Bolometric response and noise characteristics of YBCO superconductor transition edge IR detectors with relatively sharp transition and its resulting detectivity are investigated both theoretically and experimentally. The magnitude of response of a fabricated device was obtained for different bias currents and modulation frequencies. Also dependency of intrinsic noise of the device on the bias current in the vicinity of critical temperature was studied for various values of chopping frequencies. Using the measured and calculated bolometric response and noise characteristics, we found and analyzed the device detectivity versus frequency for different bias currents. The detectivity versus chopping frequency of the device did not decrease following the response strongly, due to the decrease of the noise at higher frequencies up to 1KHz, resulting in maximum detectivity around the modulation frequency of 100Hz. We also improved the detectivity of the device through the increase of the surface absorption by using a novel infrared absorber, which is made of a Copper-Carbon composite, coated in a low temperature process. Within the modulation frequency range studied in this investigation, comparison of device responsivity before and after the coating is also presented.