# Calculating secondary turns on transformer

#### SiCEngineer

Joined May 22, 2019
187
I am designing a transformer for a high voltage converter. The topology is a push-pull converter. My method is to have a 200V primary generate 4x750V secondary windings, each feeding a voltage multiplier to generate 1500V. Then connect these in series and generate the final 6kV.

So far I have calculated the primary turns using the formula:
Npri = V*10^8/(4.44*F*B*Ae), giving me 20 turns for a frqeuency of 300kHz, B of 75mT, and an Ae of 0.991cm^2.

However when attempting to use the attached equation to determine my secondary turns with Faraday's Law, my secondary turns are calculated as 169 when rounded up, for a Vo1 of 753 to account for diode drops, a period of 3.33uS, 150mT flux swing (2xoperating flux) and 0.991x10^-4 (the area again but this time in metres? I was going off the equation which seems to use metres)

This gives a turns arrangement of [20 20 169 169 169 169] for my two primary and four secondaries respectively. This seems excessive, since this is a turns ratio of 169/20 = 8.45, which given my primary voltage of 200V should generate 1690V... but I originally only needed the 750V across each sec winding.

Where am I going wrong? Does this mean that my primary turns will have to increase due to the large number of secondary windings to get my correct voltage ratio, since these values seem to be the minimum required values. If I calculate the primary turns according to the voltage ratio and the secondary turns required I would need 2 x 45 turns on the primary.

Does this suggest the core or the material I am using is not suitable?

I am new to transformer design so as much detail as possible is appreciated. Thanks!

Joined Jul 18, 2013
20,458
Your secondary turns are a direct ratio of the primary turns.
Max.

#### SiCEngineer

Joined May 22, 2019
187
Your secondary turns are a direct ratio of the primary turns.
Max.
Okay, great. But in this case, with a turns ratio of 3.75, my secondary turns would be 75x4 turns. This would then no longer satisfy the equation that I have attached to the original question (?) therefore can we guarantee that the transformer would operate as desired?

Joined Jul 18, 2013
20,458
Normally this is the ratio required.
A small percentage could be added for any losses.
Max.

#### SiCEngineer

Joined May 22, 2019
187
Normally this is the ratio required.
A small percentage could be added for any losses.
Max.
So if my turns on the secondary do not satisfy the attached equation thats okay?

Joined Jul 18, 2013
20,458
As long as you end up with the required result.
When winding on a secondary or overwind, I first place ~ a 10turn winding in order to find the exact ratio. On powering the primary.
(#turns/volt).
Max.

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#### SamR

Joined Mar 19, 2019
2,047
As Max said it's a turns ratio. However, the length of top turns is NOT equal to the length of bottom turns. So you tweak it to measurement by adding or subtracting turns. The more actual turns, the easier to tweak since one turn is a smaller percentage of the total length of wire. This is a bit of oversimplification since turns are only one part of the equation.

#### SiCEngineer

Joined May 22, 2019
187
As Max said it's a turns ratio. However, the length of top turns is NOT equal to the length of bottom turns. So you tweak it to measurement by adding or subtracting turns. The more actual turns, the easier to tweak since one turn is a smaller percentage of the total length of wire. This is a bit of oversimplification since turns are only one part of the equation.
So what is the purpose of the equation, and Faraday's Law, if the turns ratio is simply used to calculate the turns on the secondary. If the number of turns is less than reqired number calculated by the equation, I would expect there would be issues in the transformer but that seems to not be the case?

#### SamR

Joined Mar 19, 2019
2,047
Calculations are for a perfect world where all materials precisely match the exact specification used in the equation. In real life, there is the Aw S**T Factor to be considered.

#### MrAl

Joined Jun 17, 2014
7,511
I am designing a transformer for a high voltage converter. The topology is a push-pull converter. My method is to have a 200V primary generate 4x750V secondary windings, each feeding a voltage multiplier to generate 1500V. Then connect these in series and generate the final 6kV.

So far I have calculated the primary turns using the formula:
Npri = V*10^8/(4.44*F*B*Ae), giving me 20 turns for a frqeuency of 300kHz, B of 75mT, and an Ae of 0.991cm^2.

However when attempting to use the attached equation to determine my secondary turns with Faraday's Law, my secondary turns are calculated as 169 when rounded up, for a Vo1 of 753 to account for diode drops, a period of 3.33uS, 150mT flux swing (2xoperating flux) and 0.991x10^-4 (the area again but this time in metres? I was going off the equation which seems to use metres)

This gives a turns arrangement of [20 20 169 169 169 169] for my two primary and four secondaries respectively. This seems excessive, since this is a turns ratio of 169/20 = 8.45, which given my primary voltage of 200V should generate 1690V... but I originally only needed the 750V across each sec winding.

Where am I going wrong? Does this mean that my primary turns will have to increase due to the large number of secondary windings to get my correct voltage ratio, since these values seem to be the minimum required values. If I calculate the primary turns according to the voltage ratio and the secondary turns required I would need 2 x 45 turns on the primary.

Does this suggest the core or the material I am using is not suitable?

I am new to transformer design so as much detail as possible is appreciated. Thanks!
What exactly are you saying that does not work out?
Once you determine the primary turns the denominator becomes a constant so the only thing left is the turns ratio.
But please elaborate so we can tell what you are doing. Show some calculations that would help.

#### SamR

Joined Mar 19, 2019
2,047
Consider that the equation uses not only the number of turns (easy enough to count) and the precise diameter of the coil. Which coil? 1st layer? 2nd layer? etc. You can gee whiz it and use the avg diameter but this has added a degree of inaccuracy to the calculation. Hence measure the output and trim the secondary turns to fit. Then there is crossover and spacing between turns also.