L7 5 2 2 Thevenin Equivalent Impedance

Determining the Thevenin impedance of a circuit by finding the equivalent impedance

>> All right. In our previous video,

we found that the Thevenin
equivalent voltage, V_Th,

was equal to 6.25 angle 51.34 degrees.

Once again, I'm going to be
using this shorthand notation

of representing the polar coordinates
of the impedances of the phasors

as opposed to writing 6.25e to the j51.34.

All right. With the Thevenin voltage,

we need now simply to determine

the Thevenin equivalent impedance

and we're going to do that
each of three different ways.

This first method is what we'll refer
to as the Equivalent Impedance method.

It works when we have
only independent sources or no sources.

This equivalent impedance method
that we're going to show first

does not work if the circuit you're
analyzing has dependent sources.

So, this approach requires us to deactivate
any independent sources present.

In this case, there's
an independent voltage source here

which we deactivate by turning it to zero

and thus replacing it with a short circuit.

Then, looking back into
the circuit from the terminals AB

and determining what the equivalent
impedance is that we would see

looking back in that way.

Well, hopefully you can see pretty
easily that with the source deactivated-

replaced with short-circuit,

it brings this capacitor and
this resistor in parallel,

-and that parallel combination is
in series with the j50-Ohm resistor

such that the impedance seen
looking back into these terminals,

Z Thevenin, will equal Z parallel
plus the j50-Ohm inductor.

So, Z parallel is equal to

20 times minus j25 divided by 20 minus j25,

which turns out to equal
12.2 minus j9.8 Ohms.

So finally, Z Thevenin then is equal to Zp;

12.2 minus j9.8 plus the j50,

and that then equals 12.2 plus j40.2 Ohms.

Z Thevenin, bringing it up here,

then rewriting it just to show what
we've got to show our incomplete model.

Our complete model involves the Z Thevenin
equaling 12.2 plus j40.2 ohms

and our claim then is that
this Thevenin equivalent circuit

has the same terminal characteristics
at the AB terminals

as our original more complicated circuit.