Magnetic coupling through an autotransformer is not perfect. There is a coefficient of coupling whose numerical value is less than unity.
I have had it pointed out to me that my SPICE simulation of an autotransformer doesn’t account for a less-than-unity coefficient of coupling across the magnetic path. The idealized result of that can be seen as follows:
Figure 1 Autotransformer step-up with unity coupling coefficient.
Figure 2 Autotransformer step-down with unity coupling coefficient.
I guess it’s time for me to say “mea culpa.” I must be getting careless in my old age. However, the two models above can be embellished to account for their non-unity coupling coefficients along the following lines:
Figure 3 Autotransformer step-up with non-unity coupling coefficient.
Figure 4 Autotransformer step-down with non-unity coupling coefficient.
The two additional inductances are by definition not coupled to each other while the L1 and L2 are “mutual inductances” in their respective illustrations. Mutual inductance as a topic unto itself can be examined at many sources. For purposes of this autotransformer model, this is one:
Numerical values in the SPICE model can be adjusted as needed for more precise coupling coefficient modeling.
This article was originally published on EDN.
John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).