Tech Design.....
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An Discussion of Stored Energy/Linear Distortion, Part I.
Figure 1. Driver having poor burst response.     Figure 2. Driver having good burst response.
The base frequency response of these
two drivers (figures 1 and 2) can be
observed at the T=0 axis (back plane
of the plots). As can be seen,the
drivers have very different raw
frequency response and the CDS plots
give an indication of how the
irregularities in the frequency response
translate into linear distortion. A perfect
driver with flat response form 0 Hz to
infinity would show a flat 0dB line at
T=0 and nothing for T>0. (Such a
response can typically be obtained
from a wide bandwidth amplifier or
preamplifier.)

Figure 3 shows thew CSD plot for an
electrical filter with a 4nd order
bandpass response (2nd order HP and
2nd order LP) which represents the
desired acoustic target for a midrange
response in a hypothetical speaker
system. Note that it is far from perfect
and suffers its own linear distortion and
stored energy compared to a perfectly
flat response. However, depending on
how well the crossover filter is
designed, we would expect the CSD
plot for either driver to have the same
characteristics when connected to its
filter. Any deviation from this behavior
indicates some residual linear
distortion relative to the true bandpass
response. (See
Part 2 for a discussion
of stored energy in crossovers.)

Figures 4 and 5 then show the CSD
results for drivers 1 and 2,
respectively, in combination with their
respective digital crossover filters
constructed to yield the targeted band
pass response. Both plots show some
deviation from that presented in Figure
3, thus we can conclude that neither
crossover filter represents the perfect
linear correction to transform the raw
driver response into the targeted
bandpass response. This is a result of
both some error in the digital transfer
functions indicating a residual level of
linear distortion, and possible nonlinear
components in the driver response
(nonlinear distortion). However, it is
also clear that with their respective
filters in place both system perform
very closely to the ideal and will have
similar characteristics with regard to
linear distortion and stored energy.

The conclusions to be drawn here are:
that linear distortion tests on a raw
driver are not necessarily
representative of the behavior of the
driver when connected to a carefully
designed crossover network; linear
distortion is just that, a linear effect,
and can be corrected by application of
linear networks to shape the response
to the desired target; different system
which have similar impulse, frequency
or CSD plots will have similar burst and
stored energy characteristics. The
advantage of using drivers which have
smoother raw response is that the
crossover filters and response shaping
required to obtain the desired acoustic
targets can be much simpler.
Figure 1. Driver 1 frequency response and CSD.
Figure 2. Driver 2 frequency response and CSD.
Figure 3. Frequency and CSD plot of 4nd order band pass filter.
Figure 4. Frequency and CSD plot of Drive 1/filter combination
Figure 5. Frequency and CSD plot of Drive 2/filter combination