We are developing X-ray microcalorimeters based on Ti/Au transition-edge sensors (TES). Among sensors we have fabricated, one with a Cu absorber at the center of the TES shows a particularly good X-ray energy resolution: 1.56 eV at 250 eV and 2.5 eV at 5.9 keV. In this paper, a detailed study of its impedance and noise is presented. The noise is not explained by a sum of known sources. The magnitude of unexplained noise is largest when the sensitivity of the TES on temperature ( α) and on current ( β) are the highest. The observed relation between the noise level and sensitivity suggests a source of thermal fluctuations inside the TES or between the TES and the absorber. We also found that β is linearly correlated to the product of α and current, which limits the effective sensitivity that is expressed as α/(1+ β).
