The MLZ series of inductors is not designed for power conversion (buck, boost, etc.), but instead for power supply filtering. This means that a) the windings are not optimized for low skin losses, and b) the magnetic core is not optimized for low core loss. From a circuit design perspective, this means the boost regulator will be less efficient.
If efficiency is not what you're after -- if you simply care for functionality and compactness -- then I don't see any problem using MLZ (or other "ferrite choke") inductors, as long as your circuit doesn't overheat. In practice, this means sticking to low power levels. Just ensure the current rating covers your needs (with healthy margin), and evaluate the power supply thoroughly.
There are three main issues that come to my mind:
- Wire resistance: you already took it into account.
- Wire inductance: you already took it into account, too (more on this later).
- Transmission line effects: these will affect your circuit if the wires have a length which is comparable or greater than the minimum wavelength of the "signal".
About point 3: since you are not concerned with signal integrity (your "signal" is the power rail to the relay) you only need to worry if your switching times are too quick (some energy could be reflected back from the line toward your transistor ad fry it). If you switch the MOSET relatively slowly the frequency content of the "step" (a ramp, actually) won't hit that limit and you won't have problems, apart from higher power dissipation in the MOSFET during switching, but given the extremely low duty cycle of the system it is of little concern here probably.
Anyway LTspice has two different models that can represent transmission lines: a lossy one and a non-lossy one. Excerpts from the online guide:
T. Lossless Transmission Line
Symbol Name: TLINE
Syntax: Txxx L+ L- R+ R- Zo= Td=
L+ and L- are the nodes at one port. R+ and R- are the nodes for the
other port. Zo is the characteristic impedance. The length of the line
is given by the propagation delay Td.
This element models only one propagation mode. If all four nodes are
distinct in the actual circuit, then two modes may be excited. To
simulate such a situation, two transmission-line elements are
required. See the schematic file
.\examples\Educational\TransmissionLineInverter.asc to see an example
simulating both modes of a length of coax.
and:
O. Lossy Transmission Line
Symbol Name: LTLIN
Syntax: Oxxx L+ L- R+ R-
Example:
O1 in 0 out 0 MyLossyTline .model MyLossyTline LTRA(len=1 R=10 L=1u
C=10n)
This is a single-conductor lossy transmission line. N1 and N2 are the
nodes at port 1. N3 and N4 are the nodes at port 2. A model card is
required to define the electrical characteristics of this circuit
element.
Model parameters for Lossy Transmission Lines
[...table with all parameters omitted...]
Point 2 is more problematic, especially when switching the relay OFF: you could have an inductive kickback that destroys your MOSFET due to the wire inductance. Note that the diode across the relay won't protect you in this case. Thus a protection Zener at the switching transistor output (between drain and ground, cathode connected to drain) may be necessary to dampen that inductive kickback.
An article on the subject is here (not directly related to your specific case, though).
Best Answer
The next step after MMGM's excellent answer is to put a few numbers from his datasheet into the calculator from Mark B's answer at
Averaging the inside and outside diameter (6mm and 10mm) we get radius 0.4cm and MMGM's 10 turns. Datasheet has "Ae=7.83mm^2" so enter 0.0783 (cm^2) in the "Area" box and it will calculate a coil radius. Enter 4300 for relative permeability (datasheet calls it ui, calc calls it k, these things happen!) and the calculator confirms inductance 0.168mh, pretty close... So far so good.
Now the crucial question : will the coil take 10 amps?
There is another calculator to answer that on the same site... Enter the radius (0.004m this time!) 10 turns, k=4300 again. And new, the "Flux density near saturation" from the N30 data sheet - B = 380mT = 0.38T, and click the link to "current" above.
For this core size and material, with these turns, and this saturation flux density, the calculator says "0.177 amps".
So, no...
As an experiment, try a 4cm radius, 1cm^2 area, 9 turns, same material. The first calculator says 0.174mh, again pretty close. The second now says 1.96 amperes which is heading in the right direction, but a MUCH bigger coil...
So, as MMGM says, magnetics design is hard.
But that was a first step. Now try some different core materials (lower ui=k, larger cores, lower inductances, and see where you get.
(Also bear in mind that 10A DC may translate to 20A or more at AC. Try designing for 1A,5V until you have something working)