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Orbital and physical parameters of eclipsing binaries from the ASAS catalogue -- I. A sample of systems with components' masses between 1 and 2 M$_\odot$

We derive the absolute physical and orbital parameters for a sample of 18 detached eclipsing binaries from the \emph{All Sky Automated Survey} (ASAS) database based on the available photometry and our own radial velocity measurements. The radial velocities (RVs) are computed using spectra we collected with the 3.9-m Anglo-Australian Telescope and its \emph{University College London Echelle Spectrograph} and the 1.9-m SAAO Radcliffe telescope and its \emph{Grating Instrument for Radiation Analysis with a Fibre Fed Echelle}. In order to obtain as precise RVs as possible, most of the systems were observed with an iodine cell available at the AAT/UCLES and/or analyzed using the two-dimensional cross-correlation technique (TODCOR). The RVs were measured with TODCOR using synthetic template spectra as references. However, for two objects we used our own approach to the tomographic disentangling of the binary spectra to provide observed template spectra for the RV measurements and to improve the RV precision even more. For one of these binaries, AI Phe, we were able to the obtain an orbital solution with an RV $rms$ of 62 and 24 m s$^{-1}$ for the primary and secondary respectively. For this system, the precision in $M \sin^3{i}$ is 0.08%. For the analysis, we used the photometry available in the ASAS database. We combined the RV and light curves using PHOEBE and JKTEBOP codes to obtain the absolute physical parameters of the systems. Having precise RVs we were able to reach $\sim$0.2 % precision (or better) in masses in several cases but in radii, due to the limited precision of the ASAS photometry, we were able to reach a precision of only 1% in one case and 3-5 % in a few more cases. For the majority of our objects, the orbital and physical analysis is presented for the first time.