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8-14
Such an estimate may be easily obtained from a graph of the function once
the breakpoint locations have been determined.
The procedure is as fol-
lows:
1.
Locate visually the points where the slope is steepest (in
either the positive or negative direction).
2.
Estimate the slope of the curve at these points by drawing
triangles or counting squares on the graph.
3.
Form the difference between the maximum positive slope and
the maximum negative slope.
This is the total slope change
required, between the two points where maximum slope occurs.
Note that in subtracting two slopes of opposite sign,
the
magnitudes are added.
If there are several points'of maxl-
mum positive and negative slopes, choose a pair of such
points near each other where the slope difference is large.
4.
Divide the total slope change between these two points by
the number of breakpoints in this interval.
This gives
the average slope change per breakpoint in the "worst
case" region.
The slope actually required may be some-
what greater, since not all segments will have the same
slope change.
However, this estimate is a good one to use
as a starting point.
8.4.5
Example of Slope Amplification
As an example of a function requiring slope amplification, see Figure 8.6.
This curve was initially drawn free-hand on a sheet of graph paper and in-
serted in the X-Y plotter.
Breakpoints and function values were set direct-
ly by observing the plotter, not the DVM.
Hence there was no need to tabu-
late the function.
Thus the curve offers a good example
~f
graphical setup
procedure as well as of slope amplification.
Breakpoint location was determined by following the rules in Paragraph 8.4.1.
There are 4 relatively straight portions and 3 relatively "curvy" portions.
$ince the function appears to curve about the same amount in each curve re-
gion, the nine available breakpoints were equally distributed - three per
region.
Note that the breakpoints have been marked according to the SEG-
MENT SELECTOR position that will be used in setting them.
The pattern goes:
OFF, 2, 3, 4, ••• , 9, 10, OFFo
As mentioned previously, position 1 is
skipped.
The greatest positive slope occurs at the left side; the greatest negative
slope occurs just past the first peak; these facts are obvious by inspec-
tion of the graphe
Graphical determination of the slopes indicates that the positive slope is
about 5e5, and the negative slope about -6.
The difference in slopes is
11.S.
Since there are three breakpoints between these two points, the
average slope change per segment is 11.5/3 or 3.9.
It is somewhat question-
able whether a slope multiplier of 4 will be adequate, since some of these
breakpoints will require greater slope change than others
o
However, it may
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