EAI 580 Reference Handbook page 82

8-4
2. Start out by locating the areas where the function is
nearly straight; the individual segments in such areas
may be relatively long. In between these areas will be
the areas of rapid slope change; the breakpoints should be
concentrated here.
3. As a general rule, it does not pay to locate two break-
points closer together than about 4% of full scale (i.e.,
0
0
04 unit, or 004 volt on a ten-volt computer)o If two
breakpoints are spaced more closely than this, they tend
to "blend" into one because of the characteristics of di-
odes, which are not perfect switches. This effect, which
"rounds off the corners" of the function, gives a smoother
output and is beneficial, provided it is used to advantage
in determining breakpoint locations. In case of very sharply
curved functions, it may be necessary to space breakpoints
as close as 2% of full scale (0.02 unit).
As an example, consider Figure 8.2.
This curve represents
an arbitrary function, scaled on a unit basis, so that both
input x and output f(x) vary from zero to unity. The pro-
cedure starts by noting the two areas where the function
is almost straight, namely 0
<
x
<
0.2 and 0.6
<
x
<
0 0 8.
There would be little point i; putting any breakpoi;t here,
so the process starts by drawing two fairly long segments
to appr6ximate the function over these intervals
o
The intervals from 002 to 0 0 6 and from 0.8 to 1.0 are the
intervals where the function curves noticablyo Since this
is a relatively "mild" function, it may be easily approxi-
mated by ten segments
0
Hence, there are nine breakpoints
to be determined. (Note that the number
of~akpoints
is
one less than the number of segments. For example, a two-
segment function would have one breakpoint - where the two
segment joined; a three-segment function would have two
breakpoints, and so on. The endpoints of the interval are
fixed, and are not counted as breakpoints o )
We have nine breakpoints to divide between the two intervals of rapid slope-
change
0
Since the first interval is longer, and the slope changes somewhat
more in this interval, more breakpoints should be put in this interval
o
Based on a 6-3 split, the breakpoint location in Figure 8.2 was determined.
The above rules and example are intended only as a general guide.
8.4.2 DFG Setup Theory
In order to understand the DFG setup procedure, one particular aspect of
the electrical theory of DFG's should be explained. Mistakes are less
likely to occur if the operator has some knowledge of why various steps
are taken, hence, this summary.