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BUILDING BLOCK FUNCTIONS-FOUNDATION OF DESIGN
Note that the first two and last operations are used to
save and restore the sign of the result. The quotient is
available in the DAR.
If greater precision is needed, the contents of the DAR
before quotient sign restoration can be saved, the DAR
cleared,
and
conditional
subtractions
continued.
However, before the conditional subtractions can be
continued, the carry value must be restored. (The carry
should always be equal to the complement of the sign of
the partial remainder.) Restoration of carry may be
accomplished by adding and then subtracting the divisor
(appropriately shifted) from the partial remainder.
4.2 Realizing Relaxation Oscillators
There are several ways that oscillators may be realized
with the 2920. One method utilizes a simple relaxation
technique
to
implement
a
sawtooth
waveform
generator. The sawtooth waveform may then be altered
using
piece-wise
linear
transformations.
Another
method consists of implementing an unstable second
order filter, which is described in a subsequent section.
4.2.1 Reset Technique For Relaxation Oscillator
A simple sawtooth oscillator can be implemented as
follows: Once each sample period, subtract a positive
value
Kl from a register. If the result of the subtraction
becomes less than zero add a second positive value K2 to
the register.
K2 must be greater than K I.
The
oscillator
generates
samples
of
a
negative
sloped sawtooth waveform which has a frequency of
(KlIK2) fs where fs is the sample rate. The amplitude
ranges between
K2 and O. The values for Kl and K2 may
be constants or variables. If the value of the step size
constant
KI
is a function of another waveform or exter-
nal voltage, a frequency modulation or voltage con-
trolled oscillator resul ts.
The output of the oscillator corresponds to a sequence
of samples of a sawtooth waveform. If a different
waveform is desired, either filtering or waveform
modification is necessary. Caution must be exercised
when linear filtering is used since the samples of a
sawtooth represent samples of a signal that is not band
limited. Therefore, the higher harmonics of the original
sawtooth may beat with harmonics of the sampling fre-
quency to produce spurious frequency components. If
the bandwidth of the waveform modifying filter is too
4-6
wide, some spurious components could pass through
producing the equivalent of a small amplitude modula-
tion on the output. Very narrow-band waveform modi-
fying filters may be difficult to realize, and may produce
additional problems if the oscillator is frequency or
phase modulated.
A non-linear transformation of the oscillator output can
modify the samples so that they correspond to samples
of a more band-limited signal, even when the oscillator
is being used in a variable frequency mode. The most
effective band limiting transformation is one that con-
verts the sawtooth waveform to a sine wave.
Although the 2920 cannot exactly realize a sine wave
transformation, it can execute a piecewise linear
approximation of arbitrary accuracy. Figure 4-2 shows
a transformation for use with a relaxtion oscillator with
K2
=
+1.0.
OUTPUT
+1.0
-1.0
\
\
/
\
I
V
/
/
I
INPUT
Figure 4-2. Transformation for Conversion of
Sawtooth Waveform to Clipped
Triangle
The transformation shown in Figure 4-2 can be realized
using a combination of overflow-saturation and abso-
lute magnitude functions. (Note that, in Figure 4-2, if
the function represented by the dotted portion is
realized, overflow saturation
will
convert the waveform
to the solid line version.)
The parameters of the transformation can have a
marked effect on the harmonic content of the
waveform. The transformation of Figure 4-2 cancels all
even harmonics with ratio of the amplitude of the nth
odd harmonic to the fundamental being given by the
relationships:
p(n)
=
sin
(nrr/3)
n
2
rr/3
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