<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The electromagnetic properties of an <formula formulatype="inline"> <tex>${\rm MgB}_{2}$</tex></formula> superconductor depend on a matrix metal. Therefore, the design principles of an <formula formulatype="inline"><tex>${\rm MgB}_{2}$</tex></formula> magnet are greatly affected by the matrix metal of the conductor. A ferromagnetic matrix requires a complex non-linear modeling whereas in case of non-magnetic matrix the models developed for LTS magnets can be adopted. In this paper a design analyses of linear and non-linear <formula formulatype="inline"><tex>${\rm MgB}_{2}$</tex></formula> coils are compared. Also, feasibility of linear model in non-linear case is studied. As an example a design scheme of a <formula formulatype="inline"><tex>$\mu$</tex></formula>-SMES solenoid with <formula formulatype="inline"><tex>${\rm MgB}_{2}$</tex></formula>-W/Fe and <formula formulatype="inline"><tex>${\rm MgB}_{2}$</tex></formula>-SiC/Nb/AgMg wires is outlined. </para>