I am building a boost converter 12VDC-24VDC with output current of \$I_{out}=250\:\mathrm{mA}\$ and input current of around \$I_{in}=600\:\mathrm{mA}\$ and need to design an inductor for it. I've calculated that the inductance has to be \$L=125\:\mathrm{\mu H}\$, the switching frequency is 400kHz.
I have a ferrite core with 5mm diameter and 20mm length (I can cut it if necessary) and permeabillity of 12. I am also using 32 AWG wire (because of skin effect) which has a diameter of 0.2mm and \$R=538.3\:\Omega\$ for 1000m.
The equation of cylindrical coil is \$L=\frac{N^2\cdot\mu_o\cdot\mu\cdot A}{l}\$ where \$N\$ is number of turns, \$\mu_o\$ is permeabillity of free space \$\mu\$ is relative permeabillity of the core, \$A\$ is cross section area of coil and \$l\$ is length of the coil.
There are dozens of ways one can design an indutor based of number of turns and the length of coil, but increasing the length also increases the resistance of the inductor.
So what is the maximum resistance the inductor can have under these circumstances, how can I calculate it? So I know later on what length to take, and from this the number of turns.
EDIT:
I've calculated the inductance based on the equations found on this website, page 40.
Input ripple current: \$\Delta I=0.2*0.6=0.12A\$
Duty cycle: \$D=\frac{24-12}{24}=0.5\$
Inductance: \$L=\frac{12*0.5}{0.12*400000}=125\mu H\$
Best Answer
Skin effect does not mean that you have to use thin wire, it only means that you don't get all the benefit of using thicker wire.
Your calculated inductance sounds way too high for 400kHz operation (maybe an order of magnitude or so). I suggest you double-check the calculation.
You can get lower DC resistance in two ways- use thicker wire (but you only benefit with the diameter of the wire rather than the diameter squared above the skin depth) or you can use multiple thin wires in parallel (ideally in a Litz arrangement, but a simple slow twist is much better than nothing).
If your inductor is high resistance you'll get I^2R losses from the wire (effectively series resistance) on top of the core losses (which look like a frequency-dependent parallel resistance) and your DC-DC efficiency will suffer.