Pre-Project

We will admit that the following values are given :

• Band pass
• Maximal distorsion d
• Matching impedance at primary and at secundary
• power to transmit
• Applied voltage , which gives the minimum thickness of dielectric between primary and secundary and continuous current that will flow thru the windings.

We will first compute an iron core transformer without air gap. First thing to do is quickly estimating maximal induction using the maximal admissible distorsion. It's clear that the most unfavourable working condition for computing constraints on B is at low cutting frequency . Since power is known, along with primary matcheing impedance , peak voltage will be :

For a sine primary current of frequency , the flux of B will be sine (neglecting saturation and non linear effects) of the same frequency and can be writtent , or equivalently . Since we have , this yields , from which the miminum NS product needed is obtained. At this stage, N is unknown and one must use an empirical estimation of S. Section in square centimeters is about : égale à :

We will take about 10% security (at least 20 % for an air gap transformer) for taking core losses into account, which yields the final section S (of course, it must be the closest commercial upper value to the section computed). The number of turns at the primary can then be deduced, then the number of turns for the secundary using impedance ratio and after that, windings resistances can be estimated. We recall that wire gauge tes determined by maximum admissible copper losses and that, if turn ratio is n, gauge ratio between secundary and primary wire is . The choice made, one must check that windings dimensions are compatible with core window (applying a suitable security coefficient of some percents). It is now possible to compute primary inductance (core beeing selected, mean field lines length can be found in data sheets) and to check if that inductance is enough to insure a low cut of . If not, number of turns must be increased (or a bigger core selected). In the case of an air gap transformer, inductance is obtained with air gap length (see above). Windings are now completely designed. Leakage indcutance must now be computed and high-cut checked. If this constraint is not fulfilled, multiple windings are to be done. If required band pass cannot still be obtained, changing core material must be considered (but not before that stage!).