Choke designing could be an interesting field to study.
Particularly, let’s talk about toroid inductors.
Let’s start with the core,
Cores can be made of several materials. Like, iron powder; ferrite; Nano-crystalline and silicon steel etc. The selection depends on the operation of the inductors.
When the operating frequency goes up, you got to select ferrite or nano-crystalline. Iron powder or steel would introduce a high core losses during the high frequency operations.
When you have to design a choke with high DC bias, selecting ferrite as the core material would make your inductance to get drop drastically.
So NO, you cannot use ferrite for dc bias. Steel core with air gaps would suit for dc bias operations.
Iron powder cores stand in the middle with relatively low “Al” values than ferrite.
What is “Al” value..? will come to that later.
So as you have selected the core type with respect to the operation, now you have to decide about the other constraints.
Dimension plays a major role if you are going to use the choke in a PCB or inside some enclosure.
Losses or the efficiency would depend on the number of turns or diameter of the copper which you going to use. With smaller copper and higher turns would obviously add higher
resistance, which sometimes you might have to take into your design calculations as well.
Whatever you design, finally you got to make that thing for real. If the selected core is not large enough to wind the number of turns which you had calculated, it cannot be manufactured.
That’s about selecting the core,
Now let’s move on to maths.
Below is the equation for inductance of an air gap toroid core,
N=number of turns
A=core cross section (mxm)
l= air gap length (m)
µ̥=permeability of free space
Now once you select an iron powder or ferrite core, you can google for the data sheet for the core.
There he would do the calculations for you and state something called Al value.
So you can just use Al value and do your calculation as below,
And also these datasheets give you pretty much every information you need to know, Like the curves and graphs for properties of the core with varying frequency and current.