You have a set of requirements …. you have a needed output power which is some output current at some voltage. Your input voltage is known as is the frequency. You need to design your transformer to deliver as best as possible energy per unit time from the input to the output. This means efficiency matters….

How do you make a transformer as efficient as possible for some given size? The idea is to balance core and copper losses while further trying to make RMS current densities equal in all windings…

Let’s start with the latter….how do you make the current densities equal in all windings?

Current density is just the ratio of current to cross-sectional wire area. Most transformer windings carry different currents and so would need differing cross sectional wire areas….

A good rule of thumb is to shoot for 2A/mm^2 ~ 4A/mm^2 as a current density. You can go higher than this, say up to 20A/mm^2 if the DCR of the winding is quite low; low enough so that winding power loss is fairly small compared with the power being delivered through the transformer.

Now what causes power loss in a winding? It is the current and resistance of that winding. Your current is likely fixed, and you have no control over it. The current is a function of the power required; that is….power in and power out.

The resistance though you can control to some extent. By using larger gauge wire, you decrease the DCR. By using fewer turns you also decrease the DCR.

Of course, turns are something that while you have control over must also be some minimum amount to avoid saturating the core. The core carries flux from the PRI to the SEC’s and this flux is a function of PRI winding turns. Core power loss is proportional to core flux so the less flux the lower the core power loss, but while more turns mean less flux and less core power loss it also means more DCR for some particular wire gauge which means more winding power loss…..It is a balancing act which should be performed correctly.

What do you do?

- I suggest you start by choosing wire sizes that balance the wire ampacity for each winding.
- Then choose an appropriate flux density for the core you are using. For instance, if ferrite, go with say half the MAX value, so perhaps 0.24T.
- Use this, the core area and the applied volt-sec’s (or Amp-Henry’s for an inductor or flyback transformer) to find PRI turns.
- Then find your SEC turns by using a turns ratio that gives you the output voltages you are looking for.
- Now using the core manufacturer’s graphs or equation for power loss per unit volume (along with the published core volume), calculate the core power loss for your flux density at your switching frequency. Make note of this value….
- Then using the path length per turn for the wires you chose, calculate the DCR of the windings. Using the RMS currents in each winding calculate the power loss of the windings. Sum these losses and compare them with the core loss.
- If the copper losses are higher than the core losses reduce turns and/or increase wire size. This will lower the DCR’s and hence lower copper losses.
- Reducing turns increases core flux and core power loss so you will need to re-calculate the core flux density with the new turns and use this core flux density to obtain a new core power loss.
- Compare the new sum of the windings losses to the new core loss and keep adjusting in an iterative manner until your core and summed copper winding losses are nearly equal.
- It will be virtually impossible to get them exactly equal but if you can get them “close” this should be sufficient. You can always then make minor changes to wire size even if it means the ampacity of each winding is no longer equal. You want them to be “close” to the same but for instance, if

coming down one wire gauge allows for the turns needed to lower core flux density so it is more balanced with the sum of copper losses then you should do so.

I have found you do not need to be particularly exact for the balancing. If you are using a graph and not an equation for core power loss then getting an exact loss off the graph is difficult; again, exactness is not required. Also, the path length per turn for the windings is more precise if you increase it each tiny bit as you stack the windings on top of each other as the path length increases the further up the stack the next winding is. Again though I have found this level of detail is not always needed.

The basic idea is you want the power losses to be fairly distributed over the entire volume of the transformer. Having one or two “hot spots” and other “cooler” spots is not good as much of the insulation such as enamel and taping within the transformer has poor thermal conductivities and so heat energy doesn’t move very well until the temperature difference is perhaps too much. Plus, it will tend to move from the hot spots to the cooler spots within the transformer as well as to the surfaces. This will cause an excessive temperature rise within the transformer, compared with a well-balanced power loss transformer, as heat moves inward before moving outward to the surfaces to be removed.

By having all the heat being generated over the entire volume of the transformer the generated heat is not as much in any given area and it will radiate outward in all directions to find a cooler surface where it can be removed either by convection, conduction or radiation.