JP2000124764A - Strip-shaped piezoelectric resonator for frequency filter - Google Patents

Strip-shaped piezoelectric resonator for frequency filter

Info

Publication number
JP2000124764A
JP2000124764A JP10298732A JP29873298A JP2000124764A JP 2000124764 A JP2000124764 A JP 2000124764A JP 10298732 A JP10298732 A JP 10298732A JP 29873298 A JP29873298 A JP 29873298A JP 2000124764 A JP2000124764 A JP 2000124764A
Authority
JP
Japan
Prior art keywords
resonator
electrodes
active portion
strip
piezoelectric
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
JP10298732A
Other languages
Japanese (ja)
Inventor
Yasudai Fujii
靖大 藤井
Masato Yamamoto
正人 山本
Hideaki Hiramitsu
秀明 平光
Hirobumi Ozeki
博文 尾関
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Niterra Co Ltd
Original Assignee
NGK Spark Plug Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by NGK Spark Plug Co Ltd filed Critical NGK Spark Plug Co Ltd
Priority to JP10298732A priority Critical patent/JP2000124764A/en
Publication of JP2000124764A publication Critical patent/JP2000124764A/en
Pending legal-status Critical Current

Links

Abstract

PROBLEM TO BE SOLVED: To increase the band width of a piezoelectric resonator with its simple constitution when the resonator is used to a frequency filter by polarizing the resonator over its front face and in its thickness direction, providing the electrodes on the main surfaces of both sides of the resonator, excluding the electrodes on both sides and at both end of the resonator to form an inactive part at the using end part. SOLUTION: The electrodes 3 and 4 are formed on both sides of a piezoelectric resonator 1a using a thin plate-like piezoelectric magnetic plate 2 consisting of lead zirconate titanate PZT, and the inactive parts Y having no electrodes are prepared on both sides and at both ends of the plate 2 with main surfaces having the electrodes 3 and 4 used as the active parts X, respectively. Both parts X and Y are polarized over the front face and in the thickness direction of the resonator 1a. A piezoelectric ceramic sintered body is obtained by pressing and burning a raw material of a prescribed composition and then polished to obtain the plate 2 of the prescribed thickness. Then the electrodes 3 and 4 are formed on both sides of the plate 2 by the screen printing and by means of the silver paste. Thus, the parts X includes the electrodes 3 and 4 and the parts Y include no electrodes 3 and 4.

Description

【発明の詳細な説明】DETAILED DESCRIPTION OF THE INVENTION

【0001】[0001]

【発明の属する技術分野】本発明は、無線器等に用いら
れるものであって、複数の圧電共振子を直並列に組み合
わせたラダー型圧電周波数濾波器等に用いられる短冊状
圧電共振子に関する。
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a strip-shaped piezoelectric resonator used for a radio device or the like and used for a ladder-type piezoelectric frequency filter or the like in which a plurality of piezoelectric resonators are combined in series and parallel.

【0002】[0002]

【従来の技術】この種の周波数濾波器は、厚肉小容量の
直列共振子と、薄肉大容量の並列共振子とをL型接続し
てなる基本単位回路を複数段接続し、これをケース内に
収納した構成よりなっている。この従来の各共振子は、
圧電磁器板の両面に全面電極を形成し、厚み方向に分極
して短冊状に構成される。この短冊状圧電共振子からな
る並列共振子(P)及び直列共振子(S)は、図18で
示すように周波数濾波回路を構成する。
2. Description of the Related Art A frequency filter of this type is constituted by connecting a plurality of basic unit circuits each having an L-shaped connection of a thick-walled, small-capacitance series resonator and a thin-walled, large-capacity parallel resonator. It is configured to be stored inside. Each of the conventional resonators
Electrodes are formed on both sides of the piezoelectric ceramic plate, and are polarized in the thickness direction to form a strip. The parallel resonator (P) and the series resonator (S) formed of the strip-shaped piezoelectric resonators constitute a frequency filtering circuit as shown in FIG.

【0003】[0003]

【発明が解決しようとする課題】上述の短冊状共振子に
あっては、電界方向及び分極方向が振動方向と異なる圧
電横効果を利用しており、このため、電界方向及び分極
方向が振動方向と一致する圧電縦効果を利用した圧電共
振子に比して、電気機械結合係数(K31)が低い。ま
た、このため、共振周波数frと、反共振周波数faと
の差であるΔfが比較的小さく、周波数濾波器に用いた
場合に、帯域幅が狭くなるという問題を生じていた。特
に、近年、デジタル通信の普及に伴って、広帯域の濾波
器が求められており、このことは大きな解決課題となっ
ている。本発明は、このような短冊状共振子の問題点を
簡易な構成により解決することを目的とするものであ
る。
In the above-described strip-shaped resonator, the piezoelectric transverse effect in which the electric field direction and the polarization direction are different from the vibration direction is used. The electromechanical coupling coefficient (K 31 ) is lower than that of a piezoelectric resonator using the piezoelectric longitudinal effect that matches the above. For this reason, Δf which is the difference between the resonance frequency fr and the anti-resonance frequency fa is relatively small, and there has been a problem that the bandwidth becomes narrow when used in a frequency filter. In particular, in recent years, with the spread of digital communication, a broadband filter has been demanded, and this is a major problem to be solved. An object of the present invention is to solve such a problem of the strip resonator with a simple configuration.

【0004】[0004]

【課題を解決するための手段】本発明は、全面にわたっ
て厚さ方向に分極され、かつ表裏の主面に電極を備える
と共に、その両端部の表裏で電極を除くことにより、該
両端部に非活性部を形成してなることを特徴とする周波
数濾波器に用いられる短冊状圧電共振子である。
SUMMARY OF THE INVENTION According to the present invention, an electrode is polarized in the thickness direction over the entire surface, and electrodes are provided on the front and back main surfaces. This is a strip-shaped piezoelectric resonator used for a frequency filter characterized by forming an active portion.

【0005】この圧電共振子において、直列共振子とし
て用いられるものにあっては、前記活性部の長さが全長
に対して51.8〜86.9%としたものは、実験よ
り、共振周波数と、反共振周波数との差Δfが大きく良
好となり、特に、約58%以上では優れた値を示し、広
帯域の周波数濾波器用の共振子として適していることが
確認された。
[0005] In this piezoelectric resonator, when the length of the active portion is set to 51.8 to 86.9% with respect to the total length of the resonator used as a series resonator, the resonance frequency is determined by experiments. And the difference Δf from the anti-resonance frequency became large and good. In particular, an excellent value was obtained at about 58% or more, and it was confirmed that this was suitable as a resonator for a wide-band frequency filter.

【0006】また、並列共振子として用いられるものに
あって、前記活性部の長さが全長に対して59.3〜7
9.9%としたものは、Δfが大きく良好となり、特
に、約71%以上では優れた値を示し、広帯域の周波数
濾波器用の共振子として適していることが確認された。
Further, in the parallel resonator, the length of the active portion is 59.3 to 7 with respect to the total length.
In the case of 9.9%, Δf was large and good, and particularly, when it was about 71% or more, it showed an excellent value, and it was confirmed that it was suitable as a resonator for a broadband frequency filter.

【0007】ここで、両端部を、表裏で入出力電極を含
めて山形状に削って形成された非活性部を備えるように
した構成が提案される。かかる構成にあっては、圧電磁
器板を表裏全面に電極を形成して分極した短冊状素子を
あらかじめ形成し、その両端部で表裏を傾斜状に削っ
て、電極を除去することにより、請求項1記載の素子を
形成したものである。
Here, there is proposed a configuration in which both ends are provided with inactive portions formed by shaving a mountain shape including input and output electrodes on both sides. In such a configuration, a piezoelectric element is formed on the front and back surfaces of the piezoelectric ceramic plate in advance to form a polarized strip-shaped element, and the front and back surfaces are slanted at both ends to remove the electrodes. 1 is formed.

【0008】[0008]

【発明の実施の形態】図1,2について本発明に係る短
冊状圧電共振子1aを説明する。この圧電共振子1a
は、表裏に電極3,4が形成されたチタン酸ジルコン酸
鉛(PZT)からなる薄板状圧電磁器板2の両端部に、
表裏に電極のない非活性部Y,Yを備え、電極3,4の
ある主面を活性部Xとしたものであり、活性部,非活性
部ともに全面にわたって厚さ方向に分極(矢線Ps)し
てなるものであって、図18の周波数濾波器に適用され
る直列共振子Sまたは並列共振子Pとして用いられる。
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A strip-shaped piezoelectric resonator 1a according to the present invention will be described with reference to FIGS. This piezoelectric resonator 1a
Are provided at both ends of a thin piezoelectric ceramic plate 2 made of lead zirconate titanate (PZT) having electrodes 3 and 4 formed on the front and back,
Non-active portions Y, Y having no electrodes are provided on the front and back sides, and the main surface on which the electrodes 3, 4 are provided is an active portion X. Both the active portion and the non-active portion are polarized in the thickness direction over the entire surface (arrow Ps). ) And used as a series resonator S or a parallel resonator P applied to the frequency filter of FIG.

【0009】ここで、この短冊状圧電共振子1aの形成
手段を、図13,14に従って、詳しく示す。
Here, means for forming the strip-shaped piezoelectric resonator 1a will be described in detail with reference to FIGS.

【0010】Pb ,ZrO ,TiO ,S
,Nb ,Cr を、Pb
{(Sb1/2 Nb1/20.01(Cr1/2
Nb1/ 0.04Zr0.49Ti0.46}O
組成式になるように、所定量秤量して調合し、これを湿
式ボールミルにて水を加えて、48時間一次粉砕し、乾燥
後、800 ℃にて2時間仮焼した後、湿式法によりさらに
水及びPVA系バインダーを加えて、72時間二次粉砕
し、平均粒径約0.5μmとする。ここで得られたスラ
リーを噴霧乾燥を行なって顆粒にする。次に一軸加圧成
形機を用いて、厚さ2.0mm×40mm角の大板にプ
レス成形する。このときの成形密度は、4.6g/cm
である。次に940℃の大気雰囲気にて16時間焼成を
行なって、圧電磁器焼結体とする。この焼結体を表裏面
で厚さ方向に研磨し、直列共振子Sとして用いるものは
厚さ0.495 mmとし、並列共振子Pとして用いるものは厚
さ0.175mm として、圧電磁器板2を得る。
Pb 3 O 4 , ZrO 2 , TiO 2 , S
b 2 O 3 , Nb 2 O 5 , Cr 2 O 3 are converted to Pb
{(Sb 1/2 Nb 1/2 ) 0.01 (Cr 1/2
Nb 1/2) 0.04 Zr 0.49 Ti 0.46} so that the composition formula of O 3, formulated by weighing predetermined amounts, which was added to water in a wet ball mill for 48 hours primary pulverization After drying and calcining at 800 ° C. for 2 hours, water and a PVA-based binder are further added by a wet method, followed by secondary grinding for 72 hours to obtain an average particle size of about 0.5 μm. The slurry obtained here is spray-dried into granules. Next, it is press-formed into a large plate having a thickness of 2.0 mm × 40 mm square using a uniaxial pressing machine. The molding density at this time was 4.6 g / cm 3
It is. Next, baking is performed in an air atmosphere at 940 ° C. for 16 hours to obtain a piezoelectric ceramic sintered body. The sintered body is polished in the thickness direction on the front and back surfaces to obtain a piezoelectric ceramic plate 2 having a thickness of 0.495 mm for a series resonator S and a thickness of 0.175 mm for a parallel resonator P.

【0011】次に、圧電磁器板2の表裏面に、電極3,
4を銀ペーストによりスクリーン印刷を行なった。この
とき、図14イで示すように、図中上面に形成される電
極3,4を所定のストライプパターン10(非活性部に
は銀ペーストが塗布されないパターン)にてスクリーン
印刷する。ここで電極3,4のある活性部Xの幅はあら
かじめ印刷パターンで調整しておく。
Next, on the front and back surfaces of the piezoelectric ceramic plate 2, electrodes 3,
4 was screen printed with a silver paste. At this time, as shown in FIG. 14A, the electrodes 3 and 4 formed on the upper surface in the figure are screen-printed in a predetermined stripe pattern 10 (a pattern in which a silver paste is not applied to inactive portions). Here, the width of the active portion X having the electrodes 3 and 4 is adjusted in advance by a printing pattern.

【0012】この印刷後、720℃にて焼付け、焼付け
後に、非活性部Y,Yを含めて、部分電極3,4が形成
された表裏全面を覆うように、上塗乾燥銀11を塗布し
(図14ロ参照)、80℃、35kV/cm で15分間、直
流電圧を印加して分極(矢線Ps)する。この分極後
に、表裏の上塗銀10を有機溶剤で洗浄して除去する。
その後、得られた大板素子(図14ハ参照)を、鎖線L
で示すように、短冊状に切断して圧電共振子1aを得
る。このときの切断寸法例は、直列共振子Sとして用い
られるものにあっては、長さ3.28×幅0.66×厚
0.495(mm)とし、並列共振子Pとして用いられ
るものにあっては、長さ3.49×幅1.00×厚0.
175(mm)とする。
After the printing, baking is performed at 720 ° C., and after baking, top coating dry silver 11 is applied so as to cover the entire front and back surfaces including the partial electrodes 3 and 4 including the inactive portions Y and Y ( A DC voltage is applied at 80 ° C. and 35 kV / cm for 15 minutes to polarize (arrow Ps). After this polarization, the front and back overcoated silver 10 is removed by washing with an organic solvent.
Thereafter, the obtained large plate element (see FIG.
The piezoelectric resonator 1a is obtained by cutting into a strip shape as shown in FIG. An example of the cut dimensions at this time is that the length used in the series resonator S is 3.28 × width 0.66 × thickness 0.495 (mm), and that the parallel resonator P is used. There is a length 3.49 x width 1.00 x thickness 0.
175 (mm).

【0013】而して、図1,2で示すように、表裏の主
面に電極3,4が形成されて、これを活性部Xとし、両
端部で、表裏面に電極3,4が形成されていず、これを
非活性部Y,Yとし、かつ全面に渡って、厚み方向に分
極された共振子S,Pが形成される。そして、この共振
子S,Pは図18で示す周波数濾波器に適用される。
As shown in FIGS. 1 and 2, electrodes 3 and 4 are formed on the front and back main surfaces, and these are used as active portions X. At both ends, electrodes 3 and 4 are formed on the front and back surfaces. The resonators S, P polarized in the thickness direction are formed over the entire surface as inactive portions Y, Y. The resonators S and P are applied to the frequency filter shown in FIG.

【0014】上述の手段により製造され、かつ上述の寸
法外径で切り出された、活性部Xの長さ割合の異なる多
数の試料を、共振周波数と反共振周波数との差Δf(kH
z ),100kHzでの静電容量Cf (pF),共振周波数fr
,周波数定数fr ×L(Hzm),反共振周波数fa ,周
波数定数fa ×L(Hzm ),圧電横効果の電気機械結合
係数K31,さらにQm につき夫々測定した。その結
果、表1,2のようになった。
A large number of samples manufactured by the above-described means and having different length ratios of the active portion X, which are cut out at the above-mentioned outer diameter, are subjected to a difference Δf (kH) between the resonance frequency and the anti-resonance frequency.
z), capacitance Cf (pF) at 100 kHz, resonance frequency fr
, Frequency constant fr × L (Hzm), antiresonant frequency fa, frequency constant fa × L (Hzm), electromechanical coupling coefficient K 31 of the piezoelectric transverse effect, and Qm. The results are as shown in Tables 1 and 2.

【0015】尚、左右部分の非活性部Y,Yの幅は、両
端からの寸法を等しくすることが望ましく、これが左右
不均一であるとΔfが若干低下することが、別途確認さ
れている。
It is desirable that the widths of the inactive portions Y, Y in the left and right portions are equal in dimension from both ends, and it is separately confirmed that Δf is slightly reduced when the width is nonuniform.

【0016】ここで、次の表1は、上述の構成からなる
直列共振子Sの活性部Xの長さ割合と各種特性の関係を
示す。
Here, Table 1 below shows the relationship between the length ratio of the active portion X of the series resonator S having the above-described configuration and various characteristics.

【0017】[0017]

【表1】 [Table 1]

【0018】次に、図3〜図7は、上述の結果を夫々グ
ラフとして、本発明に係る直列共振子Sにあって、活性
部Xの長さ割合と各種特性との関係を示すものである。
FIGS. 3 to 7 are graphs showing the above results, and show the relationship between the length ratio of the active portion X and various characteristics in the series resonator S according to the present invention. is there.

【0019】ここで、図3は、共振周波数fr と反共振
周波数fa との差Δfと活性部Xの長さ割合との関係を
示すグラフである。このグラフと表1から直列共振子と
して用いられる圧電共振子1aにあって、全長Lに対す
る活性部Xの長さlの割合(以下長さ割合という)を5
1.8〜86.99%としたものは、共振周波数と、反
共振周波数との差Δfが約28kHz以上となりであり
良好であり、特に、約58%以上ではΔfが約29kH
z以上となり優れた値を示し、周波数濾波器として適し
ていることが確認された。ちなみに、活性部の長さ割合
100%(表裏面に対し全面電極としたもの)は、Δf
は約26kHzであった。
FIG. 3 is a graph showing the relationship between the difference Δf between the resonance frequency fr and the anti-resonance frequency fa and the length ratio of the active portion X. From this graph and Table 1, in the piezoelectric resonator 1a used as a series resonator, the ratio of the length l of the active portion X to the total length L (hereinafter referred to as length ratio) is 5
In the case of 1.8 to 86.99%, the difference Δf between the resonance frequency and the anti-resonance frequency is about 28 kHz or more, which is good. In particular, when about 58% or more, Δf is about 29 kHz.
z or more, showing an excellent value, and it was confirmed that it was suitable as a frequency filter. Incidentally, the length ratio of the active portion of 100% (the front surface and the back surface are all electrodes) is Δf
Was about 26 kHz.

【0020】図4は、静電容量Cf(測定周波数f=10
0KHz)と活性部Xの長さ割合との関係を示すグラフであ
る。このグラフから、活性部Xの長さ割合が小さくなる
に従って、静電容量Cfが低減することが解る。ところ
で、直列共振子Sは、静電容量が小さいほうが良く、こ
のため、活性部Xの長さ割合が低下しても、問題がない
こととなる。
FIG. 4 shows the capacitance Cf (measured frequency f = 10
6 is a graph showing the relationship between the active portion X and the length ratio of the active portion X. This graph shows that the capacitance Cf decreases as the length ratio of the active portion X decreases. Incidentally, the smaller the capacitance of the series resonator S, the better. Therefore, even if the length ratio of the active portion X is reduced, there is no problem.

【0021】図5はQmと活性部Xの長さ割合との関係
を示すグラフである。このグラフから、活性部Xの長さ
割合が変化しても、その値に若干のバラツキはあるもの
の、全体としては、Qmには大きな変化がないことが解
る。
FIG. 5 is a graph showing the relationship between Qm and the length ratio of the active portion X. From this graph, it can be seen that, even when the length ratio of the active portion X changes, the value does not vary greatly, although the value slightly varies.

【0022】図6は周波数定数(fr ×L)と活性部X
の長さ割合との関係を示すグラフである。このグラフか
ら、周波数定数(fr ×L)は活性部Xの長さ割合減少
にともない漸減することが解る。ここで、L=一定であ
り、従って、このグラフは周波数fr の特性変化に対応
する。
FIG. 6 shows the frequency constant (fr × L) and the active portion X.
6 is a graph showing the relationship with the length ratio. From this graph, it can be seen that the frequency constant (fr × L) gradually decreases as the length ratio of the active portion X decreases. Here, L = constant, so this graph corresponds to the characteristic change of the frequency fr.

【0023】図7は電気機械結合係数K31と活性部X
の長さ割合との関係を示すグラフである。このグラフか
ら活性部Xの長さ割合が約73%で、電気機械結合係数
が最大となることが解る。
[0023] Figure 7 is an electromechanical coupling coefficient K 31 and the active portion X
6 is a graph showing the relationship with the length ratio. The ratio of the length of the active portion X from the graph of about 73%, the electromechanical coupling coefficient K 3 1 it can be seen that the maximum.

【0024】次の表2は、上述の構成からなる並列共振
子Pの活性部Xの長さ割合と各種特性の関係を示す。
Table 2 below shows the relationship between the length ratio of the active portion X of the parallel resonator P having the above configuration and various characteristics.

【0025】[0025]

【表2】 [Table 2]

【0026】図8〜図12は、並列共振子Pに用いるも
のに関する、上述の結果をグラフで示したものである。
ここで、図8は、Δfと活性部Xの長さ割合との関係を
示すグラフである。このグラフと表2から、並列共振子
として用いられるものにあって、活性部Xの長さ割合を
59.3〜79.9%としたものは、共振周波数と、反
共振周波数との差Δfが約23kHz以上と良好であ
り、特に、約71%以上ではΔfが約25kHz以上と
なって優れた値を示し、広帯域周波数濾波器として適し
ていることが確認された。ちなみに、活性部の長さ割合
100%(表裏面に対して全面電極としたもの)は、Δ
fが約22kHzであった。
FIGS. 8 to 12 are graphs showing the above-mentioned results for the parallel resonator P. FIG.
Here, FIG. 8 is a graph showing the relationship between Δf and the length ratio of the active portion X. From this graph and Table 2, the one used as the parallel resonator and having the length ratio of the active portion X of 59.3 to 79.9% is the difference Δf between the resonance frequency and the anti-resonance frequency. Is as good as about 23 kHz or more, and particularly at about 71% or more, Δf is about 25 kHz or more, showing an excellent value, and it was confirmed that the Δf is suitable as a broadband frequency filter. Incidentally, the length ratio of the active portion of 100% (the front surface and the back surface are all electrodes) is Δ
f was about 22 kHz.

【0027】図9は、静電容量Cf(測定周波数f=10
0KHz)と活性部Xの長さ割合との関係を示すものであ
る。このグラフから、活性部Xの長さ割合が小さくなる
に従って、Cfが低減することが解る。
FIG. 9 shows the capacitance Cf (measured frequency f = 10
0 KHz) and the length ratio of the active portion X. From this graph, it is understood that Cf decreases as the length ratio of the active portion X decreases.

【0028】図10はQmと活性部Xの長さ割合との関
係を示すものである。このグラフから、活性部Xの長さ
割合が変化しても、Qmには大きな変化がないことが解
る。
FIG. 10 shows the relationship between Qm and the length ratio of the active portion X. From this graph, it can be seen that Qm does not change significantly even when the length ratio of the active portion X changes.

【0029】図11は周波数定数fa ×Lと活性部Xの
長さ割合との関係を示すものである。このグラフから、
周波数定数fa ×Lは活性部Xの長さ割合が減少して
も、変化がないことが解る。
FIG. 11 shows the relationship between the frequency constant fa × L and the length ratio of the active portion X. From this graph,
It can be seen that the frequency constant fa × L does not change even if the length ratio of the active portion X decreases.

【0030】図12は電気機械結合係数K31と活性部
Xの長さ割合との関係を示すものである。このグラフか
ら活性部Xの長さ割合が69.3〜76.5%で、電気
機械結合係数K31が特に優れたものとなることが解
る。
FIG. 12 shows a relationship between the length ratio of the electromechanical coupling coefficient K 31 and the active portion X. The ratio of the length of the active portion X from the graph in 69.3 to 76.5%, it can be seen that the that the electromechanical coupling coefficient K 31 were particularly excellent.

【0031】このように、表1,2及び図3〜図12で
理解されるように、厚さの異なる直列共振子Sと並列共
振子Pとはいずれも、活性部Xの長さ割合との関係にお
いて、同様の特性を示し、非活性部Y,Yが増加し、活
性部Xの長さが減少することが解る。また、Qmは、活
性部Xの長さが100%(表裏面に対して全面電極)の
ときに比して大きな変化がなかった。
As can be understood from Tables 1 and 2 and FIGS. 3 to 12, the series resonators S and the parallel resonators P having different thicknesses each have the same length ratio as the active portion X. It can be seen that the same characteristic is exhibited, the non-active portions Y, Y increase, and the length of the active portion X decreases. Further, Qm did not change much as compared with the case where the length of the active portion X was 100% (the entire surface electrode on the front and back surfaces).

【0032】さらに、温度依存性を確認するために、共
振周波数fr 及び反共振周波数faにつき、活性部Xの
長さ割合を異ならした各試料に、−35℃〜85℃の温
度変化を付与し、その最大値と最小値の差を常温時の共
振周波数fr 及び反共振周波数fa と比較してみたとこ
ろ、0.2〜0.4%程度であり、活性部Xが100%
のときとほとんど変わらなかった。このことから、活性
部Xの長さ割合は、温度特性に変化を与えるものではな
いことを確認した。さらに耐熱性の指標としてリフロー
(230〜250℃)後の経時変化を調べたが、活性部
Xの長さに依存し、劣化するような知見は得られなかっ
た。
Further, in order to confirm the temperature dependence, a temperature change of -35 ° C. to 85 ° C. was applied to each sample having a different length ratio of the active portion X for the resonance frequency fr and the anti-resonance frequency fa. When the difference between the maximum value and the minimum value is compared with the resonance frequency fr at normal temperature and the anti-resonance frequency fa, it is about 0.2 to 0.4%, and the active portion X is 100%
It was almost the same as at the time. From this, it was confirmed that the length ratio of the active portion X did not change the temperature characteristics. Further, a change with time after reflow (230 to 250 ° C.) was examined as an index of heat resistance. However, it was not found that deterioration depending on the length of the active portion X was caused.

【0033】而して、短冊状共振子にあって、これら
は、電界方向及び分極方向が振動方向と異なる圧電横効
果を利用しており、このため、電界方向及び分極方向が
振動方向と一致する圧電縦効果を利用した圧電共振子に
比して、電気機械結合係数が低く、共振周波数frと、
反共振周波数faとの差であるΔfが比較的小さく、周
波数濾波器に用いた場合に、帯域幅が狭くなるという問
題を生じていたが、以上の実験で確認されたように、短
冊状圧電共振子1の両側に、非活性部Y,Yを形成する
ことによりΔfが増加するため、上述の欠点を補うこと
ができることとなる。
Thus, the strip-shaped resonators utilize a piezoelectric transverse effect in which the direction of the electric field and the direction of polarization are different from the direction of vibration, and therefore, the direction of the electric field and the direction of polarization match the direction of vibration. Electromechanical coupling coefficient is lower than a piezoelectric resonator using the piezoelectric longitudinal effect, and the resonance frequency fr
The difference Δf, which is the difference from the anti-resonance frequency fa, is relatively small, and when used in a frequency filter, there has been a problem that the bandwidth is narrowed. By forming the non-active portions Y, Y on both sides of the resonator 1, Δf increases, so that the above-mentioned disadvantage can be compensated.

【0034】一方、図15,16は、圧電磁器板の、そ
の両端部にテーパ状の非活性部Y,Yを形成した構成し
た短冊状圧電共振子1bを示す。
15 and 16 show a strip-shaped piezoelectric resonator 1b in which a piezoelectric ceramic plate is formed with tapered inactive portions Y, Y at both ends.

【0035】かかる短冊状圧電共振子1bの製造手段を
図17のフローチャートで説明する。ここで、上記実施
例と異なる点は、圧電磁器組成に、Pb{(Sb1/2
Nb1/20.01(Cr1/2 Nb1/2
0.04Zr0.49Ti .46}O に代えて、
Pb{(C 1/3 Nb2/30.1 Zr0.
441 Ti0.459 }O +1.0 重力%Sb
で表される組成式のものを用い、また成形にプレス
成形法に代えて、混練物の押出成形を用いたことにあ
る。圧電磁器板2の形成以降の過程にあって、圧電磁器
板2の表裏面には、全面に渡って、電極3,4を形成す
る。そして、電極3,4間に、80℃、35KV/cm で1
5分間、直流電圧を印加して分極(矢線Ps)する。
The manufacturing method of the strip-shaped piezoelectric resonator 1b will be described with reference to the flowchart of FIG. Here, the difference from the above embodiment is that the piezoelectric ceramic composition has PbP (Sb 1/2
Nb 1/2 ) 0.01 (Cr 1/2 Nb 1/2 )
0.04 Zr 0.49 Ti 0 . Instead of the 46} O 3,
Pb {(C 0 1/3 Nb 2/3 ) 0.1 Zr 0.
441 Ti 0.459 } O 3 +1.0 Gravity% Sb 2 O
Used as a composition formula represented by 3 and instead of the press molding for molding, lies in using the extrusion molding of the kneaded material. In the process after the formation of the piezoelectric ceramic plate 2, the electrodes 3 and 4 are formed on the front and back surfaces of the piezoelectric ceramic plate 2 over the entire surface. Then, between the electrodes 3 and 4, 1 at 80 ° C. and 35 KV / cm.
Polarization (arrow Ps) is performed by applying a DC voltage for 5 minutes.

【0036】この分極後に大板素子(図14ハ参照)
を、鎖線Lで示すように、短冊状に切断する。このとき
の切断寸法例は、図13と同様に、直列共振子Sとして
用いられるものにあっては、長さ3.28×幅0.66
×厚0.595(mm)とし、並列共振子Pとして用い
られるものにあっては、長さ3.49×幅1.00×厚
0.175(mm)とする。
After this polarization, a large plate element (see FIG. 14C)
Is cut into strips as shown by a chain line L. An example of the cut size at this time is, as in FIG. 13, the length used for the series resonator S is 3.28 × width 0.66.
× thickness 0.595 (mm), and for a parallel resonator P, the length is 3.49 × width 1.00 × thickness 0.175 (mm).

【0037】そして、このように得られた短冊状素子の
両端部を、表裏から電極3,4を含めてテーパ状に削成
し、該両側にテーパ状非活性部Y,Yを形成し、而し
て、図15,16の短冊状圧電共振子1bが構成され
る。
Then, both ends of the strip-shaped element thus obtained are cut into a tapered shape including the electrodes 3 and 4 from the front and back, and tapered inactive portions Y and Y are formed on both sides. Thus, the strip-shaped piezoelectric resonator 1b shown in FIGS.

【0038】かかる構成にあっては、その製造手段で明
らかなように、圧電磁器板2の表裏全面に電極3,4を
形成して、分極し、これを切り出した後、短冊状素子の
両端部で表裏を傾斜状に削って、電極3,4を除去する
ことにより非活性部Y,Yを形成したものであるから、
その製造過程において、分極用の電極を表裏全面に形成
した電極3,4をそのまま用いることができ、上塗乾燥
銀の塗布とその除去を要しない利点がある。
In this configuration, as is apparent from the manufacturing method, the electrodes 3 and 4 are formed on the entire front and back surfaces of the piezoelectric ceramic plate 2, polarized, cut out, and then cut at both ends of the strip-shaped element. Since the inactive portions Y and Y are formed by shaving the front and back sides of the portion in an inclined manner and removing the electrodes 3 and 4,
In the manufacturing process, the electrodes 3 and 4 in which the electrodes for polarization are formed on the entire front and back surfaces can be used as they are, and there is an advantage that it is not necessary to apply and remove dry silver on top coat.

【0039】上述の手段により製造した、直列共振子S
にあって、そのテーパ状非活性部Y,Yの稜角θ=60
°とした試料を、共振周波数と反共振周波数との差Δf
(kHz ),100KHzでの静電容量Cf (pF),共振周波数
fr ,周波数定数fr ×L(Hzm ),反共振周波数fa
,周波数定数fa ×L(Hzm ),圧電横効果の電気機
械結合係数K31,さらにQm につき、夫々測定した。
The series resonator S manufactured by the means described above
And the ridge angle θ of the tapered inactive portions Y, Y = 60
° and the difference Δf between the resonance frequency and the anti-resonance frequency.
(KHz), capacitance Cf (pF) at 100 KHz, resonance frequency fr, frequency constant fr × L (Hzm), antiresonance frequency fa
, The frequency constant fa × L (Hzm), the electromechanical coupling coefficient K 31 of the transverse piezoelectric effect, and the Qm.

【0040】表3は、その特性値を示すものである。こ
こで、表中「従来例」とは、上述した短冊状素子の両端
部に非活性部Y,Yを削成する前の素子の特性を示した
ものである。
Table 3 shows the characteristic values. Here, "conventional example" in the table shows the characteristics of the element before the inactive portions Y, Y are formed at both ends of the strip-shaped element described above.

【0041】[0041]

【表3】 [Table 3]

【0042】上述の試料の出力波形を別途調べたとこ
ろ、副共振(スプリアス)が発生することなく、整った
共振波形を示していることが確認された。
When the output waveform of the above-mentioned sample was separately examined, it was confirmed that the sample exhibited a well-balanced resonance waveform without occurrence of a subresonance (spurious).

【0043】上述したように、図15,16のテーパ状
の非活性部Y,Yを備えた構成にあっても、上述の図
1,2の構成と同様に、共振周波数fr と、反共振周波
数faとの差Δfが向上し、さらには、電気機械結合係
数K31も向上した。このため広帯域の周波数濾波器と
して適していることが確認された。
As described above, even in the configuration having the tapered non-active portions Y, Y shown in FIGS. 15 and 16, the resonance frequency fr and the anti-resonance improved difference Δf between the frequency fa is further electromechanical coupling coefficient K 31 was also improved. Therefore, it was confirmed that the filter was suitable as a broadband frequency filter.

【0044】[0044]

【発明の効果】本発明は、短冊状の圧電磁器板の全面に
わたって厚さ方向に分極されたものにあって、圧電共振
子の両側部に表裏に電極の無い非活性部Y,Yを形成し
たものであり、これにより、共振周波数と、反共振周波
数との差Δfが向上した。
According to the present invention, the strip-shaped piezoelectric ceramic plate is polarized in the thickness direction over the entire surface, and non-active portions Y, Y having no electrodes are formed on both sides of the piezoelectric resonator. As a result, the difference Δf between the resonance frequency and the anti-resonance frequency was improved.

【0045】このため、この短冊状圧電共振子を直列共
振子及び並列共振子に適用した場合に、これらは、電界
方向及び分極方向が振動方向と異なる圧電横効果を利用
しており、このため、電気機械結合係数K31が低く、
共振周波数frと、反共振周波数faとの差であるΔf
が比較的小さいとされていたが、両側部に非活性部を形
成することにより、広帯域の周波数濾波器に用いられる
短冊状圧電共振子の欠点を改善することができ、周波数
濾波器の帯域幅を広くすることができる。しかも、表裏
面の電極の端部を省略するだけで、容易に非活性部を形
成でき、このため、製造が容易であり、従って、簡便に
周波数濾波器特性の向上を図ることができる。
For this reason, when this strip-shaped piezoelectric resonator is applied to a series resonator and a parallel resonator, they use a piezoelectric transverse effect in which the direction of electric field and the direction of polarization are different from the direction of vibration. , the electromechanical coupling coefficient K 31 is low,
Δf which is the difference between the resonance frequency fr and the anti-resonance frequency fa
Was relatively small, but by forming inactive portions on both sides, it was possible to improve the disadvantages of the strip-shaped piezoelectric resonator used in a wide-band frequency filter, and to reduce the bandwidth of the frequency filter. Can be widened. Moreover, the inactive portion can be easily formed only by omitting the end portions of the electrodes on the front and back surfaces, and therefore, the manufacture is easy, and therefore, the frequency filter characteristics can be easily improved.

【図面の簡単な説明】[Brief description of the drawings]

【図1】本発明に係る短冊状圧電共振子1aの斜視図で
ある。
FIG. 1 is a perspective view of a strip-shaped piezoelectric resonator 1a according to the present invention.

【図2】短冊状圧電共振子1aの縦断側面図である。FIG. 2 is a longitudinal sectional side view of a strip-shaped piezoelectric resonator 1a.

【図3】直列共振子Sに用いられる圧電共振子1aにお
いて、Δfと活性部の長さ割合を示すグラフ
FIG. 3 is a graph showing Δf and a length ratio of an active portion in the piezoelectric resonator 1a used for the series resonator S.

【図4】直列共振子Sに用いられる圧電共振子1aにお
いて、100KHzでの静電容量Cfと活性部の長さ割合を示
すグラフ
FIG. 4 is a graph showing the capacitance Cf at 100 KHz and the length ratio of the active portion in the piezoelectric resonator 1a used for the series resonator S.

【図5】直列共振子Sに用いられる圧電共振子1aにお
いて、Qm と活性部の長さ割合を示すグラフ
FIG. 5 is a graph showing Qm and a length ratio of an active portion in the piezoelectric resonator 1a used for the series resonator S.

【図6】直列共振子Sに用いられる圧電共振子1aにお
いて、周波数定数(fr ×L)と活性部の長さ割合を示
すグラフ
FIG. 6 is a graph showing a frequency constant (fr × L) and a length ratio of an active portion in the piezoelectric resonator 1a used for the series resonator S;

【図7】直列共振子Sに用いられる圧電共振子1aにお
いて、電気機械結合係数K31と活性部の長さ割合を示
すグラフ
[7] In the piezoelectric resonator 1a used in the series resonator S, the graph showing the length ratio of the electromechanical coupling coefficient K 31 and the active portion

【図8】並列共振子Pに用いられる圧電共振子1aにお
いて、Δfと活性部の長さ割合を示すグラフ
FIG. 8 is a graph showing Δf and a length ratio of an active portion in the piezoelectric resonator 1a used for the parallel resonator P.

【図9】並列共振子Pに用いられる圧電共振子1aにお
いて、静電容量Cf と活性部の長さ割合を示すグラフ
FIG. 9 is a graph showing the capacitance ratio between the capacitance Cf and the length of the active portion in the piezoelectric resonator 1a used for the parallel resonator P.

【図10】並列共振子Pに用いられる圧電共振子1aに
おいて、Qm と活性部の長さ割合を示すグラフ
FIG. 10 is a graph showing Qm and a length ratio of an active portion in the piezoelectric resonator 1a used for the parallel resonator P.

【図11】並列共振子Pに用いられる圧電共振子1aに
おいて、周波数定数(fa ×L)と活性部の長さ割合を
示すグラフ
FIG. 11 is a graph showing a frequency constant (fa × L) and a length ratio of an active portion in the piezoelectric resonator 1a used for the parallel resonator P.

【図12】並列共振子Pに用いられる圧電共振子1aに
おいて、電気機械結合係数K31と活性部の長さ割合を
示すグラフ
[12] In the piezoelectric resonator 1a for use in the parallel resonator P, a graph showing the length ratio of the electromechanical coupling coefficient K 31 and the active portion

【図13】製法を示すフローチャート図である。FIG. 13 is a flowchart showing a manufacturing method.

【図14】分極手段を示す説明図である。FIG. 14 is an explanatory view showing a polarization means.

【図15】本発明の他の構成に係る短冊状圧電共振子1
bの斜視図である。
FIG. 15 shows a strip-shaped piezoelectric resonator 1 according to another configuration of the present invention.
It is a perspective view of b.

【図16】短冊状圧電共振子1bの縦断側面図である。FIG. 16 is a longitudinal sectional side view of a strip-shaped piezoelectric resonator 1b.

【図17】短冊状圧電共振子1bの製法を示すフローチ
ャート図である。
FIG. 17 is a flowchart showing a method of manufacturing the strip-shaped piezoelectric resonator 1b.

【図18】短冊状圧電共振子からなる並列共振子P及び
直列共振子Sを用いた周波数濾波回路図である。
FIG. 18 is a circuit diagram of a frequency filtering circuit using parallel resonators P and series resonators S made of strip-shaped piezoelectric resonators.

【符号の説明】 1a,1b 短冊状圧電共振子 2 圧電磁器板 3 電極 4 電極 X 活性部 Y,Y 非活性部 S 直列共振子 P 並列共振子[Description of Signs] 1a, 1b Strip-shaped piezoelectric resonator 2 Piezoelectric ceramic plate 3 Electrode 4 Electrode X Active part Y, Y Non-active part S Series resonator P Parallel resonator

─────────────────────────────────────────────────────
────────────────────────────────────────────────── ───

【手続補正書】[Procedure amendment]

【提出日】平成10年10月21日(1998.10.
21)
[Submission date] October 21, 1998 (1998.10.
21)

【手続補正1】[Procedure amendment 1]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図3[Correction target item name] Figure 3

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図3】 FIG. 3

【手続補正2】[Procedure amendment 2]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図4[Correction target item name] Fig. 4

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図4】 FIG. 4

【手続補正3】[Procedure amendment 3]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図5[Correction target item name] Fig. 5

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図5】 FIG. 5

【手続補正4】[Procedure amendment 4]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図6[Correction target item name] Fig. 6

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図6】 FIG. 6

【手続補正5】[Procedure amendment 5]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図7[Correction target item name] Fig. 7

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図7】 FIG. 7

【手続補正6】[Procedure amendment 6]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図8[Correction target item name] Fig. 8

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図8】 FIG. 8

【手続補正7】[Procedure amendment 7]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図9[Correction target item name] Fig. 9

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図9】 FIG. 9

【手続補正8】[Procedure amendment 8]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図10[Correction target item name] FIG.

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図10】 FIG. 10

【手続補正9】[Procedure amendment 9]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図11[Correction target item name] FIG.

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図11】 FIG. 11

【手続補正10】[Procedure amendment 10]

【補正対象書類名】図面[Document name to be amended] Drawing

【補正対象項目名】図12[Correction target item name] FIG.

【補正方法】変更[Correction method] Change

【補正内容】[Correction contents]

【図12】 FIG.

───────────────────────────────────────────────────── フロントページの続き (72)発明者 平光 秀明 名古屋市瑞穂区高辻町14番18号 日本特殊 陶業株式会社内 (72)発明者 尾関 博文 名古屋市瑞穂区高辻町14番18号 日本特殊 陶業株式会社内 Fターム(参考) 5J108 AA07 BB04 CC04 CC05 CC13 KK07  ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Hideaki Hiramitsu 14-18 Takatsuji-cho, Mizuho-ku Nagoya-shi Inside Japan Special Ceramics Co., Ltd. (72) Inventor Hirofumi Ozeki 14-18 Takatsuji-cho Mizuho-ku Nagoya-shi Co., Ltd. F-term (reference) 5J108 AA07 BB04 CC04 CC05 CC13 KK07

Claims (4)

【特許請求の範囲】[Claims] 【請求項1】全面にわたって厚さ方向に分極され、かつ
表裏の主面に電極を備えると共に、その両端部の表裏で
電極を除くことにより、該両端部に非活性部を形成して
なることを特徴とする周波数濾波器に用いられる短冊状
圧電共振子。
An inactive portion is formed at both ends by being polarized in the thickness direction over the entire surface and having electrodes on the front and back main surfaces, and removing the electrodes on the front and back of both ends. A strip-shaped piezoelectric resonator used for a frequency filter characterized by the following.
【請求項2】直列共振子として用いられるものにあっ
て、前記活性部の長さが全長に対して51.8〜86.
9%であることを特徴とする請求項1記載の周波数濾波
器に用いられる短冊状圧電共振子。
2. A device used as a series resonator, wherein the length of the active portion is 51.8 to 86.
The strip-shaped piezoelectric resonator used in the frequency filter according to claim 1, wherein the frequency is 9%.
【請求項3】並列共振子として用いられるものにあっ
て、前記活性部の長さが全長に対して59.3〜79.
9%であることを特徴とする請求項1記載の周波数濾波
器に用いられる短冊状圧電共振子。
3. A resonator used as a parallel resonator, wherein the length of the active portion is 59.3 to 79.
The strip-shaped piezoelectric resonator used in the frequency filter according to claim 1, wherein the frequency is 9%.
【請求項4】圧電磁器板の両端部を、表裏で入出力電極
を含めてテーパ状に削って形成された非活性部を備える
ことを特徴とする請求項1記載の周波数濾波器に用いら
れる短冊状圧電共振子。
4. The frequency filter according to claim 1, further comprising an inactive portion formed by tapering both ends of the piezoelectric ceramic plate including the input / output electrodes on both sides thereof. Strip-shaped piezoelectric resonator.
JP10298732A 1998-10-20 1998-10-20 Strip-shaped piezoelectric resonator for frequency filter Pending JP2000124764A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP10298732A JP2000124764A (en) 1998-10-20 1998-10-20 Strip-shaped piezoelectric resonator for frequency filter

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP10298732A JP2000124764A (en) 1998-10-20 1998-10-20 Strip-shaped piezoelectric resonator for frequency filter

Publications (1)

Publication Number Publication Date
JP2000124764A true JP2000124764A (en) 2000-04-28

Family

ID=17863559

Family Applications (1)

Application Number Title Priority Date Filing Date
JP10298732A Pending JP2000124764A (en) 1998-10-20 1998-10-20 Strip-shaped piezoelectric resonator for frequency filter

Country Status (1)

Country Link
JP (1) JP2000124764A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20040033094A (en) * 2002-10-11 2004-04-21 제원전자 주식회사 Quartz crystal base manufacturing method
CN103975525A (en) * 2011-09-30 2014-08-06 高通Mems科技公司 Cross-sectional dilation mode resonators
US10003888B2 (en) 2011-11-29 2018-06-19 Snaptrack, Inc Transducer with piezoelectric, conductive and dielectric membrane

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20040033094A (en) * 2002-10-11 2004-04-21 제원전자 주식회사 Quartz crystal base manufacturing method
CN103975525A (en) * 2011-09-30 2014-08-06 高通Mems科技公司 Cross-sectional dilation mode resonators
JP2014529274A (en) * 2011-09-30 2014-10-30 クォルコム・メムズ・テクノロジーズ・インコーポレーテッド Cross-sectional expansion mode resonator
US9270254B2 (en) 2011-09-30 2016-02-23 Qualcomm Mems Technologies, Inc. Cross-sectional dilation mode resonators and resonator-based ladder filters
US10003888B2 (en) 2011-11-29 2018-06-19 Snaptrack, Inc Transducer with piezoelectric, conductive and dielectric membrane
US10735865B2 (en) 2011-11-29 2020-08-04 Snaptrack, Inc. Transducer with piezoelectric, conductive and dielectric membrane

Similar Documents

Publication Publication Date Title
JP3259678B2 (en) Piezoelectric ceramic composition
JP3282576B2 (en) Piezoelectric ceramic composition
US7245060B2 (en) Piezoelectric resonator, method for manufacturing the same, piezoelectric filter, and duplexer
JP3733860B2 (en) Piezoelectric element and manufacturing method thereof
US5057801A (en) Filter device of piezo-electric type including divided co-planar electrodes
JPH11308070A (en) Piezoelectric body element
JP2000124764A (en) Strip-shaped piezoelectric resonator for frequency filter
JP3562402B2 (en) Piezoelectric ceramic material and surface wave device using the same
GB2350478A (en) Piezoelectric device
JP3733861B2 (en) Method for polarizing laminated piezoelectric material
JP4449331B2 (en) Piezoelectric ceramic and piezoelectric ceramic element using the same
JPH05327397A (en) Saw device
JP2000114914A (en) Thin strip-shaped piezo-resonator used for frequency filter
JP2000134061A (en) Piezoelectric resonator used for frequency filter
JPH0993078A (en) Piezoelectric device
JP3639994B2 (en) Energy confinement type piezoelectric vibrator of thickness longitudinal vibration fundamental wave and manufacturing method thereof
JP3646619B2 (en) Piezoelectric ceramic composition and piezoelectric ceramic element using the same
JPH05139824A (en) Piezoelectric ceramic composition
JP4479089B2 (en) Piezoelectric ceramic composition and piezoelectric ceramic element using the same
JP2881251B2 (en) Piezoelectric resonator
JPH0763129B2 (en) Method for manufacturing piezoelectric ceramic resonator
JPH05267744A (en) Polarization of piezoelectric ceramic
JP2000216451A (en) Manufacture of piezoelectric element for filter
JP3301901B2 (en) Piezoelectric resonator
JP3111564B2 (en) Piezoelectric ceramic composition