SPEAKER 1: In this sequence, are going to
look at a whole bunch of techniques for analyzing circuits.
Think of these as your tool chest. So you are embarking on 6.002 and going on
to build lots of useful electronic
systems. But before we go and build these systems, much like a carpenter who
needs to go build a house, much like a carpenter has to go and buy a set of
tools from the local store, we need to go and make sure that you have the tools
in your tool chest to analyze these circuits. This tool chest will
include things like the KVL KCL
method, the Node method and so on. But before I begin talking about these
techniques for
your tool chest, I'd like to do a extremely quick review--as is my usual
practice--of what you've covered so far.
So remember our EECS playground. We've gotten into this place by
promising that we are going
to observe the lumped matter discipline. By observing the discipline
recall that the complexities
of Maxwell's equations and the differential equations that you have to
solve-- the partial differential
equations-- goes away. And you're left with very simple linear equations.
And you will see a lot of that today. As you make the lumped matter discipline,
you end up with these lumped elements, like resistors and voltage sources
and so on.
And what you do with these lumped elements is we can label what are called the
branch variables or the
terminal variables for these lumped elements, OK?
So for example, v is the voltage across the element. And i is the current
through the element.
The power consumed by the element is given by vi. Continuing with our review,
the lumped matter discipline
enables us to create the lumped circuit abstraction. So you take
these lumped elements and you connect them
with ideal wires. So in this case, I have a resistor which is a lumped
element, a voltage source. And I connect them with these ideal wires.
And what you end up with is called a lumped circuit. But this is your
lumped circuit abstraction.
Well as we made the transition from physics to EECS by adhering to the lumped
matter discipline.
I had discussed in the last sequence that Maxwell's equations turn into very
simple algebraic equations.
And these are captured by Kirchoff's voltage and current laws, called KVL and
KCL.
So KVL says that for all loops in your circuit, the sum of the voltages around
the loops add up to zero.
Similarly for all the nodes in the circuit, the currents that enter into a node
add up to zero.
And in the same matter, if I just summed the currents leaving a node, they also
add up to zero.
So whether you sum the currents entering the node or currents leaving a node,
they would add up to zero by KCL.
And the beauty of this was by adhering to lump matter discipline, recall the
complexities Maxwell's
equations whether an integral form or differential form went away.
And we were now left with extremely simple algebraic expressions of the
sort. And you will see shortly that you will end up solving extremely
simple linear equations
as we analyze circuits. So as one example here is a linear circuit.
It has one, two, three, four, five, six elements. It's got a voltage source of
a voltage v zero. It's got a resistor, r one and so on and so forth. So for
this circuit according to our abstraction and the laws of KVL and KCL, the
following
are going to be true. So for instance if I look at node a, then according to
KCL,
the currents entering the node must be zero. So in other words, the current
here is ica.
And I can sum to that the current entering from the d direction.
So that would be plus ida. And then there is a current from the ba direction
and iba.
Those are going to sum to zero. Now I can multiply the whole thing by minus 1.
And that would give me the sum of the currents leaving the node are also going
to be zero. So that is KCL.
Now I can also write KVL in this case for this loop, for instance, here. For
this loop I can add up the voltages around the loop. And by KVL they must add
up to zero. So for example if I look at the voltage vca, I can add that to the
next voltage here. That is to vab and then add that to the
final voltage, vbc. And by KCL-- None so all of those must add up to be zero.
Now if you go back to our circuit here that you see on the left hand side, I am
going to show you a little demo that will look at these currents, ica, ida, and
iba, and also look at the voltages, vcabab and bbc and actually go and look at
the circuit, make the measurements, and show that they indeed sum up to zero.
Not surprising. KVL and KCL really work. And so the demo should also work. OK.
So let's go and do our demo.