The spatially resolved broad-band spectroscopy with Very Long Baseline Interferometry (VLBI) is one of the few methods that can probe the physical conditions inside blazar jets. We report on measurements of the magnetic field strength in parsec-scale radio structures of selected bright Fermi blazars, based on fitting the synchrotron spectrum to VLBA images made at seven frequencies in a 4.6 -- 43.2 GHz range. Upper limits of B <= 10^-2 -- 10^2 G (observers frame) could be placed on the magnetic field strength in 13 sources. Hard radio spectra (-0.5 <= a <= +0.1, S_nu ~ nu^a) observed above the synchrotron peak may either be an indication of a hard energy spectrum of the emitting electron population or result from a significant inhomogeneity of the emitting region.
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