  Transition Edge Sensors (TESs) are the selected technology for future
spaceborne X-ray observatories, such as Athena, Lynx, and HUBS. These missions
demand thousands of pixels to be operated simultaneously with high
energy-resolving power. To reach these demanding requirements, every aspect of
the TES design has to be optimized. Here we present the experimental results of
tests on different devices where the coupling between the x-ray absorber and
the TES sensor is varied. In particular, we look at the effects of the diameter
of the coupling stems and the distance between the stems and the TES bilayer.
Based on measurements of the AC complex impedance and noise, we observe a
reduction in the excess noise as the spacing between the absorber stem and the
bilayer is decreased. We identify the origin of this excess noise to be
internal thermal fluctuation noise between the absorber stem and the bilayer.
Additionally, we see an impact of the coupling on the superconducting
transition in the appearance of kinks. Our observations show that these
unwanted structures in the transition shape can be avoided with careful design
of the coupling geometry. Also the stem diameter appears to have a significant
impact on the smoothness of the TES transition. This observation is still
poorly understood, but is of great importance for both AC and DC biased TESs.
