We study a class of superconductive radiation detectors in which the absorption of energy occurs in a long superconductive strip while the readout stage is provided by superconductive tunnel junctions positioned at the two ends of the strip. This configuration has been extensively studied in the last years almost invariably using two superconducting materials one of which, with a lower gap, used to fabricate the junctions, has the role of a trap for the nonequilibrium quasiparticles. In this work we study in detail the signal formation and the performances of such a device based on a single superconducting material, i.e. one without traps. We show that the trap-free device is capable both of imaging and energy resolution. We calculate the detector response in the form of collected charges at the two junctions, for Ta and Al devices and discuss a few features, specific to the trap-free detector, which can facilitate a rapid characterization of the device before use under radiation.