An approach for studying the performance of phase-coherent devices under high-frequency conditions is presented. The necessity of dealing with a scattering matrix that depends on the external frequency is emphasized, in order to provide an adequate theoretical framework for present tunnelling devices at frequencies comparable with the inverse of the electron transit time. As an example, a simple bound state resonant tunnelling transistor is studied. Its admittance parameters are computed showing that its amplifying properties are strongly degraded at THz frequencies. The present approach provides an original path for studying the ultimate quantum high-frequency limit for nanometric field effect transistors.