Two detection systems, electro-optical system and photo-conducting system, are tested by the method suggested previously for determining the boundaries of broadband terahertz radiation in time-domain spectroscopy. From a series of measurements the error in determining the operation ranges is calculated. The terahertz spectrometer with an electro-optical detector based on a ZnTe (110) crystal of thickness $2\{\text {mm}} $ has the operation spectral range of $0.059 {-} 1.092\{\text {THz}} $. The detector utilizing an iPCA-21-05-1000-800-h photo-conducting antenna with the same source of signal demonstrates a wider operation band ranging from 0.017 to $1.6\{\text {THz}} $. The method developed makes it possible to experimentally compare the parameters of the considered terahertz spectrometers obtained under the same quality of adjustment.