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# Improved Transformer Voltage Regulation Using Mathematical Prediction

Voltage regulation of transformers for no load and full load voltages.

So you’ve chosen a bobbin, wire, PRI turns, etc… now you want to spec an output voltage under LOADED conditions and determine the SEC turns needed to meet those voltages…

Your output voltage drops when the SEC is LOADED compared when it’s at NO LOAD.

The question becomes, can this be predicted with a fair degree of accuracy? In many cases, the answer is yes.

Let’s use a fairly simple example of an EI57 bobbin that requires **150T’s on the PRI **in order to not saturate the core. **The input voltage is 100VAC @ 400Hz and the ****power rating is 200VA.**

See the bobbin below:

Let’s say we have chosen to use 0.50mm diameter wire for the PRI.

You have also chosen 0.8mm diameter wire for the SEC.

Ok… let’s determine a length per turn… this will be an average length per turn and while not exactly correct it should be close enough to get you close enough…

Looking at the bobbin we will shoot for the “middle” distance for both the horizontal and vertical lengths.

This would be the average of length A and C for the horizontal and the average of D and B for the vertical.

These are:

Now there are 2 horizontal paths and 2 vertical paths needed for one complete trip around the bobbin, so the total distance per turn is 2H + 2V…

Ok so now let’s find the PRI DCR…

Ok, we know with a 200VA rating that the PRI current is 2A. The voltage lost due to the PRI DCR is, therefore:

This means the voltage we will use when trying to determine the SEC turns is not 100V, but is rather **100V – 1.73V = 97.4V**

Now, we need an equation for the SEC turns that accounts for SEC voltage loss due to SEC DCR and uses this above reduced PRI voltage. This equation can be found as follows:

Now let’s find the needed SEC turns…

Now what this tells you is that with 79T’s on the SEC and 150T’s on the PRI you can apply 100V to the PRI and get out 50V on the SEC @ 4A.

Now you can spec the turns ratio as:

Clearly this is not simply 2:1 which is what some people may expect. In other words, **the SEC turns should not be 75T’s**, which is half the PRI turns. In order to get half the applied PRI voltage out at the SEC when the SEC is loaded you need 79T’s.

*There is a need for more SEC turns than the ratio of what voltage is being applied at **the PRI to what voltage you’d like to see at the SEC.*

This accounts for a majority of the loss and while there are other, less important, factors that affect regulation it is the DCR of the windings and the voltage lost across those DCR’s that account for a majority of the difference between LOADED and NO LOAD output voltages…

This is how you should call out voltages at both LOAD and NO LOAD for voltage regulation of transformers.[/vc_column_text][/vc_column][/vc_row]