At the above nonuniform distribution of fi <\/sub><\/em>\u00a0<\/sub>the magnitude\u00a0 of amplitude ripples in the passband depends on a relative passband width of a filter [4] (Fig. 1, plot 1).<\/p>\n Fig.1. Relationships between amplitude ripples in passband and relative passband width: nonuniform (1) and uniform (2) frequency distribution.<\/p><\/div>\n In the case of uniform distribution of the channel frequencies fi\u00a0 <\/sub><\/em>\u00a0= fi- <\/sub><\/em>1\u00a0 <\/sub>\u00a0+df<\/em> , where df <\/em>=(fmax <\/sub><\/em>\u00a0-\u00a0\u00a0 <\/sub>fmin<\/sub><\/em>)\/(MC<\/sub><\/em> -1), an amplitude of ripples hardly depend on the passband width\u00a0 (Fig. 1,\u00a0 plot 2).\u00a0 Here fmax <\/sub><\/em>\u00a0and\u00a0\u00a0 <\/sub>fmin<\/sub><\/em> are the maximum and minimum channel frequencies of the passband respectively.<\/p>\n A slope of the amplitude response arising at the frequency distribution indicated is easy to be compensated by adjusting the apertures of sub-filters.<\/p>\n Referring to computations, the greater the number of channels\u00a0 in a slanted transducer, the narrower the passband width. As an example, Fig. 2 shows the relative transition bandwidth (TBW) and the passband amplitude ripples\u00a0 Da<\/em> as\u00a0 functions of the number of channels MC<\/sub><\/em> for a filter with the relative passband width BW=20%.<\/p>\n Fig.2. Relation ships of transition bandwidth (TBW) and passband ripples ( ) on channel number ( =60 pairs).<\/p><\/div>\n From\u00a0 Fig. 2\u00a0 one sees that the transition-band width can be decreased about by 15% at amplitude ripples not exceeding 0.1 dB and comparatively small number of channels, MC<\/sub><\/em>\u00a0 =10\u00b830.<\/p>\n For the filters with the small number of acoustic channels\u00a0 MC <\/sub>\u00a0<\/em>\u00a0=10\u00b830,\u00a0\u00a0 the\u00a0\u00a0 electrode\u00a0\u00a0 shape\u00a0\u00a0 of\u00a0 slanted transducers approaches the stepped one, as shown in Fig. 3b. Unlike slanted transducers with continually varying electrode width and period (Fig.3a) these transducers can be called quasi-slanted (QST).<\/p>\n Fig.3. Electrode shape of conventional slanted IDT (a) and quasi-slanted IDT (b).<\/p><\/div>\n QST is a set of parallel acoustic channels, each of which has a uniform electrode width, period, and aperture A i<\/sub><\/em> in the direction of SAW propagation. The like straight electrodes in the adjacent channels are electrically connected in equipotential stepped electrodes using connection layers with the apertures dAi<\/sub><\/em>\u00a0 (Fig. 3b). The computation\u00a0 yields that if the ratio dAi <\/sub>\/Ai<\/sub><\/em> <15\u00b820, then the effect of connection layers on the frequency responses of the filter can be disregarded.<\/p>\n As was mentioned above diffraction effects and SAW flow beam deviation still considerably distort characteristics of slanted transducers based filters. Fig. 4 shows the experimental amplitude response for two structurally identical filters with the different transducer apertures W1<\/sub>=80<\/em>l<\/em> and W2<\/sub>=120<\/em>l<\/em> . At the insufficient filter aperture, W1<\/sub>=80<\/em>l, <\/em>the characteristic distortions are the appearance of pronounced amplitude ripples near the low-frequency limit of the passband, the narrowing of the passband, and the broadening of the high-frequency transition band of the filter. The above distortions of the amplitude\u00a0 response\u00a0 arise owing to the SAW beam steering and diffraction. To one or another degree they are typical for all substrate materials (quartz, lithium niobate, lithium tantalate). These effects primarily show up in the filters with the low shape factor SH=1.2\u00b81.4, where the mean slope of the edge electrodes of slanted transducers must\u00a0 be\u00a0 far\u00a0 more greater than the slope in the transducers having the same passband but\u00a0 worse shape factor SH=1.5\u00b82.5.<\/p>\n Fig.4. Comparison of responses two identical slanted filters with different apertures: 1- W1=80l; 2-W2=120l.<\/p><\/div>\n Increasing of an aperture of slanted and quasi-slanted transducers decreases distortions. However, with the increase in an aperture ,<\/em> the transducer capacity CT<\/sub><\/em>\u00a0 also proportionally increases and the radiation resistance Ra<\/sub><\/em> decreases, complicating filter-load matching. To solve the problem transducers with serial-connected electrode sections[5] are commonly used (see fig.5). The multi-section transducers decrease CT<\/sub><\/em>\u00a0 by a factor ps<\/sub>2<\/sup><\/em> (ps<\/sub><\/em> is the number of sections) and increase the input impedance of the filter. The implementation of such multi-section transducers allows the optimization of their equivalent aperture in order to minimize amplitude ripples and insertion loss of quasi-slanted SPUDT filters.<\/p>\n Fig.5. Structures of multi-section transducers: a \u2013 two-section IDT; b \u2013 three-section IDT.<\/p><\/div>\n To analyze QST filters, a modified equivalent circuit model [6] has been used. This model takes into account second-order effects and fairly accurately describes the filter characteristics with due regard for loads and matching circuits.<\/p>\n Withdrawal\u00a0 weighted transducers were used in order to achieve the needed filter selectivity [2]. In this case, we employed an optimization procedure that provides the maximum\u00a0 rejection in the stop-band at the fixed transducer lengths.<\/p>\n To obtain the desired amplitude and phase responses we corrected the channel apertures and channel positions in the direction of SAW propagation.<\/p>\n A\u00a0 performance of slanted electrodes with varying width is the difficult stage in the fabrication of conventional\u00a0 slanted SPUDT filters. The slanted electrodes are divided along their aperture into 500\u00b81000 fragments. As a result, the number of flashes and, hence, the production time abruptly increase.<\/p>\n The use of quasi-slanted SPUDT substantially simplifies\u00a0 the photomask fabrication. In this case, the main problem is the creation of connection layers. The layout of these layers may be different (Fig. 6).<\/p>\n Fig.6. Variants of connection layers performance: a \u2013 trapezoid; b \u2013 slanted rectangles, c \u2013 rectangles.<\/p><\/div>\n If the elements of connection layers are alike and have the\u00a0 form\u00a0 of a trapezoid (Fig. 7a) or rectangle (Fig. 7b), the number of flashes during the photomask production is considerably reduced.<\/p>\n Fig. 7. Frequency responses of 210 MHz filter on ST-quartz In the case that these layers are of the form of parallel rectangles, the total number of flashes is also substantially reduced providing an optimization procedure is used. This procedure minimizes the required number of flashes, depending on a the pre-set overlap of adjacent layers.<\/p>\n Thus,\u00a0 the\u00a0 total number of flashes during the fabrication of the photomask for QST filters can be reduced by a factor of 3\u00b810 as compared with the conventional slanted SPUDT.<\/p>\n 4. EXPERIMENTAL RESULTS<\/p>\n Several QST filters with different relative passband widths in the range 2-70% have been designed for mobile, wireless, and satellite communication systems.<\/p>\n Two narrow-band 210 MHz filters with the passband width BW3=4.5 MHz (or 2.1%), and SH\u00bb1.5 have been fabricated on the ST-cut quartz and XYs\/1120<\/sup>-cut lithium tantalate substrates. Both the filters involve per 9 sub-filters with one withdrawal weighted DART SPUDT and one bi-directional transducer.<\/p>\n The aperture of the quartz filter was 500 mm . The input and output transducers used two series-connected electrode sections L1<\/sub>=120<\/em>l<\/em>\u00a0 and L2<\/sub>=140<\/em>l\u00a0 <\/em>long (Fig. 5a).<\/p>\n The aperture of the filter on LiTaO3<\/sub> was\u00a0 650mm, by L1<\/sub>=140<\/em>l<\/em> and L2<\/sub>=180<\/em>l<\/em>. Each of the transducers involved three series-connected electrode sections.<\/p>\n The frequency responses of the filters are depicted in Fig. 7 and Fig. 8, respectively.<\/p>\n Fig. 8. Frequency responses of 210 MHz filter on XYs\/112o LITaO3 (in passband - 0.5 dB\/Div and 0.6 MHz\/Div).<\/p><\/div>\n Resistive loss of the filter on LiTaO3<\/sub> were higher, because the number of series-connected electrode sections was greater. However, insertion loss of this filter (IL=11.2 dB) were 3 dB less than those of the quartz filter (IL=14.4 dB).\u00a0 Both the filters were housed in SMD 9.0x7.0x1.6 mm packages.<\/p>\n The frequency responses of the middle-band 280 MHz filter\u00a0 with the\u00a0 passband\u00a0 BW3=20.5 MHz\u00a0 (or \u00bb7%)\u00a0 are \u00a0shown in Fig. 9. The filter involved two withdrawal weighted TES SPUDTs [7]. Insertion loss were IL=7.7 dB and\u00a0 SH(40\/3)=1.4. The YZl-cut LiNbO3<\/sub> substrate has been used. The filter package was SMD 5.0x5.0x1.2 mm.<\/p>\n The wide-band 75 MHz filter with the passband BW3=15 MHz (or 20%) involved two quasi-slanted NCF SPUDTs [8] L1<\/sub>=53<\/em>l<\/em> and L2<\/sub>=61<\/em>l<\/em>long. The transducers used the block weighting of electrode sections [4]. Fig. 10 shows the frequency responses of the 75 MHz filter. The insertion loss were IL=10.8 dB and shape factor was SH(40\/3)=1.3. SMD 13.3x6.5x1.6 mm package have been used.<\/p>\n Fig.9. Frequency\u00a0 responses of 280 MHz filter on YZl-LiNbO3 (in passband - 0.5 dB\/Div and 3.0 MHz\/Div).<\/p><\/div>\n The frequency responses of the extra wide-band 350 MHz filter with the passband BW3=250 MHz (or 70%) are shown in Fig. 11. Two unweighted bi-directional QST L1<\/sub> =20<\/em>l<\/em>\u00a0 and\u00a0 L2<\/sub> =30<\/em>l\u00a0 <\/em>in length have been used. The filter\u00a0 had untuned insertion loss IL=34.4 dB and the shape-factor SH(30\/3)=1.08; passband amplitude ripples were less than 1.0 dB. The YZ-cut LiNbO3<\/sub> substrate has been mounted in the SIP-4M package.<\/p>\n![\"Fig.1.](\"https:\/\/butis-m.ru\/wp-content\/uploads\/2014\/07\/Pic261.jpg\")
<\/a><\/a><\/a><\/a><\/a>PHOTOMASK DESIGN<\/h2>\n
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(in passband - 0.5 dB\/Div and 0.6 MHz\/Div).<\/p><\/div>\n<\/a><\/a>