A Symbolic Analysis of Relay and Switching Circuits

47
The general network of Fig. 26 contains n(n + 1)
elements. It can be shown that for any ~iven s~lection
'of a-numbers at least n of the elements will be superfluous.
It follows that any symmetric function of n
variables can be raalized With at most n 2 elements.
Equations from Given operatin~ Characteristics.
In general,
there is a certain set of independent variables
A, B, a, ••• Which may be s\ntches, exte~lellY operated
or protective relays. Thera is also a set of depend~nt
variables x, y, z •••• Which represent relays, motors or
other devi~es to be controlled by the c1rcuit. It 1s
required to find a network which ~1vas
for each possible
comtanetion of values of the independent variables, the
correct value s for all the dependent variables. The
followin~ principles gi va
the general method of solution.
1.- Additional dependent variables must be
introduced for each added phase of operation of 8
sequential system.
Thus if it is desired to construct
.8 system which operates in three steps, two additional
v8riables must be introduced to represent th~
beginnir~
of the last t\'Vo st!3ps. These additional variables
may rep~esent
contacts on a stepping switch or relays
Which lock in sequentially.
Similarly each required
time de18~T wl11 reqt1.ire a nevv variable, representing