This course explains how to analyze circuits that have alternating current (AC) voltage or current sources. Circuits with resistors, capacitors, and inductors are covered, both analytically and experimentally. Some practical applications in sensors are demonstrated.
5.1 Transformers
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Del curso dictado por Georgia Institute of Technology
Linear Circuits 2: AC Analysis
54 calificaciones
De la lección
Module 5: Transformers
Conoce a los instructores
Dr. Bonnie H. FerriProfessor
Electrical and Computer Engineering
Dr. Joyelle HarrisDirector of the Engineering for Social Innovation Center
School of Electrical and Computer Engineering
Welcome back to Linear Circuits.
Today we are going to begin our discussion of transformers.
This lesson is essentially just going to present transformers as a device and
describe the physics behind how they work.
This concept of transformers is apparently an extensive one.
And so to help make it a little bit easier to learn, it's
been broken up into several smaller pieces so that it is nicely compartmentalized.
In the previous lesson, we talked about maximum power transfer in AC systems.
Sometimes to get maximum power transfer,
transformers are actually used for the impedance matching that was discussed.
But we're going to talk about transformers generally and
look at a number of different places that they turn up and are used.
The objectives for this lesson are to identify physical transformers and
their circuit representations and
then to describe the physical function of transformers.
This is representative of a transformer.
Here, the gray is indicative of a ferrous metal core.
So ferrous meaning that it's got some iron in it.
And the reason behind it being ferrous is,
ferrous materials hold magnetic fields very well.
Then we have two coiled wires,
represented in these somewhat orange-ish colored coils here.
So this side, as we put a current through it,
is going to generate a magnetic field, according to Ampere's Law,
which we've already discussed when we talked about inductors.
When the magnetic field is established in this coil, because of this ferrous core,
it's going to then have an impact on the other coil, since now there is
a magnetic field that is moving through this second coil, this second inductor.
So when we put them together in this configuration, we call it a transformer.
It doesn't necessarily have to be quite like this,
the only thing that makes it a transformer is this idea of mutual induction.
The current going through one coil
generates a magnetic field that has an impact or an effect on the other coil.
When we do circuit diagrams, they will be drawn somewhat like this,
where we basically have two inductors that are placed side-by-side.
And the dots here are representative of reference directions,
the reference directions that are present in transformers
with regard to the directions of these coils.
So it's possible that you could coil this the opposite direction,
in which case you would move one dot down to the other side.
This lets you know whether this magnetic
field is basically working in the same direction or
the opposite direction that the magnetic field is coming from the other coil.
In these systems, we're typically going to connect
one side to a source and the other side to a mode.
So to help distinguish the two sides of the transformer, we will refer to one side
as the primary winding or the primary and the other is the secondary winding.
And typically, the primary winding relates to the winding that is connected to your
power source, and the secondary winding is connected to some sort of load.
It's entirely possible to flip the direction of the transformer, and
then you could then change calling the other the Primary and
then the previous one the Secondary.
It really doesn't particularly matter,
it's just to keep things clear as to which side you're referring to.
As far as the relationship of magnetic field and
current, first of all we know about Ampere's Law.
As current flows through the coil, it generates a magnetic field.
The other thing that makes these devices operate is Faraday's Law of Induction.
Faraday's Law of Induction states that a changing magnetic flux leads to a voltage.
We're not going to get into the finer details of Faraday's law of induction, but
to be able to talk a little bit about it,
we need to have some idea of what magnetic flux is.
So if we take some sort of closed loop, and
we make a surface that connects all of the sides of this loop, And
then we count the amount of b fields or the magnetic fields that's
going through this surface and then divide it by the area of this surface,
that gives us magnetic flux which is represented by capital C.
This is somewhat similar to the way that we calculated current.
We calculated the amount of charge that was moving through some surface in time.
So it's a similar kind of idea.
Faraday's Law of Induction states that changing magnetic flux
leaves two voltages, which means that if the B field here is constant,
there's no changing magnetic flux.
So, zero voltage, which is why inductors behave like wires if you let the currents
flow through them stay constant in time.
So, the implication of this is that transformers are AC devices.
In order for them to work, the way that we've described,
you need to have an alternating current.
If the current is DC or if it's constant in time,
it doesn't quite have the same impact as it would if the current were alternating.
There's two primary models for analyzing transformers in a linear sense.
The first is the linear transformer model, where it uses impedances for the analysis,
impedances for the two coils as well as impedance for the mutual induction.
This is primarily used in communications applications.
The Ideal Transform Model is primarily used for power transfer applications.
It requires a few different assumptions to be made
that are never quite actually true, but they generally give us a good idea of how
the transformer is going to operate in a certain circumstance.
For ideal transformer models, we're simply going to be making use of the voltages and
the number of coil turns for the analysis.
To summarize, we just introduced transformers as a circuit device,
described their physical behavior, and then introduced the two analysis modes.
In the next lesson, we'll start by talking about the first of these,
the linear transformer model, to see how we can use it for analysis.
Until then.
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