## 1 Introduction  
Ferroelectric thin-film materials (FE) demonstrate high nonlinearity of dielectric properties (the dependence of the permittivity on the strength of the applied electric field), which makes them promising materials for electrically tunable devices of microwave electronics. The advantages of ferroelectrics at microwaves are: high dielectric nonlinearity, relatively low losses, shirt switching time (\(\sim\)10\({}^{-11}\) s), high operating power with low energy consumption in control circuits and high radiation resistance [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. Among the ferroelectrics studied today, the most attractive for use at microwaves are perovskite oxide materials, which are capable of forming multicomponent solid solutions whose electrophysical properties can be changed in broad limits [11; 12; 13; 14]. The most studied ferroelectric material for microwave applications is barium-strontium titanate Ba\({}_{\bf x}\)Sr\({}_{1-x}\)TiO\({}_{3}\) (BST) [3; 4; 5], in which the formation of a solid solution occurs due to the substitution of A-site atom in ABO\({}_{3}\) perovskite structure. At the same time, there are a number of ferroelectrics, in which the formation of a solid solution occurs due to the B-site substitution [15; 16]. Among them the barium titanate-stannate BaTi\({}_{x}\)Sn\({}_{1-x}\)O\({}_{3}\) (BTS) is a potentially promising material for electrically tunable applications. Depending on the ratio of the concentrations of Ti and Sn atoms, the value of the relative dielectric permittivity of BTS solid solution in the maximum can reach significant values (2-3) \(\times\) 10\({}^{4}\)[15]; the introduction of chemically more stable Sn atoms into a solid solution instead of Ti can lead to a decrease in through conductivity and dielectric losses, to a significant increase in the electrical strength of the material, and, as a result, to the possibility of increasing the applied electric field and increasing the dielectric nonlinearity [16]. A number of papers have been published that investigate the structural and electrophysical properties of BTS thin films [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34], including works dedicated to microwave investigations [25; 34; 35]. The studied films were obtained by chemical solution deposition [22; 23; 36], ion-plasma sputtering [17; 18; 19; 29; 30; 34; 35], sol-gel technology [24; 25; 26; 27; 28; 31; 32] and laser ablation [33]. In the vast majority of works, experimental data on dielectric losses in FE capacitive structures are given for the frequency range of 1 kHz-1 MHz. These data do not allow us to draw a conclusion about the applicability of the obtained films at microwaves. In addition, it should be noted that the high dielectric nonlinearity of capacitive elements based on the studied films (tunability up to 72%) is demonstrated exclusively in plane-parallel metal-dielectric-metal (MDM) structures, i.e., in cases when the film is formed on a conducting electrode [22; 23; 24; 28; 29; 30; 33; 35], while in works devoted to the growth of FE layers on dielectric materials data on tunability from 15 to 46% are given [25; 26; 27; 31; 32; 34; 36], and only on expensive monocrystal substrates. The design of MDM capacitors allows the use of small control voltages to change the capacitance, but exactly because of it, the use of such structures is possible only in small-signal devices. However, one of the main potential advantages of FE devices over semiconductor analogues, namely the ability to operate at high power levels, can only be realized in a planar design on a dielectric substrate. Therefore, more investigations are necessary in order to obtain enhanced tunability of BTS thin films on dielectric substrates with high Q-factor and low cost. As one such substrate material, polycrystalline aluminum oxide can be proposed.