The paper presents a method for calculation of the main paraxial and energy parameters of a high-resolution astronomical spectrograph with a single echelle grating in a wide spectral range, without cross-dispersion elements. We consider two variants of the system design, namely, with a fixed grating (spectrograph) and with a movable grating (monochromator). Based on the analysis of the spectral resolution dependence on the echelle grating characteristics and the collimated beam diameter, the limits of the achievable maximum spectral resolution of the system are determined. The results obtained in this work can simplify the choice of the starting point for spectrograph designing. As an example of the presented method application design of the spectrograph for the Large Solar Telescope-coronagraph LST-3, operating in the spectral range of 390-900 nm, with spectral resolving power of R=200,000 and minimum diffraction efficiency of the echelle grating I g>0.68, is considered.