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

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to surface acoustic wave (SAW) filters, and more particularly to a ladder-type SAW filter suitable for an RF (Radio Frequency) filter provided in pocket and mobile telephones, such as automobile phone set and portable phones.

2. Description of the Prior Art

In Japan, an automobile phone or portable phone system has a specification in which a transmission frequency band is ±8.5 MHz about a center frequency of 933.5 MHz. The ratio of the above transmission band to the center frequency is approximately 2%.

Recently, SAW filters have been employed in automobile phone or portable phone systems. It is required that the SAW filters have characteristics which satisfy the above specification. More specifically, it is required that the pass band width is so broad that 1) the ratio of the pass band to the center frequency is equal to or greater than 2%, 2) the insertion loss is small and equal to 5 dB-2 dB, and 3) the suppression factor is high and equal to 20 dB-30 dB.

In order to satisfy the above requirements, SAW filters are substituted for conventional transversal filters. Generally, SAW elements are so connected that a ladder-type filter serving as a resonator is formed.

FIG. 1 is an equivalent circuit of a SAW filter disclosed in Japanese Laid-Open Patent Publication No. 52-19044. A SAW filter 1 shown in FIG. 1 comprises a SAW resonator 3 in a series arm 2, and a SAW resonator 5 in a parallel arm 4. The equivalent parallel capacitance C_OB of the resonator 5 in the parallel arm 4 is larger than the equivalent parallel capacitance C_OA of the resonator 3 in the series arm 2.

The SAW filter 1 shown in FIG. 1 has a characteristic shown in FIG. 2. A curve 6 shows an attenuation quantity v. frequency characteristic of the SAW filter 1. As indicated by arrows 7 shown in FIG. 2, the suppression factor increases as the equivalent parallel capacitance C_OB increases. However, as the equivalent parallel capacitance C_OB increases, the band width decreases, as indicated by arrows 8, and the insertion loss increases, as indicated by an arrow 9. Hence, the characteristic deteriorates, as indicated by a broken line 10. When trying to obtain a suppression factor equal to or larger than 20 dB, the band width is decreased so that the ratio of the pass band to the center frequency is equal to or smaller than 1%, and does not satisfy the aforementioned specification of the 800 MHz-band radio systems.

SUMMARY OF THE INVENTION

It is a general object of the present invention to provide a SAW filter in which the above disadvantages are eliminated.

A more specific object of the present invention is to provide a SAW filter having a large band width, a large suppression factor, and a small insertion loss.

The above objects of the present invention are achieved by a SAW filter comprising: a first SAW resonator (21, R1A, R1B) having a pair of terminals and a predetermined resonance frequency (f_rp), the first SAW resonator being provided in a parallel arm (24) of the SAW filter; a second SAW resonator (23) having a pair of terminals and a predetermined resonance frequency (f_rs) approximately equal to the predetermined antiresonance frequency of the first SAW resonator (f_ap), the second SAW resonator being provided in a series arm (24) of the SAW filter; and an inductance element (25, L1) connected in series to the first SAW resonator.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings, in which:

FIG. 1 is an equivalent circuit diagram of a conventional SAW filter;

FIG. 2 is a graph of a characteristic of the conventional SAW filter shown in FIG. 1;

FIG. 3 is a circuit diagram of a SAW filter according to the present invention;

FIG. 4 is a block diagram of the basic structure of a filter circuit using a resonator;

FIGS. 5A, 5B and 5C are diagrams showing a one-terminal-pair SAW resonator;

FIGS. 6A and 6B are diagrams showing frequency characteristics of impedance and admittance of the one-terminal-pair SAW resonator;

FIGS. 7A to 7C are diagrams showing an immittance characteristic of a SAW resonator and a filter characteristic of the filter shown in FIG. 3 using that SAW resonator;

FIGS. 8A to 8C are diagrams showing the characteristics of the conventional SAW filter shown in FIG. 1;

FIGS. 9A and 9B are diagrams showing effects obtained when an inductance is connected in series to a resonator;

FIGS. 10A and 10B are diagrams showing effects obtained when n one-terminal-pair resonators are connected in series;

FIGS. 11A and 11B are diagrams showing an aperture length dependence on a parallel-arm resonator;

FIGS. 12A to 12C are diagrams showing an aperture length dependence on a series-arm resonator;

FIG. 13 is a circuit diagram of a SAW filter according to a first embodiment of the present invention;

FIG. 14 is a diagram showing a band characteristic of the filter shown in FIG. 13;

FIGS. 15A and 15B are diagrams showing effects obtained when an inductance is added to a parallel-arm resonator;

FIG. 16 is a plan view of the structure of the SAW filter shown in FIG. 13 with a lid removed therefrom;

FIG. 17 is a cross-sectional view taken along a line XVII--XVII shown in FIG. 16;

FIG. 18 is a diagram of a SAW filter according to a second embodiment of the present invention;

FIG. 19 is a diagram showing a band characteristic of the filter shown in FIG. 18;

FIGS. 20A and 20B are diagrams showing effects based on the ratio of the aperture length of the parallel-arm resonator to the aperture length of the series-arm resonator;

FIG. 21 is a diagram of a SAW filter according to a third embodiment of the present invention;

FIG. 22 is a diagram showing a band characteristic of the filter shown in FIG. 21;

FIG. 23 is a diagram of a SAW filter according to a fourth embodiment of the present invention;

FIG. 24 is a diagram showing a band characteristic of the filter shown in FIG. 23;

FIG. 25 is a circuit diagram of a SAW filter according to a fifth embodiment of the present invention;

FIG. 26 is a diagram showing a band characteristic of the filter shown in FIG. 25;

FIG. 27 is a circuit diagram of a SAW filter according to a sixth embodiment of the present invention;

FIG. 28 is a diagram showing a first one-terminal-pair SAW resonator shown in FIG. 27;

FIG. 29 is a diagram showing a band characteristic of the filter shown in FIG. 27;

FIG. 30 is a diagram showing the influence of the reflector setting position on the width of a ripple;

FIG. 31 is a plan view of the structure of the SAW filter shown in FIG. 27 with a lid removed therefrom;

FIG. 32 is a diagram showing a variation of the first one-terminal-pair SAW resonator shown in FIG. 27;

FIG. 33 is a diagram showing another variation of the first one-terminal-pair SAW resonator shown in FIG. 27;

FIG. 34 is a circuit diagram of a SAW filter according to a seventh embodiment of the present invention;

FIG. 35 is a diagram showing the relation between the film thickness of the electrode and the ripple occurrence position;

FIG. 36 is a diagram showing a state in which a ripple arising from reflectors of a parallel-arm resonator has been dropped into a high-frequency attenuation pole;

FIGS. 37A, 37B and 37C are diagrams showing a film thickness' dependence on the pass band characteristic of a resonator-type filter;

FIGS. 38A and 38B are diagrams showing the results of an experiment concerning the film thickness' dependence on the insertion loss and the ripple occurrence position;

FIG. 39 is a diagram of a first one-terminal-pair SAW resonator according to an eighth embodiment of the present invention;

FIG. 40 is a diagram showing a band characteristic of the SAW filter shown in FIG. 39;

FIG. 41 is a diagram showing a variation of the first one-terminal-pair SAW resonator used in the eighth embodiment of the present invention;

FIG. 42 is a plan view of a structure which realizes inductors used in the filter shown in FIG. 13;

FIG. 43 is a diagram of another structure which realizes inductors used in the filter shown in FIG. 13;

FIG. 44 is a circuit diagram of a SAW filter according to an eleventh embodiment of the present invention;

FIG. 45 is a perspective view of the SAW filter shown in FIG. 44;

FIGS. 46A and 46B are diagrams showing an immittance characteristic of a SAW resonator in which the resonance frequency is higher than the antiresonance frequency;

FIGS. 47A, 47B and 47C are diagrams showing variations in the band characteristic of the ladder-type filter observed when the difference between the resonance frequency and the antiresonance frequency increases from zero;

FIGS. 48A and 48B are diagrams showing how to measure the characteristics of the SAW resonator;

FIG. 49 is a graph showing admittance and immittance characteristics of SAW resonators in the series arm and the parallel arm;

FIG. 50 is a diagram showing the frequency' dependence on the product of bx;

FIG. 51 is diagram showing an equivalent circuit in which a part of the circuit shown in FIG. 44 is expressed by means of L and C;

FIG. 52 is a diagram showing the relation between |bx_max| and Δf/f_rs ;

FIG. 53 is a diagram showing the relation between k² and τ;

FIG. 54 is a circuit diagram of a SAW filter according to a twelfth embodiment of the present invention;

FIG. 55 is a perspective view of the SAW filter shown in FIG. 54;

FIG. 56 is a diagram showing a filter characteristic of the SAW resonator shown in FIG. 53;

FIG. 57 is a diagram showing a characteristic obtained when an output-side admittance of the filter shown in FIG. 64 is reduced;

FIGS. 58A and 58B are circuit diagrams of unit sections;

FIGS. 59A, 59B and 59C are circuit diagrams showing multi-connections of unit sections;

FIG. 60 is a diagram showing a connection of two four-terminal circuits and an interface therebetween;

FIGS. 61A, 61B and 61C are circuit diagrams showing unit section connecting ways;

FIG. 62 is a diagram showing how n unit sections are cascaded;

FIGS. 63A, 63B and 63C are circuit diagrams showing how ladder-type circuits are configured using the unit sections;

FIG. 64 is a circuit diagram of a receptionconventionalr₁ 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 increases 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=l/r_p (r_p : electric resistance of the parallel-arm resonator), and therefore the following expression can be obtained:

r+50r·g+2500g=r_s +50(r_s /r_p)+2500(l/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·ρ_o /N_s·W·t)+50·(l_s /l_p)·(N_p /N_s)·(t_p·t_s)+2500·N s·W·t_s /(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_os /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 the 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 T0 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 F2.

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 saw filter comprising:

a first saw resonator having a pair of terminals and a predetermined resonance frequency (f_rp), said first saw resonator being provided in a parallel arm of the saw filter;

a second saw resonator having 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), said second saw resonator being provided in a series arm of the saw filter; and

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

2. The saw filter as claimed in claim 1, wherein an aperture length (Ap) of the first saw resonator is larger than an aperture length (As) of the second saw resonator.

3. The saw filter as claimed in claim 1, wherein a number (Np) of electrode finger pairs of the first saw resonator is larger than a number (Ns) of electrode finger pairs of the second saw resonator.

4. The saw filter as claimed in claim 1, wherein the first saw resonator comprises an exciting interdigital electrode and first and second reflectors respectively located on opposite sides of the exciting electrode so that β is equal to 0.4, said β being defined in the following equation:

d=(n+β)·λ

wherein d denotes a distance between the exciting electrode and each of the first and second reflectors, n is an integer, β is a real number equal to or less than 1, and λ denotes a period of the exciting interdigital electrode corresponding to the resonance frequency.

5. The A saw filter as claimed in claim 1, wherein comprising:

a first saw resonator having a pair of terminals and a predetermined resonance frequency (f_rp), said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having 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), said second saw resonator being provided in a series arm of the saw filter, wherein

the first and second saw resonators are formed on a piezoelectric substrate including at least one of LiTaO₃ and LiNbO₃;

the first saw 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.

6. The A saw filter as claimed in claim 1, wherein comprising:

a first saw resonator having a pair of terminals and a predetermined resonance frequency (f_rp), said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having 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), said second saw resonator being provided in a series arm of the saw filter, wherein

the first and second saw resonators are formed on a piezoelectric substrate including at least one of LiTaO₃ and LiNbO₃;

the first saw 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.

7. The saw filter as claimed in claim 1, wherein said inductance element comprises a bonding wire.

8. The saw filter as claimed in claim 1, wherein said inductance element comprises:

a ceramic package accommodating a filter chip, the first and second saw resonators being formed on the filter chip; and

a microstrip line which is formed on the ceramic package and extends between, and interconnects, the first saw resonator and a terminal.

9. The saw filter as claimed in claim 1, wherein said inductance element comprises:

a filter chip, the first and second saw resonators being formed on the filter chip; and

a microstrip line which is formed on the filter chip and extends from the first saw resonator.

10. 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 respectively provided in 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 a predetermined antiresonance frequency of the first saw resonator (f_ap), said second saw resonators being provided in a series arm of the saw filter; and

inductance elements (Ls) respectively connected in series to the second saw resonators.

11. The saw filter as claimed in claim 10, wherein:

each of the first saw resonators comprises an exciting interdigital electrode and first and second reflectors respectively located on opposite sides of the exciting electrode so that β is equal to 0.4, said β being defined in the following equation:

d=(n+β)·λ

wherein d denotes a distance between the exciting electrode and each of the first and second reflectors, n is an integer, β is a real number equal to or smaller than 1, and λ denotes a period of the exciting interdigital electrode corresponding to the resonance frequency.

12. The saw filter as claimed in claim 11, wherein each of said inductance elements comprises:

a ceramic package accommodating a filter chip, the first and second saw resonators being formed on the filter chip; and

microstrip lines which are formed on the ceramic package and respectively extend between, and interconnect, the second saw resonators and corresponding terminals.

13. The saw filter as claimed in claim 11, wherein each of said inductance elements comprises:

a filter chip, the first and second saw resonators are formed; and

microstrip lines which are formed on the filter chip and extend respectively from the second saw resonators.

14. 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 the predetermined antiresonance frequency of the first saw resonator (f_ap), said second saw resonators being provided in a series arm of the saw filter; and

inductance elements respectively connected in series with the first saw resonators in the parallel arms.

15. A saw filter comprising:

a first saw resonator having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonator being provided in a series arm of the saw filter, wherein:

the second resonance frequency (f_rs) is higher than the first antiresonance frequency (f_ap), and

a difference between the second resonance frequency and the first antiresonance frequency is equal to a value which provides an allowable ripple range and an allowable insertion loss.

16. The A saw filter as claimed in claim 15, wherein comprising:

a first saw resonator having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonator being provided in a series arm of the saw filter, wherein:

the second resonance frequency (f_rs) is higher than the first antiresonance frequency (f_ap), and

a difference between the second resonance frequency and the first antiresonance frequency is equal to a value which provides an allowable ripple range and an allowable insertion loss, wherein:

the first and second saw resonators are formed on a piezoelectric substrate;

the second saw comprises an interdigital electrode which is formed on the piezoelectric substrate and which has a predetermined period; and

a normalized value, obtained by normalizing said difference by the second resonance frequency, is larger than zero #x2205;002 and smaller than α, as defined by the following equation: ##EQU14##

wherein P is a ratio of an electrostatic capacitance, based on an aperture length and a number of finger pairs of the interdigital electrode of the second saw resonator, to an electrostatic capacitance, based on an aperture length and a number of finger pairs of an interdigital electrode of the first saw resonator.

17. The A saw filter as claimed in claim 15, wherein comprising:

a first saw resonator having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonator being provided in a series arm of the saw filter, wherein:

the second resonance frequency (f_rs) is higher than the first antiresonance frequency (f_ap), and

a difference between the second resonance frequency and the first antiresonance frequency is equal to a value which provides an allowable ripple range and an allowable insertion loss, wherein:

the first and second saw resonators are formed on a piezoelectric substrate;

the second saw resonator comprises an interdigital electrode which is formed on the piezoelectric substrate and which has a predetermined period;

said piezoelectric substrate comprises 36° Y-cut X-propagation LiTaO₃ ; and

Cop/Cos is less than 1.8, wherein Cop and Cos are the electrostatic capacitances of the first saw resonator and the second saw resonator, respectively; and

the predetermined period of the interdigital electrode of the second saw resonator is selected so that said normalized ratio a normalized value, obtained by normalizing said difference by the second resonance frequency, is larger than zero #x2205;007 and is smaller than a, as defined by the following equation: ##EQU15##

wherein P is a ratio of an electrostatic capacitance, Cop/Cos, based on an aperture length and a number of finger pairs of the interdigital electrode of the second saw resonator, to an electrostatic capacitance, based on an aperture length and a number of finger pairs of an interdigital electrode of the first saw resonator.

18. The A saw filter as claimed in claim 15, wherein comprising:

a first saw resonator having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonator being provided in a series arm of the saw filter, wherein:

the second resonance frequency (f_rs) is higher than the first antiresonance frequency (f_ap), and

a difference between the second resonance frequency and the first antiresonance frequency is equal to a value which provides an allowable ripple range and an allowable insertion loss, wherein:

Cop/Cos is less than 1.8, wherein Cop and Cos are the electrostatic capacitances of the first saw resonator and the second saw resonator, respectively; and

the first and second saw resonators are formed on a piezoelectric substrate;

the second saw resonator comprises an interdigital electrode which is formed on the piezoelectric substrate and which has a predetermined period;

said piezoelectric substrate comprises 64° Y-cut X-preparation LiNbO₃ ; and

the predetermined period of the interdigital electrode of the second saw resonator is selected so that said normalized ratio a normalized value, obtained by normalizing said difference by the second resonance frequency, is larger than zero #x2205;0073 and is smaller than α, as defined by the following equation: ##EQU16##

wherein P is a ratio of an electrostatic capacitance, Cop/Cos, based on an aperture length and a number of finger pairs of the interdigital electrode of the second saw resonator, to an electrostatic capacitance, based on an aperture length and a number of finger pairs of an interdigital electrode of the first saw resonator.

19. The A saw filter as claimed in claim 15, wherein comprising:

a first saw resonator having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonator being provided in a parallel arm of the saw filter; and

a second saw resonator having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonator being provided in a series arm of the saw filter, wherein:

the second resonance frequency (f_rs) is higher than the first antiresonance frequency (f_ap), and a difference between the second resonance frequency and the first antiresonance frequency is equal to a value which provides an allowable ripple range and an allowable insertion loss, wherein:

Cop/Cos is less than 1.8, wherein Cop and Cos are the electrostatic capacitances of the first saw resonator and the second saw resonator, respectively; and

the first and second saw resonators are formed on a piezoelectric substrate;

the second saw resonator comprises an interdigital electrode which is formed on the piezoelectric substrate and which has a predetermined period;

said piezoelectric substrate comprises 41° Y-cut X-propagation LiNbO₃ ; and

the predetermined period of the interdigital electrode of the second saw resonator is selected so that said normalized ratio a normalized value, obtained by normalizing said difference by the second resonance frequency, is larger than zero #x2205;0074 and is smaller than α, as defined by the following equation: ##EQU17##

wherein P is a ratio of an electrostatic capacitance, Cop/Cos, based on an aperture length and a number of finger pairs of the interdigital electrode of the second saw resonator, to an electrostatic capacitance, based on an aperture length and a number of finger pairs of an interdigital electrode of the first saw resonator.

20. A saw filter comprising:

a plurality of first saw resonators, each having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonators being connected in respective, parallel arms of the saw filter; and

a plurality of second saw resonators, each having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonators being connected in a series arm of the saw filter, wherein: the first and second saw resonators are connected so as to form a ladder-type filter structure,

the second resonance frequency is higher than or equal to the first antiresonance frequency,

a first outermost arm, closest to either an input or an output of the saw filter, is said series arm and a second outermost arm,

closest to a remaining one of the input and the output, is one of the parallel arms, and

the respective one of the second saw resonators connected in the first outermost arm has an impedance smaller than that of each of remaining second saw resonators connected in the series arm and located interiorally of said saw filter, relatively to said respective one of the second saw resonators connected in the first outermost arm.

21. The saw filter as claimed in claim 20, wherein the respective one of the first saw resonators connected in the second outermost arm has an admittance smaller than that of each of remaining first saw resonators connected respectively in the parallel arms and located interiorally of said saw filter, relatively to said respective one of the first saw resonators connected in the second innermost arm.

22. The saw filter as claimed in claim 20, wherein the impedance of said respective one of the second saw resonators is half that of each of the remaining second saw resonators.

23. The saw filter as claimed in claim 21, wherein the impedance of said respective one of the second saw resonators is half that of each of the remaining second saw resonators.

24. The saw filter as claimed in claim 20, wherein:

a first electrostatic capacitance based on a first product is larger than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said one of the second saw resonators in the first outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining second saw resonators, a number of finger pairs thereof, and said dielectric constant.

25. The saw filter as claimed in claim 20, wherein each of said remaining second saw resonators in the series arm comprises a plurality of component saw resonators connected in series and each of the plurality of component saw resonators has the same capacitance as said respective one of the second saw resonators connected in the first outermost arm.

26. The saw filter as claimed in claim 21, wherein:

a first electrostatic capacitance based on a first product is larger smaller than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said one of the first saw resonators in the second outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining first saw resonators, a number of finger pairs thereof, and said dielectric constant.

27. The saw filter as claimed in claim 21, wherein each of said remaining second saw resonators in the series arm comprises a plurality of component saw resonators connected in series and each of the plurality of component saw resonators has the same impedance as said respective one of the second saw resonators connected in the first outermost arm.

28. The saw filter as claimed in claim 21, wherein the admittance of said respective one of the first saw resonators is half that of each of the remaining first saw resonators.

29. The saw resonator as claimed in claim 21, wherein:

a first electrostatic capacitance based on a first product is smaller than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said one of the first saw resonators in the second outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining first saw resonators, a number of finger paris pairs thereof, and said dielectric constant.

30. The saw resonator as claimed in claim 21, wherein each of said remaining first saw resonators in the respective parallel arms comprises a plurality of component saw resonators connected in parallel and each of the plurality of component saw resonators has the same capacitance as said respective one of the first saw resonators connected in the second outermost arm.

31. The saw filter as claimed in claim 23, wherein:

a first electrostatic capacitance based on a first product is larger than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said respective one of the second saw resonators connected in the first outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining second saw resonators, a number of finger pairs thereof, and said dielectric constant.

32. The saw filter as claimed in claim 23, wherein each of said remaining second saw resonators in the series arm comprises a plurality of component saw resonators connected in series and each of the plurality of component saw resonators has the same capacitance as said respective one of the second saw resonators connected in the first outermost arm.

33. The saw resonator as claimed in claim 28, wherein:

a first electrostatic capacitance based on a first product is smaller than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said respective one of the first saw resonators connected in the second outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate, and the second product is a product of an aperture length of each of said remaining first saw resonators, a number of finger pairs thereof and said dielectric constant.

34. The saw resonator as claimed in claim 28, wherein each of said remaining first saw resonators connected in the respective parallel arms comprises a plurality of component saw resonators connected in parallel and each of the plurality of component saw resonators has the same capacitance as said respective one of the first saw resonators connected in the second outermost arm.

35. A saw filter having an input and an output, comprising:

a plurality of first saw resonators, each having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonators being connected in respective, parallel arms of the saw filter; and

a plurality of second saw resonators, each having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonators being connected in a series arm of the saw filter, wherein:

the first and second saw resonators are connected so as to form a ladder-type filter structure,

the second resonance frequency is higher than or equal to the first antiresonance frequency, and

a first outermost arm, closest to one of the input and the output of the saw filter, comprises said series arm and a second outermost arm, closest to the other of the input and the output, comprises one of the parallel arms, and the respective first saw resonator connected in the second outermost arm has an admittance smaller than that of each of the remaining first saw resonators, connected in the remaining, respective parallel arms and located interiorly of said saw filter relatively to the respective first saw resonator connected in the second outermost arm.

36. The saw filter as claimed in claim 35, wherein the admittance of said one of the first saw resonators is half that of each of the remaining first saw resonators.

37. The saw filter as claimed in claim 35, wherein:

a first electrostatic capacitance based on a first product is smaller than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said one of the first saw resonators in the second outermost arm, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining first saw resonators, a number of finger pairs thereof, and said dielectric constant.

38. The saw filter as claimed in claim 35, wherein each of said remaining first saw resonators connected respectively in the parallel arms comprises a plurality of component saw resonators connected in parallel and each of the plurality of component saw resonators has the same capacitance as said respective one of the first saw resonators connected in the second outermost arm.

39. A saw filter comprising:

a plurality of first saw resonators, each having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonators being connected in respective, parallel arms of the saw filter; and

a plurality of second saw resonators, each having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonators being connected in a series arm of the saw filter, wherein:

the first and second saw resonators are connected so as to form a ladder-type filter structure;

the second resonance frequency is higher than or equal to the first antiresonance frequency;

a first outermost arm, closest to an input of the saw filter, comprises one of the parallel arms, and a second outermost arm, closest to an output of the saw filter, comprises another one of the parallel arms; and

the respective one of the first saw resonators connected in one of the first and second outermost arms has an admittance smaller than that of each of the remaining first saw resonators respectively connected in the parallel arms and located interiorly of the saw filter relatively to said respective one of the first saw resonators connected in said one of the first and second outermost arms.

40. The saw filter as claimed in claim 39, wherein the admittance of said respective one of the first saw resonators in at least one of the first and second outermost arms is half that of each of said remaining first saw resonators.

41. The saw filter as claimed in claim 40, wherein:

a first electrostatic capacitance based on a first product is smaller than a second electrostatic capacitance based on a second product;

the first product is a product of an aperture length of said respective one of the first saw resonators in at least one of the first and second outermost arms, a number of finger pairs thereof, and a dielectric constant of a substrate of the first and second saw resonators; and

the second product is a product of an aperture length of each of said remaining first saw resonators, a number of finger pairs thereof, and said dielectric constant.

42. The saw filter as claimed in claim 40, wherein each of said remaining first saw resonators connected respectively in the parallel arms comprises a plurality of component saw resonators connected in parallel and each of the plurality of component saw resonators has the same capacitance as said respective one of the first saw resonators connected in one of the first and second outermost arms.

43. A saw filter comprising:

a plurality of first saw resonators, each having a pair of terminals, a first resonance frequency (f_rp) and a first antiresonance frequency (f_ap), based on the first resonance frequency and a first capacitance ratio (τ) and higher than the first resonance frequency, said first saw resonators being connected in respective, parallel arms of the saw filter; and

a plurality of second saw resonators, each having a pair of terminals, a second resonance frequency (f_rs) and a second antiresonance frequency (f_as), based on the second resonance frequency and a second capacitance ratio (τ) and higher than the second resonance frequency, said second saw resonators being provided in a series arm of the saw filter, wherein:

the first and second saw resonators are connected so as to form a ladder-type filter structure;

the second resonance frequency is higher than or equal to the first antiresonance frequency;

a first outermost arm, closest to an input of the saw filter, is said series arm and a second outermost arm, closest to an output of the saw filter, is also said series arm; and

one of the second saw resonators connected in a respective one of the first and second outermost arms has an impedance smaller than that of each of remaining second saw resonators provided in the series arm and located interiorally of said saw filter, relatively to said one of the second saw resonators.

44. The saw filter as claimed in claim 43, wherein the impedance of said one of the second saw resonators is half that of each of the remaining second saw resonators.

45. The saw filter as claimed in claim 43, wherein each of said remaining second saw resonators in the respective series arms comprises a plurality of saw resonators connected in series and each of the plurality of component saw resonators has the same capacitance as said one of the second saw resonators provided in the at least one of the first and second outermost arms.

46. The saw filter comprising:

a first saw resonator having a pair of terminals and a predetermined resonance frequency (f_rp), said first saw resonator being provided in a respective parallel arm of the saw filter; and

a second saw resonator having a pair of terminals and a predetermined resonance frequency (f_rs) approximately equal to or higher than a predetermined antiresonance frequency of the first saw resonator (f_ap), said second saw resonator being provided in a series arm of the saw filter, a first electric resistance (rs) of an interdigital electrode of said second saw resonator being smaller than a second electric resistance (rp) of an interdigital electrode of said first saw resonator.

47. The saw filter as claimed in claim 46, wherein:

an aperture length (ls) of the interdigital electrode of said second saw resonator is smaller than that (lp) of the interdigital electrode of said first saw resonator; and

a number (Ns) of finger pairs of the interdigital electrode of said second saw resonator is larger than a number (Np) of finger pairs of the interdigital electrode of said first saw resonator.

48. The saw filter as claimed in claim 46, wherein a film thickness of the interdigital electrode of said first saw resonator is smaller than a film thickness of the interdigital electrode of said second saw resonator.

49. A band-pass filter comprising:

a plurality 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 and a series-arm resonator located at the first stage;

a pair of input terminals commonly connected to the plurality of saw filters;

a plurality of pairs of output terminals respectively connected to the plurality of saw filters;

an inductance element, located between at least one of the saw filters and the pair of input terminals and connected in parallel to said at least one of the saw filters; and

a capacitance element connected in series between said inductance element and said series-arm resonator.

50. A band-pass filter comprising:

a plurality of saw filters having respective pass bands and saw resonators and each having at least a first stage;

a pair of input terminals commonly connected to the plurality of saw filters;

a plurality of pairs of output terminals respectively connected to the plurality of saw filters;

a first one of the saw filters comprises a series-arm saw resonator, located at the first stage of said first one of the saw filters, and a parallel-arm saw resonator, connected to said series-arm saw resonator;

a second one of the saw filters comprises a parallel-arm saw resonator, located at the first stage of said second one of the saw filters, and a series-arm saw filter connected to said parallel-arm saw resonator located at the first stage of the second one of the saw filters; and

a line used for phase rotation and connected in series between one of the pair of input terminals and the second one of the saw filters.

51. The band-pass filter as claimed in claim 50, further comprising an inductance element located between the first one of the saw filters and the pair of input terminals, and connected in parallel to the first one of the saw filters.

52. The band-pass filter as claimed in claim 51, further comprising a capacitance element connected in series between said inductance element and the series-arm resonator of said first one of the saw filters.

53. The saw filter as claimed in claim 1, wherein:

a product of an aperture length (Ap) and a number of (Np) of electrode finger pairs of the first saw resonator is larger than a product of an aperture length (As) and a number (Ns) of electrode finger pairs of the second saw resonator.

54. The saw filter as claimed in claim 7, further comprising input and output terminals and wires connected to said input and output terminals, wherein said bonding wire is longer than at least one of the wires which is connected to said input and output terminals.

55. The saw filter as claimed in claim 7, further comprising:

a ceramic package to support said first and second saw resonators; and

a metal terminal formed on said ceramic package and coupled to an external terminal.

56. The saw filter as claimed in claim 14, wherein at least two of said inductance elements have different values of inductances.

57. The saw filter as claimed in claim 14, wherein at least two of the first saw resonators in the parallel arms of said saw filter have different values of capacitances.

58. The saw filter as claimed in claim 14, further comprising input and output terminals and wires connected to said input and output terminals, wherein at least one of said inductance elements comprises a bonding wire which is longer than at least one of the wires connected to said input and output terminals.

59. The saw filter as claimed in claim 14, further comprising:

a ceramic package to support said first and second saw resonators; and

a metal terminal formed on said ceramic package and coupled to an external terminal.

60. The saw filter as claimed in claim 16, wherein the normalized value is larger than 1/[1.3416(τ+100)-τ].