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The direct integration on the high-resistivity substrate of a source-follower stage significantly improves the overall detector performance as the detector capacitance is buffered from the capacitive load of the external preamplifier. In principle this would allow full exploitation of the benefits of sub-picofarad anode capacitance (e.g., down to few tens of fF for Silicon Drift Detectors) in terms of spectroscopic resolution and processing speed. However, as the product of transconductance and output resistance of on-chip JFETs is typically limited to about 10 or even less due to technological constraints, the signal transfer of the JFET source-follower stage significantly departs from the ideal behavior, especially at sub-picofarad detector capacitances. In this paper we analyze in detail the actual performance of the on-chip source follower stage and its impact on the achievable noise and time performance of the detection system.