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De Haas-van Alphen oscillations are studied for Fermi surfaces (FS)illustrating the model proposed by Pippard in the early sixties, namely thelinear chain of orbits coupled by magnetic breakdown. This FS topology isrelevant for many multiband quasi-two dimensional (q-2D) organic metals such as$\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ and$\theta$-(BEDT-TTF)$_4$CoBr$_4$(C$_6$H$_4$Cl$_2$) which are considered indetail. Whereas the Lifshits-Kosevich model only involves a first orderdevelopment of field- and temperature-dependent damping factors, second orderterms may have significant contribution on the Fourier components amplitude forsuch q-2D systems at high magnetic field and low temperature. The strength ofthese second order terms depends on the relative value of the involved dampingfactors, which are in turns strongly dependent on parameters such as themagnetic breakdown field, effective masses and, most of all, effectiveLand\'{e} factors. In addition, the influence of field-dependent Onsager phasefactors on the oscillation spectra is considered.

Recent developments in the determination of the amplitude and phase of quantum oscillations for the linear chain of coupled orbits