  The next generation of Far-infrared and X-ray space observatories will
require detector arrays with thousands of transition edge sensor (TES) pixel.
It is extremely important to have a tool that is able to characterize all the
pixels and that can give a clear picture of the performance of the devices. In
particular, we refer to those aspects that can affect the global energy
resolution of the array: logarithmic resistance sensitivity with respect to
temperature and current ($\alpha$ and $\beta$ parameters, respectively),
uniformity of the TESs and the correct understanding of the detector thermal
model. Complex impedance measurement of a TES is the only technique that can
give all this information at once, but it has been established only for a
single pixel under DC bias. We have developed a complex impedance measurement
method for TESs that are AC biased since we are using a MHz frequency domain
multiplexing (FDM) system to readout an array. We perform a complete set of AC
impedance measurements for different X-ray TES microcalorimeters based on
superconducting TiAu bilayers with or without normal metal Au bar structures.
We discuss the statistical analysis of the residual between impedance data and
fitting model to determine the proper calorimeter thermal model for our
detectors. Extracted parameters are used to improve our understanding of the
differences and capabilities among the detectors and additionally the quality
of the array. Moreover, we use the results to compare the calculated noise
spectra with the measured data.
