In our paper, we present a new design for a single-grating tunable spatial heterodyne spectrometer (SHS). Our design simplifies the change of the center wavelength (Littrow wavelength) thus one can quickly tune the system to an arbitrary spectral range. Furthermore, we introduce a new calibration method that provides superior calibration accuracy over the generally used formulas involving small angle approximations. We also present considerations about the general usability of the SHS technique in broadband measurements and propose different strategies to improve the signal-to-noise ratio.