BEAM From the Ground Up is a
BEAM
Reference Library
site.
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Connecting Nv nets
Getting in synch
The vast majority of Nv
nets are either loops of Nv
neurons,
or several such loops connected together (given that a
"loop" can consist of just 2 Nv
neurons).
Loops of Nv
neurons
are generally called "cores,"
and are described by a numeric prefix denoting the number of
Nv
neurons
they contain -- Bicore (2), Tricore (3), Quadcore /
Quadracore (4, the most common form), Quincore (5), Hexcore
(6), Septcore (7), Octacore (8), etc.
Bad
nomenclature warning!
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You should be aware that there's also a
beast called the Monocore
-- this is not a loop of a single
Nv
neuron,
but rather a more-loosely connected pair
of bicores.
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As a general rule, connecting two cores
together results in a synchronized group of circuits -- the
fastest one causes the other(s) to synchronize to it. This
"bossy" core
(generally a bicore)
is termed the "master," the others are termed
"slaves."
The simplest set of Nv
loops -- the master / slave bicore pair
First, we'll rotate the diagram around a bit
(note that this doesn't change anything in an
electrical sense):
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This circuit is a master / slave bicore
pair (often referred to in a fairly misleading shorthand as
a "master / slave bicore"). Here, the suspended
bicore is the master (green), and acts as a
"pacemaker" for the whole circuit. The former grounded
bicore is the slave (blue), and operates in a
subservient fashion (but more on that in a bit).
The following description of the slave
bicore
and its behavior comes courtesy of Wilf
Righter
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In normal operation the slave bicore
is a kind of complementary Nu
Neuron
with feedback. This is best explained with a
diagram:
Assume a stable condition where:
The outputs of the master are 1
and 0,
the inputs of the slave are 1 and 0,
the outputs of the slave are 0 and 1.
Therefore the voltage across the slave
coupling resistors (Vsr) = 0V and the voltage
across the slave capacitors (Vsc) = 0V. Now
assume the master bicore has just flipped
it's bits.
The master outputs are now 0 and
1,
the slave inputs are still 1 and 0,
the slave outputs are still 1 and 0.
Therefore Vsr=Vcc and Vsc=0V and the
slave capacitors start to charge / discharge
through the "coupling" resistors. So far, no
different from two Nu neurons (integrators)
delaying a step input by their RC time
constant.
The slave inputs 1 and 0 charge towards
opposite values and when either of the slave
inputs reaches the switching threshold at
approximately 1/2 Vcc, the corresponding slave
output starts to switch from 1 or 0 to 0 or 1. Now
feedback occurs, which is quite different from the
Nu neuron and more like an Nv
neuron.
When the first output changes, this change is
capacitively coupled into the other slave
input and causes that input, already near 1/2 Vcc,
to cross its threshold, which in turn causes the
second output to change, which is capacitively
coupled into the first input. The second RC node
with the larger time constant plays no role in the
timing of the slave bicore, and the RC
components can be eliminated. This positive
feedback results in an rapid voltage change at both
slaves' input towards the value as the
corresponding master outputs. During this
rapid change, each slave capacitor charge is
"dumped" through the slave input protection
diodes so that the voltage across the caps and
resistors rapidly changes to 0V. At that point the
following stable condition exists:
The master outputs are 0 and
1,
the slave inputs are 0 and 1,
the slave outputs are 1 and 0
Vsr = 0V and Vsc = 0V
The process repeats when the master
bicore again flips its bits in the opposite
direction.
The formula for the delay time of a 74HC/ACxx
slave bicore is approximately 0.7*R*C.
The time constant of the master bicore
is much trickier to calculate (especially when
components are closely matched) since the switching
threshold is close to 0V across the suspended
resistor (i.e. on the flat part of the exponential
discharge curve). This is what makes the
master bicore
time constant relatively-long for a given RC, and
quite sensitive to preemptive triggering by
"feedback" from the load. A rule of thumb used for
determining the 74HC/AC04
or 74HC/AC240
type master bicore
time constant is that it's approximately 1.4*R*C.
Based on the requirement for 90 degree phase delay
between master and slave bicore, the
same RC components can be used in both.
The 90 degree phase shift means that the
slave bicore's
output changes occur half-way in time between the
master bicore's
output changes.
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Meanwhile, what is (inaccurately)
referred to as a monocore,
is really just a master / slave bicore
pair with a simpler connection than what we saw above:
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