of Microprocessors

SIGNAL ROUTING 279
First, the set of modules in the system, including outputs from the interface
DACs, are divided into groups. The modules chosen to form a group should
form a compatible set, that is, in a real patching situation the interconnections
among elements of the group would be a maximum and "outside"
connections to other groups would be a minimum. Since the matrix size is
proportional to the square of the number of modules in the group, the size of
the individual submatrices can be dramatically reduced. In fact, it is easy to
show that the theoretical reduction in overall matrix size is proportional to
the number of subgroups it is broken into if the subgroups are equal in size.
For example, if a matrix were broken into five equal-sized subgroups, then
the total number of switches would be one-fifth as large.
Of course, in a practical system one subgroup must be able to connect
to another. Therefore, "communications" input columns and output rows for
the subgroup must be added as in Fig. 8-3. The limit on subdivision is
reached when the quantity of switches devoted to communications exceeds
that saved by the subdivision.
Other methods are available for reducing switch count and are, of
course, widely used in very large switching matrices such as a telephone
central office. The basic idea in all of these is to concentrate the myriad of
inputs into a few "buses" with one set of switches and then distribute the
buses to the desired outputs with another set of switches. If the number of
buses remains constant, then the number of switches increases linearly with
increases in input and output count rather than exponentially. The difficulty
with such schemes in patching a synthesizer is that their fundamental assumption,
that a small number of inputs are connected to outputs, is not
valid. One will generally find that a large fraction of available inputs, outputs,
and modules are used in a significant number of patches.
SUBGROUP I MODULES
SUBGROUP 2 MODULES
, ,
I~-
l~ ~I -
LL
I
•
-I-
~
,-__L-'-
---;:::::=....-
COMMUNICATION
SUBGROUP I MATRIX CONNECTIONS SUBGROUP 2 MATRIX
Fig. 8-3. SUbgroup organization of switching matrix