RF transformer design with ferrite cores – saturation calcs

Ferrite cored inductors and transformers saturate at relatively low magnetising force.

#61 material example

Lets work through an example of a FT50-61 core with 10t primary at 3.5MHz.

Magnetic saturation is one limit on power handling capacity of such a transformer, and likely the most significant one for very low loss cores (#61 material losses are very low at 3.5MHz).

Let’s calculate the expected magnetising impedance @ 3.5MHz.

Zm=0.966+j144Ω, |Zm|=144Ω.

Above is the manufacturers B/H curve for #61 material. Lets take the saturation magnetising force conservatively as 2Oe=2*1000/(4*pi)=159A/m (or At/m for a multi turn coil).

The ID of a FT50 core is 7.15mm, so magnetic path length l=0.00715*pi=0.0225m.

So, we take saturation current as Is=Hs*l/t=159*0.0225/10=0.358A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.358*144=51.6Vpk. This corresponds to about 25W in a 50Ω system.

Increasing the number of turns decreases Is for a given Hs, and increases Zm which reduces I for a given applied voltage. For example in this example, a 12t primary has |Z|=207, Is=0.298A, Vs=61.7Vpk which corresponds to a 43% 50Ω power increase.

#43 material example

Lets work through an example of a 2643625002 core with 3t primary at 3.6MHz (Small efficient matching transformer for an EFHW).

Magnetic saturation is one limit on power handling capacity of such a transformer. For lossier materials, heat dissipation is likely to be the practical limit in all but low duty cycle applications, but lets calculate the saturation limit.

Let’s calculate the expected magnetising impedance @ 3.6MHz.

Zm=94.1+j197Ω, |Zm|=218Ω.

Above is the manufacturers B/H curve for #43 material. Lets take the saturation magnetising force conservatively as 1Oe=1*1000/(4*pi)=79.6A/m (or At/m for a multi turn coil).

The ID of a 2643625002 core is 7.29mm, so magnetic path length l=0.00729*pi=0.0229m.

So, we take saturation current as Is=Hs*l/t=79.6*0.0229/3=0.607A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.607*218=132Vpk. This corresponds to about 175W in a 50Ω system. This transformer would not withstand such high power continuously, but pulses or bursts to that level would remain in the substantially linear range of the material characteristic.

Conclusions

  • Magnetic saturation is one limit on power handling capacity of ferrite inductors and transformers.
  • For very loss cores, magnetic saturation is likely to be the significant limit on power handling.

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