L3 5 2 Techniques to DetermineThevenin Model

Demonstrates Thevenin Equivalent Circuit techniques

In this video we're gonna demonstrate
the technique for determining the Thevenin

equivalent circuit by looking at
a relatively simple circuit and

going through the different steps
you will be using to do this.

The first thing we need to determine
is the open circuit voltage.

The Thevenin voltage or
the voltage in our Thevenin model.

Consists of a Thevenin voltage which
we pointed out is just the open

circuit voltage.

So in this case we need to know
what the voltage between a and

b is with nothing connecting a and b.

As you look at this, you can see then,

that the open circuit voltage
is the voltage across R2.

Now, we can use any method we want
to determine the voltage across R2.

We could calculate the current
running through these.

Which, because this open circuit,

we should point out there is no current-
[SOUND] Going through that branch.

That means that these two
resistors are in series.

And by definition the current is
[INAUDIBLE] the same through both of them.

So we could calculate the current
through those two resistors and

we multiply R2 by that current and

that would give us the Open circuit
volts through the volts across R2,

we're gonna also use our voltage divider
which was developed, we derive a voltage

formula by taking advantage of the fact
that those two cells are in series.

So let's just do that.

V open circuit, is equal to then,
V sub s, times.

R2 over R1 + R2.

For this circuit, that is our V Thevenin.

So to get the open circuit
voltage using any of the voltage,

any of the certain analysis techniques
that you have to determine the voltage

across the open terminals.

Next, we need to determine
the thevenin resistance.

And at that point, we will have
our thevenin equivalent circuit.

Now we're gonna see there are at
least three different methods for

determining the thevenin resistance.

And we're going to Demonstrate each of
those models on the simple circuit.

The first method takes advantage
of the definition of R Thevenin,

you'll recall from our previous video
we said that R Thevenin was defined

as the ratio of the open circuit
voltage to the short circuit current.

Now in the previous slide we determine
that the open circuit voltage

which is the voltage across our
to in this case which was vs so

times R two over R one
plus R two.Now we need

to determine what the short circuit
current is by short circuit currently mean

if we short The wire between
the two terminals A and

B and then determine what that current is
that flows through that short circuit.

That's the short circuit current.

Well, in this case the short circuit
pulls the voltage here to zero.

So, there would be no
current going through R2.

And the short circuit current then is
simply the current that would be flowing

through R 1 or I short circuit is
equal to V sub S divided by R 1.

So you've been using this
first method method 1 we say

then that open the R thevenin is equal
to the ratio of the open circuit voltage

short circuit current, we form that And
say that R 7 is equal to V

open circuit divided by I short
circuit which is equal to V sub

S times R 2 over R 1 plus R 2.

That's our open circuit voltage

divided by the short circuit
current which is V sub S.

Over R one.

Well, the v of s is cancelled.

We take this one over our one in
the denominator, invert and multiply, and

we get then that our Is equal

to R 1 R 2 over R 1 +
R 2 At least it works

if you've got an independent source in the
circuit that you're attempting to model.

Method one then is determine
the open circuit voltage and

the short circuit current using any
circuit analysis method you'd like.

And then forming the ratio of
the open circuit voltage to the short

circuit current.

The second method works
when all you have or

the only types of sources you
have are independent sources.

It works only with independent

Sources and in this method,
or to apply this method,

we deactivate any of the sources present.

And by deactivate,

we mean the same thing that we did back
when we were talking about super position.

When you deactivate a voltage source,
you turn the voltage source to zero.

Or in this case, or

a voltage source turned to 0 is
effectively a short circuit.

So having deactivated the independent
sources present, we then calculate

the resistance seen looking
back into the circuit.

Well, looking back into it with this
point pulled to ground by deactivating

the voltage source, we see then that R1
and R2 are in parallel with each other.

And the resistance that we see
going back into the ab terminals is

R1R2 over R1 + R2.

Which is the same result
we got on the previews.

Using the previews method.

The third method, involves applying
a test voltage at the terminals, and

pushing the current back into the circuit,
pushing the current back into the circuit.

After deactivating the sources.

This is somewhat like going back
to our power training analogy, or

an automobile analogy.

It'd be like sort of
turning off the engine, and

then blowing back into the exhaust pipe,
and measuring

the resistance to the movement of air
going back into the Into the exhaust pipe.

So, Method 3,
deactivate the independent sources.

If you have dependent sources present,
don't deactivate them.

Deactivate just the independent sources,
and then

apply a test voltage We'll call it V Test,
VT for test.

That's not the Thevenin volt,
it's just V Test which will

force a test current to
flow back into the circuit.

Again, after we have
deactivated the source.

The resistance that we feel going
back into it is simply the ratio

of the test voltage divided
by the test current.

So our approach now requires us to

come up with an equation or
more than one equation.

It allows us then to by
just algebraic manipulation

form the ratio of Vtest over Itest.

Let's just do it.

It's easier to show that
it is to tell about it.

When we apply this,

after deactivating the voltage source,
we see that we have only one node here.

And that node is in fact,
at least in this circuit, The voltage,

our test voltage being Test.

So, let's write a node equation here at
this node in terms of the node voltage

V Test.

The current leaving this node going
through R1 is going to be V Test divided

by R1,
is the current leaving going this way.

The current coming down here
through R2 Is gonna be added to it

plus V test divided by R2.

Now you'll notice that I test
is directed into the nodes, so

that would be minus I test equals 0.

Now let's factor out the common
V test here Times 1 over R1

plus 1 over R2 and take I test to
the other side as a positive I test.

Getting a common denominator
we have then V test time

R1 plus R2 over R1 times R2.

Is equal to I test.

Now that we've got a factor
of the test on this side,

I test on that side divide both sides by
I test, divide both sides by this term

here and
we get that then v test over I test

Which is our R thevenin is = R1,

R2 over R1 + R2.

Which is the same resistance we
determined through the other two methods.

So, again, this approach drives home the
idea that what this Thevenin resistance

represents is the restriction or
the resistance seen

looking back into
the terminals of our circuit.

Let's review then, determining
we find the open circuit voltage

using any method of
circuit analysis we want

we then use one of three methods
to determine our thevenin.

The first method works When you have at
least one independent source present.

Method one then is too short
between the output terminals and

determine the short circuit current and

then form the ratio V open circuit
divided by high short circuit.

That's method one.

Method two works only if you
have independent sources

and with only independent sources present,
And deactivate the independent sources.

In this case, we had a voltage
source that we shorted out.

Had it been a current source, we would
have opened circuited that current source,

and then determined the resistance,

the equivalent resistance seen
looking back in from a to b.

Method two works only if
independent sources are present.

Method three works when you have both
independent and dependent sources.

If you have dependent sources, if you have
independent sources you deactivate Any

of the independent sources by replacing
voltage sources with short circuits, and

current sources with open circuits, and

then apply a test voltage
to the terminals.

And then using algebraic
manipulation techniques,

derive the ratio of V test over I test.

Three different options.

Some options work under all circumstances,

other options work only at
given certain circumstances.

And in the next two or three videos, we'll
go through and give examples demonstrating

each of these three techniques in
somewhat more complicated circuits.