![\"Fig.](\"https:\/\/butis-m.ru\/wp-content\/uploads\/2014\/07\/Pic74.jpg\")
<\/a>Fig. 1. Typical structures of resonator filters with longitudinal coupling: (a) asymmetric (first and second modes) and (b) symmetric (first and third modes).<\/p><\/div>\n
The characteristics are realized by the corresponding\u00a0spatial arrangement of IDTs and reflecting lattices\u00a0that ensures the required interaction between resonance\u00a0modes for various filter designs. Usually, to realize the\u00a0required characteristics, the filters are made of two or\u00a0three units connected in series and topologically combined\u00a0into a single design.<\/p>\n
In this study, we consider modified structures and\u00a0the methods of improving the parameters of LCRFs.\u00a0These methods involve IDTs and reflecting lattices with\u00a0a modulated electrode period. The cases of partially\u00a0modulated transducers and so-called dispersive IDTs\u00a0realizing linear frequency modulation (LFM) within\u00a0the IDT length are considered. The use of these structures
\nmakes it possible to reduce the insertion loss in filters\u00a0and to improve the uniformity of the characteristics\u00a0in the passband. In particular, the authors of [3] attribute the reduction of the insertion loss to decreased generation of spurious bulk waves.<\/p>\n
1. FILTERS BASED ON PARTIALLY MODULATED IDTS<\/h2>\n
As a result of the filter synthesis, distances Li between the structure elements ensuring the required filter characteristics may be considerably different from typical gaps between the electrodes in IDTs and lat-tices. If distances Li are too small, problems of fabrication arise. In contrast, if Li are greater than the typical gap width, additional loss occurs owing to the effect of LSAW scattering by topological inhomogeneities [4].<\/p>\n
An effective solution of the above-mentioned problems is to adjust the periods of IDT electrodes and of the lattices adjoining the gap under consideration in order to smooth the LSAW transition from one structural element to another. Then, the periods of most of the electrodes in the central parts of IDTs and lattices remain unchanged, thus ensuring the arrangement and interaction of acoustic resonances similar to the arrangement and interaction needed for realization of the required characteristics.<\/p>\n
Owing to the change of the character of boundary inhomogeneities in the period-modulation zone, the phase relationships between resonance structures exhibit variations. To develop the filter more adequately, these variations should be taken into account. An additional gap correction is made for reconstructing the original shape of the characteristics. Usually, two or three iterations ensure the convergence of the filter characteristics to the original design parameters for the filter on equidistant IDTs.<\/p>\n
Obviously, the results of development depend on the accuracy of the model used for the filter analysis. In this study, we use a modified model of equivalent circuits with the spatial arrangement of elementary sections uniquely related to the position of the electrode boundaries. To make the analysis more reliable, we calculate the charge distribution in irregular electrode lattices by solving the electrostatic problem [5], thus making it possible to improve the accuracy of the calculated filter characteristics.<\/p>\n
Figure 2 presents the experimental characteristics of a two-cascade RF with LAC. The structure of the RF is shown in Fig. 1b (first to third modes) in a 50-\u03a9 circuit with no matching elements. The filter is made on the YX1-36 \u00b0 cut of lithium tantalate. The relative thickness of the aluminum film is 6.5%. There are 44 and 36 electrodes for the central IDT and side IDTs, respectively. In each of the transducers adjoining the inter-IDT gap, three electrodes were modulated by period.<\/p>\n
<\/a>Fig. 2. Experimental characteristics of a two-cascade RF with LAC with the partially modulated electrode period; curve 1 is group delay time \u03c4.<\/p><\/div>\n
The insertion loss in the filter amounted to about 1.4 dB at the relative passband of 3.5% and a selectivity greater than 50 dB. Note that the insertion loss in the filters of this type is, on average, 0.3 to 0.5 dB less than that in conventional LCRFs that are based on equidistant IDTs.<\/p>\n
2. FILTERS BASED ON DISPERSIVE IDTS<\/h2>\n
The above-described designs of LCRFs can be considered a particular case of filters in which the electrode period varies according to a given relationship along the entire IDT length. The transducers of this type are usually employed in dispersive delay lines to realize a frequency-dependent delay and can, by analogy, be called dispersive IDTs (DIDTs). The structures of DIDTs and lattices with modulated periods of reflecting fingers ensure a more flexible approach to formation of resonances and arrangement of resonance peaks within the required passband [6], thus allowing realization of filters with better parameters than those of LCRFs on equidistant elements. In particular, a wider passband, a lower insertion loss, and a deeper rejection in the stop band, i.e., the total improvement of the filter parameters, can be achieved under the various conditions of requirements imposed on the filter.<\/p>\n
For determining the basic properties of dispersive\u00a0IDTs, we have investigated test transducers (Fig. 3)\u00a0with the linear variation of effective frequency\u00a0Fi(Fi=v\/2di, where\u00a0di\u00a0is the spatial \u00a0period of an electrode pair).\u00a0The test structures were made on the YX1-36\u00b0\u00a0cut of\u00a0LiTaO3\u00a0with an aperture of\u00a050\u03bb. The transducers were\u00a0made with linearly modulated spatial electrode periods;\u00a0the relative frequency deviation Fig. 3. Test structures with different dispersion directivities: (a) the negative sign of the dispersion, (b) the positive sign of dispersion,and (c) the frequency characteristics of structures (curve\u00a01) (a) and (curve 2) (b).<\/p><\/div>\n In Fig. 3c, we present the characteristics of the\u00a0transducers for different signs of the mutual dispersion\u00a0(Figs. 3a, 3b); the film thickness is about 5%. It is seen\u00a0that the difference between the insertion losses in the\u00a0structures with different combinations of the dispersion\u00a0signs is about 5.4 dB. The asymmetry of the dispersive\u00a0transducer radiation is due to the displacement of effective\u00a0reflection centers toward the low-frequency IDT\u00a0edge relative to the SAW radiation centers. The phenomenon\u00a0leads to an increase in the radiation flux\u00a0toward the high-frequency edge.<\/p>\n The experimental data show that, in dispersive IDTs\u00a0with unsplit electrodes, an effect of the unidirectional\u00a0SAW radiation toward the high-frequency IDT section\u00a0arises. This effect can be used for additional reduction\u00a0of the insertion losses in LCRFs. It should be noted that\u00a0the unidirectional character of radiation of dispersive\u00a0IDTs is most effective in the structure of the first and\u00a0second modes (Fig. 1a), where the transducers\u2019 directivities are opposite. The filters of this type have dimensions smaller than those of the structures of the first and third modes and are easier to assemble.<\/p>\n For the comparative evaluation of the efficiency of using dispersive IDTs in resonator SAW filters, we have developed identical two-cascade LCRFs with a central frequency of about 315 MHz.<\/p>\n The first filter consisted of a pair of two-mode resonator units connected in series (the first and second modes, see Fig. 1a). Each IDT included 36 electrodes; the frequency deviation was 2.3%. The relative Al-film thickness was about 6%. To achieve the required passband (2%), a central reflecting equidistant grating (screen) was applied; it ensured the necessary magnitude of the acoustic coupling between the input and output resonators.<\/p>\n The structure of the second LCRF was analogous, although it consisted only of equidistant transducers and lattices. The design parameters of both filters were the same. The experimental characteristics of the filters in a 50\u03a9 circuit are presented in Fig. 4.<\/p>\n Fig. 4.\u00a0Amplitude\u2013frequency characteristics of the LCRF with (curve\u00a01) dispersion of the IDT electrode width and (curve\u00a02) equidistant\u00a0electrodes.<\/p><\/div>\n Thus, the results indicate that LCRFs that are based on\u00a0dispersive transducers exhibit smaller (by about 0.6 dB)\u00a0losses and have more uniform amplitude\u2013frequency\u00a0characteristics in the band. Note that the experimental\u00a0parameters of the filters are in fairly good agreement\u00a0with the calculated results, thus indicating that the adequacy\u00a0of the model developed for the calculation of filters\u00a0of this type. Possible realization of asymmetric filters that ensure\u00a0effective operation in narrower and wider passbands is\u00a0illustrated in Fig. 5, where the experimental characteristics\u00a0of the filters made on YX1-\u00a036\u00b0\u00a0LiTaO3\u00a0cut are\u00a0depicted. The filters have relative passbands of 1.5 and\u00a03.5%. The insertion losses in the filters were 2.2 and 1.9dB, respectively, in the 50\u03a9 circuit. The signal attenuationin the stop bands was greater than 40 dB at 40-and 3-dB-level rectangularity coefficients of about 2.<\/p>\n
\n<\/a>
\nwhere\u00a0Fh\u00a0and\u00a0F1\u00a0are the highest and the lowest frequencies\u00a0corresponding to the edge IDT electrodes, respectively,\u00a0and\u00a0F0\u00a0is the central frequency of the structure.\u00a0The relative thickness of the aluminum film on the test\u00a0samples varied from 1 to 6%.<\/p>\n<\/a><\/a>