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Band pass

We have seen how leakage inductances of windings can be computed (or at least estimated). It's clear that those inductances will tent to limit performances of a transformer in high frequencies. To make that point more precise, we will enrich the original equivalent schema of the real transformer. First of all, it must be noticed that winding a wire on a core creates both inter-turns and inter-windings capacitances. A winding can thus be seen as a trasnmission line :

Complete computation of propagation modes along such a line is possible, but tedious unless inter-turns capacitance is neglected. Generally however, a winding is heavily damped and we can assume without problem that spread capacitances can be modelled as localized components. This yields to the following schema (we neglect leakage resistance between windings and core!) :

At low frequencies, one can neglect the effect of parasitic capacitances, and , assuming a pure resistive load tex2html_wrap_inline552 at the secundary, the system of equations (5) gives an approximate schema :

Where tex2html_wrap_inline554 is primary inductance, that is self-inductance of the primary winding alone (linked to tex2html_wrap_inline498 in (5), that cannot be neglected at low frequencies), which can be computed knowing core parameters (see section on reluctance). We have then a high-pass filter, and putting :
the low cut frequency is :


If input generator's impedance is non zero, one must add it to tex2html_wrap_inline562. In the case of a valve amplifier output transformer, that impedance will be the plate resistance of the output tube.

For high cur, we will not include in our computation the parasitic capacitances of windings. We have then the schema :

Where tex2html_wrap_inline564 is total leakage inductance seen at primary. We have now a low-pass filter whose cutting frequency is, putting : tex2html_wrap_inline566, given by :


If parasitic capcaitances are taken into account (and reduced to primary by tex2html_wrap_inline570), it will appear a damped LC circuit of oscillating frequency :

Generally, this frequency is higher than high-cut created by leakage inductances and its effect consist mainly in slightly lowering band-pass. In some rare occasions, damped oscillations can appear (to be controlled on square wave with a scope).

next up previous
Next: Distorsion Up: Tansformer Previous: Leakage inductances computation

Stephane Puechmorel
Tue Jul 8 14:22:42 WET DST 1997