# Transformers as Inductors (Weird Results)

If a transformer's primary and secondary are connected in series, then the total inductance of the result, is greater than the summation of each coil separately.

That is to say: $L_{total} > (L_p + L_s)$.

I've seen the math for this and understand it well enough; but the thing is, if I connect an xfmrs coils in series and then short the primary (so that there is a direct path to the secondary) the result is significantly greater than the inductance of the secondary by itself: this I don't understand.

I understand that the short is not zero (unless one is using a super conductor), and that there is going to be current through the primary, but there seems to be more to it. For instance, if I short the secondary (instead of the primary), the LCR meter reads MUCH higher than as if the coils were just connected in series!

I want to make sure that my LCR meter is correct, because if this phenomenon holds true, then I would like to take advantage of this in a filter circuit.

Can someone help me to understand what's going on?

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Did you upload that image to flicker and set it as copyrighted? If so, that will greatly diminish the likelihood of someone editing your post and inline the image. (I'll give you an upvote to help your rep go > 10, so you can add the image yourself.) –  Madmanguruman Oct 23 '12 at 16:06
Thanks Madmanguruman, I appreciate the upvote. Until I'm able to post an image, I give anyone the permission to use the flicker image however they wish. –  musicisphysics Oct 23 '12 at 16:15

Shorting one winding and measuring the other gives you the leakage inductance, which is a result of imperfect coupling between the two windings, and is a function of the physical construction of the transformer.

Depending on your needs, it can have a practical application - zero voltage switching full-bridge converters often use the leakage inductance of the transformer to assist with the ZVS transitioning of the primary MOSFETs - but in general, transformers are designed to minimize this parameter by a variety of means (winding interleaving, etc.)

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Thanks again @Madmanguruman. Does the 3 to 4 connection in the "In Series with Shorted Primary" scenario contribute to the result in any way. That is: if one were to simply measure the inductance between 6 & 4 with a shorted primary, would this be equivalent to the "In Series with Shorted Primary" scenario? –  musicisphysics Oct 23 '12 at 17:13
–  musicisphysics Oct 23 '12 at 17:27
The connection between 3 and 4 isn't a 'magnetic path' in my opinion (it would go around the core, not through it), so I don't believe it would impact the measurement whatsoever. Also, the short between pins 1 and 3 isn't a magnetic path, so I would tend to believe that it too is not material in your leakage inductance measurement. –  Madmanguruman Oct 23 '12 at 19:53
I guess it goes by the formula of equivalent inductance$L= L_11 + L_2 \pm 2M$ where $M$ is the value mutual inductance. In $\pm$, + is taken if both the windings have current in same direction and minus if otherwise.