![\"Fig.1](\"https:\/\/butis-m.ru\/wp-content\/uploads\/2014\/05\/Pic1.jpg\")
<\/a>Fig.1 Structure of quasi-rectangle slanted filter<\/p><\/div>\n
Transducers can be performed as quasi-slanted ones\u00a0[5]. In this case a set of parallel acoustic channels have a\u00a0uniform electrode widths, periodicity, and aperture An in\u00a0the direction of SAW propagation for an each channel.\u00a0The like straight electrodes in the adjacent channels are
\nelectrically connected in equipotential stepped electrodes\u00a0using connection layers with the apertures dAn. \u00a0A\u00a0simulation yields that if the ratio dAn \/An is about 15\u00b820,\u00a0then the effect of connection layers on the frequency\u00a0responses of the filter can be disregarded. These\u00a0intermediate layers can be used for a connection with\u00a0additional busbars by horizontal strips as shown on Fig.2.<\/p>\n
<\/a>Fig.2 Layout fragment for intermediate channels<\/p><\/div>\n
A transfer function of the n-channel may be derived as<\/p>\n
Hn(f) = HIn(f) x HOn*(f),<\/p>\n
where HIn(f) and HOn*(f) are transfer function and\u00a0complex conjugate one of input and output transducers\u00a0correspondingly.<\/p>\n
In contrast to ordinary slanted filter transfer functions\u00a0of sub-filters differ each from other because of different\u00a0finger number for each channel. Therefore, an overall amplitude response of quasi-rectangle slanted filter (QRST) may be expressed by:<\/p>\n
Because sub-filter lengths are identical, high and low frequency transition bandwidths are identical too. They are close to a high frequency transition band for an ordinary slanted filter with the same weighting functions. So a frequency response of such filter becomes more symmetrical. Because specifications for the most of filters require symmetrical responses a use of QRST allows to reduce a filter lengths. Besides diffraction distortions are smaller because of more homogeneous metalization along propagation directions for SAW with different frequencies.<\/p>\n A design of quasi-rectangular slanted filters is based on the synthesis of high frequency transition band requirements. Both transducers are synthesized so that to provide required transition bandwidth and rejection level, i.e. a length of high-frequency channel limits transducer lengths as a whole. A finger structure of other lower frequency channels depends on the fixed length of a transducers. Fingers that positioned out of transducers edges are disregarded. Last existing fingers of every channel that have to be connected to the opposite busbars are connected to additional busbars as shown in Fig.2.<\/p>\n Finger structures of cut layers differ from initial weighting. That\u2019s why transition bandwidth and out-ofband rejection for low frequency region can vary from high frequency one. But this difference is insignificant for most withdrawn weighted or unweighted transducers that widely used for such filter synthesis.<\/p>\n As an example simulated responses of filters based on an ordinary slanted transducer (plot 2) and QRST (plot 1) are shown in Fig.3.<\/p>\n Fig 3 Comparison of simulation responses of quasirectangular (plot #1) and ordinary slanted filters<\/p><\/div>\n It should be mentioned that in comparison with a length of ordinary transducer Lor a length of QRST equals Lo \u00bb Lor *Fmin\/Fmax , where Fmin and Fmax are minimal and maximal central frequency of sub-filters.<\/p>\n Experimental responses of the 77 MHz filter based on QRST are shown in Fig. 4. The filter is fabricated on 112o-LiTaO3 substrate. The first SPUDT transducer was unweighted and the second one was withdrawn weighted. The number of active layers was 25. The relative bandwidth of the filter was more than 15% and its shape factor for levels 40 dB and 3 dB is 1.17. A use of QRSTs allowed to reduce metal pattern.<\/p>\n Fig.4 Experimental responses of quasi-rectangular 77 Usually tap weights for any given electrode of ST are the same for every channel across an aperture. Segmenting of an entire slanted filter into a discrete layer structure allows to synthesize these layers with different weighting functions. The frequency response of transition bandwidth regions is mainly determined by responses of \u00a0sub-filters that are adjacent to respective edges of a transducer aperture. So channels closed to passband edge frequencies are more responsible for transition band and out-of-band rejection.<\/p>\n In order to improve a rejection withdrawal weighted transducer is usually used. Central layers mainly yield insertion loss (IL) of the slanted filter. If a filter length is fixed unweighted transducers can provide minimal IL.<\/p>\n A structure of such partially-weighted slanted\u00a0transducer(PWST) that corresponds to the design Fig.5 Transducer structure with partially weighted layers.<\/p><\/div>\n It should be mentioned that there are a few\u00a0limitations for such PWSTs synthesis. These limitations\u00a0are caused by requirement of electrical connections\u00a0between layers. A synthesis procedure was designed to\u00a0simulate correct layer structures of partially weighted\u00a0transducers. As initial data a number of unweighted and\u00a0withdrawn weighted layers and weighing function of\u00a0lateral layers are set. The synthesis algorithm provides\u00a0weights simulation of every layer accounting limitation\u00a0mentioned above. Besides optimization procedure is used\u00a0in order to minimize out-of-band rejection.<\/p>\n Simulations show that IL of filters based on PWST are closer to unweighted transducers but better out-of-band rejection can be provided. Three responses corresponding to different slanted filter structure are shown in Fig.6. All filters have transducers of the same lenghts and SPUDT finger structure but have different weighting. 112o-LiTaO3 was used as a substrate.<\/p>\n Fig.6 Frequency responses of slanted filter: Because numbers of non-zero weights are different for withdrawal weighted layers the correction of layer apertures is required to provide a desirable passband response.<\/p>\n As an example the distribution of layer apertures corresponding to partially-weighted filter is shown in Fig.7. Apertures of lateral layers exceed ones of central layers by 8-9 dB to provide a flat passband response. As the additional advantage of PWST may be mentioned that such distribution of apertures allows to decrease distortions caused by diffraction effects because of larger apertures of lateral layers.<\/p>\n<\/a><\/p>\n<\/a><\/a>
MHz filter on 112o on LiTaO3 substrate<\/p><\/div>\nIII. PARTIALLY-WEIGHTED SLANTED TRANSDUCERS<\/h2>\n
\napproach mentioned above is shown in Fig.5. The QRST\u00a0has different weighting for central and lateral layers:\u00a0lateral channels are withdrawal weighted but central ones\u00a0are unweighted. Intermediate layers between lateral\u00a0layers and unweighted ones are withdrawal weighted too\u00a0but weighting functions for these layers are different. In\u00a0order to provide straight electrical connections between\u00a0fingers of adjacent layers the number of zero weights is\u00a0decreased continuously from lateral layers to unweighted\u00a0ones.<\/p>\n<\/a>
\n- Positions of zero weights of an every layer which is\u00a0closer to a transducer center have to coincide with\u00a0corresponding zero-weights of a previous layer, i.e. a\u00a0number of zero-weights of the layer can not be more than\u00a0one for adjacent more faraway layers.
\n- Weight distributions of high frequency and low\u00a0frequency layers are different, there is a shift by one\u00a0weight between coincident layers.<\/p>\n<\/a>
1 \u2013 filter based on unweighted transducers;
2 - filter based on partially-weighted transducers
3 \u2013 filter based on withdrawn-weighted transducers<\/p><\/div>\n