Designing Transformers with J.C.Maxwell

[popilin]

As a DIYer, all your work with a solder, (and all Classical Electrodynamics too) whith exception of Thermionic Effect and Semiconductor Theory (Quantum Mechanics), came from only four equations and two constitutive relationsand You must at least see them one time in your life. Eq.(1) to (4) are called Maxwell Equations due to his creator James Clerk Maxwell.
If You are afraid of Mathematical Physics, skip the Theory after take a look on Maxwell Eq.!-Mandatory-
Well, go to Transformers
Eq.(51) is the well known

Np = (Upx10^8)/(√2 π f S B)

Where: Np=Number of primary turns Up=RMS Primary Voltage in Volts f=frequency in Hz S=Area of the core in cm2 B=Magnetic Field in Gauss
Nothing to say, all You must Know it.
Eq.(37) can be placed in the form

Lp = (4 π μ S Np^2)/(9 lx10^8)

Where: Lp=Primary Indutance in Henry μ=Permeability of the Core l=magnetic path length in cm
No Matter What You do, PP or SE Transformers, is very important because of bottom end response of a Transformer.We tend to think high u exotic materials can help...Wrong, u is a fuction of almost everything, like frequency, temperature, oil price, etc. and at low frequency generaly is low, furthermore if You have an air gap

μ(Real World)=(l μ)/(l+le μ)

Where: le=Air Gap in cm
Much lower yet!!!
If You think making PP don´t have an Air Gap, You must have perfect lamination!!!
The only way is as ever, bigger core or more turns.Because the number of turns is squared, has more efect on L.

For SE lovers, OPT are PIA, don´t worry, I had deduced a long time ago Eq.(41)

Np = (Lp iDCx10^8)/(S B)

Where: iDC=Primary DC current in Amper B=Half allowable B of the core in Gauss

Recipe:Choose the bottom end frequency, with Eq.(53) can calculate Lp, iDC is given by the operation point of your output valve, B is obtained in the lamination datasheet, and S... is given by "Art of Transfomers"
For a 30W SE 211/VT4C/845 16cm2 and a good standard GOSS is enough.
Check the turns with Eq.(37) and choose the bigger.
Estimation formulae for S are all "Rule of Tumb", the correct calculation is a bit dificult.
The rest of the story is "The Art of Transformers":Winding Techniques to reduce L disperse, capacitance, increase insulation, and many more.
In coclusion: Don´t waste your money, standard grade GOSS (M6) is enough, if double-C much better, You only need High Flux to avoid saturation and a thin hysteresis curve for best linearity.The thinner the lamination the less energy loss.


Cheers!

[popilin]

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