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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. 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 1 kHz, resulting in maximum detectivity around the modulation frequency of 100 Hz. We also improved the responsivity 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 paper, comparison of device detectivity before and after coating is also presented.