0:13

So far in the course we have talked

about converters containing only inductors, capacitors and switches.

We've ignored one of the other primary elements

used in switching converters, namely the magnetic transformer.

So, for the next several lectures, we're

going to discuss converters with transformers what the

basic circuits are, and how to model them

and extend what we already know to understand

the operation of transformer isolated converters.

0:44

There are a number of reasons

to incorporate a transformer into a converter.

One of the major ones is when safety requirements require that we have

transformer isolation from the power line now one

way to do this is to put a 60 cycle transformer at the input of our system.

But 60 cycle or 50 cycle transformers elsewhere

in the world these transformers are very heavy

and, and large and now a days we generally try to avoid them whenever we can.

1:17

the size of the transformer scales more or less inversely with frequency.

So if we can build a transformer that

operates at the converter switching frequency, say 100 kilohertz

instead of 60 or 50 hertz the size of the transformer

and its weight can be reduced by a very large margin.

Here's an example of a what a iPhone charger that plugs into the a.

120 volt 60 cycle wall and produces a five volt output to drive

the USB connected devices and power them. Inside this

charger unit is, is a fly back converter which

is a transformer isolated version of the buck boost converter.

And it contains a high frequency

transformer that operates at the switching frequency.

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Another reason to use a transformer is when we

have a large step up or step down of voltage.

Suppose we wanted, we had 100 volts and we wanted to make one volt.

We could build a buck converter and operate it at

a duty cycle of 1%, but such a small duty

cycle may have, may mean that the conduction time of

the transistor is equal to the switching times of the transistors.

And we find then that the efficiency is very low.

And most of the time, we're switching instead of conducting.

So instead, we could build a converter that

includes a transformer, that has a turns ratio,

and use the turns ratio to do most of the work of stepping down the voltage.

And that converter then operates at a much

higher duty cycle, where the efficiency is better.

3:22

Here's a diagram of a transformer that is

a physical magnetic transformer, it has multiple windings,

each with some number of turns, so winding one has

n1 turns, winding two has n2 turns, and so on.

And we've labeled the voltages and currents of each winding.

3:57

To understand how a converter works that contains a transformer like this.

We need to first model the transformer.

And to write a set of equations that describe the behave, its behavior.

What we're going to do is to

employ this equivalent circuit model for the transformer.

4:34

is internal to the model and is modelling

things that are going on inside the transformer.

So we replace our physical transformer with this equivalent circuit model.

And this equivalent circuit model has elements

that we can solve using standard circuit analysis.

So the equivalent circuit model we will use is most

of the time, is this simple first order model that

contains an ideal transformer. Inside these dotted lines.

5:04

and then in parallel with one of the windings of the ideal transformer is an

inductor that is called the magnetizing inductance of the transformer.

'Kay?

So there isn't actually a physical extra inductor put on our transformer.

This is built into the transformer.

And everything inside this dashed line

is a equivalent circuit that is modelling correctly, the

terminal equations between the voltages and currents of the windings.

5:34

Okay, the definig equations of the ideal transformer, we'd seen before the

voltage of each winding divided by its turns is equal for all of the windings.

So V1 over N1 equals V2 over N2 and so on, and

this makes the voltages scale according to the turns ratios of the ideal transformer.

5:56

The equations of the currents going into the windings of the ideal transformer.

is this one.

And this is, again we've seen before also, the sum of the amp turns flowing into the

dots of the ideal transformer is zero. Now in addition to the ideal transformer,

we're adding one more element. this L sub N is called the magnetizing

inductance, and its current, I sub N, is called the magnetizing current.

6:27

The magnetizing inductance is actually real.

And the way to see that is to do the thought experiment

of, suppose we connect something up to our transformer, like some AC voltage.

Connect it up to our primary winding.

And suppose we disconnect all the other windings.

So there, winding two and winding three here are simply open circuited.

What do we expect this to, to do do?

7:18

And the magnetizing inductance then actually models

that inductance.

So the magnetizing inductance referred to the first

winding, where it's drawn here, is the inductance

that you would get if you simply put in one turns of wire on the core.

7:52

it has to obey volts second balance.

The average value of the voltage applied to this inductor must be zero.

So we can apply volt second balance to find the steady state behavior.

Of the, of circuits containing physical magnetic transformers.

8:10

Magnetizing inductnace also explains why you can't put DC through a transformer.

So we can't, for example,

apply a DC voltage, Vg, to our transformer.

Because at DC, the magnetizing inductance being an inductor has zero impedance,

its impedance goes to a short circuit at DC and then shorts out our DC voltage.

And if we apply a DC voltage volt seconds won't balance on, on LM.

8:42

The magnetizing inductance is a physical inductor in that sense.

It models magnetization of the transformer core.

The transformer core has a BH characteristic.

If you apply too many volt seconds to the transformer core

it will saturate and the transformer will turn into a short circuit.

Which generally is bad in most of our converters.

9:07

so if

the applied volt seconds on the winding is too large,

what happens when you apply a voltage is we integrate.

So by the by Faraday's law, the flux in the core

is given, or proportional to the integral of the applied voltage.

As we apply volage, we integrate up the BH loop.

When we get into saturation, then the current

in the windings and the magnetizing inductance becomes

very large.

And magnetizing inductance essentially turns into a short circuit.

Which is called saturation of the transformer,

and it's generally something we want to avoid.

9:47

So then, we apply volt-second balance to

transformers when we analyze converters that contain them.

So the procedure here is that we replace the physical transformer

with this equivalent circuit model that contains an ideal transformer

plus a magnetizing inductance in parallel with one of the windings.

And then we apply volt second balance to this magnetizing inductance just

like we do to any other inductor in the converter and as

we've been doing a in the past and understanding how the volt

seconds balance then is part of the analysis of, of the converter.

10:28

Okay we sometimes use the terminology

transformer reset and transformer reset is the

mechanism by which the converter circuit makes

the volt seconds balance on the transformer.

In many converter circuits it's not easy to add a transformer.

We have to add additional circuitry to

make the transformer reset and get the volt

second balance to happen.

10:56

So we're going to discuss that with respect to a transformer

isolated version of the buck converter known as the forward converter.

To understand how the transformer gets reset and

how we can get the volt second to balance.

11:12

One last point this equivalent circuit model is a simple

first order model that is adequate for most things we're

going to do in the analysis of converters but if

desired, we can further refine this model to model other things.

So for example, if we want to model the resistance of the

windings, like we've done in the, in previous exercises for modeling losses

in inductors, we can model resistance of the windings of the

transformer by putting resistors in series with each of these windings.

11:58

Sometimes we model what's called core loss in the transformer, and we can do that

by putting a resistor in parallel with

a magnetizing inductance, traditional way to do that.

And sometimes we model what are called leakage inductances that

are effectively series inductances in series with these windings.

12:16

Okay, we're not going to model those in this course but they do exist, there are

higher order effect in the transformer but there

were times where we need to, to include them.

12:28

So in the upcoming lectures we're going to use this transformer model

to understand how some of the

basic transformer isolated converter circuits work.

We're going to look at transformer isolated versions of a buck converter.

And the buck-boost converter.

And we'll apply this model and

understand the transformer reset, generalizing our ideas

of volt-second balance and charge balance to

include volt-second balance on the magnetizing inductance.

I'll also briefly list some of the other common transformer-isolated converters.