Surface acoustic wave filter

Abstract

A SAW filter includes a first SAW resonator having a pair of terminals and a predetermined resonance frequency (f_rp), the first SAW resonator being provided in a parallel arm of the SAW filter. A second SAW resonator has a pair of terminals and a predetermined resonance frequency (f_rs) approximately equal to a predetermined antiresonance frequency of the first SAW resonator (f_ap). The second SAW resonator is provided in a series arm of the SAW filter. An inductance element is connected in series to the first SAW resonator.

Description

conventional
B=jx
C=jb
D=1−bx   (3).
Hence, the following equation (4) can be obtained from the equation (2) using the above ABCD parameters: $\begin{array}{cc}\tan h\left(\gamma \right)=\sqrt{\mathrm{bx}/\left(\mathrm{bx}-1\right)}.& \left(4\right)\end{array}$
When 0<bx<1, that is, when b and x have the same sign and are small values, the entire circuit shown in FIG. 4 has a pass band characteristic. When bx<0 or bx>1, that is, when the b and x have different signs or the product of bx is a large value, the circuit shown in FIG. 4 has an attenuation characteristic.

In order to qualitatively understand the frequency characteristics of b and x, the impedance and admittance of the SAW resonators will not be considered.

As shown in FIG. 5A, a SAW resonator having pair of terminals comprises an interdigital electrode 40 (see “Nikkel Electronics”, November 29, pp.76-pp.98, 1976). A reference number 41 indicates a pair of electrodes, 42 indicates an aperture length (crossing width), and 43 indicates an interdigital electrode period. When the resistance of the interdigital electrode 40 is neglected, the SAW resonator shown in FIG. 5A has an equivalent circuit 45 shown in FIG. 8B, in which C₀ denotes the electrostatic capacitance of the interdigital electrode 40, C₁ and L₁ denote equivalent constants. Hereinafter, the equivalent circuit 45 is depicted by symbol 46 shown in FIG. 5C.

FIGS. 6A and 6B qualitatively show an impedance vs. frequency characteristic (A) of the equivalent circuit shown in FIG. 5B, and an admittance vs. frequency characteristic (B) thereof. The characteristics shown in FIGS. 6A and 6B are double resonance characteristics in which two resonance frequencies f_r and f_a exist. It will be noted that a resonator having a crystal has a double resonance characteristic. When the resonators respectively having a double resonance characteristic are arranged in the series and parallel arms, respectively, and an antiresonace frequency f_ap of the parallel arm is made approximately equal to a resonance frequency f_rs of the series arm, a circuit can be configured which has a band-pass-type filter characteristic having the center frequencies f_ap and f_rs. This is because, as shown in an immittance vs. frequency characteristic shown in FIG. 7A, the relation 0<bx<1 is satisfied in a frequency range around the center frequency f_ap≈f_rs and that frequency range is a pass band, while the relation bx>1 is satisifed in a frequency range slightly away from the center frequency and the relation bx<0 is satisfied in a frequency range far away from the center frequency, the latter two frequency ranges serving as attenuation bands. Hence, the SAW filter shown in FIG. 4 has a qualitative filter charateristic 47 shown in FIG. 7B.

A description will now be given of the factors that determine the band width in the resonator-type SAW filters. As is seen from FIGS. 7A and 7B, the band width is mainly dependent on the difference between the resonance frequency f_r and the antiresonance frequency f_a of each of the two resonators. The band width increases as the above difference increases, while the band width decreases as the difference decreases. The resonance frequency f_r and the antiresonance frequency f_a can be determined using the following equations, using the equivalent circuit constants shown in FIG. 5B: $\begin{array}{cc}{f}_r=1/\left[2·\pi \sqrt{\left(C_1\times L_1\right)}\right]& \left(5\right)\\ f_a=f_r·\sqrt{\left(1+1/\tau \right)}& \left(6\right)\\ \tau =C_0/C_1& \left(7\right)\end{array}$
where τ denotes the capacitance ratio. The ratio of the pass band to the center frequency (Δf/f_o) is mainly dependent on the difference between f_r and f_a, and is therefore expressed in the following expression, using the equations (6) and (7):
Δf/f_o=2(f_a−f_r)/(f_a+f_r)=2/(4τ+1)   (8).

It can be seen from the equation (8) that the capacitance ratio τ is the main factor which determines the ratio of the pass band to the center frequency. However, as set forth in Japanese Laid-Open Patent Publication No. 52-19044, the capacitance ratio is much dependent on the type of substrate material used for the interdigital electrode. For example, an ST-cut crystal having a small electromechanical coupling coefficient has a capacitance ratio τ equal to or greater than 1300, while a 36° Y-cut X-propagation LiTaO₃ substrate having a large electromechanical coupling coefficient has a capacitance ratio τ of approximately 15. The ratio of the pass band to the center frequency is 0.04% for ST-cut crystal, and 3.3% for the 36° Y-cut X-propagation LiTaO₃ substrate. Hence, the band width is much dependent on the substrate material.

The band width decreases as the equivalent parallel capacitance C_OB increases in order to improve the side lobe suppression factor according to Japanese Laid-Open Patent Publication No. 52-19044.

The above phenomenon will now be described with reference to FIGS. 8A, 8B and 8C. As is seen from the previous description of the principle of the present invention, as the admittance value increases while f_r and f_a of the parallel resonator (see, FIG. 8C) are kept constant, the product of bx has a negative sign and increases, as shown in FIG. 8A. However, the bx product increases around the center frequency, and hence the range of bx>1 increases. Hence, the pass band in which the relation 0<bx<1 stands is narrowed, and a sufficient pass band cannot be obtained. This phenomenon is indicated by arrows in FIG. 8B.

The following two conditions must be satisfied in order to eliminate the above disadvantages. The first condition is to increase the difference between the resonance frequency f_r and the antiresonance frequency f_a in at least one of the resonators provided in the series and parallel arms (see FIG. 8C). The second condition is to increase either the impedance or admittance of the above-mentioned one of the resonators. As the impedance or admittance increases, the side lobe attenuation quantity increases. When the above two conditions awe satisfied, the side lobe attenuation quantity can be improved while the pass band is improved or prevented from being narrowed.

Regarding the first condition, it is effective to provide an inductor L connected in series to a SAW resonator having a pair of terminals in order to increase the difference between f_r and f_a. FIGS. 9A and 9B respectively show an impedance vs. frequency characteristic of a SAW filter in which an inductor having an inductance of 8 nH is connected to a resonator, and an admittance vs. frequency characteristic thereof. The parameters of the equivalent circuits of the SAW resonators used for obtaining the characteristics are illustrated in FIGS. 9A and 9B.

FIG. 9A shows an impedance characteristic curve 50 obtained before the inductor L is connected to the resonator, and an impedance characteristic curve 51 obtained after the inductor is connected thereto. FIG. 9B shows an admittance characteristic curve 52 obtained before the inductor L is connected to the resonator, and an admittance characteristic curve 53 obtained after the inductor L is connected thereto.

It can be seen from FIG. 9A that the inductance L increases the distance between the resonance frequency f_r and the antiresonance frequency f_a. In the graph of FIG. 9A, the distance is increased by approximately 30 MHz. This is because, as shown in FIG. 9A, the inductance L functions to shift the impedance characteristic curve of the original resonator upwards to the plus side by ωL, and hence the resonance frequency f_r changes to f_r′. In this case, the antiresonance frequency f_a has little variation. The admittance, which is the reciprocal of the impedance, changes, as shown in FIG. 9B. In this case, the resonance frequency f_r changes to f_r′.

Regarding the aforementioned second condition, the admittance value increases due to the inductance L, as shown in FIG. 9B. However, as shown in FIG. 9A, the impedance value decreases in frequencies outside of the pass band. Hence, if the inductance L is added to the resonator provided in the series arm, it is necessary to provide an additional means for increasing the impedance value. The above additional means is, for example, an arrangement in which a plurality of identical SAW resonators are connected in series to each other (cascaded).

FIGS. 10A and 10B show an impedance characteristic curve 56 of a resonance arrangement in which n identical SAW resonators, each having a pair of terminals, are cascaded. As shown in FIGS. 10A and 10B, the impedance value of the resonance arrangement having the n cascaded resonators is n times that of the single resonator. The resonance frequency of the resonator with the inductor L connected thereto is f_r″. That is, the difference between f_r″ and f_a of the resonance arrangement with the inductor L connected thereto is slightly smaller than the difference between f_r′ and f_a of a single resonator with the inductor L connected thereto. However, the difference between f_r″ and f_a of the resonance arrangement with the inductor L connected thereto is larger than that without the inductor L. It is possible to further increase the difference between the resonance frequency and the antiresonance frequency by using a larger inductance L.

In order to increase the band width, it is also possible to select the antiresonance frequency f_ap of the parallel arm resonator and the resonance frequency f_rs of the series arm resonator so that f_rs>f_ap. In this case, the condition bx<0 occurs around the center frequency, and hence the aforementioned pass band condition is not satisfied. Hence, there is a possibility that an insertion loss and a ripple may increase. However, by controlling Δf=f_vs−f_ap, it is possible to substantially suppress the increase in the insertion loss and the ripple and to expand the increase in the pass band.

A description will now be given of embodiments of the present invention. The embodiments which will be described are based on a simulation. Hence, this simulation will be described first, as well as the results of comparisons between the experimental results and the simulation in order to show the validity of the simulation.

The equivalent circuit shown in FIG. 5B easily simulates the characteristic of the SAW resonator having a pair of terminals, while that equivalent circuit is not suitable for simulating, with high accuracy, variations in the number of figure pairs, the aperture length and the electrode thickness, and the effects of a reflector. With the above in mind, the inventors have proposed an improved simulation which uses a Smith's equivalent circuit model and expands a transfer matrix to analyze the SAW resonators (see O. Ikata et al., “1990 ULTRASONIC SYMPOSIUM Proceedings, vol. 1, pp.83-pp.86, 1990; the disclosure of which is hereby incorporated by reference).

FIG. 11A is a graph showing the results of the simulation (calculation) for an arrangement in which a SAW resonator having a pair of terminals is disposed in the parallel arm. FIG. 11B is a graph showing the results of the experiment on an arrangement in which a one-terminal-pair SAW resonator including an interdigital electrode made of Al-2% Cu and having a film thickness of 1600 Å is disposed in a parallel arm, and bonding wires (L=1.5 nH) having a length of 3 mm are connected to the interdigital electrode. It can be seen from FIGS. 11A and 11B that the calculation values match the experiment values with respect to variations in the resonance points (f_r1, f_r2, f_r3) as well as the attenuation quantities observed around the resonance points for different aperture lengths (a=60, 150, 300 μm).

FIG. 12A is a graph showing the results of the simulation for an arrangement in which a SAW resonator having a pair of terminals is disposed in the series arm (see, FIG. 12C). The bonding pads used in the experiment which will be described later were slightly large, and the simulation was carried out taking into account a stray capacitance 0.5 pF of the bonding pads. FIG. 12B is a graph showing the results of the experiment on an arrangement in which a SAW resonator having a pair of terminals is disposed in the series arm. It can be seen from FIGS. 12A, 12B and 12C that the antiresonance frequencies f_a1, f_a2 and f_a3 do not depend on the aperture length and that the simulation results match the experimental results regarding variations in the attenuation quantity around the resonance frequencies.

Hence, it will be apparent from the above that the results of a simulation of the filter with the combination of the resonators disposed in the parallel and series arms match the results of the experiment. The embodiments described below are based on the result of simulations.

FIG. 13 shows a SAW filter 60 according to a first embodiment of the present invention. In Japan, an automobile and portable telephone system has a specification in which the ±8.5 MHz range about a center frequency of 933.5 MHz is a transmission band for mobile telephones and the ±8.5 MHz range about a center frequency of 878.5 MHz separated from 933.5 MHz by −55 MHz is a
where d is the distance between the center of the electrode 131 and each of the reflectors 132 and 133, n is an arbitrary integer, β is a real number equal to or less than 1, and λ is the period of the interdigital electrode 131 corresponding to its resonance frequency.

The number of finger pairs of each of the reflectors 132 and 133 is 50. The resonators respectively equipped with the reflectors are indicated by the symbol “*” shown in FIG. 27. The resonators R3B and R5B respectively provided in the parallel arms 63 and 64 respectively have two reflectors in the same manner as the resonator R1B.

The filter 130 shown in FIG. 27 has a band characteristic indicated by a curve 134 shown in FIG. 29. As compared to the characteristic curve 85 of the filter 80 (FIG. 13), the insertion loss in the filter 130 is improved, as indicated by an arrow 135. A ripple r_p arises from the arrangement of the reflectors 132 and 133.

A description will now be given of the reason why the reflectors 132 and 133 are arranged in the above-mentioned manner. The influence of the ripple r_p observed when β is changed from 0 to 0.5 is illustrated by a curve 140 shown in FIG. 30. The smallest ripple width can be obtained at a point 141 at which β is 0.4.

FIG. 31 shows a SAW filter device 150 functioning as the filter 130 shown in FIG. 27. In FIG. 31, parts that are the same as parts shown in the previously described figures are given the same reference numbers as previously. The filter device 150 comprises reflectors 132, 133, 151, 152, 153 and 154.

Variations of the one-terminal-pair SAW resonators R1B, R3B and R5B will now be described.

FIG. 32 shows a first variation R1Ba, which comprises interdigital electrodes 180 and respectively arranged on both sides of the exciting interdigital electrode 131. Each of the interdigital electrodes 180 and 181, which functions as a reflector, is an electrode in which the electric load thereof is of a short-circuit type.

FIG. 33 shows a second variation R1Bb, which comprises strip array type electrodes 167 and 166 respectively arranged on both sides of the electrode 131.

A description will now be given of a seventh embodiment of the present invention with reference to FIG. 34, in which parts that are the same as parts shown in the previously described figures are given the same reference numbers. A SAW filter 170 shown in FIG. 34 comprises two SAW resonators R2 and two resonators R4 respectively provided in the series arm 61, and three SAW resonators R1B, R3B and R5B respectively provided in the parallel arms 62, 63 and 64. Two inductors Ls are provided in the series arm 61, as shown in FIG. 34.

The filter 170 is obtained by replacing the resonators R1, R3 and R5 shown in FIG. 23 with the resonators R1B, R3B and R5B shown in FIG. 28. As has been described previously, the reflectors 132 and 133 shown in FIG. 28 are positioned so that the condition β=0.4 is satisfied. The filter 170 has a loss of the pass band smaller than that of the filter 110 shown in FIG. 23, and a suppressed ripple.

A description will now be given of an eighth embodiment of the present invention, which is intended to eliminate the ripple r_p shown in FIG. 29. First of all, a means for effectively eliminating the ripple r_p arising from the reflectors will be described.

The inventors simulated the relationship between the frequencies at which the ripple r_p is observed and the electrode thickness. In the simulation, the effects resulting from increasing the film thickness of the electrode are replaced by increasing the ratio between the acoustic impedance (Z_m) obtained under the electrode and the acoustic impedance (Z_o) of the free surface. As described in the aforementioned Ikata document, an increase in the electrode thickness increases the weight thereof. Hence, it is possible to consider that an increase in the electrode thickness is proportional to an increase in a discontinuous quantity of the acoustic impedance. With the above in mind, the following equation was prepared:
Q=Z_o/Z_m=V_o/V_m=1+k²/2+α(t)   (9)
where V_o and V_m respectively denote sound velocities on the free surface and under the electrode, k² is the electromechanical coupling coefficient, and t is the film thickness of the electrode. Then α(t) was changed as a parameter proportional to the film thickness t.

From the equation (9), the center frequency f_o of the filter is written as follows:
f_o=2f_o′/(1+Q)   (10).
The equation (10) is consistent with the well-known experimental result in which, as the film thickness increases, the center frequency decreases from the center frequency f_o′ obtained when there is no discontinuity of the acoustic impedance. The results of the simulation show that, as α(t) increases, that is, the film thickness increases, the frequency position at which the ripple r_p appears shifts toward the high-frequency range of the pass band, as indicated by an arrow 180 shown in FIG. 35, and finally drops into the attenuation pole on the high-frequency side of the pass band. It will be noted that a ripple r_s shown in FIG. 35 is caused by the reflectors of the resonators provided in the series arm.

FIG. 36 shows an attenuation quantity vs. frequency characteristic obtained when α(t)=0.05. A ripple resulting from the reflectors of the resonators in the parallel arms is located in the attenuation pole on the high-frequency side of the pass band. That is, there is no ripple in the pass band. In addition, the graph of FIG. 36 shows that the insertion loss is very small. In FIG. 36, the resonance frequencies of the resonators in the parallel and series arms are calibrated so that they are located at the frequency position which is 15 MHz higher than the original frequency position in order to obtain a center frequency of 932 MHz, because the center frequency of the pass band decreases according to the equation (10).

The inventors fabricated chips and measured the band characteristic thereof in order to study the relation to the actual film thickness.

FIGS. 37A, 37B and 37C respectively show band characteristic curves 185, 186 and 187 for film thicknesses of 2000 Å, 3000 Å and 4000 Å. In practice, the center frequency is varied by changing the film thickness. The graphs of FIGS. 37A, 37B and 37C have been calibrated by changing the period of the interdigital electrode.

A ripple r_p resulting from the resonators in the parallel arms is superimposed on the characteristic curve 185 for a film thickness of 2000 Å. As the film thickness increases, the ripple r_p shifts to higher frequencies. The experimental results shown in FIGS. 37A, 37B and 37C are consistent with the aforementioned results of the simulation.

However, an insertion loss arising from a bulk wave, which cannot be calculated by simulation, and a resistance loss appear as the film thickness increases (see Ebata et al., “SURFACE ACOUSTIC WAVE RESONATOR ON LiTaO₃ SUBSTRATE AND ITS APPLICATION TO OSCILLATORS FOR USE IN VTR”, Journal of the Institute of Electronics and Communication Engineers of Japan, vol. J66-C, No.1, pp.23-pp.30, 1988). Further, the correlation between the above insertion loss and the resistance loss is also a very important factor.

FIG. 38A shows a curve 190 of the insertion loss resulting from the bulk wave, and a resistance loss curve 191. A curve 192 shows an experimental characteristic curve. The insertion loss is approximately equal to the resistance loss when the film thickness is 2500 Å. Then, the total loss mainly resulting from the insertion loss starts to increase when the film thickness is approximately 3500 Å.

A curve 193 shown in FIG. 38B indicates the frequency position f_rp of the ripple r_p as a function of the identical film thickness of the exciting electrode 131 and the reflectors 132 and 133 shown in FIG. 28. It is concluded, based on the graphs in FIGS. 38A and 38B of FIG. 38, that the optimum film thickness that results in no ripple and little insertion loss is between 2600 Å and 4000 Å. The above optimum film thickness can be normalized by the period λ_p (4.4 μm at 932 MHz see FIG. 28) of the resonators in the parallel arm substantially determined by the center frequency of the filter. The normalized optimum film thickness is between 0.06 and 0.09.

The eighth embodiment of the present invention is based on the results of the above consideration by the inventors.

FIG. 39 shows a first one-terminal-pair SAW resonator 200 used in the SAW filter according to the eighth embodiment. The resonator 200 comprises an exciting electrode 201, and two reflectors 202 and 203 respectively located on both sides of the electrode 201. The electrode 201 and the reflectors 202 and 203 are made of aluminum (Al) or a mixture or alloy of Al and a few percentage of other metal by weight. The film thickness t₁ of each of the electrodes and the reflectors 202 and 203 is equal to 0.06-0.09 times the electrode period λ_p. A SAW filter, in which the resonator 200 is applied to each of the resonators R1B, R3B and R5B shown in FIGS. 27 and FIG. 34, has a band characteristic indicated by a curve 205 shown in FIG. 40. It can be seen from FIG. 40 that there is no ripple in the pass band. Use of an Al alloy improves the breakdown power performance, as compared to use of Al, Cu or Ti can be mixed with Al.

FIG. 41 shows a variation 210 of the SAW resonator 200. The resonator 210 shown in FIG. 41 comprises an exciting interdigital electrode 211, and two reflectors 212 and 213 respectively located on both sides of the electrode 211. The electrode 211 and the reflectors 212 and 213 are made of Au. The optimum film thickness of the electrode 211 and the reflectors 212 and 213 is determined, taking into account the above-mentioned phenomenon caused due to the influence of an increase in the weights of the electrode 211 and the reflectors 212 and 213. Since the ratio of the density of Al to that of Au is 2.7/18.9, equal to 0.143, the optimum film thickness t₂ is determined by multiplying the optimum film thickness t₁ by 0.143, and is equal to 0.0086-0.013 times the electrode period λ_p. A SAW filter obtained by applying the resonator 210 to each of the resonators R1B, R3B and R5B has a band characteristic similar to the characteristic shown in FIG. 40, and does not have any ripple in the pass band.

A description will now be given of the structure of the inductors L1, L2 and L3 shown in FIG. 13 according to a ninth embodiment of the present invention, with reference to FIG. 42, in which parts that are the same as parts shown in FIG. 16 are given the same reference numbers. As shown in FIG. 42, zigzag microstrip lines 220 and 221 are formed on the ceramic package 81 and are connected to the terminals 84₋₃ and 84₋₅. Ends of the microstrip lines 220 and 221 are connected to the ground. The pattern width of each of the microstrip lines 220 and 221 is 100 μm, and the distance between the microstrip lines 220 and 221 and the ground is 0.5 mm. When the dielectric constant of the ceramic package 81 is equal to 9, the inductance values of the microstrip lines 220 and 221 are equal to 2 nH.

A description will now be given, with reference to FIG. 43, of a tenth embodiment of the present invention which is another structure of the inductors L1, L2 and L3. In FIG. 43, parts that are the same as parts shown in FIG. 16 are given the same reference numbers as previously. Two zigzag microstrip lines 230 and 231 respectively connected to the resonators R1 and R2 are formed on the filter chip 82. Terminals 85₋₃ and 85₋₅ are connected to ends of the microstrip lines 230 and 231. Each of the microstrip lines 230 and 231 is 3000 Å thick, 60 μm wide and 2 mm in length. When the dielectric constant of the filter chip (LiTaO₃) 82 is equal to 44, the inductance of the microstrip lines 230 and 231 are equal to 2.2 nH.

It is possible to form inductors by suitably combining the bonding wire 86₋₃, the microstrip line 220 on the ceramic package 81 and the microstrip line 230 on the filter chip 82.

A description will now be given, with reference to FIG. 44, of a SAW filter 240 according to an eleventh embodiment of the present invention. The eleventh embodiment of the present invention is configured as follows. First, the resonance frequency f_rs of the resonators in the series arm is made higher than the antiresonance frequency f_ap of the resonators in the parallel arms in order to increase the pass band width. Second, Δf≡f_rs−f_ap is selected so that the pass band does not have an extremely large loss.

The previously described embodiments of the present invention require that f_ap=f_rs. However, as long as this condition is maintained, the pass band cannot be increased. In order to increase the pass band, the present inventors considered a condition f_ap<f_rs, as shown in FIGS. 46A and 46B. It is apparent from FIGS. 46A and 46B that bx<0 within a range f_ap<f<f_rs and hence this frequency range is changed to an attenuation band according to the aforementioned theory. However, in practice, the product bx can be maintained at a very small value by limiting Δf=(f_rs−f_ap), and the above frequency range can practically function as a pass band without any substantial attenuation.

FIGS. 47A, 47B and 47C show band characteristics of a ladder-type filter obtained when the Δf=(f_rs−f_ap) increases from zero. The filter used in the experiment has a piezo-electric substrate made of LiTaO₃ having an electromechanical coupling coefficient of 0.05, and an Al interdigital electrode having a film thickness of 3000 Å. The structure of the electrode is one of two basic units connected so as to form a ladder-type structure, as shown in FIG. 44. Each of the basic units comprises a first resonator in the parallel arm and a second resonator in the series arm. In order to form the input and output parts of the filter in symmetry to each other, a third resonator is provided in another parallel arm of the final stage. A plurality of basic units are cascaded so as to form a ladder-type structure in order to increase the side lobe suppression factor to a practical value.

However, the insertion loss increases as the number of basic units to be cascaded increases. Hence, it is preferable to determine the number of basic units to be cascaded, taking into account an actual filter specification. The filter being considered is intended to realize a loss equal to or less than 2 dB and a side lobe suppression factor equal to or higher than 20 dB. The interdigital electrode of each of the resonators in the parallel and series arms is designed to have an aperture length of 180 μm and 50 finger pairs. The ratio P=(Cop/Cos) obtained when Cop and Cos are electrostatic capacitances of parallel-arm and series-arm, respectively, is 1 because the electrodes of all the resonators have identical specifications.

FIG. 47A shows a band characteristic when Δf=0. FIG. 47B shows a band characteristic when Δf=10 MHz. The band characteristic shown in FIG. 47B is improved so that the pass band width (in which a loss equal to or less than 2.5 dB is ensured) is increased to 40 MHz, while the band characteristic shown in FIG. 47A has a pass band width of 22 MHz. It can be seen from FIGS. 47A and 47B that the pass band width is improved particularly for low frequencies. Further, the band characteristic shown in FIG. 47B has an improved side lobe suppression factor. More particularly, the side lobe suppression factor is improved to 20 dB from 19 dB.

There is a limit regarding improvement due to increase in Δf. FIG. 47C shows a band characteristic when Δf=19 MHz. The pass band width slightly deteriorates at high frequencies, and this deterioration is approximately equal to 2.5 dB, which will increase the ripple in the pass band. In FIG. 47C, a ripple amounting to approximately 1.0 dB, which is the allowable ripple limit, is observed. When Δf is further increased, the insertion loss and the in-band ripple increase. Hence, an increase of Δf=19 MHz is the limit.

The product bx obtained when Δf=19 MHz was examined. In the experiment, a SAW resonator provided in a parallel arm shown in FIG. 44 and a SAW resonator provided in a series arm shown therein were separately fabricated. The admittance of the resonator in the parallel arm was measured by means of a circuit configuration shown in FIG. 48A, and the impedance of the resonator in the series arm was measured by means of a circuit configuration shown in FIG. 48B. The measurement of admittance and impedance was carried out by measuring S21 by means of a network analyzer. The measured values of S21 were inserted into equations shown in FIGS. 48A and 48B, and the impedance Z_p and the admittance Y_p were calculated.

A frequency characteristic shown in FIG. 49 was obtained, which shows the imaginary part of the admittance or impedance, that is, the value of b or x. The frequency dependence of the product bx is as shown in FIG. 50. It can be seen from FIG. 50 that the product bx is negative and is a small value within f_ap<f<f_rs. The maximum absolute value |bx_max| of the product bx is given when: $f=\sqrt{f_{\mathrm{ap}}·f_{\mathrm{rs}}}$
and was equal to 0.06 for the embodiment being considered. That is, when value |bx_max| is equal to or smaller than 0.06, and deterioration of the insertion loss can be reduced and the in-band ripple can be suppressed to 1 dB or less. If Δf>19 MHz, the value of |bx_max| increases, and both the insertion loss and the in-band ripple will increase to 1 dB or greater. This value is not practical. As a result, the value of |bx_max| is a an upper-limit indicator of characteristic deterioration, and determines the allowable value of Δf.

The above consideration will be generalized. FIG. 51 is an equivalent circuit diagram of a ladder-type filter obtained by approximating the SAW resonators by the double resonance circuits of LC. The impedance Z_s of the SAW resonator in the series arm and the admittance Y_p of the SAW resonator in the parallel arm are expressed as follows: $\begin{array}{cc}\begin{array}{c}{Z}_s=\mathrm{jx}\\ =\left[-j\left({\omega }_{\mathrm{rs}}^2-{\omega }^2\right)\right]/\left[C_{\mathrm{os}}\left({\omega }_{\mathrm{as}}^2-{\omega }^2\right)\right]\end{array}& \left(11\right)\\ {{\rm Y}}_p=\mathrm{jb}& \left(12\right)\\ \text{[}=\left[{jC}_{\mathrm{op}}\left({\omega }_{\mathrm{ap}}^2-{\omega }^2\right)\right]/\left({\omega }_{\mathrm{rp}}^2-{\omega }^2\right)\text{]}& \\ =\left[-j{C}_{\mathrm{op}}\left({\omega }_{\mathrm{ap}}^2-{\omega }^2\right)\right]/\left({\omega }_{\mathrm{as}}^2-{\omega }^2\right)& \end{array}$
where ω_rs, ω_as, ω_rp, ω_ap are respectively the resonance and antiresonance frequencies of the series-arm resonator and the resonance and antiresonance frequencies of the parallel-arm resonator, and τ is the capacitance ratio (inherent in the substrate). The above resonance and antiresonance frequencies as well as the capacitance ratio are written as follows: ${\omega }_{\mathrm{rs}}=2{\mathrm{\pi f}}_{\mathrm{rs}}=1/\sqrt{C_{1s}{L}_{1s}\lambda }$ ${\omega }_{\mathrm{as}}=2{\mathrm{\pi f}}_{\mathrm{as}}={\omega }_{\mathrm{\tau s}}\sqrt{1+1/\tau }$ ${\omega }_{\mathrm{rp}}=2{\mathrm{\pi f}}_{\mathrm{rp}}=1/\sqrt{C_{1p}{L}_{1p}}$ ${\omega }_{\mathrm{ap}}=2{\mathrm{\pi f}}_{\mathrm{ap}}={\omega }_{\mathrm{rp}}\sqrt{1+1/\tau }$ $\tau =C_{0s}/C_{1s}=C_{0p}/C_{1p}.$

The product bx is calculated from the equations (11) and (12) as follows:
bx=−[C_0p·(ω_ap²−ω²)·(ω_rs−ω²)]/[C_0s·(ω_rp²−ω²)·(ω_as²−ω²)]  (13)
The angular frequency ω which makes the product bx have a pole is obtained from δ(bx)/δω=0, and is expressed as follows: $\begin{array}{cc}=\sqrt{{\omega }_{\mathrm{ap}}·{\omega }_{\mathrm{rs}}}.& \left(14\right)\end{array}$
The value obtained by inserting the above into the equation (13) is the maximum value of the product bx in the pass band. That is,
bx_max=−[C_0p·(1+1/τ)]/[C_0s·{1+1/(τ·Δω/ω_rs}⁻²]  (15)
where
Δω=ω_rs−ω_ap=2π·Δf   (16)

FIG. 52 shows a relation between bx_max and Δf/f_rs obtained by plotting the equation (15) as a parameter P=C_0p/C_0s. The hatched area shown in FIG. 52 corresponds to the condition such that the allowable value of the product bx is equal to or smaller than 0.06 obtained by the experiment. Hence, the allowable value α of Δf/f_rs dependent on P=C_0p/C_0s can be determined, and is written as follows, by inserting |bx_max|=0.06 into the equation (15): $\begin{array}{cc}\alpha =1/\left[\sqrt{P\left({\tau }^2+\tau \right)/0.06}-\tau \right].& \left(17\right)\end{array}$

The capacitance ratio τ depends on the substrate material, and is approximately 15 for 36° Y-cut X-propagation LiTaO₃ according to the experiment. Hence, the equation (17) can be rewritten as follows:
α=6.67×10⁻²/(4.22√{square root over (P)}−1)   (18).
When P=1, then α=0.02, and Δf=19 MHz for the embodiment shown in FIG. 47 having f_rs of 948 MHz. That is, the equation (18) stands.

An increase in Δf is effective for a piezoelectric substrate material having a small capacitance ratio τ, that is a substrate material having a large electromechanical coupling coefficient. The equation (17) is obtained for such a substrate material.

The capacitance ratio τ is proportional to the reciprocal of the electromechanical coupling coefficient k². The value of the ratio τ for 64° Y-cut X-propagation LiNbO₃ (k²=0.11) and the value of the ratio τ for 41° Y-cut X-propagation LiNbO₃ are respectively 6.8 and 4.4. The above values are obtained using the τ value of 36° Y-cut X-propagation LiTaO₃ and k²=0.05 (see K. Yamanouchi et al., “Applications for Piezoelectric Leaky Surface Wave”, 1990 ULTRASONIC SYMPOSIUM Proceedings, pp.11-pp.18, 1990).

FIG. 53 shows the relation between the capacitance ratio τ and the electromechanical coupling coefficient k², which is obtained using the values of k² and τ of 36° Y-cut X-propagation LiTaO₃ and using such a relation that k² is proportional to the reciprocal of τ.

From the relation shown in FIG. 53, the values of the capacitance ratios τ of 64° and 41° Y-cut X-propagation LiNbO₃ substrates can be obtained and are equal to 6.8 and 4.4, respectively.

The structure of the embodiment shown in FIGS. 44 and 45 will now be described. The SAW filter 240 comprises a 36° Y-cut X-propagation LiTaO₃ substrate 241, and has dimensions of 1.5 mm×2 mm×0.5 mm. From the input side of the filter 240, a parallel-arm resonator Rp1, a series-arm resonator Rs1, a parallel-arm resonator Rp2, a series-arm resonator Rs2, and a parallel-arm resonator Rp3 are arranged in that order. Each of the resonators has reflectors (short-circuit type) 242 respectively provided on both sides of the electrode having an aperture length of 180 μm and 50 finger pairs. Each of the reflectors 242 has 50 finger pairs.

The parallel-arm resonators are the same as the series-arm resonators except for the periods of the interdigital electrodes. The period λ_p of the electrode of each parallel-arm resonator is 4.39 μm (the ratio between the pattern width and the gap is 1:1 and hence the pattern width is approximately 1.1 μm (=λ_p/4), and the period of the electrode of each series-arm resonator is 4.16 μm (the pattern width is 1.04 μm (=λ_s/4)).

The respective periods are selected using the following equations so that the resonance frequencies (f_rp, f_rs) of the respective resonators are equal to the respective predetermined values (f_rp=893 MHz, f_rs=942 MHz):
λ_s=V_m/f_rs
λ_p=V_m/f_rp
where V_m is the sound velocity of the surface wave propagating in the 36° Y-cut X-propagation LiTaO₃ crystal for an electrode thickness of 3000 Å, and is experimentally 3920 m/s.

The SAW filter 240 having the above structure has a band-pass characteristic having a broad pass band and a low loss, as shown in FIG. 47C, in which Δf=19 MHz. When only the pattern width λ_p in FIG. 45 is changed to 4.35 μm, then Δf becomes 10 MHz, and the characteristic shown in FIG. 47B is obtained. The electrode is made of an Al-Cu alloy and is 3000 Å thick, and is arranged so that the surface wave is propagated in the X direction of the piezoelectric substrate 241.

A description will now be given of piezoelectric substrates other than 36° Y-cut X-propagation TiTaO₃. The capacitance ratio τ of 64° Y-cut X-propagation LiNbO₃ is 6.8, and an equation corresponding to the equation (17) is written as follows:
α=1.47×10⁻¹/(4.37√{square root over (P)}−1)   (19)

The capacitance ratio τ of 41° Y-cut X-propagation LiNbO₃ is 4.4, and an equation corresponding to the equation (17) is written as follows:
α=2.273×10⁻¹/(4.52√{square root over (P)}−1)   (20)
As the τ value decreases, that is, the electromechanical coupling coefficient increases, α increases, and the characteristic deteriorates little even if Δf increases.

A description will now be given of a twelfth embodiment of the present invention with reference to FIGS. 54 through 57. A SAW filter 250 according to the twelfth embodiment of the present invention is a ladder-type SAW filter having a plurality of basic units (unit sections), each having a SAW resonator in the parallel arm and a SAW resonator in the series arm, and establishes image impedance matching between adjacent unit sections in order to reduce a loss at each connection node. With the above arrangement, it becomes possible to reduce the insertion loss in the pass band.

The twelfth embodiment of the present invention was made with the following consideration. As shown in FIGS. 58A and 58B, a band-pass characteristic can be obtained by means of at least one parallel-arm resonator and at least one series-arm resonator. The ladder-type connection comprising one parallel-arm resonator and one series-arm resonator is the unit section of the filter.

It is desirable that the resonance frequency of the series-arm resonator be equal to or higher than the antiresonance frequency of the parallel-arm resonator. Two unit sections respectively shown in FIGS. 58A and 58B are available. The series arm of the unit section shown in FIG. 58A

FIG. 61A shows a connection having poor impedance matching, and the condition of the equation (23) is not satisfied. The reflection factor Γ obtained by viewing the right circuit from the interface b-b′ is expressed as follows:
Γ=(Z_sY_p)/(2+Z_sY_p)   (24).
The values of the Z_s and Y_p of a practical element are not equal to zero, and hence the reflection factor Γ thereof is not zero.

In a connection shown in FIG. 61B, an image impedance Z_i1 obtained by viewing the left circuit from the interface b-b′ is obtained as follows, using the equation (21): $\begin{array}{cc}{Z}_{\mathrm{i1}}=\sqrt{Z_s/Y_p\left(1+Z_s{Y}_p\right)}.& \left(25\right)\end{array}$
An image impedance Z_i2 obtained by viewing the right circuit from the interface b-b′ can be obtained using the equation (22). It will be noted that Z_i2=Z_i1. Hence, the impedance matching is established, and the reflection factor Γ at the interface b-b′ is zero. The above holds true for a connection shown in FIG. 61C.

A description will now be given of a method for cascading a plurality of unit sections in the manner shown in FIG. 61B or 61C. FIG. 62-(A) shows a circuit comprising n unit sections (n>2), in which the connection method shown in FIG. 61B and the connection method shown in FIG. 61C are alternatively employed. It will be seen from the above description that there is no reflection at each interface.

The circuit shown in (A) of FIG. 62 can be modified, as shown in (B) of FIG. 62, in which two resonators respectively in adjacent parallel nodes are integrated and two adjacent resonators in the series arm are also integrated. The series-arm resonator closest to the input of the filter has an impedance value half that of the resonators located inside the above series-arm resonator. Similarly, the parallel-arm resonator closest to the output of the filter has an admittance value half that of the resonators located inside the above parallel-arm resonator.

FIGS. 63A, 63B and 63C show configurations obtained by applying the above modifying method shown in FIG. 62 to the configurations shown in FIGS. 59A, 59B and 59C, respectively. More particularly, FIG. 63A shows an impedance matching method corresponding to the matching method shown in FIG. 59A, in which either the input or output of the filter is the series arm and the other is the parallel arm. In the configuration shown in FIG. 63A, the impedance of the series-arm resonator located at one end of the filter is half that of each inner series-arm resonator, and the admittance of the parallel-arm resonator located at the other end of the filter is half that of each inner parallel-arm resonator.

FIG. 63B shows an impedance matching method corresponding to the matching method shown in FIG. 59B. In the configuration shown in FIG. 63B, each of two parallel-arm resonators located at respective ends thereof has an admittance value half that of the inner parallel-arm resonator.

FIG. 63C shows an impedance matching method corresponding to the matching method shown in FIG. 59C. In the configuration shown in FIG. 63C, each of the two series-arm resonators located at respective ends thereof has an impedance value half that of the inner series-arm resonators.

A further description will now be given of the twelfth embodiment of the present invention based on the above-mentioned concept. The SAW filter 250 according to the twelfth embodiment has the equivalent circuit shown in FIG. 54, and the practical structure shown in FIG. 55. As shown in FIG. 54, it has three series-arm resonators Rs1, Rs2 and Rs3, and three parallel-arm resonators Rp1, Rp2 and Rp3. Each of the six resonators has an identical aperture length (90 μm), and an identical number of finger pairs (100). Each of the resonators has two short-circuit-type reflectors respectively located on two opposite sides of the interdigital electrode in order to increase Q. Each of the reflectors has approximately 100 finger pairs. The series-arm resonators Rs1, Rs2 and Rs3 have an identical finger period (λ_s) of 4.191 μm. The parallel-arm resonators Rp1, Rp2 and Rp3 have an identical finger period λ_p of 4.38 μm, which is different from the value of λ_s.

FIG. 64 shows a
where g denotes a conductance component, and b denotes a susceptance. Further, it will be assumed that the impedance of each series-arm resonator is expressed as follows:
Z_s=r+j·x   (27)
where r denotes a resistance component, and x denotes a reactance component.

Under the above assumptions, the frequency characteristics of g, b, r and x are as shown in FIG. 71. The susceptance component b (indicated by the dot chained line) of the admittance Y_p of the parallel-arm resonator has the largest value at the resonance frequency f_rp, at which the sign thereof changes from + to −. Further, the susceptance component b becomes zero at the antiresonance frequency f_ap, at which the sign thereof changes from − to +. The conductance component g (one-dot chain line) has the largest value is at the resonance frequency f_rp, and rapidly decreases and approaches zero. The value of the conductance component g assumes only the plus sign.

The reactance component x (indicated by the solid line in FIG. 71) of the impedance Z_s of the series-arm resonator becomes zero at the resonance frequency f_rs, and the largest value at the antiresonance frequency f_as. Further, the sign of the reactance component x changes from + to −, and approaches zero from the minus side in a range higher than f_as. The resistance component r gradually increases from zero to the largest value at the antiresonance frequency f_as, and then gradually decreases. The resistance component r assumes only the plus sign.

In order to obtain a filter characteristic, the antiresonance frequency f_ap of the parallel-arm resonator is equal to or slightly smaller than the resonance frequency f_rs of the series-arm resonator.

A graph depicted in the lower portion of FIG. 71 shows the band characteristic of the filter circuit. The pass band is formed around f_ap≈f_rs, and the other frequency range serves as an attenuation range. It can also be seen from FIG. 71 that b and x are respectively zero around the center frequency of the pass band. Hence, the pass band characteristic of the filter is determined by only r and g, and the following is obtained:
S21=100/(100+r+50r·g+2500 g)   (28).
Since r>0 and g>0, S21 becomes smaller than 1 as both r and g increase, and the insertion loss written as 20log, ¦S21¦ also increases. Hence, the insertion loss decreases as both r and g are closer to zero.

A description will now be given of a consideration concerning which part of the interdigital electrode is related to the resistance component r and the conductance component g. The above consideration takes into account a resistance r₁ inserted in the equivalent circuit shown in FIG. 5B. The resistance r₁ is the sum of the electric resistance component of the interdigital electrode and an acoustic resistance component corresponding to an energy loss encountered while bulk waves generated from ends of the fingers are propagated inside the substrate. The resistance component resulting from emission of bulk waves is little dependent on the shape of the interdigital electrodes, and is hence proportional to the electric resistance r₁ of the interdigital electrode. Particularly, r=r₁ around the center frequency of x=0.

The conductance component g of the admittance of the parallel-arm resonator is proportional to the conductance 1/r₁ of the electric resistance of the interdigital electrode.

The following equation is known:
r=l_s·ρ_O/(N_s·W·t)   (29)
where ρ_O denotes the resistivity of the fingers of the interdigital electrodes, W denotes the width of each finger, t denotes the film thickness of each finger, l_s denotes the aperture length of the series-arm resonator, and N_s denotes the number of finger pairs.

The conductance component g is obtained as follows if the same substrate and the same metallic film as those used in the series-arm resonator are employed:
g=N_p·W·t/(l_p·ρ_O)   (30)
where l_p denotes the aperture length of the parallel-arm resonator, and the N_p denotes the number of finger pairs. It will be noted that ρ_O, W and t in the parallel-arm resonator are almost the same as those in the series-arm resonator.

Hence, an increase in the insertion loss in the equation (28) is expressed as follows:
r+50r·g+2500g=l_s·ρ_O/(N_s·W·t)+50·(l_s/l_p)·(N_p/N_s)+2500·N_p·W·t/(l_p·ρ_O).   (31)

It can be seen from equation (31) that the insertion loss of the series-arm resonator becomes smaller as the aperture length l_s decreases and the number N_s of finger pairs increases, and that the insertion loss of the parallel-arm resonator becomes smaller as the aperture length l_p increase and the number N_p of finger pairs decreases. Particularly, the insertion loss can be effectively reduced when l_s/l_p<1 and N_p/N_s<1, that is, when the aperture length of the series-arm resonator is smaller than that of the parallel-arm resonator, and the number of finger pairs of the series-arm resonator is larger than the number of finger pairs of the parallel-arm resonator.

The reason for the above will now be described. In equation (31), r=r_s (r_s: electric resistance of the series-arm resonator), and g=1/r_p (r_p: electric resistance of the parallel-arm resonator), and therefore the following expression can be obtained:
r+50r·g+2500 g=r_s+50(r_s/r_p)+2500(1/r_p).
Hence, an increase in the insertion loss can be suppressed when (r_s/r_p)<1, that is, r_s<r_p.

If l_s is too short, a loss resulting from diffraction of the surface wave takes place. If l_p is too long, a decrease in Q of the parallel-arm resonator due to resistance increase appears, and the side lobe suppression factor is deteriorated. Hence, there is a limit on l_s and l_p.

The equation (31) can be modified as follows:
r+50r·g+2500g=l_s·ρ₀/(N_s·W·t_s)+50·(l_s/l_p)·(N_p/N_s)+(t_p·t_s)+2500·N_p·W·t_p/(l_p·ρ_O)   (32)
where t_s denotes the film thickness of the metallic film forming the interdigital electrode of the series-arm resonator, and t_p denotes the film thickness of the metallic film forming the interdigital electrode of the parallel-arm resonator. Hence, the insertion loss can be reduced when t_p/t_s.

It is possible to use resonators, each having two different metallic films having different resistivity values (ρ_os, ρ_op) and to arrange these resonators in the parallel and series arms, so that ρ_op/ρ_op<1 can be satisfied. However, this is not practical in terms of mass productivity.

A further description will be given, with reference to FIGS. 67 and 68, of the fifteenth embodiment based on the above concept. A piezoelectric substrate 241 is formed of 36° Y-cut X-propagation LiTaO₃, and an electrode is made of Al and 3000 Å thick.

Conventionally, in each of the parallel and series arms, l_s=l_p=90 μm, and N_p=N_s=100. In the present embodiment, l_s=45 μm and N_s=200 in the series arm, while l_p=180 μm and N_p=50 in the parallel arm. That is, l_p>l_s, and N_s>N_p. Further, l_s/l_p=0.25, and N_p/N_s=0.25. The electrostatic C_O of the interdigital electrode based on the product of the number of finger pairs and the aperture length is kept constant.

In FIG. 69, solid line 281 indicates the characteristic of the present embodiment, and broken line 282 indicates the characteristic of the conventional filter. The conventional filter has an insertion loss of 2.5 dB, while the present embodiment has an insertion loss of 2.0 dB. That is, the insertion loss is improved by 0.5 dB, in other words, 25%. Further, since an increased number of finger pairs of the series-arm resonator is used, the breakdown power performance is improved, and the applicable maximum power is improved by 20%.

In the present embodiment, a diffraction loss appears when l_s is equal to or less than 30 μm, and them side lobe starts to deteriorate when l_p is equal to or larger than 300 μm. Hence, the l_s and l_p are limited to the above values. It can be seen from the above that the insertion loss in the pass band is improved by decreasing the electric resistance of the series-arm and increasing the electric resistance of the parallel arm (decreasing the conductance). It is also possible to use a parallel-arm resonator having a film thickness larger than that of the series-arm resonator. Even with this structure, it is possible to reduce the insertion loss in the pass band.

A description will now be given, with reference to FIG. 72, of a wave filter according to a sixteenth embodiment of the present invention. The wave filter (branching filter) shown in FIG. 72 comprises two SAW filters F1 and F2 having input terminals connected to a pair of common signal terminals TO via common nodes a and b. The SAW filter F1 has a pair of signal terminals T1, and the SAW filter F2 has a pair of signal terminals T2. A pair of signal lines l_h and l_c connects the nodes a and b to the SAW filter F1, and another pair of signal lines l_h and l_c connects the nodes a and b to the SAW filter

The SAW filter F1 comprises a series-arm SAW resonator Rso, and a parallel-arm SAW resonator Rp, which resonators are configured as has been described previously. The resonator Rso is connected to the common node a, and hence serves as a resonator of the first stage of the SAW resonator F1. A plurality of pairs, each pair of series-arm resonator and parallel-arm resonator are cascaded in the SAW filter F1. The SAW filter F2 is configured in the same manner as the SAW filter F1.

The SAW filters F1 and F2 respectively have different band center frequencies. For example, the SAW filter F1 has a band center frequency f₁ of 887 MHz, and the SAW filter F2 has a band center frequency f₂ of 932 MHz. In this case, the frequency f₁ is lower than the frequency f₂.

FIG. 73 is a Smith's chart of the wave filter shown in FIG. 72. In FIG. 72, P indicates the pass band of the wave filter. A indicates a low-frequency-side attenuation band, and B indicates a high-frequency-side attenuation band. It can be seen from FIG. 73 that the characteristic impedance of the circuit shown in FIG. 72 is equal to 50 Ω, while the impedances of the attenuation bands A and B are greater than 50 Ω. This means that the wave filter shown in FIG. 72 has the impedance characteristics of the respective band-pass filters.

A description will now be given, with reference to FIGS. 74 and 75, of a wave filter according to a seventeenth embodiment of the present invention. In FIG. 74, parts that are the same as parts shown in the previously described figures are given the same reference symbols.

As has been described previously, the SAW filters F1 and F2 satisfy the condition f₁<f₂. If the SAW band-pass filters F1 and F2 have characteristics as shown in FIG. 75, the filter F1 is maintained in a high-impedance state within the pass band frequency band of the filter F2. In this case, there is no need to provide an impedance matching circuit M to the filter F1, and the same characteristic as the characteristic of the filter F2 alone can be obtained.

However, the filter F2 does not have a high impedance within the low-frequency attenuation band A thereof, and crosstalk may take place. Hence, it is necessary to increase the impedance within the low-frequency attenuation band A of the filter F2.

An impedance matching circuit M for increasing the impedance in the low-frequency attenuation band A thereof is connected between the nodes a and b and the filter F2. The impedance matching circuit M includes an inductor L, which is a high-impedance element for rotating the phase of signal. The inductor L has an inductance of, for example, 6 nH. The inductor L can be formed with, for example, a metallic strip line made of, for example, gold, tungsten, or copper, and formed on a glass-epoxy or ceramic substrate. The strip line formed on the glass-epoxy substrate has a width of 0.5 mm and a length of 11 mm, and the strip line formed on the ceramic substrate has a width of 0.2 mm and a length of 6 mm.

As shown in FIG. 75, the impedance matching circuit M provided for the filter F2 rotates the phase in the direction indicated by the arrow, and the impedance of the filter F2 in the low-frequency attenuation band A can be increased.

FIG. 76 shows a wave filter according to an eighteenth embodiment of the present invention. In FIG. 76, parts that are the same as parts shown in the previously described figures are given the same reference symbols. The wave filter shown in FIG. 76 can be obtained by connecting a capacitor C, which corrects the quantity of phase rotation of the inductor L, in series between the inductor L and the series-arm resonator Rso. There is a possibility that a suitable impedance matching may be not obtained by means of only inductor L. As shown in a Smith's chart shown in FIG. 77, the phase is rotated in the direction indicated by the arrow shown in FIG. 77 first, and is rotated by means of the inductor L second.

FIG. 78 shows a wave filter according to a nineteenth embodiment of the present invention. The filter F1 comprises the series-arm SAW resonator Rso and the parallel-arm SAW resonator Rp, which are connected so that the series-arm resonator is located at the first stage of the filter F1. The parallel-arm SAW resonator Rpo of the filter F is located at the first stage of the filter F. A line S for use in phase rotation is connected in series to the SAW filter F2. It is possible to increase the impedance of the filter F1 within the high-frequency attenuation band B thereof even by an arrangement such that only the filter F1 has the series-arm resonator of the first stage. In this case, the resonator of the first stage of the filter F2 is the parallel-arm resonator Rpo connected in parallel to the pair of common signal terminals T0, and the low-frequency attenuation band A of the filter F2 (corresponding to the pass band of the filter F1 does not have a high impedance. Hence, according to the present embodiment, the phase rotation line S is connected in series to the filter F2.

As shown in FIG. 79, the direction of phase rotation caused by the line S is opposite to the directions shown in FIGS. 75 and 77. However, as shown in FIG. 80, suitable matching of the filter F2 can be obtained. In this case, the length of the line S formed on the glass-epoxy substrate is approximately 25 mm, and the length of the line S formed on the ceramic substrate is approximately 26 mm.

A variation of the configuration shown in FIG. 78 can be made by providing the inductor L in the same manner as shown in FIG. 74. It is also possible to further provide the capacitor C in the same manner as shown in FIG. 76.

The band center frequencies f₁ and f₂ of the sixteenth through nineteenth embodiments of the present invention are not limited to 887 MHz and 932 MHz.

The present invention is not limited to the specifically disclosed embodiments, and variations and modifications may be made without departing from the scope of the present invention.

Claims

1. A band-pass filter having a pair of band-pass filter input common signal terminals and plural pairs of band-pass filter output signal terminals, comprising:

a pair of SAW band-pass filters having respective pass bands and comprising a plurality of one-port SAW acoustic wave resonators connected in a multiple ladder structure, each having at least a first stage located at a side of the pair of band-pass filter input common signal terminals and a series-arm resonator located at the first stage, a pair of input terminals and a pair of output terminals;

the pair of band-pass filter input common signal terminals being commonly connected to the respective pairs of input terminals of the pair pair of SAW band-pass filters;

the plurality of pairs of band-pass filter output signal terminals being respectively connected to the respective pairs of output terminals of the pair pair of SAW band-pass filters; and

an inductance element located between at least one side of only one of the SAW band-pass filters located at the first stage and the pair of band-pass filter input terminals and directly connected between the respective pair of input terminals of the at least one of the SAW filters and thereby in parallel to said at least one of the SAW filters one of the common signal terminals, and no inductance element being located between the other of the band-pass filters and one of the common signal terminals.

2. A SAW filter comprising:

a plurality of first SAW resonators, each having a pair of terminals and a predetermined resonance frequency (f_rp), said first SAW resonators being connected in respective, parallel arms of the SAW filter;

a plurality of second SAW resonators, each having a pair of terminals and a predetermined resonance frequency (f_rs) approximately equal to an antiresonance frequency (f_ap) of each of the first SAW resonators, said second SAW resonators being provided in series arms of the SAW filter; and

inductance elements respectively connected in series with the first SAW resonators in the parallel arms and formed of wires.

3. The SAW filter as claimed in claim 2, further comprising:

a package accommodating the first and second resonators and the inductance elements; and

lead terminals extending from interiorly of the package to exteriorly thereof, said wires of the inductance elements being bonded to said lead terminals.

4. A band-pass filter having a predetermined pass-band characteristic and comprising:

a plurality of SAW resonators connected in a ladder formation, said plurality of resonators being connected in respective serial arms and parallel arms; and

bonding inductance elements, said parallel arms of said ladder formation being connected to ground via respective said bonding inductance elements.

5. The band-pass filter as claimed in claim 4, wherein said bonding inductance elements comprise wires.

6. A band-pass filter having a pair of band-pass filter input terminals and plural pairs of band-pass filter output terminals, comprising:

a pair of SAW filters having respective, different pass bands and each SAW filter having a pair of SAW filter input terminals and a pair of SAW filter output terminals and comprising a plurality of one-port SAW resonators connected in a ladder structure between the input and output terminals and including at least a first stage having a series-arm SAW resonator connected to one of the pair of input terminals;

a pair of SAW filters having respective pass bands and comprising a plurality of one-port SAW resonators connected in a ladder structure, each having at least a first stage located at a side of the pair of band-pass filter input terminals and a series-arm resonator located at the first stage, a pair of input terminals and a pair of output terminals;

the pair of band-pass filter input terminals being commonly connected to the respective pairs of input terminals of the pair of SAW filters;

the plurality of pairs of band-pass filter output terminals being connected to the respective pairs of output terminals of the pair of SAW filters.

7. A band-pass filter having a predetermined pass-band characteristic and comprising:

a plurality of SAW resonators connected in a ladder configuration of respective serial arms and parallel arms, said plurality of SAW resonators being connected in respective said serial arms and parallel arms; and

bonding inductance elements respectively connecting said parallel arms of said ladder configuration to ground.

8. An acoustic wave filter comprising:

a first acoustic wave resonator having a pair of terminals and a predetermined resonance frequency (frp), said first acoustic wave resonator being provided in a parallel arm of the acoustic wave filter on a LiTaO₃ substrate; and

a second acoustic wave resonator having a pair of terminals and a predetermined resonance frequency (frs) approximately equal to a predetermined antiresonance frequency of the first acoustic wave resonator (fap), said second acoustic wave resonator being provided in a series arm of the acoustic wave filter on the LiTaO₃ substrate; and

an inductance element connected in series with the first acoustic wave resonator in the parallel arm, the inductance element functioning to increase the admittance of the parallel arm and decrease the resonance frequency, wherein

the first acoustic wave resonator comprises an exciting interdigital electrode and first and second reflectors, each of which comprises either aluminum or an aluminum alloy containing a few weight percentage of metal, other than aluminum; and

the respective film thicknesses of the exciting interdigital electrode and the first and second reflectors are in a range of from 0.06 to 0.09 times the period of the exciting interdigital electrode.

9. An acoustic wave filter comprising:

a first acoustic wave resonator having a pair of terminals and a predetermined resonance frequency (frp), said first acoustic wave resonator being provided in a parallel arm of the acoustic wave filter on a LiTaO₃ substrate; and

a second acoustic wave resonator having a pair of terminals and a predetermined resonance frequency (frs) approximately equal to a predetermined antiresonance frequency of the first acoustic wave resonator (fap), said second acoustic wave resonator being provided in a series arm of the acoustic wave filter on the LiTaO₃ substrate; and

an inductance element connected in series with the first acoustic wave resonator in the parallel arm, the inductance element functioning to increase the admittance of the parallel arm and decrease the resonance frequency, wherein

the first acoustic wave resonator comprises an exciting interdigital electrode and first and second reflectors, each of which comprises either gold or a gold alloy containing a few weight percentage of metal other than gold; and the respective film thicknesses of the exciting interdigital electrode and the first and second reflectors are in a range of from 0.0086 to 0.013 times the period of the exciting interdigital electrode.

10. An acoustic wave filter comprising:

a plurality of first acoustic wave resonators on a single piezoelectric substrate, each having a pair of terminals and a predetermined resonance frequency (frp), said first acoustic wave resonators being connected in respective, parallel arms of the acoustic wave filter;

a plurality of second acoustic wave resonators on the piezoelectric substrate, each having a pair of terminals and a predetermined resonance frequency (frs) approximately equal to the predetermined antiresonance frequency of the first acoustic wave resonator (fap), said second acoustic wave resonators being provided in a series arm of the acoustic wave filter; and

inductance elements respectively connected to ground in series with the first acoustic wave resonators in the parallel arms.

11. A band-pass filter having a pair of band-pass filter common signal terminals and plural pairs of band-pass filter signal terminals, comprising:

a first band-pass filter having a pass band, having a band center frequency and comprising a plurality of acoustic wave resonators connected in a multiple ladder structure, having at least a first stage located at a side of the pair of band-pass filter common signal terminals, a pair of input terminals and a pair of output terminals;

a second band-pass filter having a different pass band from the pass band of the first band-pass filter, having a band center frequency which is larger than the band center frequency of the first band-pass filter and comprising a plurality of acoustic wave resonators connected in a multiple ladder structure, having at least a first stage located at a side of the pair of band-pass filter common signal terminals, a pair of input terminals and a pair of output terminals;

the pair of band-pass filter common signal terminals being commonly connected to the first and second band-pass filters;

the plurality of pairs of band-pass filter signal terminals being respectively connected to the first and second band-pass filters; and

only one impedance matching circuit located only between the first stage of the second band-pass filter and the common signal terminals.

12. The band-pass filter as claimed in claim 11, wherein the impedance matching circuit includes an inductor.

13. The band-pass filter as claimed in claim 12, wherein the inductor is formed with a metallic strip line.

14. The band-pass filter as claimed in claim 13, wherein the metallic strip line is formed on a ceramic package.

15. The band-pass filter as claimed in claim 11, wherein said impedance matching circuit includes an inductor and a capacitor.

16. A band-pass filter comprising:

a first band-pass filter having a pass band, having a band center frequency and comprising a plurality of acoustic wave resonators connected in a multiple ladder structure, having at least a first stage and a series-arm resonator located at the first stage, a pair of input terminals and a pair of output terminals;

a second band-pass filter having a different pass band from the pass band of the first band-pass filter, having a band center frequency which is larger than the band center frequency of the first band-pass filter and comprising a plurality of acoustic wave resonators connected in a multiple ladder structure, having at least a first stage and a parallel-arm resonator located at the first stage, a pair of input terminals and a pair of output terminals;

a pair of band-pass filter common signal terminals commonly connected to the first and second band-pass filters;

a plurality of pairs of band-pass filter signal terminals respectively connected to the first and second band-pass filters;

a circuit element used for phase rotation and connected between at least one of the pair of common signal terminals and the second band-pass filter.

17. The band-pass filter as claimed in claim 16, wherein the circuit element comprises a line formed on a glass-epoxy substrate or a ceramic substrate.

18. The band-pass filter as claimed in claim 16, wherein the circuit element comprises an inductance element.

19. The band-pass filter as claimed in claim 18, wherein the circuit element further comprises a capacitance element coupled to the inductance element.

20. A band-pass filter having a predetermined pass-band characteristic and comprising:

a plurality of acoustic wave resonators connected in a ladder formation, said plurality of resonators being connected in respective serial arms and parallel arms; and

bonding inductance elements, said parallel arms of said ladder formation being connected to ground via respective said bonding inductance elements, wherein:

a package in which the band-pass filter is mounted, contains a piezoelectric substrate and the ground; and

the plurality of acoustic wave resonators are on the piezoelectric substrate.

21. A band-pass filter having a predetermined pass-band characteristic and comprising:

a plurality of acoustic wave resonators connected in a ladder formation, said plurality of resonators being connected in respective serial arms and parallel arms; and

bonding inductance elements, said parallel arms of said ladder formation being connected to ground via respective said bonding inductance elements, wherein:

a package in which the band-pass filter is mounted contains a piezoelectric substrate;

the plurality of acoustic wave resonators are on the piezoelectric substrate; and

a first electric resistance (Rs) of an interdigital electrode of a acoustic wave resonator provided in a series arm, is smaller than a second electric resistance (Rp) of an interdigital electrode of a acoustic wave resonator provided in a parallel arm which is next to the series arm.

22. A band-pass filter having a predetermined pass-band characteristic and comprising:

a plurality of acoustic wave resonators connected in a ladder formation, said plurality of resonators being connected in respective serial arms and parallel arms; and

bonding inductance elements, said parallel arms of said ladder formation being connected to ground via respective said bonding inductance elements, wherein:

the plurality of acoustic wave resonators are on a piezoelectric substrate; and

the bonding inductance elements are respectively connected to the ground outside the piezoelectric substrate.