We show that Si MOSFETs, AlGaN/GaN HEMTs, AlGaAs/InGaAs HEMTs, and p-diamond FETs with feature sizes ranging from 20 nm to 130 nm could operate at room temperature as THz spectrometers in the frequency range from 120 GHz to 9.3 THz with different subranges corresponding to the transistors with different features sizes and tunable by the gate bias. The spectrometer uses a symmetrical FET with interchangeable source and drain with the rectified THz voltage between the source and drain being proportional to the sine of the phase shift between the voltages induced by the THz signal between gate-to-drain and gate-to-source. This phase difference could be created by using different antennas for the source-to-gate and drain-to gate contacts or by using a delay line introducing a phase shift or even by manipulating the impinging angle of the two antennas. The spectrometers are simulated using the multi-segment unified charge control model implemented in SPICE and ADS and accounting for the electron inertia effect and the distributed channel resistances, capacitances and Drude inductances.