JP3964078B2 - Distributed constant filter - Google Patents

Description

【００３４】
と表わされる。ここで分母有理多項式ｇ（ｓ）は群遅延特性が平坦である多項式とし、例えばベッセルの多項式等とする。
【００３５】
次に、この分母有理多項式の振幅特性を、群遅延特性に悪影響を与えることなく分子有理多項式で補正するとともに、分子有理多項式の虚根の組により、阻止帯域に伝送零点を設ける。さらに、振幅特性が通過帯域でできるだけ平坦となるように、分子有理多項式の実根の組で振幅特性の補正を行なう。このようにして、分母有理多項式および目的とするフィルタ特性に対応して分子有理多項式が定まる。
【００３６】
そして、このようにして定まった多項式から、図３に回路図の例を示すような、基準化低域通過フィルタが定まる。この基準化低域通過フィルタにおいては、並列あるいは直列のはしご型の接続の段数がフルビッツ多項式の次数に相当し、この例では６段である。また、直列に接続された２つの並列共振回路は、分子有理多項式のそれぞれ実根および虚根の組に相当する回路部である。
【００３７】
これら実根および虚根の組に相当する回路部のうち、虚根の組に相当する直列共振回路の回路素子は共に正の値であり、実際の回路で実現可能である。一方、実根の組に相当する並列共振回路の回路素子はどちらか一方が負の値となり、このままでは実際の回路として実現することはできない。
【００３８】
そこで、次に、多重結合回路部への等価変換を行なう。すなわち、図３に示した回路を、虚ジャイレータを用いて図４に示すような回路への等価変換を行なう。そして、この図４に示した回路の中で、虚ジャイレータを含む２つの並列共振回路を含む部分に着目して、図５（ａ）に示すような回路を扱う。この回路に対して、同図（ｂ）に示すように、虚ジャイレータを５つ含む回路を考えると、これら（ａ）および（ｂ）に示した回路は、互いのパラメータを適切に置き換えることにより両者が等価となることが分かる。なお、図５（ｂ）中のＬおよびＣはそれぞれ回路素子がインダクタンスおよび容量であることを示し、その値は示していない。また同様に、ｊは虚ジャイレータを示し、その値は示していない。また、虚ジャイレータｊの符号は特に示していない場合は、＋または−のある定数の値を持つ虚ジャイレータであるものとする。これらは以下の図６〜図８においても同様である。
【００３９】
これらの結果、図３に示した基準化低域通過フィルタは、図４および図５の等価変換を経て、図６に示すような等価な基準化低域通過フィルタに変換される。
【００４０】
この図６に示す等価な基準化低域通過フィルタに、さらに虚ジャイレータと理想トランスを導入し、回路素子をすべて並列の同じ値の容量に等価変換することにより、図７に示すような等価基準化低域通過フィルタが得られる。この図７に示す等価基準化低域通過フィルタは、図３に示した基準化低域通過フィルタと厳密に全く等価なものである。なお、この等価変換を行なった段階での虚ジャイレータの符号は図７に示す通りの複合の取り方の自由度がある。
【００４１】
次に、この基準化低域通過フィルタを、周波数変換およびインピーダンス変換して、目的の帯域通過特性を有する帯域通過フィルタへ変換する。このとき、図７の回路中の容量は周波数変換により並列共振回路となるが、虚ジャイレータは変化せずにそのままとなる。この際、フィルタの入力端と出力端の対称性をよくするため、出力端に理想トランスを含む虚ジャイレータを挿入してある。この虚ジャイレータを挿入することで、出力端におけるフィルタの出力インピーダンスが出力アドミッタンスに変換されるが、フィルタの振幅特性・群遅延特性等の伝送特性は変わらない。これにより、図８に示すような帯域通過フィルタが得られる。
【００４２】
さらに、虚ジャイレータをπ型の定リアクタンス素子の接続で実現すると、目的の帯域通過フィルタは図９に示すような回路構成となる。この帯域通過フィルタにおいて、結合回路の定リアクタンス素子は、通過帯域近辺での狭帯域近似により、電界結合または磁界結合で実現できる。
【００４３】
ここで、同図中の17・18・19・20・21・23・24の７個の結合回路の定リアクタンス素子と、11・12・13・14の４つの共振回路（共振子）とを１つの多重結合回路部とする。そして、17は第１共振子11とその外側の回路とをカスケード接続する第１結合回路、18は第１共振子11と第２共振子12とをカスケード接続する第２結合回路、19は第２共振子12と第３共振子13とをカスケード接続する第３結合回路、20は第３共振子13と第４共振子14とをカスケード接続する第４結合回路、21は第４共振子14と外側の回路とをブリッジ接続する第５結合回路、22は第２結合回路18と第４結合回路20の外側をブリッジ結合する第６結合回路、23は第１結合回路17と第５結合回路21の外側をブリッジ接続する第７結合回路である。
【００４４】
これら第１結合回路17〜第７結合回路23および第１共振子11〜第４共振子14で実現された多重結合回路部によって数１で示した式における分子有理多項式ｆ（ｓ）の１組の実根および１組の虚根に相当する回路部分を実現するには、定リアクタンス素子で実現されている第１結合回路17〜第７結合回路23の符号の組合せは、次のａ〜ｄの組合せとなる。
ａ：第６および第７結合回路22・23がともに負符号（−）であり、第１〜第５結合回路17〜21はその内の１または３個が正符号（＋）で残りが負符号である
。
ｂ：第６および第７結合回路22・23がともに正符号であり、第１〜第５結合回路 17〜21はその内の２または４個が正符号で残りが負符号である。
ｃ：第６結合回路22が負符号、第７結合回路23が正符号であり、第１〜第５結合回路17〜21はその内の０または２または４個が正符号で残りが負符号である。
ｄ：第６結合回路22が正符号、第７結合回路23が負符号であり、第１〜第５結合回路17〜21はその内の１または３または５個が正符号で残りが負符号である。
【００４５】
第１結合回路17〜第７結合回路23の符号の組合せがこのようなａ〜ｄの組合せとなるのは、前記多項式を実現する第１結合回路17から第７結合回路23の電界結合あるいは磁界結合の組合せは等価変換により決められ、その組合せは、電界結合を（−）で、磁界結合を（＋）で表記すると、表１に示す20通りとなることによるものである。
【００４６】
【表１】

【００４７】
この帯域通過フィルタにおける各結合回路17〜23の定リアクタンス素子は、通過帯域近辺での狭帯域近似により、負符号または正符号の定リアクタンス素子がそれぞれ電界結合または磁界結合、あるいは容量またはインダクタで実現することができる。
【００４８】
次に、狭帯域近似を行なった結果得られた帯域通過フィルタの回路の実施例の回路図を図１に示す。この例は、第６結合回路22が負符号、第７結合回路23が正符号であり、第１〜第５結合回路17〜21が負符号である上記ｃの組合せを選んだ例である。
【００４９】
さらに、本発明の分布定数フィルタについて、図１に示した帯域通過フィルタの実施例を分布定数フィルタで実現した構成例を図２に平面図で示す。
【００５０】
図２に示す本発明の分布定数フィルタの構成例は誘電体基板上に分布定数回路素子としての導体パターンで形成されており、この例においては、６個の円形の共振子40〜45がＥ₁₁₀ モードで使用されている。
【００５１】
このような本発明の分布定数フィルタにおいて、図２中の結合部48〜56は図１中の多重結合回路部の第１〜第７結合回路31〜39に、図２中の共振子40〜45は図１中の共振回路（共振子）25〜30にそれぞれ対応するものである。そして、各共振子40〜45の共振モードがＥ₂₁₀ モードの場合、図２中に示すように、それぞれの共振子の外周の周りに90度おきに電界最大点があり、この部分で電界結合ができる。また、電界最大点の中間点すなわち電界最大点から45度ずつずれた点の位置に磁界最大点があり、この部分で磁界結合ができる。なお、図２において導体パターンで形成された各共振子40〜45中に示す矢印を付した曲線は図の紙面に平行な磁界の向きを表し、それらの内側の・印および×印はそれぞれ図の紙面に垂直な電界の向きを表している。このような配置を利用して、図２に示すように、６つの共振子40〜45を結合させた目的の帯域通過フィルタとしての分布定数フィルタを構成することができる。そして、図２では48〜54・56が電界結合、55が磁界結合となっている。
【００５２】
このような本発明の分布定数フィルタによれば、図１に示したような正確な等価回路の帯域通過フィルタを各素子毎に正確に図２に示した導体パターンとして実現できることから、正確な設計手法により設計して簡単な回路で構成して実現することができるとともに、与えられた特性に対して最少の素子数・パターン数でフィルタを構成できることから、低素子感度で低損失な特性の分布定数フィルタとなる。
【００５３】
しかも、本発明の分布定数フィルタによれば、分子多項式の次数の増加に対し、分母多項式の次数の増加が同じ次数で済むことから、特願平11−150150号における提案よりも、与えられた数の共振子で実現できる分子有理多項式の次数をより多くすることができ、複雑な特性のフィルタを実現する上での制約が少なくて済むという、実用上極めて有用な分布定数フィルタとなる。
【００５４】
なお、以上はあくまでも本発明の実施の形態の例示であり、本発明はこれらに限定されるものではなく、本発明の要旨を逸脱しない範囲で種々の変更や改良を加えることは何ら差し支えない。例えば、分布定数フィルタを構成する共振子の導体パターンには、他の形状の共振器パターンを用いてもよい。また、図２に示した実施例における電界結合と磁界結合との組合せを、前記ａ〜ｄに対応したＡ〜Ｄの他の組合せとしてもよい。
【００５５】
【発明の効果】
以上により、本発明によれば、複素周波数ｓの偶関数であって少なくとも１組の実根および少なくとも１組の虚根を持つ分子有理多項式と複素周波数ｓの６次以上のフルビッツ多項式である分母有理多項式とから成る回路網関数で伝達関数が表わされた基準化低域通過フィルタを周波数変換することにより得られ、不平衡分布定数回路で実現された、周波数帯域通過特性を有する分布定数フィルタであって、前記分子有理多項式の１組の実根および１組の虚根ならびにそれらに対応する前記分母有理多項式に相当する回路部は、第１〜第４共振子と、前記第１共振子とその外側の回路とをカスケード結合する第１結合回路と、前記第１共振子と第２共振子とをカスケード結合する第２結合回路と、前記第２共振子と第３共振子とをカスケード結合する第３結合回路と、前記第３共振子と第４共振子とをカスケード結合する第４結合回路と、前記第４共振子とその外側の回路とをカスケード結合する第５結合回路と、前記第２結合回路と第４結合回路の外側をブリッジ結合により結合する第６結合回路と、前記第１結合回路と第５結合回路の外側をブリッジ結合により結合する第７結合回路とから成る多重結合回路部を１つ以上有する多共振子フィルタで実現されており、前記第１〜第７結合回路は、下記Ａ〜Ｄの電界結合と磁界結合との組合せ、すなわち
Ａ：前記第６および第７結合回路が電界結合であり、前記第１〜第５結合回路はその内の１または３個が磁界結合で残りが電界結合である。
Ｂ：前記第６および第７結合回路が磁界結合であり、前記第１〜第５結合回路はその内の２または４個が磁界結合で残りが電界結合である。
Ｃ：前記第６結合回路が電界結合、第７結合回路が磁界結合であり、前記第１〜第５結合回路はその内の０または２または４個が磁界結合で残りが電界結合である。
Ｄ：前記第６結合回路が磁界結合、第７結合回路が電界結合であり、前記第１〜第５結合回路はその内の１または３または５個が磁界結合で残りが電界結合である。
【００５６】
としたことにより、通過帯域の振幅特性および群遅延特性が同時平坦特性で、かつ阻止帯域に伝送零点を持つ周波数帯域通過特性を有し、正確な設計手法により設計して簡単な回路で構成して実現することができるとともに、複雑な特性のフィルタを実現する上での制約がなく、共振子間における意図しない結合を抑制して寄生的な特性劣化を抑制した、低素子感度で低損失な特性の分布定数フィルタを提供することができた。
【図面の簡単な説明】
【図１】本発明による帯域通過フィルタの実施例を示す回路図である。
【図２】図１に示す帯域通過フィルタの実施例を分布定数フィルタで実現した構成例を示す平面図である。
【図３】本発明における基準化低域通過フィルタの例を示す回路図である。
【図４】本発明における等価変換した基準化低域通過フィルタの例を示す回路図である。
【図５】（ａ）および（ｂ）は本発明における基準化低域通過フィルタに対する等価変換の例を示す回路図である。
【図６】本発明における等価変換した基準化低域通過フィルタの例を示す回路図である。
【図７】本発明における等価変換した基準化低域通過フィルタの例を示す回路図である。
【図８】本発明における等価変換した帯域通過フィルタの例を示す回路図である。
【図９】本発明による帯域通過フィルタの構成例を示す回路図である。
【図１０】（ａ）および（ｂ）はそれぞれ帯域通過フィルタの通過帯域における振幅特性および群遅延特性を示す線図である。
【図１１】従来の帯域通過フィルタの構成例を示すブロック図である。
【図１２】従来のフィルタの阻止帯域における伝送零点を実現するための構成例を示す回路図である。
【図１３】従来のフィルタの阻止帯域における伝送零点を実現するための構成例を示すブロック図である。
【図１４】従来のフィルタの阻止帯域における伝送零点を実現するための構成例を示す回路図である。
【符号の説明】
17、32、49・・・・・第１結合回路
18、33、50・・・・・第２結合回路
19、34、51・・・・・第３結合回路
20、35、52・・・・・第４結合回路
21、36、53・・・・・第５結合回路
22、37、54・・・・・第６結合回路
23、38、55・・・・・第７結合回路
11、25、41・・・・・第１共振子
12、26、42・・・・・第２共振子
13、27、43・・・・・第３共振子
14、28、44・・・・・第４共振子[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a distributed constant filter used as a band-pass filter in an RF stage of a mobile communication device or the like for removing interference signals and noise. More specifically, the amplitude characteristics and group delay characteristics of a pass band are simultaneous flat characteristics. In addition, the present invention relates to a distributed constant filter having a transmission zero in the stop band, having a simplified structure, suppressing loss, and improving performance.
[0002]
[Prior art]
For example, when the same antenna is shared by the transmission circuit and the reception circuit, the transmission circuit of the mobile communication device such as an analog or digital mobile phone or a radio telephone and the high-frequency circuit unit such as the RF stage of the reception circuit are transmitted. In order to separate the frequency band from the reception frequency band, or to attenuate harmonics generated based on the nonlinearity of the amplifier circuit, in order to remove unwanted signal waves such as interference waves and sideband waves other than the desired signal wave For example, a band pass filter (band pass filter: BPF) is often used.
[0003]
Such a band-pass filter as a filter for a communication device is generally realized and configured as a filter circuit having a desired band characteristic by connecting a plurality of series resonant circuits or parallel resonant circuits composed of various circuit elements. However, the filter circuit unit may be composed of unbalanced distributed constant lines such as a microstrip line and a strip line because the filter circuit part can be reduced in size and electrical characteristics as a high frequency circuit are good. Many.
[0004]
In a bandpass characteristic filter with strict specifications such as waveform transmission, the amplitude characteristics and group delay characteristics of the passband are simultaneous flat characteristics and the stopband as shown in the diagrams of FIGS. 10 (a) and 10 (b). It was necessary to create a transmission zero point, and a complicated circuit configuration was required for its realization.
[0005]
A method of directly configuring a bandpass filter having such characteristics with a clear design theory has not been known so far, and various filters have been used to construct a filter empirically.
[0006]
For example, as shown in the block diagram of FIG. 11, first, paying attention only to the amplitude characteristics, a desired amplitude whose pass band has a flat amplitude characteristic and has a transmission zero in the stop band by a filter having a known configuration. The filter 1 having the characteristics but having no consideration for the group delay characteristic is designed, and then the group delay characteristic of the passband is set in order to compensate for the group delay characteristic of the filter 1 to obtain a desired group delay characteristic as a whole. A device has been devised in which a phase equalizer 2 having an all-pass characteristic to be flattened is added thereto. According to this method, the phase or group delay characteristic is improved while adding the phase equalizer 2 to the filter 1.
[0007]
[Problems to be solved by the invention]
However, in general, such phase equalization and correction are less effective, and there is a problem that a sufficient correction effect cannot be obtained. In addition, since the circuit is configured with more circuit elements than necessary, the circuit configuration is wasted, and conversely, the amplitude characteristics due to the incomplete all-pass characteristics of the phase equalizer 2 are reduced. There has been a problem that there are significant adverse effects such as an adverse effect and an increase in loss due to circuit complexity.
[0008]
On the other hand, conventionally, mainly two methods have been known for realizing the transmission zero in the filter stop band. One is to implement a transmission zero point by inserting a parallel resonator or a series resonator in series or in parallel in the filter, or a combination thereof. For example, as shown in the circuit diagram of FIG. 12, the transmission zero point is set in the stop band outside the pass band by the combination 5 of the parallel resonator and the series resonator with respect to the filter having the band pass characteristic by the resonators 3 and 4. It is to form.
[0009]
In another method, the transmission zero point is realized by branching the transmission path into two, combining the respective paths with the same amplitude, and the phases reversed.
[0010]
For example, as shown in the block diagram of FIG. 13, the circuit is divided into two, and the two ports 6 and 7 have a relationship in which the output amplitude is the same and the phase is 180 degrees different at a certain frequency. As a result, the output obtained by synthesizing these outputs becomes a transmission zero at that frequency.
[0011]
In general, the latter method is easier to implement, and a filter can be realized with a circuit configuration that actually has less loss.
[0012]
Furthermore, as a modification of the latter, a method using a simple reactance feedback path is also known, but in this method, the exact design theory and method for synthesizing the filter from the target network function are not known, Approximate or empirical usage is used. For example, as shown in a circuit diagram in FIG. 14, a transmission zero point is formed by a filter unit 8 which is a normal filter and a coupling circuit 9 corresponding to a branch circuit or a feedback path.
[0013]
However, this method has the effect of reducing loss by simplifying the circuit, but since the exact design method for filter synthesis is not known, the design is approximate, so only approximate characteristics can be obtained. However, there was a problem that the characteristics were insufficient.
[0014]
Conventionally, there has also been known a method in which a ladder-type circuit is combined with a method for generating these transmission zeros, and then a group delay is corrected by a phase equalizer. According to such a configuration, a band-pass characteristic filter having a flat transmission band amplitude characteristic and a group delay characteristic and having a transmission zero in the stop band can be obtained.
[0015]
However, even with this method, the design is approximate, so that accurate characteristics cannot be obtained, and the circuit configuration is complicated. Further, such a filter has a problem that transmission loss increases or only approximate and insufficient characteristics can be obtained, and the loss particularly when constituted by a distributed constant filter such as a microstrip circuit is remarkable. Met.
[0016]
In view of the above problems, the present inventor proposed in Japanese Patent Application No. 10-337219 a method for directly constructing a bandpass filter having a desired characteristic as described above with a clear design theory. In Hei 11-150150, the amplitude characteristics and the group delay characteristics are simultaneously flat characteristics in the pass band, and have a band pass characteristic with a transmission zero in the stop band, and a simple circuit designed by an accurate design method A bandpass filter with low element sensitivity and low loss was proposed.
[0017]
The band-pass filter of Japanese Patent Application No. 11-150150 is a denominator that is an even function of complex frequency s, which is a numerator rational polynomial having at least one set of real roots and at least one set of imaginary roots, and a Hurwitz polynomial of complex frequency s. A distributed constant filter having frequency band pass characteristics, obtained by frequency conversion of a standardized low pass filter whose transfer function is represented by a network function consisting of rational polynomials, and realized by an unbalanced distributed constant circuit. The circuit portion corresponding to the real or imaginary root of the molecular rational polynomial includes a first coupling circuit that cascade-couples the first and second resonators, and the first resonator and a circuit outside thereof. A second coupling circuit that cascade-couples the first resonator and the second resonator, a third coupling circuit that cascade-couples the second resonator and a circuit outside thereof, and the first coupling circuit; A multi-resonator filter having two or more unit coupling circuit units each composed of a fourth coupling circuit that couples the outside of the three coupling circuit by bridge coupling, and the first coupling circuit and the third coupling circuit are combined. The same combination of electric field coupling or magnetic field coupling, and the first coupling circuit, the third coupling circuit, and the second coupling circuit are different combinations of electric field coupling or magnetic field coupling, which correspond to the actual roots. The unit coupling circuit unit is configured such that the second coupling circuit and the fourth coupling circuit are each composed of a coupling circuit of the same type of electric field coupling or magnetic field coupling, and the unit coupling circuit unit corresponding to the imaginary root is the second coupling circuit. And the fourth coupling circuit is composed of different types of coupling circuits of electric field coupling or magnetic field coupling, respectively.
[0018]
However, in the proposal in Japanese Patent Application No. 11-150150, in order to realize a coupling circuit portion corresponding to one set of real roots or one set of imaginary roots of a molecular rational polynomial, more than 3.5 stages of resonators per set are required. It is necessary to connect two 3.5-stage resonators in a cascade to realize a coupling circuit unit corresponding to one set of real roots and one set of imaginary roots. there were. In addition, as the number of root pairs of numerator rational polynomials increases, the number of resonators that is an integer multiple of 3.5 is required. For this reason, there is a limitation on the number of roots of the molecular rational polynomial that can be realized with a given number of resonators, and there is a point to be improved that there is a limitation in realizing a filter with complex characteristics.
[0019]
The present invention has been devised in view of the above problems, and its purpose is a band pass in which the amplitude characteristic and the group delay characteristic are simultaneous flat characteristics in the pass band characteristic, and the transmission band is zero in the stop band. An object of the present invention is to provide a distributed constant filter that has a characteristic, is theoretically accurate, has a simplified structure, suppresses loss, and can improve the performance.
[0020]
[Means for Solving the Problems]
The distributed constant filter of the present invention is a denominator rational polynomial that is an even function of a complex frequency s, which is a numerator rational polynomial having at least one set of real roots and at least one set of imaginary roots, and a 6th-order or more Hurwitz polynomial of complex frequency s. This is a distributed constant filter having a frequency band pass characteristic obtained by frequency-converting a standardized low-pass filter whose transfer function is expressed by a network function consisting of The circuit unit corresponding to one set of real roots and one set of imaginary roots of the numerator rational polynomial and the corresponding denominator rational polynomials includes the first to fourth resonators, the first resonator, and the outside thereof. A first coupling circuit that cascade-couples the first circuit, a second coupling circuit that cascade-couples the first resonator and the second resonator, and a cascade of the second resonator and the third resonator. A third coupling circuit that couples, a fourth coupling circuit that cascade-couples the third resonator and the fourth resonator, a fifth coupling circuit that cascade-couples the fourth resonator and the circuit outside thereof, A multiplex circuit comprising a sixth coupling circuit coupling the outside of the second coupling circuit and the fourth coupling circuit by bridge coupling, and a seventh coupling circuit coupling the outside of the first coupling circuit and the fifth coupling circuit by bridge coupling. It is realized by a multi-resonator filter having one or more coupling circuit sections, and the first to seventh coupling circuits are a combination of electric field coupling and magnetic field coupling of A to D below. is there.
A: The sixth and seventh coupling circuits are electric field coupling, and one or three of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field coupling.
B: The sixth and seventh coupling circuits are magnetic couplings, and two or four of the first to fifth coupling circuits are magnetic couplings and the rest are electric field couplings.
C: The sixth coupling circuit is an electric field coupling, the seventh coupling circuit is a magnetic field coupling, 0, 2 or 4 of the first to fifth coupling circuits are magnetic field couplings, and the rest are electric field couplings.
D: The sixth coupling circuit is magnetic field coupling, the seventh coupling circuit is electric field coupling, one, three or five of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field coupling.
[0021]
DETAILED DESCRIPTION OF THE INVENTION
According to the distributed constant filter of the present invention, a circuit unit corresponding to a set of real roots and a set of imaginary roots of a numerator rational polynomial of a network function and a corresponding denominator rational polynomial is replaced with a multiple coupling circuit unit configured as described above. Since it is realized by a multi-resonator filter having one or more, it is possible to configure and realize a circuit theoretically accurately, simplifying the structure of the filter, suppressing loss and improving performance.
[0022]
The minimum order required for the amplitude characteristic and the group delay characteristic to be flat simultaneously in the passband, which is the target characteristic of the distributed constant filter of the present invention, and to have a transmission zero (attenuation pole) in the stopband is 4 for the molecular rational polynomial. The second and denominator rational polynomials are sixth order. In other words, the order of the molecular rational polynomial is 4th or higher with at least one pair of real and imaginary roots. Further, the order of the Hurwitz polynomial of the denominator rational polynomial is an order that is at least two orders higher than the order of the numerator rational polynomial (degree of the numerator + 2 ≦ degree of the denominator), and the order of the Hurwitz polynomial that is the denominator rational polynomial is This corresponds to the number of resonators constituting the distributed constant filter.
[0023]
A circuit unit corresponding to the fourth-order numerator rational polynomial and the sixth-order denominator rational polynomial includes a first coupling circuit that cascade-couples the first to fourth resonators, the first resonator, and a circuit outside the first resonator, A second coupling circuit that cascade-couples the first resonator and the second resonator, a third coupling circuit that cascade-couples the second resonator and the third resonator, a third resonator, and a fourth resonator; A fourth coupling circuit that cascade-couples, a fifth coupling circuit that cascade-couples the fourth resonator and the circuit outside thereof, and a sixth coupling that couples the second coupling circuit and the outside of the fourth coupling circuit by bridge coupling The circuit is realized by a multi-resonator filter having one or more multiple coupling circuit sections including a first coupling circuit and a seventh coupling circuit that couples the outside of the first coupling circuit and the fifth coupling circuit by bridge coupling. 7 coupling circuit is a combination of electric field coupling and magnetic field coupling The sixth and seventh coupling circuits are electric field couplings, and the first to fifth coupling circuits are one or three of which are magnetic field couplings and the rest are electric field couplings, or the sixth and seventh coupling circuits. Is the magnetic field coupling, and two or four of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field couplings, or the sixth coupling circuit is electric field coupling, and the seventh coupling circuit is magnetic field coupling. In the first to fifth coupling circuits, 0, 2 or 4 of them are magnetic field coupling and the rest are electric field couplings, the sixth coupling circuit is magnetic field coupling, the seventh coupling circuit is electric field coupling, In the fifth coupling circuit, one, three or five of them are magnetic field coupling and the rest are electric field coupling.
[0024]
Although the distributed constant filter of the present invention is realized by an unbalanced distributed constant circuit, each coupling circuit of such a multiple coupling circuit section is connected between resonators by charges on each resonator of the multiple coupling circuit section. It can be realized by coupling of electric fields, or similarly coupling of magnetic fields between resonators by current.
[0025]
The sixth and seventh coupling circuits can also be realized by, for example, lumped constant reactance elements, coupling of electric fields by charges on the resonators at both ends bridge-coupled by them, or coupling of magnetic fields by current.
[0026]
According to the distributed constant filter of the present invention, the network function representing the transfer function of the standardized low-pass filter is an even function of the complex frequency s and has at least one set of real roots and at least one set of imaginary roots. Since it is composed of a numerator rational polynomial and a denominator rational polynomial that is a 6th-order or higher Hurwitz polynomial of complex frequency s, the amplitude passband characteristic is corrected by a set of real roots of the numerator rational polynomial. In addition, an attenuation pole, which is a transmission zero point that is given a frequency with a set of imaginary roots, can be generated in the vicinity of the pass band, so that the amplitude characteristic and the phase characteristic are compared with the pass band characteristic of the filter. Band pass characteristics that ensure sufficient attenuation by the transmission zero point in the stop band while ensuring the desired simultaneous flat characteristics for the amplitude characteristics and group delay characteristics by individually imposing conditions It can be obtained a filter having.
[0027]
By using an unbalanced distributed constant circuit such as a microstrip circuit, an ideal transformer and gyrator can be easily realized, and a series resonant circuit and a parallel resonant circuit can also be easily realized. It is possible to obtain a distributed constant filter having a simplified circuit configuration including an unbalanced distributed constant circuit.
[0028]
In order to realize the distributed constant filter of the present invention, the characteristic of the standardized low-pass filter is first determined by a Hurwitz polynomial having a phase linear characteristic that is a denominator rational polynomial, and then a complex frequency that is a numerator rational polynomial. The imaginary root of the even function of s is specified so that the transmission zero is arranged at a desired frequency, and the real root of the molecular rational polynomial is determined so that the amplitude characteristic is flat in the passband.
[0029]
Next, a normalized low-pass filter using the network function composed of the numerator rational polynomial and the denominator rational polynomial as a transfer function is synthesized.
[0030]
Next, a negative value element is converted into an actual positive value element by equivalent conversion, and after frequency conversion to bandpass characteristics, equivalent conversion to an unbalanced distributed constant circuit is performed to realize a distributed constant filter.
[0031]
Hereinafter, the distributed constant filter of the present invention will be described in detail.
[0032]
As an implementation example of the minimum order of the distributed constant filter of the present invention, the numerator rational polynomial is a fourth-order polynomial f (s) having a pair of real and imaginary roots, and the denominator rational polynomial is a sixth-order Hurwitz polynomial g (s ), The network function is a function of the complex frequency s = jω,
[0033]
[Expression 1]

[0034]
It is expressed as Here, the denominator rational polynomial g (s) is a polynomial having a flat group delay characteristic, such as a Bessel polynomial.
[0035]
Next, the amplitude characteristic of the denominator rational polynomial is corrected with a numerator rational polynomial without adversely affecting the group delay characteristic, and a transmission zero is provided in the stopband by a set of imaginary roots of the numerator rational polynomial. Furthermore, the amplitude characteristic is corrected with a set of real roots of the numerator rational polynomial so that the amplitude characteristic is as flat as possible in the passband. In this way, the numerator rational polynomial is determined corresponding to the denominator rational polynomial and the target filter characteristic.
[0036]
From the polynomial thus determined, a standardized low-pass filter as shown in an example of a circuit diagram in FIG. 3 is determined. In this standardized low-pass filter, the number of parallel or series ladder-type connections corresponds to the order of the Hurwitz polynomial, and in this example is six. The two parallel resonant circuits connected in series are circuit portions corresponding to pairs of real and imaginary roots of the molecular rational polynomial, respectively.
[0037]
Among the circuit portions corresponding to the real root and imaginary root pairs, the circuit elements of the series resonance circuit corresponding to the imaginary root pair are both positive values and can be realized with an actual circuit. On the other hand, one of the circuit elements of the parallel resonant circuit corresponding to the real root set has a negative value, and cannot be realized as an actual circuit as it is.
[0038]
Therefore, next, equivalent conversion to the multiple coupling circuit unit is performed. That is, the circuit shown in FIG. 3 is equivalently converted into a circuit as shown in FIG. 4 using an imaginary gyrator. In the circuit shown in FIG. 4, the circuit shown in FIG. 5A is handled by paying attention to the part including two parallel resonant circuits including the imaginary gyrator. If a circuit including five imaginary gyrators is considered for this circuit as shown in FIG. 5B, the circuits shown in FIGS. 5A and 5B can be obtained by appropriately replacing each other's parameters. It turns out that both are equivalent. In addition, L and C in FIG.5 (b) show that a circuit element is an inductance and a capacity | capacitance, respectively, The value is not shown. Similarly, j indicates an imaginary gyrator and its value is not shown. Further, when the sign of the imaginary gyrator j is not particularly indicated, it is assumed that the imaginary gyrator has a constant value of + or −. The same applies to FIGS. 6 to 8 below.
[0039]
As a result, the standardized low-pass filter shown in FIG. 3 is converted into an equivalent standardized low-pass filter as shown in FIG. 6 through the equivalent conversion of FIGS.
[0040]
By introducing an imaginary gyrator and an ideal transformer to the equivalent standardized low-pass filter shown in FIG. 6 and equivalently converting all circuit elements to the same value of capacitance in parallel, an equivalent standard as shown in FIG. A low pass filter is obtained. The equivalent standardized low-pass filter shown in FIG. 7 is strictly equivalent to the standardized low-pass filter shown in FIG. It should be noted that the sign of the imaginary gyrator at the stage of performing this equivalent conversion has a degree of freedom of compounding as shown in FIG.
[0041]
Next, the standardized low-pass filter is frequency-converted and impedance-converted to be converted into a band-pass filter having a target band-pass characteristic. At this time, the capacitance in the circuit of FIG. 7 becomes a parallel resonant circuit by frequency conversion, but the imaginary gyrator remains unchanged. At this time, in order to improve the symmetry between the input end and the output end of the filter, an imaginary gyrator including an ideal transformer is inserted at the output end. By inserting this imaginary gyrator, the output impedance of the filter at the output end is converted into output admittance, but the transmission characteristics such as the amplitude characteristic and group delay characteristic of the filter are not changed. Thereby, a band pass filter as shown in FIG. 8 is obtained.
[0042]
Furthermore, when the imaginary gyrator is realized by connecting a π-type constant reactance element, the target band-pass filter has a circuit configuration as shown in FIG. In this band pass filter, the constant reactance element of the coupling circuit can be realized by electric field coupling or magnetic field coupling by narrow band approximation in the vicinity of the pass band.
[0043]
Here, the constant reactance elements of the seven coupled circuits 17, 18, 19, 20, 21, 23, and 24 in the figure and the four resonant circuits (resonators) of 11, 12, 13, and 14 One multiple coupling circuit unit is used. Reference numeral 17 denotes a first coupling circuit for cascading the first resonator 11 and its outer circuit, 18 denotes a second coupling circuit for cascading the first resonator 11 and the second resonator 12, and 19 denotes a first coupling circuit. A third coupling circuit that cascade-connects the two resonators 12 and the third resonator 13, 20 is a fourth coupling circuit that cascade-connects the third resonator 13 and the fourth resonator 14, and 21 is a fourth resonator 14 5 is a fifth coupling circuit that bridge-connects the outer and outer circuits, 22 is a sixth coupling circuit that bridge-couples the second coupling circuit 18 and the fourth coupling circuit 20, and 23 is a first coupling circuit 17 and a fifth coupling circuit. 21 is a seventh coupling circuit that bridges the outside of 21.
[0044]
One set of numerator rational polynomials f (s) in the equation shown in Equation 1 by the multiple coupling circuit unit realized by the first coupling circuit 17 to the seventh coupling circuit 23 and the first resonator 11 to the fourth resonator 14. In order to realize a circuit portion corresponding to a real root and a set of imaginary roots, combinations of signs of the first coupling circuit 17 to the seventh coupling circuit 23 realized by constant reactance elements are as follows: It becomes a combination.
a: Both the sixth and seventh coupling circuits 22 and 23 have a negative sign (-), and one to three of the first to fifth coupling circuits 17 to 21 are positive signs (+) and the rest are negative. It is a sign.
b: Both the sixth and seventh coupling circuits 22 and 23 have a positive sign, and two or four of the first to fifth coupling circuits 17 to 21 have a positive sign and the rest have a negative sign.
c: The sixth coupling circuit 22 has a negative sign, the seventh coupling circuit 23 has a positive sign, and the first to fifth coupling circuits 17 to 21 have 0, 2 or 4 positive signs, and the rest are negative signs. It is.
d: The sixth coupling circuit 22 has a positive sign, the seventh coupling circuit 23 has a negative sign, and one to three or five of the first to fifth coupling circuits 17 to 21 have a positive sign and the rest have a negative sign. It is.
[0045]
The combination of the signs of the first coupling circuit 17 to the seventh coupling circuit 23 is such a combination of a to d. The electric field coupling or the magnetic field of the first coupling circuit 17 to the seventh coupling circuit 23 that realizes the above polynomial is used. The combination of the couplings is determined by equivalent conversion, and the combination is due to the fact that the electric field coupling is represented by (−) and the magnetic field coupling is represented by (+), resulting in 20 types shown in Table 1.
[0046]
[Table 1]

[0047]
The constant reactance elements of the coupling circuits 17 to 23 in this bandpass filter are realized by electric field coupling or magnetic field coupling, or capacitance or inductor, respectively, by narrowband approximation in the vicinity of the passband. can do.
[0048]
Next, FIG. 1 shows a circuit diagram of an embodiment of a circuit of a band pass filter obtained as a result of narrow band approximation. In this example, the sixth combination circuit 22 has a negative sign, the seventh combination circuit 23 has a positive sign, and the first to fifth combination circuits 17 to 21 have a negative sign.
[0049]
Further, for the distributed constant filter of the present invention, a configuration example in which the embodiment of the bandpass filter shown in FIG. 1 is realized by the distributed constant filter is shown in a plan view in FIG.
[0050]
The configuration example of the distributed constant filter of the present invention shown in FIG. 2 is formed with a conductor pattern as a distributed constant circuit element on a dielectric substrate. In this example, six circular resonators 40 to 45 are E. Used in ₁₁₀ mode.
[0051]
In such a distributed constant filter of the present invention, the coupling sections 48 to 56 in FIG. 2 are connected to the first to seventh coupling circuits 31 to 39 of the multiple coupling circuit section in FIG. 45 corresponds to the resonance circuits (resonators) 25 to 30 in FIG. When the resonance mode of each resonator 40-45 is E ₂₁₀ mode, as shown in FIG. 2, there is an electric field maximum points every 90 degrees around the perimeter of each resonator, the electric field coupling in the moiety Can do. In addition, there is a magnetic field maximum point at the middle point of the electric field maximum point, that is, a point shifted by 45 degrees from the electric field maximum point, and magnetic field coupling can be performed at this portion. In FIG. 2, the curved lines with arrows shown in the resonators 40 to 45 formed by the conductor pattern represent the direction of the magnetic field parallel to the paper surface of the drawing, and the inside and x marks are the figures. Represents the direction of the electric field perpendicular to the paper surface. Using such an arrangement, as shown in FIG. 2, a distributed constant filter as a target band-pass filter in which six resonators 40 to 45 are coupled can be configured. In FIG. 2, 48 to 54 and 56 are electric field couplings, and 55 is magnetic field coupling.
[0052]
According to such a distributed constant filter of the present invention, an accurate equivalent circuit bandpass filter as shown in FIG. 1 can be realized as the conductor pattern shown in FIG. It can be realized by designing with a simple circuit and designing with a simple method, and a filter can be configured with the minimum number of elements and patterns for a given characteristic, so the distribution of characteristics with low element sensitivity and low loss It becomes a constant filter.
[0053]
Moreover, according to the distributed constant filter of the present invention, the order of the denominator polynomial can be increased by the same order with respect to the increase of the order of the numerator polynomial, so that it is given rather than the proposal in Japanese Patent Application No. 11-150150. It is possible to increase the order of the molecular rational polynomial that can be realized with a number of resonators, and it is a practically very useful distributed constant filter that requires fewer restrictions for realizing a filter with complex characteristics.
[0054]
Note that the above are only examples of the embodiments of the present invention, and the present invention is not limited to these, and various modifications and improvements can be made without departing from the scope of the present invention. For example, a resonator pattern of another shape may be used as the conductor pattern of the resonator constituting the distributed constant filter. Further, the combination of electric field coupling and magnetic field coupling in the embodiment shown in FIG. 2 may be other combinations of A to D corresponding to the above a to d.
[0055]
【The invention's effect】
Thus, according to the present invention, the denominator rational function is an even function of the complex frequency s, which is a numerator rational polynomial having at least one set of real roots and at least one set of imaginary roots, and a 6th-order or more Hurwitz polynomial of the complex frequency s. A distributed constant filter having a frequency band pass characteristic obtained by frequency-converting a standardized low-pass filter whose transfer function is represented by a network function consisting of a polynomial, and realized by an unbalanced distributed constant circuit. The circuit portion corresponding to one set of real roots and one set of imaginary roots of the numerator rational polynomial and the corresponding denominator rational polynomials includes the first to fourth resonators, the first resonator, and A first coupling circuit that cascade-couples an outer circuit, a second coupling circuit that cascade-couples the first resonator and the second resonator, and a cascade of the second resonator and the third resonator A third coupling circuit that couples, a fourth coupling circuit that cascade-couples the third resonator and the fourth resonator, a fifth coupling circuit that cascade-couples the fourth resonator and the circuit outside thereof, A multiplex circuit comprising a sixth coupling circuit coupling the outside of the second coupling circuit and the fourth coupling circuit by bridge coupling, and a seventh coupling circuit coupling the outside of the first coupling circuit and the fifth coupling circuit by bridge coupling. The first to seventh coupling circuits are a combination of the following electric field coupling and magnetic field coupling of A to D, that is, A: the sixth and sixth coupling circuits. Seven coupling circuits are electric field couplings, and one or three of the first to fifth coupling circuits are magnetic field couplings and the rest are electric field couplings.
B: The sixth and seventh coupling circuits are magnetic couplings, and two or four of the first to fifth coupling circuits are magnetic couplings and the rest are electric field couplings.
C: The sixth coupling circuit is an electric field coupling, the seventh coupling circuit is a magnetic field coupling, 0, 2 or 4 of the first to fifth coupling circuits are magnetic field couplings, and the rest are electric field couplings.
D: The sixth coupling circuit is magnetic field coupling, the seventh coupling circuit is electric field coupling, one, three or five of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field coupling.
[0056]
As a result, the passband amplitude characteristics and group delay characteristics are simultaneously flat, and have a frequency bandpass characteristic with a transmission zero in the stopband. In addition, there are no restrictions in realizing a filter with complex characteristics, and unintentional coupling between the resonators is suppressed to suppress parasitic characteristic deterioration, resulting in low element sensitivity and low loss. A distributed parameter filter of characteristics could be provided.
[Brief description of the drawings]
FIG. 1 is a circuit diagram showing an embodiment of a bandpass filter according to the present invention.
FIG. 2 is a plan view showing a configuration example in which the embodiment of the bandpass filter shown in FIG. 1 is realized by a distributed constant filter.
FIG. 3 is a circuit diagram showing an example of a standardized low-pass filter in the present invention.
FIG. 4 is a circuit diagram showing an example of an equivalent-converted standardized low-pass filter in the present invention.
FIGS. 5A and 5B are circuit diagrams showing an example of equivalent conversion for a standardized low-pass filter in the present invention. FIGS.
FIG. 6 is a circuit diagram illustrating an example of an equivalent-converted normalized low-pass filter according to the present invention.
FIG. 7 is a circuit diagram showing an example of an equivalent-converted normalized low-pass filter according to the present invention.
FIG. 8 is a circuit diagram showing an example of an equivalently converted bandpass filter in the present invention.
FIG. 9 is a circuit diagram showing a configuration example of a bandpass filter according to the present invention.
FIGS. 10A and 10B are diagrams showing amplitude characteristics and group delay characteristics in the pass band of the band pass filter, respectively.
FIG. 11 is a block diagram illustrating a configuration example of a conventional bandpass filter.
FIG. 12 is a circuit diagram showing a configuration example for realizing a transmission zero in a stop band of a conventional filter.
FIG. 13 is a block diagram showing a configuration example for realizing a transmission zero in a stop band of a conventional filter.
FIG. 14 is a circuit diagram showing a configuration example for realizing a transmission zero in a stop band of a conventional filter.
[Explanation of symbols]
17, 32, 49 ... 1st coupling circuit
18, 33, 50 ... 2nd coupling circuit
19, 34, 51 ... 3rd coupling circuit
20, 35, 52 ... 4th coupling circuit
21, 36, 53 ... Fifth coupling circuit
22, 37, 54 ... Sixth coupling circuit
23, 38, 55 ... Seventh coupling circuit
11, 25, 41 ... 1st resonator
12, 26, 42 ... 2nd resonator
13, 27, 43 ... Third resonator
14, 28, 44 ... 4th resonator

Claims (1)

It is transmitted by a network function consisting of a numerator rational polynomial having an even function of complex frequency s and having at least one set of real roots and at least one set of imaginary roots, and a denominator rational polynomial which is a 6th-order or more Hurwitz polynomial of complex frequency s. A distributed constant filter having a frequency band pass characteristic, obtained by frequency-converting a standardized low-pass filter in which a function is represented, and realized by an unbalanced distributed constant circuit,
A circuit unit corresponding to one set of real roots and one set of imaginary roots of the numerator rational polynomial and the corresponding denominator rational polynomials includes first to fourth resonators, the first resonator, and a circuit outside thereof. A first coupling circuit that cascade couples the second resonator, a second coupling circuit that cascade couples the first resonator and the second resonator, and a third coupling that cascade couples the second resonator and the third resonator. A circuit, a fourth coupling circuit that cascade-couples the third resonator and the fourth resonator, a fifth coupling circuit that cascade-couples the fourth resonator and an outside circuit, and the second coupling circuit And a sixth coupling circuit that couples the outside of the fourth coupling circuit by bridge coupling and a seventh coupling circuit that couples the first coupling circuit and the fifth coupling circuit by bridge coupling. Multi-resonator fill with two or more In has been realized,
The distributed constant filter, wherein the first to seventh coupling circuits are combinations of electric field coupling and magnetic field coupling of A to D below.
A: The sixth and seventh coupling circuits are electric field coupling, and one or three of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field coupling.
B: The sixth and seventh coupling circuits are magnetic couplings, and two or four of the first to fifth coupling circuits are magnetic couplings and the rest are electric field couplings.
C: The sixth coupling circuit is an electric field coupling, the seventh coupling circuit is a magnetic field coupling, 0, 2 or 4 of the first to fifth coupling circuits are magnetic field couplings, and the rest are electric field couplings.
D: The sixth coupling circuit is magnetic field coupling, the seventh coupling circuit is electric field coupling, one, three or five of the first to fifth coupling circuits are magnetic field coupling and the rest are electric field coupling.

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