This paper presents matching condition for detector at THz frequencies, which directly read signals from an integrated antenna. We use direct THz-signal detections with CMOS transistors in non-resonant plasma wave mode, which are embedded in on-chip resonating antennas. The detector detects THz envelope signals directly from the side edges of the on-chip patch antennas. The signal detection mechanism is studied in the view of the impedance conditions of the antenna and the detector. The detectors are implemented with stacked transistors structures to achieve high responsivity. The measured responsivities of the detectors with antenna impedances that were simulated to be 599.7, 912.3, 1565, and 3190.6 Omega agree well with the calculated values. Moreover, the responsivity dependence on the detector impedance is shown with two different input impedances of the detectors. Since CMOS circuit models from foundry are not accurate at frequencies higher than f(t) , the matching guideline between the antenna and the detector is very useful in designing high responsivity detectors. This study found that a detector has to have a large input impedance conjugately matched to the antenna's impedance to have high responsivity.