In the last lecture, we modeled the copper loss of the inductor of

a boost converter by inserting

an extra resistor in series effectively with the inductor in a lumped element model,

and with that model we then calculated

the effect of this resistor on the output voltage of the boost converter.

In this lecture, we're going to extend that result and construct

an equivalent circuit model to go along with the equations.

So, here are the equations that were found in the last lecture.

For this example, the first equation was from

inductor volt second balance and

the second equation we got from capacitor charge balance.

The object now is to find an equivalent circuit to go along with these equations.

The approach that we're going to take is to

view these equations as the loop and node equations of our equivalent circuit model.

Indeed, the first equation was found by finding

the average voltage around the loop where the inductor is connected.

So, this effectively is a loop equation in our model.

The second equation was found by finding the average current

flowing into the capacitor from the node where the capacitor is connected,

namely the output node.

So, we can view this equation as a node equation in our model as well.

So, what we're going to do is construct

equivalent circuits to go with each of these equations.

Now in basic circuits classes,

I hope you were taught how to take a circuit

and apply Kirchhoff's laws to find the equations.

Here we're going backwards,

we're given the equations and we want to construct a circuit.

Well, this process of going backwards turns out to not be unique.

There's more than one way to construct a circuit that satisfies these equations.

So, we have to be careful how we do it to make sure that

our resulting model has physical significance,

and my advice here is to use

the equations in the form that they come without further manipulations.

So, the first equation was found from inductor volt second balance,

we should keep it as a sum of voltages around a loop corresponding

to a Kirchhoff voltage law equation and don't manipulate this.

If you for example divided through by say R,

then this first equation would have terms that have

dimensions of current rather than voltage and you

might think then that this is a node equation with currents flowing into a node.

While that equation might be mathematically correct,

the resulting model is not physically connected to the actual converter.

So, we don't manipulate these equations or do any kind of algebra on them,

we construct circuits to go along with the equations right away.