  We present a study of the electrodynamic response of MgB2 pellets and thin
film samples exhibiting critical temperatures ranging between 26 and 38 K. We
have performed accurate measurements of the surface impedance ZS =RS+iXS as a
function of the temperature and of the magnitude of the electromagnetic field.
The temperature variation and the field dependence of ZS was measured by a
dielectric resonator cavity technique in the microwave region. In particular,
the temperature variation of the magnetic penetration depth was also determined
in the RF region by a single coil mutual inductance method. In the case of the
films, for T<TC/2 a clear exponential behavior of the penetration depth is
observed, which can be explained by a simple BCS s-wave model with a reduced
value of the energy gap. On the contrary, pellets show no evidence of
saturation, and the experimental results strictly follow a quadratic dependence
down to the lowest temperatures. This behavior can be induced by the presence
of metallic Mg inclusions that may locally depress the gap. The analysis of the
field dependence of the surface impedance in the microwave region confirms that
the electrodynamic response of MgB2 is dominated by different sources of
dissipation, depending on the sample history, likely to be ascribed to the
predominance of grain boundaries or normal regions on its surface.
