Furthermore, these LGS cuts show a natural\u00a0directivity enabling the design of natural single phase\u00a0unidirectional transducers (NSPUDTs) [4,5]. An\u00a0NSPUDT is a normal finger transducer exhibiting a\u00a0natural unidirectivity owing to anisotropic properties\u00a0of the substrate crystal. It seems that the advantages\u00a0of such an effect would have been taken for the\u00a0development of low loss SAW filters. However, for a\u00a0long time, the applications of langasite have been\u00a0limited to medium-loss filters, resonators and\u00a0impedance element structures.<\/p>\n
Development of state-of-art SPUDT or\u00a0RSPUDT based filters on LGS is hindered because\u00a0they need different types of cells owning to its direct\u00a0and reverse unidirectivity. In addition, for RSPUDT\u00a0structure, the phase difference between transduction\u00a0and reflection centers in the cells has to be close to\u00a045 degree in order to provide resonant cavities inside\u00a0the transducer. Because of the effect of natural\u00a0unidirectivity, a general solution to meet these\u00a0requirements for LGS has not been found so far.<\/p>\n
In this paper we describe a new approach to the\u00a0synthesis of low-loss filters similar to RSPUDT\u00a0based filters. Design principles as well as theoretical\u00a0and experimental results are presented.<\/p>\n
MATHMATIC MODEL<\/h2>\n
Equivalent circuit model was modified and\u00a0adapted for the simulation of different types of SAW\u00a0filters on LGS. The basic section of a transducer is\u00a0shown in Fig.1. It extends between centers of\u00a0neighboring fingers and includes three basic cells\u00a0connected with electrical circuit by transformers r.<\/p>\n
Each cell is described by the following 3x3 matrix:<\/p>\n
where Z=Zo or Zm is acoustical resistors for \u00a0free or metalized surface, respectively; L v i \u03b8 =\u03c9 \/\u00a0is the angle shift under wave propagation in the cell.; \u00a0r is transformer ratio; and v is SAW velocity. The\u00a0circuit element B superposed with electrode edges is\u00a0a complex number. It describes the second order\u00a0effects such as propagation loss Re(B) and energy\u00a0storage effect Im(B).<\/p>\n Fig.1. Equivalent circuit model representation.<\/p><\/div>\n In order to adapt the model for simulations on\u00a0LGS and describe the effect of natural unidirectivity,\u00a0an additional angle \u03c6 was included into the phase\u00a0shift for cells under fingers, i.e. \u03b8 =\u03b8 +\u03d5 m . The\u00a0sign of the angle depends on SAW propagation\u00a0direction at finger edges. It should be mentioned that\u00a0the angle is equivalent to a shift between reflection\u00a0and transduction centers in a transducer.<\/p>\n The angle \u03c6 and substrate parameters\u00a0depending on relative film thickness were determined\u00a0by experiments. The test structure is shown in Fig. 2-\u00a0a. Typical responses for different film thickness are\u00a0shown in Fig.2-b, when transducers 1 and 3 are used\u00a0as in put and output, respectively. The responses for\u00a0direct and reverse directions on LGS, when the \u00a0transducer 2 is input and transducers 1 or 3 are used\u00a0as output, are shown in Fig.2-c.<\/p>\n The analysis of responses for different film\u00a0thicknesses allows the determination of the angle \u03c6\u00a0and the dependence of reflection and energy storage\u00a0effects as the first approximation. The average \u03c6\u00a0value turns out to be around 60o. It should be noted\u00a0that the angle depends on film thickness. The angle\u00a0change is around 10% with thickness variation from\u00a00.4% to 3%. More precise tuning of these parameters\u00a0has been carried out with the development of\u00a0different types of filters on LGS substrates.<\/p>\n Fig.2. Test structure (a) and typical responses for 1-3\u00a0transducers (b) and 1-2 and 2-3 transducers (c).<\/p><\/div>\n The advantage of this model is its flexibility\u00a0with varieties of finger structures because the\u00a0parameters of cells are determined by edge positions\u00a0of electrodes. The model has been applied to the\u00a0analysis of single-phase unidirectional transducers\u00a0(SPUDT) on LGS in order to estimate their\u00a0efficiency for SPUDT filter designs.\u00a0Analysis of different electrode structures\u00a0allows the selection of basic SPUDT structures, that\u00a0can be utilized for the development of lower-loss\u00a0SAW filters on substrates with natural unidirectivity,\u00a0such as LGS. These SPUDT sections are shown in\u00a0Fig.3. It should be mentioned that the efficiencies of\u00a0the section\u2019s unidirectivity for the forward direction\u00a0(coinciding with the natural unidirectivity) and the\u00a0reverse direction are close. This feature simplifies the\u00a0development and allows better results of SPUDT\u00a0filters.<\/p>\n Fig.3. Sell structures for forward (a) and reverse\u00a0(b) directions and with reflection removed (c).<\/p><\/div>\n Because the phase between transduction and\u00a0reflection centers for SPUDT sections shown in Fig.3\u00a0is not optimal (45o), it is a problem to use these\u00a0sections for resonant SPUDT (RSPUDT) filters. The\u00a0method based on variations of electrode structures\u00a0inside a transducer region [6], has been used in order\u00a0to reach a total phase of reflections required to realize\u00a0resonant conditions in the transducer region.<\/p>\n The method consists the division of an\u00a0electrode section by elements with equal widths.\u00a0Usually a section\u2019s width is equal to the wave length\u00a0\u03bb. The element width is \u03bb\/N, where N is the number\u00a0of elements in the section. Every element can be\u00a0represented as a strip connected with opposite\u00a0transducer busbar or a free space element. So the\u00a0maximal number of layout variants for the current\u00a0section is 3N. The number of simulation variants can\u00a0be reduced significantly if some restrictions are\u00a0imposed in the synthesis algorithm. These\u00a0restrictions are listed as follows:<\/p>\n The developed design algorithm is based on an\u00a0ordinary routine applied for synthesis of RSPUDT filters. A filter structure is represented as a\u00a0combination of basic elements. Responses of the\u00a0synthesized filter are simulated for every current\u00a0structure and compare with requirements for the\u00a0filter. The error Eg between the current response and\u00a0requirements is estimated.<\/p>\n If simulated Eg is reduced for a current section\u00a0structure the structure corresponding to a minimal\u00a0error is fixed. Then a next section of the transducer is\u00a0analyzed. The optimization algorithm allows\u00a0minimizing the error after a few iterations. In this\u00a0case the simulated response becomes close to the\u00a0required.<\/p>\n Analysis of responses corresponding to current \u00a0filter structure is carried out for tuned filter. Values\u00a0of elements of matching circuits are determined\u00a0automatically for fixed circuit configuration and\u00a0termination impedances. The reliability of synthesis\u00a0results depends on both accuracy of model and\u00a0charge distribution calculation. Charge distribution\u00a0on electrodes is determined by solving the electrostatic task for each electrode configuration.<\/p>\n Figs. 4 and 5 refer to slanted filters on LGS substrate with orientation yxlt\/48.5o\/26.6o. The filter shown in Fig.4 used NSPUDT transducer and reversed one with 1\/6 \u03bb fingers. The fractional\u00a0bandwidth of the filter is 2.6%, and insertion loss is 12.4dB.<\/p>\n Fig.4 Responses of slanted filter based on NSPUDT<\/p><\/div>\n The second filter is based on SPUDT structures \u00a0shown in Fig.3. It consists of unweighted input transducer and withdrawal weighted output transducer. Weighing functions for reflectors were optimized in order to allow minimal passband ripples based on simulations. The lengths of transducers are 78 \u03bb and 120 \u03bb. respectively, with aperture of 44 \u03bb. 3 dB bandwidth of the filter is 3.6 MHz (3.1%), insertion loss is less than 10dB (9.6dB) and out of band rejection is about 50dB.<\/p>\n Experimental results (Fig.5) agree with simulations (dotted line) very well. The comparison confirms that the model we developed is adequate for the analysis of SPUDT filter on LGS. It should be mentioned that the use of novel SPUDT structures developed in the work allows to improve the SAW filters parameters over NSPUDT. Insertion loss has been reduced by 2.5 to 3dB, even with wider bandwidth and lower passband ripple.<\/p>\n Fig.5. Responses of slanted filter based on SPUDT Narrower filters have been designed by the optimization routine described above as well. The width of the basic synthesis elements is 0.125\u03bb. Maximal gap and electrode widths are restricted as 0.25\u03bb and 0.375\u03bb, respectively. The structure of these filters is shown in Fig.6. The central grating in these filters is used both as feedthrough screen and additional structure element for the synthesis of the filter responses. A fragment of electrode structure is shown in Fig.6-b. As indicated in the picture, because of irregular electrode structure, the pitches between transduction centers are variable.<\/p>\n Fig.6. Schematic of in-line RSPUDT filters (a) and fragment of electrode structure (b).<\/p><\/div>\n Performances of RSPUDT filters on the same langasite cut are shown below.<\/p>\n 3dB bandwidth of the 129 MHz filter (Fig.7) is 3.1 MHz or 2.4%, with 8.7dB insertion loss. The \u00a0filter fits in 3.8mm square package.<\/p>\n Responses of 251 MHz filter with 3dB bandwidth of 3.26MHz or about 1.3% are shown inFig.8. The pass band ripple is only 0.1 dB, with insertion loss of 7.7 dB. The filter also fits in 3.8mm square package.<\/p>\n
\n<\/a> ![\"Pic56\"](\"https:\/\/butis-m.ru\/wp-content\/uploads\/2014\/07\/Pic56.jpg\")
<\/a><\/p>\n<\/a><\/a><\/a>SYNTHESIS OF RSPUDT FILTERS<\/h2>\n
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FILTERS DESIGN<\/h2>\n
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cells shown in Fig.3.<\/p><\/div>\n<\/a>
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