With what formulas can I choose the diameter of the wire for the high frequency transformer?

 

Normally you would calculate the resistance of the wire by its length and cross-sectional area.
At higher frequencies use the length and the product of the wire circumference and its skin depth.
There are on-line calculators for skin depth.
https://www.omnicalculator.com/physics/skin-depth

More important is the proximity effect, which applies when you use windings consisting of multiple layers.
https://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)

Also bear in mind that core losses increase with frequency, so you may have to use a lower flux density for optimum efficiency

 

With what formulas can I choose the diameter of the wire for the high frequency transformer?

I don't know if there is a precise formula for an optimum wire size, but you need to start with the number of turns required and the space available. This will put an upper limit on the wire diameter. Then you need to consider your skill in winding to use a wire size close to the limit. Then you need to consider the current in the winding and the temperature rise. Skin effect may also dictate a smaller wire size and so it goes.

 

The really big question would be what you mean by "high frequency", kilo-hertz or megahertz, or maybe just 400 Hz?

 

The really big question would be what you mean by "high frequency", kilo-hertz or megahertz, or maybe just 400 Hz?

Actually, according to the TS’ other thread, try GHz.

 

Starting with a "thought good" design at a lower frequency:
Rule #1: If the coil is getting too hot, decrease the wire size but increase the number of strands to you don't run into ohmic losses.

 

I have not considered other threads posted by the TS. But without the TS providing additional information, the question is like asking "What size of tires should I put on my car".
And as the TS has presented in "information" that they are an electrical engineer, there should have been additional information provided, such a s power level and frequency band.
A high frequency power inverter transformer is quite different from an FM broadcast transmitter.

 

He never replied to questions either, on his only other post.

 

With what formulas can I choose the diameter of the wire for the high frequency transformer?

Hi there,

You do not choose the diameter, the diameter chooses you

Ok seriously, #26AWG is considered the max diameter at 100kHz, but as others have pointed out you have to check out some of those web sites, and ultimately it will depend on what kind of efficiency you are after. Skin effect is a problem as you go up in frequency.

The explanation for skin effect is interesting. It's due to the change in polarity. For AC, the change in polarity happens repeatedly so the skin effect appears repeatedly. The skin effect is most likely called that because the wire appears to conduct only near the surface which ends up looking like a 'skin'. The explanation is because the field pushes the current out from the center of the wire due to the way the angles of the field cut the wire diameter, so at first the current does not flow along the axial length of the wire. This occurs at various angles so the skin effect is not the same throughout the entire length of the wire. It takes time for the current to align with the axial center of the wire to where it could conduct normally, so the AC resistance appears to be higher, even though it is not a continuous event. As the polarity reverses, the same thing happens again. The current gets pushed out from the center of the wire for a few instants, then eventually flows normally. If the frequency decreases, the time spent where the current is being pushed more or less perpendicular to the axial center of the wire is much less than the time the current flows along the axial center of the wire and thus the overall 'effect' is reduced. If the frequency decreases to zero (DC) then the current always flows along the axial center of the wire. If the frequency increase, the rate (the number of times per second) at which the current gets pushed toward the outer surface of the wire increases and thus the effect increases.
So what we normally think of as a continuous effect, it's actually a short time effect that keeps happening over and over again and because the overall effect is uniform, we think of it as being a continuous effect and what's more is that we can use that to deal with this effect. This also tells us that the skin effect occurs even with DC but only when the current is first switched on and only lasts for as long as it takes for the current to become completely aligned with the axial center of the wire, although that would be a very short time.