Using the oscilloscope’s correlation function, acsn provides a

measurement of the auto-correlation signal–to–noise for a repetitive
waveform. At least two waveform repetitions need to be acquired in
order to calculate acsn. In addition, the period of the waveform must
be specified.

The parameter then verifies, and may adjust, the period based on the
value provided. This is crucial, because variations in disk rotation
speed make the exact length of time for a disk waveform difficult to
determine.

Using the period as a starting point, the scope performs an auto­correlation and looks for an auto-correlation peak at the period. At the
top of the peak, the pattern repeats. The scope locates the top and
notes the corresponding time so that it can determine the period. Then
it recalculates the auto-correlation using this period. The value of the
auto-correlation at the period peak, R, is used to calculate the ACSN
as:

S/N = R/(1–R),
ACSN = 10* log10 S/N.

For greater accuracy, the instrument averages several ACSN
measurements when calculating acsn. If the number of periods in the
input waveform is 26 or more, an ACSN measurement is performed for
each pattern and the result averaged. Otherwise, the scope performs
25 ACSN measurements by incrementing by 25 times the starting
point, approximately 1/25th of the input waveform’s length minus the
period of the input waveform used to perform the correlation
calculation, and then averages the result.

All individual ACSN measurements can be observed by histogramming
the acsn parameter. ACSN is limited to measuring signal–to–noise
ratios of 9.6 dB or greater.

ACSN results are presented in dB. All averaging, including statististics
and trend average, is performed on linear units. Average results are
converted to dB.

9–1

PRML

Parameter SettingsSelection of acsn in the “CHANGE PARAM” menus causes the “MORE

acsn SETUP” menu to appear. The user can adjust the mantissa,
exponent or number of mantissa digits by pressing this menu’s
corresponding button. And the associated ‘menu’ knob can be used to
adjust these. However, if a large number of digits is used, selection of
the exact frequency may be difficult. In this case, a number with fewer
digits and less precision should be chosen for the approximate
frequency, then the precision increased as desired and the exact value
chosen.

The pattern length should be set as an integral number of waveform
periods. Since these periods will be correlated with the same number of
following periods, the pattern length must be no more than half the
number of full periods available in the sweep.

Example On the screen below, a noisy 5 MHz period waveform has been

captured on Channel 2. The “pattern len” menu shows the pattern
length set to 200 ns. The value for acsn is 12.89dB.

9–2

Parameters

nlts Non-Linear Transition Shift

Definition Provides a measurement of the nonlinear transition shift for a disk drive

signal.

Description Using the oscilloscope’s correlation function, nlts measures the

nonlinear transition (adjacent location) shift. At least two full cycles of
the test sequence are required for the auto-correlation. In addition, the
period of the waveform must be specified.

The parameter then verifies, and may adjust, the pattern length based
on the value provided. This is crucial, because variations in disk
rotation speed make the exact pattern length for a disk waveform
difficult to determine.

Using the pattern length as a starting point, the oscilloscope looks for
an auto-correlation peak at the length. At the top of the peak, the
pattern repeats. The scope locates the top and notes the corresponding
time so as to determine the exact pattern length. Then it recalculates
the auto-correlation using this length. If the value of the auto-correlation
peak at the pattern length is less than .9, the nlts is not calculated. This
is because the pattern-length sections will be too uncorrelated to
provide a meaningful result. Otherwise, the pattern length value is used
to calculate nlts. Using the pattern delay value, the scope measures
the auto-correlation coefficient for the first pattern-length ‘chunk’ of the
input waveform with a second pattern-length ‘chunk’, starting from the
beginning of the input waveform at the delay value.

In order to correctly calculate nlts, the disk drive waveform must be a
pseudo-random sequence that will create an echo in an auto-correlation
calculation, corresponding to the non-linear transition shift. Typically,
this waveform is a 127-bit pattern based on a x7 + x3 + 1 polynomial,
and the NLTS echo appears at a pattern delay of 20.06% of the input
pattern length. Ideally, the value of NLTS is:

NLTS(%) = –200* Correlation Coefficient (at delay).

However, because noise in the input waveform can affect the
correlation coefficient’s value, the scope averages several NLTS
measurements to reduce the effect of noise. If the number of pseudo­random patterns in the input waveform is 26 or more, an NLTS
measurement is performed for each pattern and the result averaged.

9–3

PRML

Otherwise, the scope performs 25 NLTS measurements by
incrementing 25 times the start point —approximately 1/25’th of the
input waveform’s length minus pattern length — of the input waveform
used to perform the correlation calculation. And then averages the
resulting 25 NLTS measurements. All the individual NLTS
measurements can be observed by histogramming the nlts parameter.

The greater the number of pseudo-random pattern periods in the input
waveform, the greater the reduction in the effect of noise on the nlts
result. In order to further reduce the impact of noise, the NLTS
calculations are adjusted by dividing their value by the correlation
coefficient value at an integral number of pattern-length delays.

The following table gives the standard deviation of the nlts parameter
for varying amounts of auto-correlation signal–to–noise, and numbers
of repetitions of the pseudo-random sequence in the input waveform.
The sampling rate used was four samples/bit cell, and the input
waveform had 20% NLTS.

ACSN #Pattern

Repetitions

26 dB 2 0.44%

10 0.28%
25 0.20%

23 dB 2 0.59%

10 0.32%
25 0.26%

20 dB 2 0.65%

10 0.42%
25 0.28%

17 dB 2 1.08%

10 0.57%
25 0.35%

nlts Standard

Deviation

9–4

Parameters

Parameter SettingsSelection of the “nlts” parameter in the “CHANGE PARAM” menus

causes a “MORE nlts SETUP” menu to appear. Pressing the
corresponding menu button acesses pattern length and pattern delay
menus. The user can adjust the mantissa, exponent or number of
mantissa digits by pressing these menus’ corresponding buttons. And
the associated ‘menu’ knob can be used to adjust these. However, if a
large number of digits is used, selection of the exact frequency may be
difficult. In this case, a number with fewer digits and less precision
should be chosen for the approximate frequency, then the precision
increased as desired and the exact value chosen. The pattern length
should be set to the pattern period.

Although the scope searches for the correct pattern length, the value
provided needs to be sufficiently close to the actual pattern length for
nlts to perform the search. A 1 µsec pattern may, for example, accept
a range of 1 µsec ± 40 nsec. Within this range a value for nlts will be
provided. Otherwise “---” appears on the screen, indicating that no
measurement can be made.

The pattern delay setting is a percentage of the pattern length. The
scope will internally scale the delay value entered by the ratio of the
pattern length calculated internally to the pattern entered by the user.
Several disk drive waveform attributes can be measured by using
different delay values. The following table provides delay values to
enter for the commonly used 127-bit pseudo random sequence (x7 + x
+ 1 polynomial) when measuring various waveform attributes:

3

Waveform

Attribute

Adjacent Location 25.5 20.08%
Second Adjacent Location 30.5 24.02%
Initial Magnetization 45.5 35.83%
Interaction Interference 60.5 47.64%

Bit Cell

Location

Delay (%)

9–5

9

PRML Parameters

acsn Auto-Correlation Signal–to–Noise

Definition Provides a signal–to–noise ratio for periodic waveforms.
Description Using the oscilloscope’s correlation function, acsn provides a

measurement of the auto-correlation signal–to–noise for a repetitive
waveform. At least two waveform repetitions need to be acquired in
order to calculate acsn. In addition, the period of the waveform must
be specified.

The parameter then verifies, and may adjust, the period based on the
value provided. This is crucial, because variations in disk rotation
speed make the exact length of time for a disk waveform difficult to
determine.

Using the period as a starting point, the scope performs an auto­correlation and looks for an auto-correlation peak at the period. At the
top of the peak, the pattern repeats. The scope locates the top and
notes the corresponding time so that it can determine the period. Then
it recalculates the auto-correlation using this period. The value of the
auto-correlation at the period peak, R, is used to calculate the ACSN
as:

S/N = R/(1–R),
ACSN = 10* log10 S/N.

For greater accuracy, the instrument averages several ACSN
measurements when calculating acsn. If the number of periods in the
input waveform is 26 or more, an ACSN measurement is performed for
each pattern and the result averaged. Otherwise, the scope performs
25 ACSN measurements by incrementing by 25 times the starting
point, approximately 1/25th of the input waveform’s length minus the
period of the input waveform used to perform the correlation
calculation, and then averages the result.

All individual ACSN measurements can be observed by histogramming
the acsn parameter. ACSN is limited to measuring signal–to–noise
ratios of 9.6 dB or greater.

ACSN results are presented in dB. All averaging, including statististics
and trend average, is performed on linear units. Average results are
converted to dB.

9–1

PRML

Parameter SettingsSelection of acsn in the “CHANGE PARAM” menus causes the “MORE

acsn SETUP” menu to appear. The user can adjust the mantissa,
exponent or number of mantissa digits by pressing this menu’s
corresponding button. And the associated ‘menu’ knob can be used to
adjust these. However, if a large number of digits is used, selection of
the exact frequency may be difficult. In this case, a number with fewer
digits and less precision should be chosen for the approximate
frequency, then the precision increased as desired and the exact value
chosen.

The pattern length should be set as an integral number of waveform
periods. Since these periods will be correlated with the same number of
following periods, the pattern length must be no more than half the
number of full periods available in the sweep.

Example On the screen below, a noisy 5 MHz period waveform has been

captured on Channel 2. The “pattern len” menu shows the pattern
length set to 200 ns. The value for acsn is 12.89dB.

9–2

Parameters

nlts Non-Linear Transition Shift

Definition Provides a measurement of the nonlinear transition shift for a disk drive

signal.

Description Using the oscilloscope’s correlation function, nlts measures the

nonlinear transition (adjacent location) shift. At least two full cycles of
the test sequence are required for the auto-correlation. In addition, the
period of the waveform must be specified.

The parameter then verifies, and may adjust, the pattern length based
on the value provided. This is crucial, because variations in disk
rotation speed make the exact pattern length for a disk waveform
difficult to determine.

Using the pattern length as a starting point, the oscilloscope looks for
an auto-correlation peak at the length. At the top of the peak, the
pattern repeats. The scope locates the top and notes the corresponding
time so as to determine the exact pattern length. Then it recalculates
the auto-correlation using this length. If the value of the auto-correlation
peak at the pattern length is less than .9, the nlts is not calculated. This
is because the pattern-length sections will be too uncorrelated to
provide a meaningful result. Otherwise, the pattern length value is used
to calculate nlts. Using the pattern delay value, the scope measures
the auto-correlation coefficient for the first pattern-length ‘chunk’ of the
input waveform with a second pattern-length ‘chunk’, starting from the
beginning of the input waveform at the delay value.

In order to correctly calculate nlts, the disk drive waveform must be a
pseudo-random sequence that will create an echo in an auto-correlation
calculation, corresponding to the non-linear transition shift. Typically,
this waveform is a 127-bit pattern based on a x7 + x3 + 1 polynomial,
and the NLTS echo appears at a pattern delay of 20.06% of the input
pattern length. Ideally, the value of NLTS is:

NLTS(%) = –200* Correlation Coefficient (at delay).

However, because noise in the input waveform can affect the
correlation coefficient’s value, the scope averages several NLTS
measurements to reduce the effect of noise. If the number of pseudo­random patterns in the input waveform is 26 or more, an NLTS
measurement is performed for each pattern and the result averaged.

9–3

PRML

Otherwise, the scope performs 25 NLTS measurements by
incrementing 25 times the start point —approximately 1/25’th of the
input waveform’s length minus pattern length — of the input waveform
used to perform the correlation calculation. And then averages the
resulting 25 NLTS measurements. All the individual NLTS
measurements can be observed by histogramming the nlts parameter.

The greater the number of pseudo-random pattern periods in the input
waveform, the greater the reduction in the effect of noise on the nlts
result. In order to further reduce the impact of noise, the NLTS
calculations are adjusted by dividing their value by the correlation
coefficient value at an integral number of pattern-length delays.

The following table gives the standard deviation of the nlts parameter
for varying amounts of auto-correlation signal–to–noise, and numbers
of repetitions of the pseudo-random sequence in the input waveform.
The sampling rate used was four samples/bit cell, and the input
waveform had 20% NLTS.

ACSN #Pattern

Repetitions

26 dB 2 0.44%

10 0.28%
25 0.20%

23 dB 2 0.59%

10 0.32%
25 0.26%

20 dB 2 0.65%

10 0.42%
25 0.28%

17 dB 2 1.08%

10 0.57%
25 0.35%

nlts Standard

Deviation

9–4

Parameters

Parameter SettingsSelection of the “nlts” parameter in the “CHANGE PARAM” menus

causes a “MORE nlts SETUP” menu to appear. Pressing the
corresponding menu button acesses pattern length and pattern delay
menus. The user can adjust the mantissa, exponent or number of
mantissa digits by pressing these menus’ corresponding buttons. And
the associated ‘menu’ knob can be used to adjust these. However, if a
large number of digits is used, selection of the exact frequency may be
difficult. In this case, a number with fewer digits and less precision
should be chosen for the approximate frequency, then the precision
increased as desired and the exact value chosen. The pattern length
should be set to the pattern period.

Although the scope searches for the correct pattern length, the value
provided needs to be sufficiently close to the actual pattern length for
nlts to perform the search. A 1 µsec pattern may, for example, accept
a range of 1 µsec ± 40 nsec. Within this range a value for nlts will be
provided. Otherwise “---” appears on the screen, indicating that no
measurement can be made.

The pattern delay setting is a percentage of the pattern length. The
scope will internally scale the delay value entered by the ratio of the
pattern length calculated internally to the pattern entered by the user.
Several disk drive waveform attributes can be measured by using
different delay values. The following table provides delay values to
enter for the commonly used 127-bit pseudo random sequence (x7 + x
+ 1 polynomial) when measuring various waveform attributes:

3

Waveform

Attribute

Adjacent Location 25.5 20.08%
Second Adjacent Location 30.5 24.02%
Initial Magnetization 45.5 35.83%
Interaction Interference 60.5 47.64%

Bit Cell

Location

Delay (%)

9–5



''0350/5HPRWH&RQWURO&RPPDQGV

2SHUDWLQJWKH6FRSH5HPRWHO\

The final chapter of this manual lists the commands for
performing remote programming of the DDM and PRML
options. Refer to your
description of remote control capabilities. These commands —

DEF, PACU and PAVA by their short names — are to be used
when remotely programming DDM and PRML functions.

Remote Control Manual

for a complete

²

''0350/

)81&7,21

'(),1('()

Command/Query

'(6&5,37,21 The DEFINE com m and spec ifies the m athem atic al ex press ion to

be evaluated by a function. This command is used to control all
functions in the standard oscilloscopes and WP0X processing
packages.

&200$1'6<17$; <function> : DEFine EQN,‘<equation>’

[,<param_name>,<value>,...]

Note 1: Parameters are grouped in pairs. The first in the pair
names the variable to be modified, <param_name>, while the
second one gives the new value to be assigned. Pairs can be
given in any order and restricted to the variables to be changed.

Note 2: Space (blank) characters inside equations are optional.

48(5<6<17$; <function> : DEFine?

5(63216()250$7

SDUDPBQDPH! YDOXH! 'HVFULSWLRQ

<function> : DEFine EQN,‘<equation>’[,MAXPTS,<max_points>]
[,SWEEPS,<max_sweeps>][,WEIGHT,<weight>][,BITS,<bits>]

EQN ‘<equation>’ Function equation as defined

below
DELAY <delay> Delay by time
MAXPTS <max_points> Max. n u m b er o f p o i n t s to c o m p u t e
SWEEPS <max_sweeps> Maximum number of sweeps

3DUDPHWHUV7R6XSSRUW$GGLWLRQDO)XQFWLRQVLQ:3

BITS <bits> Number of ERES bits
UNITS <units> Physical units
WEIGHT <weight> Continuous Average weight

²

5HPRWH&RQWURO&RPPDQGV

3DUDPHWHUV7R6XSSRUW$GGLWLRQDO)XQFWLRQVLQ:3

WINDOW <window_type> FFT window function

3DUDPHWHUV7R6XSSRUW$GGLWLRQDO)XQFWLRQVLQ:3RU''0

MAXBINS <bins> Number of bins in histogram
MAX_EVENTS <max_values> Max. no. of values in histogram
CENTER <center> Horizontal center position for

histogram display.
WIDTH <width> Width of histogram display
VERT <vert_scale> Vertical scaling type

3DUDPHWHUV7R6XSSRUW$GGLWLRQDO)XQFWLRQVLQ350/

LENGTH <length> No. points to use from first

waveform
START <start> Starting point in second waveform

)XQFWLRQ(TXDWLRQV$QG1DPHV$YDLODEOH2Q$OO0RGHOV

<source> Identity
+<source> Identity

-<source> Negation
<source1> + <source2> Addition
<source1> - <source2> Subtraction
<source1><source2> Multiplication
<source1>/<source2> Ratio
AVGS(<source>) Average Summed
RESAMP(<source>) Resample (deskew)
SINX(<source>) Sin(x)/x interpolator
ZOOMONLY (<extended_source>) Zoom only (No Math)

([WHQGHG)XQFWLRQV$YDLODEOH2Q,QVWUXPHQWV:LWK:33URFHVVLQJ)LUPZDUH

ABS(<source>) Absolute Value

²

AVGC(<source>) Continuous Average
DERI(<source>) Derivative
ERES(<source>) Enhanced Resolution
EXP(<source>) Exponential (power of e)
EXP10(<source>) Exponential (power of 10)
EXTR(<source>) Extrema (Roof and Floor)
FLOOR(EXTR(<source>)) Floor (Extrema source only)

INTG(<source>[{+,-} <addend>]) Integral
LN(<source>) Logarithm base e
LOG10(<source>) Logarithm base 10
RESC([{+,-}][<multiplier>*]<source>[{+,-}<addend>]) Rescale
ROOF(EXTR(<source>)) Roof (Extrema source only)
1/<source> Reciprocal
SQR(<source>) Square

''0350/

SQRT(<source>) Square Root

))7)XQFWLRQV$YDLODEOHRQ,QVWUXPHQWVZLWK:33URFHVVLQJ)LUPZDUH

Note: The source waveform must be a time-domain signal, single segment.

FFT(<source>) Fast Fourier Transform (complex result)
REAL(FFT(<source>)) Real part of complex result
IMAG(FFT(<source>)) Imaginary part of complex result
MAG(FFT(<source>)) Magnitude of complex result
PHASE(FFT(<source>)) Phase angle (degrees) of complex result
PS(FFT(<source>)) Power spectrum
PSD(FFT(<source>)) Power density
RESC([{+,-}][<multiplier>*]<source>[{+,-}<addend>]) Rescale

3RZHU$YHUDJH)XQFWLRQV$YDLODEOHRQ,QVWUXPHQWVZLWK:33URFHVVLQJ)LUPZDUH

Note: The source waveform must be another function defined as a Fourier transform.

²

5HPRWH&RQWURO&RPPDQGV

MAG(AVGP(<function>)) PS(AVGP(<function>)) PSD(AVGP(<function>))

)XQFWLRQ(TXDWLRQVDQG1DPHV$YDLODEOHRQ,QVWUXPHQWVZLWK:3RU''0)LUPZDUH

HIST(<custom_line>) Histogram of parameter on custom line

)XQFWLRQ(TXDWLRQVDQG1DPHV$YDLODEOHRQ,QVWUXPHQWVZLWK350/)LUPZDUH

CORR(<source1>,<source2>) Cross Correlation

Source values

Note: The numbers in CUST1, CUST2, CUST3, CUST4, and
CUST5 refer to the line numbers of the selected custom
parameters.

<sourceN> : = {TA, TB, TC, TD, M1, M2, M3, M4, C1, C2,

<function> : = {TA, TB, TC, TD}
<custom_line> : = {CUST1, CUST2, CUST3, CUST4, CUST5}

<extended_source> : = {C1, C2, C3

Values to define number of points/sweeps

<max_points> : = 50 to 10 000 000
<max sweeps> : = 1 to 1000 (For standard instruments)
<max_sweeps> : = 1 to 1 000 000 (For WP01 only)
<max_sweeps> : = 1 to 50 000 (WP02 Power Spectrum only)

Values for Resample Function

<delay> : = −2e−6 to +2e−6 seconds

Values for Rescale Function

<addend> : = 0.0 to 1e15
<multiplier> : = 0.0 to 1e15

Values for Summation Average and ERES

<weight> : = {1, 3, 7, 15, 31, 63, 127, 255, 511, 1023}
<bits> : = {0.5, 1.0, 1.5, 2.0, 2.5, 3.0}

Values for FFT window function

<window_type> : = {BLHA, FLTP, HAMM, HANN, RECT}

C3

G

, C4G}

TD, M1, M2, M3, M4}

G

,C4G, TA, TB, TC,

²

''0350/

))7:LQGRZ)XQFWLRQ1RWDWLRQ

LHA
FLTP
HABMM
HANN
RECT

Blackman–Harris window

Flat Top window
Hamming window
von Hann window

Rectangular window

²

5HPRWH&RQWURO&RPPDQGV

Values for WP03 histogramming

<max bins> : = {20, 50, 100, 200, 500, 1000, 2000}
<max_events> : = 20 to 2e9 (in a 1–2–5 sequence)

<center> : = −1e15 to 1e15
<width> : = 1e−30 to 1e30 (in a 1–2–5 sequence)
<vert_scale> : = {LIN, LOG, CONSTMAX}

+LVWRJUDP1RWDWLRQ

LIN

Use linear vertical scaling for histogram display

LOG
CONSTMAX

Values for PRML correlation

<length> : = 0 to 10 divisions
<start> : = 0 to 10 divisions

G

$9$,/$%,/,7< <sourceN> : = {C3, C4} only on four-channel instruments.

<extended_source> : = {C3, C4} only on four-channel
instruments

SWEEPS is the maximum number of sweeps (Average and
Extrema only).

Note: The pair SWEEPS,<max_sweeps> applies only to the
summed averaging (AVGS).

(;$03/(*3,% The following instruction defines Trace A to compute the

summed average of Channel 1 using 5000 points over 200
sweeps:

CMD$=“TA:DEF EQN,‘AVGS(C1)’,MAXPTS,5000,SWEEPS,200”:
CALL IBWRT(SCOPE%,CMD$)

:3(;$03/( The following instruction defines Trace A to com pute the product

of Channel 1 and Channel 2, using a maxim um of 10 000 input
points:

CMD$=“TA:DEF EQN,‘C1*C2’,MAXPTS,10000”:
CALL IBWRT(SCOPE%,CMD$)

Use log vertical scaling for histogram display
Use constant maximum linear scaling for histogram

display

²