1. Minntronix Technical Note
The Contributions of Fringing Flux on Turns Ratio Measurement Accuracy
Dave LeVasseur
VP of Research & Development
Minntronix, Inc.
3-Apr-2018

2. Turns Ratio Measurement
The turns counts applied to a multi-winding magnetic component such as a transformer are usually verified through a turns ratio test. This is typically done with one of the windings chosen as the reference against which the others are compared.
Turns ratio measurement can be affected by several factors. One such factor is the fringing flux that may cause errors due to incomplete coupling of the magnetic field common to both windings.

3. Turns Ratio Affected by Fringing
…but the red windings at the top are partially skipped.
Smaller air gaps and the use of cores with higher permeability will result in reduced fringing (we can, and do perform turns ratio tests at the coil stage using high- permeability cores)
The blue and green windings are mostly encircled by the magnetic flux…

4. The red winding catches less flux so it has less voltage developed across it
Turns ratio is measured by dividing the voltage measured across a winding under test by the reference excitation voltage, V.
A reduction in flux will cause a winding to measure lower in turns than what was actually applied by winding. V
The green winding catches almost all of the flux so it’s voltage is about the same as the excitation voltage, V

5. A Real-Word Example
A transformer having three separate windings located in different positions across its winding width was found to exhibit errors when tested for turns ratio.
The ninth winding, W9, was located close to the top of the coil. Due to the EI core used to construct the transformer W9 was closer to the air gap.
W9— turns
W8— 4.0 turns
W7— 6.0 turns

6. A Real-Word Example
To illustrate the effects of fringing a movable 10T winding was added to the part in question. To obtain good coupling the other windings were connected in series for a total of 120T.
EI core interface showing location of air gap plane
10 turns spread across winding width
Measured results at +0.28% of nominal
With the 10T spread across the winding width the measured results across the additional winding was or +0.28% from actual.

7. A Real-Word Example
EI core interface showing location of air gap plane
10 turns offset, closer to the air gap
Measured results at -3.6% of nominal
When moved closer to the core’s air gap which was located near the top side of the transformer the 10-turn winding was measured to have -3.6% error due to fringing effects.

8. A Real-Word Example
EI core interface showing location of air gap plane
10 turns offset, farther from the air gap
Measured results at +5.28% of nominal
When moved farther from the core’s air gap the 10-turn winding was found to have +5.28% error due to reduced fringing of the measured winding exacerbated by fringing losses in the reference winding.

9. A Real-Word Example
The original issue with turns ratio measurement of this transformer was based on the location of W7 and W9.
With the reference winding wound across the full winding width (not shown) the error introduced due to fringing was +5% for W7 and -7% for W9.
(W8 was less affected with an error of +3% since it was more centrally-located)
W9— turns
W8— 4.0 turns
W7— 6.0 turns

10. Location of Air Gaps in EI, EE Cores
EI air gap
Switching from an EI core set to an EE core set allowed the fringing of the reference winding to more closely match that of all measured windings.
This resulted in a more reasonable specification tolerance of ±3% for all measured windings.
EE air gap

11. Location of Air Gaps in EI, EE Cores
A winding located directly over the air gap would still be subject to more fringing losses than its neighbors…

12. Location of Air Gaps in EI, EE Cores
A winding located directly over the air gap would still be subject to more fringing losses than its neighbors… but would see about the same fringing loss as a winding spread across the entire winding width.

13. Summary
Measured turns ratio may not match the actual ratio of the physical turns counts applied to the transformer or inductor due to fringing
Transformers and inductors with gapless, high-permeability cores will have turns ratio tests least affected by fringing
If the reference winding and the winding under test are equally influenced by fringing then the turns ratio test is much better able to match physical turns count
Use of EE cores may provide improved turns ratio accuracy based on the windings physical location, if they allow the reference winding and the winding under test to be subjected to similar amounts of fringing
The width of tolerance needed for a turns ratio spec is almost always a function of measurement error versus mistakes in applied turns counts.