Reactive load impedance in a transformer (Circuits I don't understand #1)

The "turns ratio squared" business is accurate as long as two conditions hold: one, you can ignore, or you take into account, the transformer's inductance, and two, the coupling between the coils is good enough.

I can't quote numbers on the coupling constant -- I'd have to do some hen- scratching on paper. But once you take the transformer's own inductance into account, on a transformer with a coupling constant of unity the turns-ratio-squared stuff is exactly right.

How do I take the transformer's own inductance into account? Would that be another way of saying, do not operate near resonance of the secondary with the load cap?

An .ac analysis, rather than .tran might show you more.

Model the transformer as an ideal transformer with parasitics outside.

The parasitics are magnetizing inductance and leakage inductance and various capacitances and ohmic losses.

So do your analysis around that model. The ideal transformer will then transform the impedances as n^2.

I took two semisters of power electronics (60 Hz, utility type power) and about all I got out of it was a good mental transformer model.

Thanks, good idea. I did, and the results here showing the relation between voltage and current at each side of the transformer:

It shows that VL1 and VL2 always differ by 20dB (turn ratio of 10) while th e current ratio is only 10 at frequencies much higher than the resonant fre quency 10 MHz. To me this suggests that impedance ratio is hundred only at a frequency higher than about 20 MHz.

I'm not sure I fully understand. Would you consider the inductance L1, L2 representing the transformer in LTSpice part of the parasitics?

That would allow you to analyze and maybe understand your situation better.

Plop down L1 and L2, two huge inductors, like megaHenries, with K=1 to approximate an ideal transformer.

Then add the known magnetizing inductance of your real transformer across the secondary as L3. Add your resonating capacitor. Now the resonant impedance C||L3 is *outside* the ideal transformer and the impedance transformation to the primary makes more sense.

Crack open your 2nd-year circuits book and review.

No.

I did that before posting. The method that was used in the book is to add a JwMI2 term for mutual inductance to the JwLI1 term for self inductance.

I used that method with mesh analysis and came up with a result that agrees with the simulation that I showed. V1/V2 always follows the turn ratio at all frequencies while I1/I2 doesn't around resonance frequency.

I am still not sure where I could be wrong

This seems to agree with me:

"Transformers match only the ?real? part of the impedance. If there is a large amount of reactance in the load, a transformer will not eliminate t hese reactive components. In fact, a transformer may exaggerate the reactiv e portion of the load impedance. This reactive component results in power t hat is reflected to the generator."

Wow, I finally managed to understand it. It's funny how you can read something over and over without it clicking until you do some hard work on your own and suddenly everything falls into place!