Method for designing a SAW resonator and computer program comprising program instructions for carrying out the method

Abstract

The present invention provides a method for designing a SAW resonator that can configure a SAW filter over a wide frequency band from several hundred MHz to several GHz by establishing a four-port transmission line model for a SAW IDT electrode instead of directly measuring the SAW characteristics of the SAW resonator, and calculating the parameters of the four-port transmission line model using initial parameters measured from a SAW resonator sample, and a computer program having program instructions for executing the method.

Description

[Technical field]

[0001] The present invention relates to a method for designing a SAW resonator, which is a resonator or bandpass filter used in mobile communication devices and the like, that converts an electrical signal into a surface acoustic wave (SAW) of a piezoelectric material using the piezoelectric effect of a piezoelectric material and then converts the converted SAW back into an electrical signal, using parameters of a four-port equivalent circuit model of a SAW IDT, such as IDT electrode capacitance, SAW phase velocity, electromechanical coupling coefficient, and attenuation constant of the IDT electrode, and a computer program having program instructions for executing the method. [Background technology]

[0002] Solid-state piezoelectric materials have been widely used in recent years in radio frequency (RF) electronic systems because the acoustic waves inside the material can be well controlled by the physical layout of the surface.

[0003] In particular, RF filters based on acoustic resonators have become important circuit components in microwave integrated systems due to their high performance, small size and low cost.

[0004] In a SAW resonator, when a time-varying electrical signal is applied to the IDT electrodes, particles in the elastic material vibrate, thus generating sound waves at the shallow surface of the piezoelectric substrate.

[0005] The physical phenomenon associated with the IDT electrodes provided on the piezoelectric substrate of the SAW resonator is very complicated to understand since electromagnetic waves are related to acoustic waves.

[0006] The electromechanical coupling coefficient (k 2 ) can be introduced to treat electromagnetic waves and acoustic waves as separate waves.

[0007] In prior publication 1 (WR Smith, HM Gerard, JH Collins, TM Reeder, and HJ Shaw, "Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model," IEEE Trans. Microw. Theory Tech., Vol. MTT-17, no. 11, pp. 856-864, Nov. 1969.) and prior publication 2 (WR Smith, HM Gerard, and WR Jones, "Analysis and Design of Dispersive Interdigital Surface-Wave Transducers," IEEE Trans. Microw, Theory Tech., Vol. MTT-20, no. 7, pp. 458-471, Jul. 1972.), Smith modeled a surface acoustic wave (SAW) device with an electromechanically coupled four-port distributed circuit in which the physical properties of the SAW in the IDT electrodes can be mathematically formulated using the electromechanical coupling coefficient, acoustic phase velocity, and acoustic energy loss. This made it easier to understand the physical characteristics of the SAW generated within the IDT electrodes.

[0008] However, the theoretically determined bulk piezoelectric material

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[0009] where v a is the phase velocity of the acoustic wave in the piezoelectric material. For BAW (Bulk Acoustic Wave) devices, the theoretically determined k 2 bulk is sufficiently accurate, but in the case of SAW devices, most of the acoustic energy is distributed on the surface of the piezoelectric substrate, so k 2However, there were problems with this method that made it unsuitable for application to SAW devices.

[0010] On the other hand, in the previous paper3 (O. Ikata, T. Miyashita, T. Matsuda, T. Nishihara and Y. Satoh, "Development of low-loss band-pass filters using SAW resonators for portable telephones," in Proc. IEEE Ultrason. Symp., 1992, pp. 111-115.), Ikata used experimental data to adjust the filter bandwidth so that it matched the experimental results. 2 It was decided.

[0011] After that, Ikata considered the metal load effect of the IDT electrode and divided the inside of the IDT electrode into a metal region and a space region, and calculated the acoustic wave phase velocity (v o , v m ) were divided.

[0012] Although such parameters are fairly accurate up to several hundred MHz, they are not accurate enough in the frequency band of several GHz, and therefore microwave circuit designs based on SAW IDTs using such existing technology have the potential to result in serious design failures. [Prior art documents] [Non-patent literature]

[0013] [Non-Patent Document 1] WR Smith, HM Gerard, JH Collins, TM Reeder, and HJ Shaw, "Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model," IEEE Trans. Microw. Theory Tech., Vol. MTT-17, no. 11, pp. 856-864, Nov. 1969.

[0014] [Non-Patent Document 2] WR Smith, HM Gerard, and WR Jones, "Analysis and Design of Dispersive Interdigital Surface-Wave Transducers," IEEE Trans. Microw, Theory Tech., Vol. MTT-20, no. 7, pp. 458-471, Jul. 1972.

[0015] [Non-Patent Document 3] O. Ikata, T. Miyashita, T. Matsuda, T. Nishihara and Y. Satoh, "Development of low-loss band-pass filters using SAW resonators for portable telephones," in Proc. IEEE Ultrason. Symp., 1992, pp. 111-115. Summary of the Invention [Problem to be solved by the invention]

[0016] The present invention provides a method for designing a SAW resonator that can configure a SAW filter over a wide frequency band from several hundred MHz to several GHz by establishing a four-port transmission line model for a SAW IDT electrode instead of directly measuring the SAW characteristics of the SAW resonator, and calculating the parameters of the four-port transmission line model using initial parameters measured from a SAW resonator sample, and a computer program having program instructions for executing the method. [Means for solving the problem]

[0017] A method for designing a SAW resonator using characteristic information of a SAW resonator according to one embodiment of the present invention includes the steps of calculating characteristic frequency information for a surface acoustic wave generated by an IDT electrode using each scattering parameter measured from a SAW resonator sample, calculating information indicating physical characteristics of the surface acoustic wave in the IDT electrode using the characteristic frequency information, and designing a SAW resonator from a transmission line circuit model of the surface acoustic wave using the calculated information indicating the physical characteristics of the surface acoustic wave.

[0018] In a preferred embodiment, the method further includes the step of calculating a capacitance per finger of the IDT electrode using the scattering parameters as one of the pieces of information indicating the physical characteristics of the surface acoustic wave.

[0019] In a preferred embodiment, the step of calculating characteristic frequency information for the surface acoustic wave includes a step of calculating a resonant frequency, an anti-resonant frequency and a spurious response frequency for the surface acoustic wave generated by the IDT electrode using the impedance or admittance of the IDT electrode converted from the scattering parameters.

[0020] In addition, preferably, the step of calculating information indicating the physical characteristics of the surface acoustic wave includes the steps of: determining a phase velocity of the surface acoustic wave in the IDT electrode using the characteristic frequency information; determining an electromechanical coupling coefficient indicating how much electrical energy can be converted into surface acoustic wave energy from the IDT electrode using the characteristic frequency information; and determining an attenuation constant of the surface acoustic wave in the IDT electrode using the characteristic frequency information.

[0021] Preferably, the step of calculating information indicating the physical characteristics of the surface acoustic wave includes a step of determining a temporary value when a frequency characteristic calculated by repeatedly applying a temporary value to the phase velocity of the surface acoustic wave in the IDT electrode while changing the temporary value is close to the calculated resonant frequency and spurious response frequency within a predetermined range as a value of the phase velocity indicating the physical characteristics of the surface acoustic wave.

[0022] Preferably, the step of calculating information indicating the physical characteristics of the surface acoustic wave includes a step of determining a temporary value when a frequency characteristic calculated by repeatedly applying a temporary value to an electromechanical coupling coefficient of the IDT electrode while changing the temporary value is close to the calculated anti-resonance frequency within a predetermined range as a value of the electromechanical coupling coefficient indicating the physical characteristics of the surface acoustic wave.

[0023] In a preferred embodiment, the step of calculating information indicating the physical characteristics of the surface acoustic wave includes a step of determining an attenuation constant so that the peak-to-peak magnitudes of the input impedance or admittance of the IDT electrode at the resonant frequency and anti-resonant frequency match the calculated resonant frequency and anti-resonant frequency.

[0024] Meanwhile, the present invention includes a computer program having program instructions capable of executing the above-mentioned method for designing a SAW resonator. Effect of the Invention

[0025] The method for designing a SAW resonator according to the present invention and a computer program having program instructions capable of executing the same have the advantage that, instead of directly measuring the SAW characteristics of a SAW resonator, a four-port transmission line model for a SAW IDT electrode is established, and parameters of the four-port transmission line model are calculated using initial parameters measured from a SAW resonator sample, and then a SAW filter can be constructed over a wide frequency band from several hundred MHz to several GHz. [Brief description of the drawings]

[0026] [Figure 1] (a) is a diagram showing a one-port SAW resonator, and (b) is a diagram showing the mechanism for the IDT electrodes of the SAW resonator in terms of an equivalent electrical circuit in order to interpret the physical characteristics of the surface acoustic wave (SAW) generated via the IDT electrodes of the SAW resonator shown in (a).

[0027] [Diagram 2] FIG. 1(a) is an enlarged view of the IDT electrode 200 of a SAW resonator, and FIG. 1(b) is a diagram showing a four-port transmission line model using an equivalent electrical path based on the i-th finger to interpret the SAW by the IDT electrode shown in FIG.

[0028] [Diagram 3] 4 is a flowchart illustrating each process of a method for designing a SAW resonator according to an embodiment of the present invention.

[0029] [Figure 4] FIG. 13 is a diagram showing an example of calculating the capacitance of an IDT electrode of a SAW resonator using a 3D field solver.

[0030] [Diagram 5] 1 is a graph of admittance Yin versus frequency of an IDT electrode of a SAW resonator, showing the frequency versus resonant frequency (f1), the anti-resonant frequency (f2), and the spurious response frequency (f3), respectively.

[0031] [Figure 6] 1 is a graph showing a relationship between a SAW phase velocity and a phase velocity ratio and a film-thickness ratio (h / Lp) obtained according to an embodiment of the present invention.

[0032] [Figure 7] 1 is a graph showing the relationship between the electromechanical coupling coefficient (k2) and the damping constant (α) and the film-thickness ratio (h / Lp) obtained according to an embodiment of the present invention.

[0033] [Figure 8] FIG. 1A shows a 3.5 stage ladder type SAW filter created to verify a design method of a SAW resonator according to one embodiment of the present invention, and FIG. 1B shows a graph of insertion loss versus frequency for the test SAW filter shown in FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] The specific contents of the method for designing a SAW resonator according to the present invention and a computer program having program instructions for executing the method will be described in detail with reference to the drawings.

[0035] FIG. 1(a) shows a one-port SAW resonator, and FIG. 1(b) shows the mechanism for the IDT electrode of the SAW resonator as an equivalent electrical path in order to interpret the physical characteristics of the surface acoustic wave (SAW) generated through the IDT electrode of the SAW resonator shown in FIG. 1(a).

[0036] 1(a), an SAW resonator forms an IDT (InterDigital Transducers) electrode 200 on a piezoelectric substrate 100, and generates a surface acoustic wave (SAW) on the surface of the piezoelectric substrate 100 in response to an electrical signal applied to the IDT electrode 200. Here, as shown in FIG. 1(a), by providing reflectors 110 and 120 on both ends of the IDT electrode 200 on the piezoelectric substrate 100, the surface acoustic wave generated in the IDT electrode 200 can be configured to be reflected by the reflectors 110 and 120 without leaking to the outside.

[0037] A SAW resonator is very difficult to interpret by itself because electrical and acoustic energies are mutually coupled. To easily solve this problem, the electromechanical coupling coefficient (k 2 ) to separate the acoustic and electrical energies, the mechanism for SAW in the IDT electrodes can be interpreted in terms of a circuit.

[0038] Conventionally, k 2 is a characteristic constant of piezoelectric material, and theoretically, it can be defined using the elastic stiffness constant (c), the piezoelectric stress constant (e), and the dielectric permittivity (ε) as shown in the following mathematical formula 1. Experimentally, the change in acoustic wave phase velocity (▽v a ) can be used to calculate

[0039]

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[0040] k according to the above mathematical formula 1 2 is the electromechanical coupling coefficient of a bulk wave, and is therefore not suitable for a SAW device in which most of the acoustic waves exist on the surface of the piezoelectric substrate.

[0041] In order to solve this problem, Smith in the above-mentioned prior art documents 1 and 2 introduces a correction factor δ and solves the problem as shown in the following mathematical formula 4.

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[0042]

number

[0043] As mentioned above

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[0044] In order to solve this problem, Ikata in the above-mentioned prior art 3 considers the mass loading effect and calculates the phase velocity of the SAW in the IDT electrode as the phase velocity (v o ) and the phase velocity of the SAW when there is metal loading (when there are fingers of the IDT electrode) m ) ratio (τ v =v o / v m ) to model the phase velocity of the SAW in the IDT electrodes.

[0045] Since the electromechanical coupling coefficient does not match using existing methods, the SAW device can be successfully designed by modifying the bandwidth of the SAW device to match. However, as the SAW operating frequency increases to several GHz, the mass loading effect becomes more nonlinear, so the Ikata method mentioned above has its limitations.

[0046] A circuit model of the IDT electrode 200 for the SAW resonator can be expressed by a four-port transmission line model as shown in FIG.

[0047] FIG. 2(a) is an enlarged view of the IDT electrode 200 of the SAW resonator, and FIG. 2(b) is a diagram showing a four-port transmission line model using an equivalent electrical path based on the i-th finger to interpret the SAW by the IDT electrode shown in FIG. 2(a).

[0048] As shown in FIG. 2(a), the IDT electrode 200 includes a number of fingers 211 to 215 and spaces 231 to 234 between each finger. Reference numeral 211 denotes the (i-2)th finger, and its width is m. (i-2) The reference numeral 212 denotes the (i-1)th finger, and its width is m (i-1) Reference numeral 213 denotes the i-th finger, whose width is m i The reference numeral 214 denotes the (i+1)th finger, whose width is m (i+1) The reference numeral 215 denotes the (i+2)th finger, whose width is m (i+2) It is.

[0049] As shown in FIG. 2A, the width of the (i-1)-th gap 231 between the (i-2)-th finger 211 and the (i-1)-th finger 212 is S (i-1) and the width of the i-th gap 232 between the (i-1)-th finger 212 and the i-th finger 213 is S i and the width of the i+1-th gap 233 between the i-th finger 213 and the i+1-th finger 214 is S (i+1) and the width of the i+2-th gap 234 between the i+1-th finger 214 and the i+2-th finger 215 is S (i+2) It is.

[0050] Here, reference numerals 211, 213, and 215 denote fingers of an input IDT electrode, that is, input fingers, and reference numerals 212 and 214 denote fingers of an output IDT electrode, that is, output fingers.

[0051] As shown in Fig. 2(a), the distance between the input fingers or the output fingers is called the period (λ) of the IDT electrodes, and half of that distance, i.e., λ / 2, is called the period length, denoted as Lp. The symbol h shown in Fig. 2(a) indicates the thickness of each finger 211, etc.

[0052] FIG. 2B is a diagram showing a four-port transmission line model using an equivalent electrical path for the i-th gap 232 and the (i+1)-th gap 233 centered on the i-th finger 213 shown in FIG. 2A.

[0053] To calculate the four-port transmission line model shown in Figure 2(b), we need to calculate the capacitance (Co) of the IDT electrode fingers and the phase velocity (v o , v m ), electromechanical coupling coefficient (k 2 ) and the SAW attenuation constant (α) must be determined.

[0054] A method for designing a SAW resonator according to an embodiment of the present invention is for designing a SAW resonator having desired characteristics by effectively determining the above-mentioned parameters.

[0055] For this purpose, a method for designing a SAW resonator according to an embodiment of the present invention may include a process according to the flowchart shown in FIG. 3, and the above-mentioned capacitance (Co) and the phase velocity (v) of the SAW with and without the mass loading effect can be calculated by the process. o , v m ), electromechanical coupling coefficient (k 2 ), the attenuation constant (α) of the SAW can be effectively calculated.

[0056] Referring to FIG. 3, each step of the method for designing a SAW resonator according to one embodiment of the present invention will be described. First, a sample is extracted for the SAW resonator to be designed, and scattering parameters of the SAW resonator are measured from the sample as initial parameters (S110).

[0057] The mass loading effect of the IDT electrode varies nonlinearly with the film-thickness ratio (h / Lp), which is the ratio of the period length (Lp) of the IDT electrode to its thickness (h) as shown in Figure 2(a).

[0058] Therefore, the aperture length (La) of the one-port SAW resonator and the number of fingers of the IDT electrode (N IDT ), the number of reflectors (N REF Test patterns can be created by varying only the section length (Lp) of the IDT electrode while keeping the same thickness (h) of the fingers, and these can be used as samples. The scattering parameters of the samples created can be measured using a VNA.

[0059] Using the scattering parameters measured as described above, the capacitance of each finger of the IDT electrode of the SAW resonator can be calculated (S120).

[0060] The measured scattering parameters are used to calculate the admittance Y as shown in Equation 3 below. in (ω) can be calculated.

[0061]

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[0062] where ω is the angular frequency and S 11 (ω) is the scattering parameter.

[0063] The above Y inFrom (ω), the total capacitance C of the SAW resonator can be calculated using the following mathematical formula 4. Here, the frequency f for the calculation is a low frequency of 100 MHz or less at which the capacitance value of the IDT electrode is stable.

[0064]

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[0065] Total capacitance C total can also be calculated using a commercial 3D field solver (e.g., HFSS, SONNET, ADS, etc.). Figure 4 shows an example of using a 3D field solver.

[0066] As shown in Figure 4, the total capacitance C total can be further expressed as the sum of detailed capacitances in the IDT electrodes, which can be shown as Equation 5 below.

[0067]

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[0068] Here, C internal is the capacitance per finger of the inner fingers excluding the fingers at both ends of the IDT electrode, and C edge is the capacitance per finger of the fingers at both ends of the IDT electrode, and C parasitic is the parasitic capacitance.

[0069] C from N different one-port SAW resonator samples internal can be calculated as shown in Figure 4. internal and C. edge is almost the same as the capacitance C of the IDT electrode fingers in the four-port SAW transmission model. o is C internal is almost the same as C internalIt can be calculated as follows.

[0070] As described above, the IDT finger capacitance can be calculated according to step S120 of FIG.

[0071] Meanwhile, as shown in FIG. 3, by using the impedance or admittance of the IDT electrode converted from the scattering parameters measured as described above, for example, by using the admittance of the IDT electrode calculated by the above-mentioned mathematical formula 3, the resonant frequency (f1), anti-resonant frequency (f2), and spurious response frequency (f3) for the surface acoustic wave (SAW) generated by the IDT electrode can be calculated.

[0072] Figure 5 shows the admittance Y of the IDT electrode versus frequency. in Graphs of are shown for the resonant frequency (f1), the anti-resonant frequency (f2), and the spurious response frequency (f3), respectively.

[0073] Here, the spurious response frequency (f3) is a response frequency due to a bulk wave generated in the IDT electrode, and corresponds to noise in the response characteristics of the SAW.

[0074] The response frequency due to such a bulk wave acts as noise in grasping the physical characteristics of the SAW, and is a factor in increasing the nonlinearity of the physical characteristics of the SAW.

[0075] In the method for designing a SAW resonator according to one embodiment of the present invention, the necessary parameters are calculated by taking into consideration the spurious response frequency (f3) due to the bulk wave, which corresponds to the noise as described above, so that it is possible to calculate the physical characteristic information of the SAW more accurately than the conventional Smith and Ikata methods.

[0076] Returning to FIG. 3 again, in step S130, the resonant frequency (f1), anti-resonant frequency (f2), and spurious response frequency (f3) for the SAW are calculated using the admittance as described above, and then a temporary value is assigned to the phase velocity of the surface acoustic wave (SAW) in the IDT electrode.

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[0077] The temporary value of the phase velocity is repeatedly applied with other values ​​until the frequency characteristic approaches the resonance frequency (f1) and the spurious response frequency (f3) within a predetermined range, and the temporary value when the frequency characteristic approaches the resonance frequency and the spurious response frequency within a predetermined range is determined as the phase velocity (v o , v m ) can be determined (S160).

[0078] It has been explained previously that the mass loading effect of the IDT electrode in the SAW resonator changes nonlinearly depending on the film-thickness ratio (h / Lp), which is the ratio of the section length (Lp) of the IDT electrode to the thickness (h) of the IDT electrode. Figure 6 shows the phase velocity (v) of the SAW when there are no fingers of the IDT electrode (when there is no mass loading effect) calculated in step S160 with respect to the film-thickness ratio (h / Lp). o ) and the phase velocity ratio (τ v ) is a graph showing the relationship between

[0079] As shown in Fig. 6, the phase velocity of the SAW without the IDT finger (v o ) and the phase velocity of the SAW when the IDT electrode fingers are present (v m ) ratio (τ v =v o / v m ) changes nonlinearly.

[0080] Returning to FIG. 3, as mentioned above, the phase velocity of the SAW (v o , v m ) is determined, the electromechanical coupling coefficient (k 2 ) can be determined (S170 to S190). This can also be determined using an iterative method, similar to the phase velocity.

[0081] A temporary value is applied to the electromechanical coupling coefficient of the IDT electrode to calculate the frequency characteristic of the SAW (S170), and it is determined whether the calculated frequency characteristic approaches the anti-resonance frequency (f2) as shown in FIG. 5 within a predetermined range (S180). Other values ​​are repeatedly applied as the temporary value of the electromechanical coupling coefficient until the frequency characteristic approaches the anti-resonance frequency (f2) within the predetermined range, and the temporary value when the frequency characteristic approaches the anti-resonance frequency (f2) within the predetermined range is determined as the electromechanical coupling coefficient (k 2 ) can be determined (S190).

[0082] In addition, it is possible to determine an attenuation constant (α) such that the peak-to-peak magnitudes of the resonant frequency and anti-resonant frequency of the impedance or admittance according to the phase velocity of the SAW and the electromechanical coupling coefficient determined as described above match the peak-to-peak magnitudes of the resonant frequency (f1) and anti-resonant frequency (f2) as shown in FIG. 5 (S200).

[0083] FIG. 7 is a graph showing the relationship between the film-thickness ratio (h / Lp) and the electromechanical coupling coefficient (k2) and the damping constant (α) obtained in step S190.

[0084] As shown in Fig. 7, the electromechanical coupling coefficient (k 2 It can be seen that the damping constant (α) changes nonlinearly with the change in the film-thickness ratio (h / Lp), while the damping constant (α) remains almost constant.

[0085] Meanwhile, FIG. 8(a) shows a 3.5 stage ladder type SAW filter including SAW resonators S1 to S4 connected in series and SAW resonators P1 to P3 connected in parallel to verify a SAW resonator design method according to one embodiment of the present invention.

[0086] The aperture length (La) of each of the series-connected SAW resonators S1 to S4 and the parallel-connected SAW resonators P1 to P3 is set to 40 μm, and the number of reflectors N ref When the number of IDT fingers (NIDT) of each of the series-connected SAW resonators S1 to S4 is set to 20, the length of each of the sections (Lp) and the number of IDT fingers (N IDT ) is as shown in FIG. 8(a).

[0087] For a test SAW filter such as that shown in FIG. 8(a), a graph of insertion loss versus frequency was calculated as shown in FIG. 8(b).

[0088] In the graph shown in Figure 8 (b), MA3 shown by the dotted line is a graph calculated by the conventional method, MA1 shown by the red solid line is a graph calculated by the method of the present invention, and MA2 shown by the black solid line is a graph of the results of simulation based on measurements.

[0089] As shown in FIG. 8(b), when comparing MA3 according to the conventional method, MA1 according to the present invention, and MA2 according to the measured simulation results, in the passband, MA3 according to the conventional method shows a large difference of up to 36 MHz in frequency bandwidth and up to 3.4 dB in insertion loss compared to MA2 according to the simulation results.

[0090] On the other hand, when comparing MA1 according to the present invention with MA2 according to the simulation results, there are minute differences of up to 4 MHz in bandwidth and up to 0.7 dB in insertion loss, which shows that the results according to the present invention are almost identical to the frequency characteristics of an actual SAW filter.

[0091] Therefore, when designing a SAW filter using known material values ​​according to conventional methods, it is difficult to design an accurate SAW filter, but according to the method presented in the present invention, it is possible to design a SAW filter very accurately even at several GHz. [Industrial Applicability]

[0092] The method for designing a SAW resonator according to the present invention and a computer program having program instructions for executing the same can be applied to software that embodies the process of the design method by an algorithm and performs the corresponding function, or to a computer that performs such function, or to equipment for designing or manufacturing a SAW resonator or filter, and thus has industrial applicability in the technical field of designing a SAW resonator or a SAW filter.

Claims

1. A method for designing a SAW resonator using characteristic information of the SAW resonator, comprising the steps of: calculating characteristic frequency information for a surface acoustic wave generated by the IDT electrode using each scattering parameter measured from the SAW resonator sample; calculating information indicative of a physical characteristic of a surface acoustic wave in the IDT electrode using the characteristic frequency information; and designing a SAW resonator from a transmission line circuit model of the surface acoustic wave using information indicating the calculated physical characteristics of the surface acoustic wave.

2. 2. The method of claim 1, further comprising the step of calculating a capacitance per finger of the IDT electrode using the scattering parameters as one of the pieces of information indicating physical characteristics of the surface acoustic wave.

3. The step of calculating characteristic frequency information for the surface acoustic wave includes:

2. The method for designing a SAW resonator according to claim 1, further comprising the step of calculating a resonant frequency, an anti-resonant frequency and a spurious response frequency for a surface acoustic wave generated by the IDT electrode using the impedance or admittance of the IDT electrode converted from the scattering parameters.

4. The step of calculating information indicative of a physical characteristic of the surface acoustic wave includes: determining a phase velocity of a surface acoustic wave in the IDT electrode using the characteristic frequency information; determining an electromechanical coupling coefficient using the characteristic frequency information, which indicates how much electrical energy can be converted from the IDT electrodes into surface acoustic wave energy; and determining an attenuation constant of a surface acoustic wave in the IDT electrode using the characteristic frequency information.

5. The step of calculating information indicative of a physical characteristic of the surface acoustic wave includes:

4. The method of claim 3, further comprising the step of determining a temporary value, when a frequency characteristic calculated by repeatedly applying a temporary value to the phase velocity of the surface acoustic wave in the IDT electrode while changing the temporary value, to be a value of the phase velocity indicating a physical characteristic of the surface acoustic wave, when the temporary value approaches the calculated resonant frequency and spurious response frequency within a predetermined range.

6. The step of calculating information indicative of a physical characteristic of the surface acoustic wave includes:

4. The method of claim 3, further comprising the step of determining a temporary value when a frequency characteristic calculated by repeatedly applying a temporary value to the electromechanical coupling coefficient of the IDT electrode while changing the temporary value approaches the calculated anti-resonance frequency within a predetermined range as a value of the electromechanical coupling coefficient indicating a physical characteristic of the surface acoustic wave.

7. The step of calculating information indicative of a physical characteristic of the surface acoustic wave includes:

4. The method for designing a SAW resonator according to claim 3, further comprising a step of determining a damping constant so that the peak-to-peak magnitudes of the input impedance or admittance of the IDT electrode at the resonant frequency and the anti-resonant frequency match the calculated resonant frequency and anti-resonant frequency.

8. A computer program comprising program instructions capable of carrying out the method for designing a SAW resonator according to any one of claims 1 to 7.

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