We've spent the last
two modules discussing procedures for designing different types of
magnetic devices. I chose several basic classes of devices to illustrate
their design. Of course, there's
quite a few others, and we can approach
those designs in a similar way in which we
write the design equations. We then manipulate them
in a way to choose a core that is large
enough to do the job, and we work out the other
parameters of the design. Here is one final example, and I'm going to just briefly
outline how it works. Let's consider an
ac inductor design. This is an inductor
that's a single-winding. We want to obtain a
given inductance, but we have to include
both core and copper loss. In the most extreme case, there may be no dc component
of current or flux, but there may be a large
ac component which causes large core loss
and large copper loss. So we might assume that we have a voltage waveform that is
some arbitrary waveform, but we can identify its volt seconds or
this area of Lambda. There's some inductor current which obeys the law V is
LDIDT for the inductor. We'll assume that we
have a geometry that's topologically equivalent to this, where there's a core in
air gap and a winding. I'll just outline the equations. We want to obtain a
specified inductance. We have the usual
equation for inductance, and that's the first constraint. To find the core loss, we need to know Delta B, the peak ac component
of flux density. It has the usual relationship that comes from Faraday's law, that B is related to the
volt-seconds Lambda. We need to calculate both the core losses
and the copper loss. The copper loss is given
by this expression that really just comes from the equation for the
resistance of the wire. This is ignoring
proximity effect, and we have our usual equation for core loss that comes
from Steinmetz equation. As usual, we can combine these, but now subject to
these constraints. Define the value of Delta B that minimizes the total loss. When we take the derivative
of the total loss, set it equal to 0, and
solve for Delta B. Then we find that this is
the optimum flux density. With that Delta B, then we can find the core K_gfe that is required to
satisfy the requirements. Here is the result in this case. So as usual then we will define a procedure where
we evaluate K_gfe, pick a color that's large enough, evaluate Delta B, and then go back and find the turns
and the wire size. When your travels,
when you encounter different types of magnetic
devices to design, you can follow this basic
approach of writing the equations of the constraints
of the total losses, finding the Delta B that
minimizes the total losses, and use that to select a large enough core and solve for the other
design parameters.