Handbook for Sound Engineers

Computer Aided Sound System Design 1367

the system, the sensitivity of the transducer , and

the filter configuration of the system:

(35-38)

where,

denotes the angle- and frequency-dependent

directivity ratio.

Correspondingly, the coherent pressure sum of

several components of a system is expressed by:

(35-39)

This formulation relates principally to Eq. 35-6 with the

equalities of and.

The loudspeaker properties and

will normally be measured and the parameters

and are defined by the manufacturer or end

user. As a result, this concept allows one to model the

full response of a multicomponent system under con-

sideration of the given filter settings, may it be a multi-

way loudspeaker or a digitally steered column. Of

course, the effect of changing crossover parameters on

the directivity characteristics can be also calculated.^41

An example is shown in Fig. 35-33.

A second step can now be taken as well. The

mechanical variability of touring line arrays or clusters

can be considered by defining either directly by its

coordinates or indirectly as a function of user-defined

parameters, such as the mounting height of the system

and the splay angles between individual cabinets.

35.2.1.3.4 Shadowing and Ray Tracing

It has been pointed out earlier, that for a large-format

loudspeaker system, the use of a single point as the ori-

gin for ray tracing- or particle-based methods is not ade-

quate. On the other hand, it is not practical to use all

individual acoustic sources as origins for the ray-tracing

process, given available computing power and the geo-

metrical accuracy of the model. But that is not neces-

sary anyway, since the ray tracing algorithm can be run

for subsets or groups of acoustic sources. Therefore rep-

resentative points have to be found, so-called virtual

center points, that can be used as particle sources,

Fig. 35-34.

Typical lower-frequency limits for the particle model

and the level of detail in common room models suggest

ray tracing sources to be spaced apart by about 0.5 to

1 m. In many cases this corresponds to one ray tracing

origin per loudspeaker cabinet. While this method of

virtual center points is significantly more accurate than

using a single source of rays for the whole array, it is

still viable with respect to the required computational

performance.

35.2.1.3.5 Additional Notes

Some other problems are also automatically resolved by

modeling the components of a loudspeaker system sepa-

rately. For example, the definition of maximum power

handling capabilities becomes straightforward. Each

component can be described individually by its maxi-

mum input level and possibly the frequency response of

the test signal. In this respect also the focus of the pro-

audio community increasingly shifts from sometimes

obscure maximum power values, as defined by the loud-

speaker manufacturer, toward the specification of maxi-

mum voltage as the entity that is directly measured and

applied in modern constant voltage amplifiers.

Finally, one should be aware of the errors made in

advanced modeling approaches like the GLL or DLL. It

is clear that the acquisition of complex data requires

more care and thus engineers will initially see signifi-

Figure 35-32. Comparison of measurement and prediction
for the LF–LF configuration of two two-way loudspeakers,
measured data at 5q angular resolution (+), complex data
at 5q angular resolution (dashed) and complex data (solid)
at 2.5q angular resolution, at 1 kHz and -octave band-
width.

10

20

30

40

30

210

60

240

90

270

120

300

150

330

(^1800)
(^1) » 3
K f
hf
AM-M-f = Kf f hf Uf
M- f
pSum rf
*nKM-f n f hn fUn f
rr– n
-------------------------------------------------------------------------exp>@–jkn rr– n
n

¦

=

EKaKn f hn f PUa n f^2

*n M-f Kn f

hn f

*n f

rn,