Turns / Core size optimization for Transformer

[I_am_learning]

Say, I want to design, 220 / 12 V 100VA transformer.
We have
V = 4.4BfNA (V is applied voltage RMS, B is peak flux Density, N is no. of turns, f is frequency, A is core cross section)
so, B = V / (4.4 f NA)

If i use iron core, there is limit to the maximum value of B without excessive saturation losses. So there is constraint for the minimum value for N*A.

But seems like we can choose N and A arbitrarily. Why not use a tiny core A and huge N if that saves money. Or the other way round if that saves money.
Whats the optimum choice?

 

[Fish4Fun]

In theory, using ideal components, there are a lot of things we can do with inductors and capacitors. In reality it is very difficult to find these ideal components. In the question about your transformer, you need to consider the Iron Losses, the impedance and the resistance in your primary in an effort to minimize no-load, nominal load and full load losses. This has been done exhaustively.

The more modern approach to limiting the costs associate with transformers is to increase frequency and manipulate duty cycle. That is, rectify the line voltage, and then use a switch (BJT, FET, IGBT) to send pulses to the transformer at switching speeds from a few kHz to hundreds of kHz. While more complicated than a simple line transformer/rectifier, the product is typically much more efficient and considerably less expensive.

Fish

 

[Bob S]

Here is a list of things you need to review

What is iron core shape? toroid, window frame, pot core, etc.?

1) core loss (hysteresis) ===> B_max
2) lamination loss (eddy currents)===> lamination thickness or ferrite
3) copper loss (coil resistance (primary and secondary))
4) coil primary inductance (power factor stuff)

Note: Low core cross section and high N creates large coil cross section and high inductance primary.

From this you will calculate
5) N turns (primary)
6) core cross section A
7) geometry (autotransformer or isolated secondary)
8) Center tapped secondary? (for full wave CT vs. full wave bridge)
7) wire gauge (primary and secondary)
8) core loss watts
9) eddy current loss watts
10) copper loss watts

What is secondary circuit?
If you are rectifying this using single phase, you need extra copper for a capacitor-input filter because of surge current every half cycle.

What do you need to minimize/mazimize?
Total power loss (watts)?
Total size (volume)
total weight (grams)
Total cost (core, copper, etc.)?

One modern approach is a "transformerless" design
Directly rectify primary power and generate high voltage dc
Use high efficiency dc-dc converter design

Bob S