I'm currently working on a project were I need to cascade several transformers (the core we use does not nearly work as good as it ought to..).

I'm using the equivalent circuit shown in (A), transformed it into an ideal transformer and equivalent circuit (B) by

dragging over the circuit on the secondary side, where $$\sigma_2 L_2 \rightarrow \sigma_2 L_2 N_1^2\\R_2\rightarrow R_2 N_1^2\\C_2 \rightarrow \frac{C_2}{N_1^2}$$

This works very well for a single transformer. When I use the same method for 2 cascaded equivalent circuits of transformers (C) to transform them into the e.c. (D)

the inductors, resistors and capacitors from the second e.c. transformer are modified accordingly (from C to D) :

$$\sigma_2 L_2 \rightarrow \sigma_2 L_2 N_1^2\\R_2\rightarrow R_2 N_1^2\\C_2 \rightarrow \frac{C_2}{N_1^2}\\C_3 \rightarrow \frac{C_3}{N_1^2}\\R_3\rightarrow R_3 N_1^2\\

\sigma_3 L_3 \rightarrow \sigma_3 L_3 N_1^2\\

R_{fe} \rightarrow R_{fe} N_1^2\\

L_3 \rightarrow L_3 N_1^2\\

\sigma_4 L_4 N_2^2\rightarrow \sigma_4 L_4 N_1^2 N_2^2\\

\sigma_4 R_4 N_2^2\rightarrow \sigma_4 R_4 N_1^2 N_2^2\\

\frac{C_4}{N_2^2} \rightarrow \frac{C_4}{N_1^2 N_2^2}

$$

The LTSpice simulation of (D) works as one would expect it to,

the problem is: the LTSpice simulation of (C) does not.

It shows a decrease in amplification after the second ideal transformer in instead of an increase.

I suspect my method might be flawed, but I can't really pin it down right now.

Does anyone have an idea what could have gone wrong / where I made a mistake ?

If you can't open the schematic, I made a screenshot, hopefully that helps?

http://imgur.com/pLg1v83

Thank you!

^{simulate this circuit – Schematic created using CircuitLab}

ASC FILES:

https://github.com/mmelchger/transformers

# EDIT:

# 1

I'm limited by the number of turns (primary <= 10 turns) and the voltage (voltage through primary inductivity < 0.2V), but require primary inductivities > 270uH with low losses and low saturation between 0.5MHz and 1.5MHz. The transformer should have a ratio of ~ 40, which is why the number of turns on the primary side matters and I'm considering cascading multiple transformers, otherwise I won't have enough space and might run into trouble with capacitive coupling and other effects. I'm using ferrite cores (Al ~ 2700nH/[turn^2] delivers a primary inductivity of 270uH for 10 turns).

Ideally the B-H curve should be linear for my use, but that's another question.

## Best Answer

There are several issues here.

Simulation (C) is failing not because of a mistake in your circuit, but due to a limitation in LTSpice itself. The secondary inductance of your transformer windings is too high! Reduce primary and secondary inductances by a factor of at least 10000 (eg. to 100 and 10000 Henries) and then the results should come out correct.

Your formulas are correct but your calculations for circuit (D) are wrong. From secondary to primary the transformers are stepping

down10:1, so N is 0.1 not 10. Therefore (for example) L3 should be 2.7uH, not 27000uH.You are driving the circuit with a current generator, so input voltage is directly proportional to impedance. Is that what you really wanted? If not then perhaps you should be using a

voltagegenerator with an appropriate series resistance (eg. 50 Ohms).