COMPOSITE RESONATOR AND ASSEMBLY

A composite resonator includes a first resonator extending in a first plane direction, a second resonator spaced apart from the first resonator in a first direction and extending in the first plane direction, a third resonator located between the first resonator and the second resonator in the first direction and configured to magnetically or capacitively connect to or electrically connect to each of the first resonator and the second resonator, and a reference conductor extending in the first plane direction, located between the first resonator and the second resonator in the first direction, and serving as a potential reference of the first resonator and the second resonator. The reference conductor surrounds at least a part of the third resonator in the first plane direction.

TECHNICAL FIELD

The present disclosure relates to a composite resonator and an assembly.

BACKGROUND OF INVENTION

A known technique involves controlling electromagnetic waves without using a dielectric lens. For example, Patent Document 1 describes a technique of refracting radio waves by changing parameters of respective elements in a structure including an array of resonator elements.

CITATION LIST

Patent Literature

Patent Document 1: JP 2015-231182 A

SUMMARY

Summary of the Invention

In the resonator elements described in Patent Document 1, even when the parameters of respective elements are changed, a maximum amount of change in phase is 180°. There is a need to provide a resonator element which can form an assembly having a high degree of design freedom.

An objective of the present disclosure is to provide a composite resonator and an assembly that can be made with a high degree of design freedom.

Solution to Problem

In the present disclosure, a composite resonator includes a first resonator extending in a first plane direction, a second resonator spaced apart from the first resonator in a first direction and extending in the first plane direction, a third resonator located between the first resonator and the second resonator in the first direction and configured to magnetically or capacitively connect to or electrically connect to each of the first resonator and the second resonator, and a reference conductor extending in the first plane direction, located between the first resonator and the second resonator in the first direction, and serving as a potential reference of the first resonator and the second resonator, and the reference conductor surrounds at least a part of the third resonator in the first plane direction.

An assembly according to the present disclosure includes a plurality of the composite resonators according to the present disclosure, in which the plurality of composite resonators are arranged in the first plane direction.

Advantageous Effect

According to the present disclosure, a composite resonator which can form an assembly having a high degree of design freedom can be provided.

DESCRIPTION OF EMBODIMENTS

Embodiments of the present disclosure will be described in detail with reference to the drawings. The embodiments described below do not limit the present disclosure.

In the following description, an XYZ orthogonal coordinate system is set, and the positional relationship between respective portions will be described by referring to the XYZ orthogonal coordinate system. A direction parallel to an X-axis in a horizontal plane is defined as an X-axis direction, a direction parallel to a Y-axis orthogonal to the X-axis in the horizontal plane is defined as a Y-axis direction, and a direction parallel to a Z-axis orthogonal to the horizontal plane is defined as a Z-axis direction. A plane including the X-axis and the Y-axis is appropriately referred to as an XY plane, a plane including the X-axis and the Z-axis is appropriately referred to as an XZ plane, and a plane including the Y-axis and the Z-axis is appropriately referred to as a YZ plane. The XY plane is parallel to the horizontal plane. The XY plane, the XZ plane, and the YZ plane are orthogonal to each other.

Overview

FIG.1illustrates an assembly in which a plurality of composite resonators are periodically arranged. In the assembly, the plurality of composite resonators periodically arranged function as an assembly. For example, the assembly functions as a spatial filter plate for a plane wave. For example, the assembly functions as a radio wave refraction plate by generating a phase difference in the plurality of composite resonators.

As illustrated inFIG.1, an assembly1includes a plurality of unit structures10and a substrate12.

The plurality of unit structures10are arranged in an XY plane direction. The XY plane direction may also be referred to as a first plane direction. That is, the plurality of unit structures10are arranged two-dimensionally. Each of the plurality of unit structures10has a resonance structure. The structure of the unit structure10will be described later. The unit structure10may be referred to as a composite resonator. The substrate12may be, for example, a dielectric substrate made of a dielectric body. The assembly1is made by two-dimensionally arranging the plurality of unit structures10having the resonance structure on the substrate12made of the dielectric body.

In the present disclosure, the assembly can be made by arranging the composite resonators of the following embodiments as illustrated inFIG.1.

First Embodiment

Configuration of Unit Structure

A configuration example of the unit structure according to a first embodiment will be described with reference toFIG.2.FIG.2is a diagram schematically illustrating the configuration example of the unit structure according to the first embodiment.

As illustrated inFIG.2, the unit structure10includes a first resonator14, a second resonator16, a reference conductor18, and a connection line path20.

The first resonator14may be arranged on the substrate12, extending on the XY plane. The first resonator14may be made of a conductor. The first resonator14may be, for example, a patch conductor formed in a rectangular shape. In the example illustrated inFIG.2, the first resonator14is illustrated as the rectangular patch conductor, but the present disclosure is not limited thereto. The first resonator14may have, for example, a linear shape, a circular shape, a loop shape, or a polygonal shape other than a rectangular shape. That is, the shape of the first resonator14may be arbitrarily changed according to the design. The first resonator14resonates by an electromagnetic wave received from the +Z-axis direction.

The first resonator14radiates an electromagnetic wave during resonance. The first resonator14radiates the electromagnetic wave to the +Z-axis direction side during resonance.

The second resonator16may be arranged on the substrate12to extend on the XY plane at a position away from the first resonator14in the Z-axis direction. The second resonator16may be, for example, a patch conductor formed in a rectangular shape. In the example illustrated inFIG.2, the second resonator16is illustrated as the rectangular patch conductor, but the present disclosure is not limited thereto. The second resonator16may have, for example, a linear shape, a circular shape, a loop shape, or a polygonal shape other than a rectangular shape. That is, the shape of the second resonator16may be arbitrarily changed according to the design. The shape of the second resonator16may be the same as or different from the shape of the first resonator14. The area of the second resonator16may be the same as or different from the area of the first resonator14.

The second resonator16radiates an electromagnetic wave during resonance. The second resonator16, for example, radiates the electromagnetic wave to the −Z-axis direction side. The second resonator16radiates the electromagnetic wave to the −Z-axis direction side during resonance. The second resonator16resonates by receiving the electromagnetic wave from the −Z-axis direction.

The second resonator16may resonate at a phase different from that of the first resonator14. The second resonator16may resonate in a direction different from the resonance direction of the first resonator14in the XY plane direction. For example, when the first resonator14resonates in the X-axis direction, the second resonator16may resonate in the Y-axis direction. The resonance direction of the second resonator16may change with time in the XY plane direction corresponding to a change with time in the resonance direction of the first resonator14. The second resonator16may radiate the electromagnetic wave received by the first resonator14with a first frequency band thereof attenuated.

The reference conductor18may be arranged between the first resonator14and the second resonator16in the substrate12. The reference conductor18may be, for example, at the center between the first resonator14and the second resonator16in the substrate12, but the present disclosure is not limited thereto. For example, the reference conductor18may be at a position where the distance from the reference conductor18to the first resonator14differs from the distance from the reference conductor18to the second resonator16. The reference conductor18has a through-hole18athrough which the connection line path20extends. The reference conductor18surrounds at least a part of the connection line path20.

The connection line path20may be made of a conductor. The connection line path20is located between the first resonator14and the second resonator16in the Z-axis direction. The Z-axis direction may also be referred to as a first direction, for example. The connection line path20may be connected to each of the first resonator14and the second resonator16. Although the connection line path20passes through the through-hole18a, the connection line path20is not in contact with the reference conductor18. The connection line path20may be magnetically or capacitively connected to each of the first resonator14and the second resonator16, for example. For example, the connection line path20may be electrically connected to each of the first resonator14and the second resonator16. The connection line path20is connected to a side of the first resonator14parallel to the X-axis direction and is connected to a side of the second resonator16parallel to the X-axis direction. The connection line path20may be a path parallel to the Z-axis direction. The connection line path20may be a third resonator.

The unit structure10magnetically or capacitively connects the first resonator14and the second resonator16or electrically connects them to be combined. By combining the three resonators, the unit structure10transmits a high frequency excited by an electromagnetic wave incident on the first resonator14through the composite resonator. The unit structure10may have any one or more functions of a phase shift, a band-pass filter, a high-pass filter, and a low-pass filter depending on the transmission characteristics of the unit structure.

The unit structure10changes the phase of the electromagnetic wave incident on the first resonator14and radiates the electromagnetic wave from the second resonator16. The amount of change in phase changes depending on the length of the connection line path20. The amount of change in phase also changes depending on the area of the first resonator14or the second resonator16.

Frequency characteristics of the unit structure according to the first embodiment will be described with reference toFIG.3.FIG.3is a graph showing the frequency characteristics of the unit structure according to the first embodiment.

InFIG.3, the horizontal axis represents the frequency [Giga Hertz (GHz)] and the vertical axis represents the gain [deci Bel (dB)].FIG.3shows a graph G1and a graph G2. The graph G1shows a transmission coefficient. The graph G2shows a reflection coefficient. The graph G1shows that insertion loss in a region from around 21.00 GHz to around 28.00 GHz is −3 dB or more and transmission characteristics are satisfactory. The graph G2shows that the reflection coefficient in the region from around 21.00 GHz to around 28.00 GHz is low. That is, the unit structure10illustrated inFIG.1has satisfactory transmission characteristics over a wide range from around 21.00 GHz to around 28.00 GHz.

The amount of change in phase of the unit structure according to the first embodiment will be described with reference toFIG.4.FIG.4is a graph showing the amount of change in phase of the unit structure according to the first embodiment.

InFIG.4, the horizontal axis represents the frequency [GHz] and the vertical axis represents the amount of change in phase [deg].FIG.4shows a graph G3. The graph G3shows the amount of shift in phase of the electromagnetic wave when the electromagnetic wave incident on the first resonator14is radiated from the second resonator16. For example, when the electromagnetic wave having a frequency around 22.00 GHz is incident on the first resonator14, the unit structure10shifts the phase of the electromagnetic wave by about −80° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency around 24.00 GHz is incident on the first resonator14, the unit structure10shifts the phase of the electromagnetic wave by about −130° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency in around 28.00 GHz is incident on the first resonator14, the unit structure10shifts the phase of the electromagnetic wave by about 135° and radiates the electromagnetic wave from the second resonator16. The unit structure10can be used as a spatial filter. The unit structure10can obtain a desired phase difference between the elements by shifting a design value of a center frequency of the spatial filter.

The unit structures10are arranged in the assembly1, and thus the electromagnetic wave transmitted through the assembly1is shifted. For example, the electromagnetic wave passing through the assembly1is shifted by about 22° at a frequency of 18.00 GHz. For example, the electromagnetic wave passing through the assembly1is shifted by about −130° at a frequency of 24.00 GHz. For example, the electromagnetic wave passing through the assembly1is shifted by about 135° at a frequency of 28 GHz.

Second Embodiment

Configuration of Unit Structure

A configuration example of a unit structure according to a second embodiment will be described with reference toFIG.5.FIG.5is a diagram schematically illustrating the configuration example of the unit structure according to the second embodiment.

As illustrated inFIG.5, a unit structure10A differs from the unit structure10illustrated inFIG.2in that the connection line path20is not a linear path parallel to the Z-axis direction. Specifically, the connection line path20of the unit structure10A differs from the unit structure10illustrated inFIG.2in that the connection line path20includes a first path portion20a, a second path portion20b, a third path portion20c, a fourth path portion20d, and a fifth path portion20e.

The first path portion20amay be a path parallel to the Z-axis direction and including one end connected to the first resonator14and the other end located between the first resonator14and the reference conductor18. The second path portion20bmay be a path parallel to the XY plane and including one end connected to the other end of the first path portion20aand the other end located between the first resonator14and the reference conductor18. The third path portion20cmay be a path parallel to the Z-axis direction and including one end connected to the other end of the second path portion20band the other end located between the second resonator16and the reference conductor18. The third path portion20cpasses through the through-hole18aof the reference conductor18. The third path portion20cis not in contact with the reference conductor18. The fourth path portion20dmay be a path parallel to the XY plane and including one end connected to the other end of the third path portion20cand the other end located between the second resonator16and the reference conductor18. The fifth path portion20emay be a path parallel to the Z-axis direction and including one end connected to the fourth path portion20dand the other end connected to the fifth path portion20e.

InFIG.5, the connection line path20has been described as including the five paths from the first path portion20ato the fifth path portion20e, but this is merely an example and does not limit the present disclosure. The number of paths included in the connection line path20may be more or less than five. The plurality of path portions may also be referred to as sub-resonators. For example, the connection line path20may have a bent portion being bent in a curved shape.

The unit structure10A changes the phase of the electromagnetic wave incident on the first resonator14and radiates the electromagnetic wave from the second resonator16. The amount of change in phase changes depending on the length of the connection line path20. The amount of change in phase also changes depending on the area of the first resonator14or the second resonator16.

Frequency characteristics of the unit structure according to the second embodiment will be described with reference toFIG.6.FIG.6is a graph showing frequency characteristics of the unit structure according to the second embodiment.

InFIG.6, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.6shows a graph G4and a graph G5. The graph G4shows a transmission coefficient. The graph G5shows a reflection coefficient. The graph G4shows that insertion loss in a region from around 22.00 GHz to around 31.40 GHz is −3 dB or more and transmission characteristics are satisfactory. The graph G5shows that the reflection coefficient in the region from around 22.00 GHz to around 31.40 GHz is low. That is, the unit structure10A illustrated inFIG.5has satisfactory transmission characteristics over a wide range from around 22.00 GHz to around 31.40 GHz.

An amount of change in phase of the unit structure according to the second embodiment will be described with reference toFIG.7.FIG.7is a graph showing the amount of change in phase of the unit structure according to the second embodiment.

InFIG.7, the horizontal axis represents the frequency [GHz] and the vertical axis represents the amount of change in phase [deg].FIG.7shows a graph G6. The graph G6shows the amount of shift in phase of the electromagnetic wave when the electromagnetic wave incident on the first resonator14is radiated from the second resonator16. For example, when the electromagnetic wave having a frequency around 22.00 GHz is incident on the first resonator14, the unit structure10A shifts the phase of the electromagnetic wave by about −65° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency in around 24.00 GHz is incident on the first resonator14, the unit structure10shifts the phase of the electromagnetic wave by about −140° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency in around 28.00 GHz is incident on the first resonator14, the unit structure10shifts the phase of the electromagnetic wave by about 110° and radiates the electromagnetic wave from the second resonator16. That is, the unit structure10A can be used as a spatial filter changing the phase of the electromagnetic wave.

The unit structures10A are arranged in the assembly1, and thus the electromagnetic wave transmitted through the assembly1is shifted. For example, the electromagnetic wave passing through the assembly1is shifted by about −65° at a frequency of 22.00 GHz. For example, the electromagnetic wave passing through the assembly1is shifted by about −140° at a frequency of 24.00 GHz. For example, the electromagnetic wave passing through the assembly1is shifted by about 110° at a frequency of 28.00 GHz.

The unit structure10can obtain a desired phase difference between the elements by arranging the elements having shifted design value of the center frequency of the spatial filter. When the unit structure10and the unit structure10A are arranged side by side in the assembly1, a difference between phases in which electromagnetic waves transmitted through the unit structures10and10A, respectively, are shifted is generated. For example, at the frequency 22.00 GHz, the phases of electromagnetic waves transmitted through the two unit structures10and10A are shifted by about 22° and about −65°, respectively, and the phase difference is 85°. For example, at a frequency of 24.00 GHZ, the phases of electromagnetic waves transmitted through the two unit structures10and10A are shifted by about −130° and about −140°, respectively, and the phase difference is 10°. For example, at a frequency of 28.00 GHz, the phases of electromagnetic waves transmitted through the two unit structures10and10A are shifted by about 135° and about 110°, respectively, and the phase difference is 25°.

Third Embodiment

Configuration of Unit Structure

A configuration example of the unit structure according to a third embodiment will be described with reference toFIG.8.FIG.8is a diagram schematically illustrating the configuration example of the unit structure according to the third embodiment.

As illustrated inFIG.8, a unit structure10B differs from the unit structure10illustrated inFIG.2in that the unit structure10B includes a connection line path20A and a connection line path20B.

In the unit structure10B, the reference conductor18includes a through-hole18aand a through-hole18b. The through-hole18ais a through-hole through which the connection line path20A passes. The through-hole18bis a through-hole through which the connection line path20B passes.

The connection line path20A may be made of a conductor. The connection line path20A is located between the first resonator14and the second resonator16in the Z-axis direction. The connection line path20A is connected to each of the first resonator14and the second resonator16. Specifically, the connection line path20A has one end connected to a side of the first resonator14parallel to the Y-axis direction and the other end connected to a side of the second resonator16parallel to the Y-axis direction. Although the connection line path20A passes through the through-hole18a, the connection line path20A is not in contact with the reference conductor18.

The connection line path20B may be made of a conductor. The connection line path20B is located between the first resonator14and the second resonator16in the Z-axis direction. The connection line path20B is connected to each of the first resonator14and the second resonator16. Specifically, the connection line path20B has one end connected to a side of the first resonator14parallel to the X-axis direction and the other end connected to a side of the second resonator16parallel to the X-axis direction. Although the connection line path20B passes through the through-hole18b, the connection line path20B is not in contact with the reference conductor18.

Frequency characteristics of the unit structure according to the third embodiment will be described with reference toFIGS.9and10.FIGS.9and10are graphs showing the frequency characteristics of the unit structure according to the third embodiment.

InFIG.9, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.9shows a graph G7and a graph G8. The graph G7shows a transmission coefficient when the electromagnetic wave incident from the X-axis direction is radiated in the X-axis direction. The graph G8shows a reflection coefficient. The graph G7shows that insertion loss in a region from around 21.00 GHz to around 28.00 GHz is about −3 dB or more and transmission characteristics are satisfactory. The graph G8shows that the reflection coefficient in the region from around 21.00 GHz to around 28.00 GHz is low. That is, the unit structure10B illustrated inFIG.8has satisfactory transmission characteristics over a wide range from around 21.00 GHz to around 28.00 GHz.

InFIG.10, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.10shows a graph G9. The graph G9shows a transmission coefficient when the electromagnetic wave incident from the X-axis direction is radiated in the Y-axis direction. As shown in the graph G9, in the transmission coefficient when the electromagnetic wave incident from the X-axis direction is radiated in the Y-axis direction, the insertion loss in a region from around 21.00 GHz to around 28.00 GHz is about −3 dB or more and transmission characteristics are satisfactory.

The unit structure10B has satisfactory transmission coefficients of the electromagnetic wave from the X-axis direction to the X-axis direction and from the X-axis direction to the Y-axis direction. That is, the unit structure10B functions as a spatial filter and has a polarizing function.

Fourth Embodiment

Configuration of Unit Structure

A configuration of the unit structure according to a fourth embodiment will be described with reference toFIG.11.FIG.11is a diagram illustrating a configuration of the unit structure according to the fourth embodiment.

As illustrated inFIG.11, a unit structure10C includes the substrate12the first resonator14, the second resonator16, the reference conductor18, the connection line path20and a third resonator22. The unit structure10C differs from the unit structure10illustrated inFIG.2in that the unit structure10C includes the third resonator22. In the unit structure10C, the reference conductor18includes an opening portion18csurrounding the third resonator22.

The third resonator22may be located between the first resonator14and the second resonator16in the Z-axis direction. The third resonator22may be located within the opening portion18cof the reference conductor18. The third resonator22may be located within the opening portion18cso as not to be in contact with the reference conductor18. That is, the third resonator22is surrounded by the reference conductor18. The third resonator22is capacitively connected to the reference conductor18.

In the present embodiment, when a wavelength of a fundamental wave of an incoming electromagnetic wave is A, a length of at least one side of the first resonator14is set to λ/2, a length of at least one side of the second resonator16is set to λ/2, and a length of at least one side of the third resonator22is set to λ/4.

Frequency characteristics of the unit structure according to the fourth embodiment will be described with reference toFIG.12.FIG.12is a graph showing frequency characteristics of the unit structure according to the fourth embodiment.

InFIG.12, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.12shows a graph G10and a graph G11. The graph G10shows the transmission coefficient from the X-axis direction to the X-axis direction. The graph G11shows the reflection coefficient of the electromagnetic wave incident in the X-axis direction. The graph G10shows that the insertion loss in a region from around 18.00 GHz to around 28.00 GHz is −2 dB or more and transmission characteristics are satisfactory. The graph G11shows that the reflection coefficient in the region from around 18.00 GHz to around 28.00 GHz is low. As shown in the graph G10, the unit structure10C has a steep attenuation characteristic in a higher frequency band than in the unit structure10illustrated inFIG.2. That is, the unit structure10C illustrated inFIG.11has satisfactory transmission characteristics over a wide range from around 18.00 GHz to around 28.00 GHz.

An amount of change in phase of the unit structure according to the fourth embodiment will be described with reference toFIG.13.FIG.13is a graph showing the amount of change in phase of the unit structure according to the fourth embodiment.

InFIG.13, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.13shows a graph G12. The graph G12shows the amount of shift in phase of the electromagnetic wave when the electromagnetic wave incident on the first resonator14is radiated from the second resonator16. For example, when the electromagnetic wave having a frequency around 18.00 GHz is incident on the first resonator14, the unit structure10C shifts the phase of the electromagnetic wave by about −37° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency around 27.50 GHz is incident on the first resonator14, the unit structure10C shifts the phase of the electromagnetic wave by about −40° and radiates the electromagnetic wave from the second resonator16. That is, even when a plurality of the resonators are provided as in the unit structure10C, the incoming electromagnetic wave can be shifted.

Variation of Fourth Embodiment

In the unit structure10C, by changing the designs of the first resonator14, the second resonator16, and the third resonator22, the amount of change in phase and the frequency band in which the phase is changed can be changed.

Frequency characteristics of the unit structure according to a variation of the fourth embodiment will be described with reference toFIG.14.FIG.14is a graph showing frequency characteristics of the unit structure according to a variation of the fourth embodiment.

InFIG.14, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.14shows a graph G13and a graph G14. The graph G13shows the transmission coefficient from the X-axis direction to the X-axis direction. The graph G13shows the reflection coefficient of the electromagnetic wave incident in the X-axis direction. The graph G13shows that the insertion loss in a region from around 21.00 GHz to around 28.00 GHz is −2 dB or more and transmission characteristics are satisfactory. The graph G13shows that the reflection coefficient in the region from around 21.00 GHz to around 28.00 GHz is low. That is, the unit structure10C illustrated inFIG.11has satisfactory transmission characteristics over a wide range from around 21.00 GHz to around 28.00 GHz.

An amount of change in phase of the unit structure according to a variation of the fourth embodiment will be described with reference toFIG.15.FIG.15is a graph showing the amount of change in phase of the unit structure according to the variation of the fourth embodiment.

InFIG.15, the horizontal axis represents the frequency [GHz] and the vertical axis represents the gain [dB].FIG.15shows a graph G15. The graph G15shows the amount of shift in phase of the electromagnetic wave when the electromagnetic wave incident on the first resonator14is radiated from the second resonator16. For example, when the electromagnetic wave having a frequency around 21.00 GHz is incident on the first resonator14, the unit structure10C shifts the phase of the electromagnetic wave by about −55° and radiates the electromagnetic wave from the second resonator16. For example, when the electromagnetic wave having a frequency around 27.50 GHz is incident on the first resonator14, the unit structure10C shifts the phase of the electromagnetic wave by about 117° and radiates the electromagnetic wave from the second resonator16. That is, even when a plurality of the resonators are provided as in the unit structure10C, the incoming electromagnetic wave can be shifted.

In the example illustrated inFIG.11, the unit structure10C includes three resonators, but the present disclosure is not limited thereto. In the present disclosure, the composite resonator may include three or more resonators. In the present disclosure, by increasing the number of resonators, a steeper attenuation characteristic can be provided in a high frequency band.

Embodiments of the present disclosure have been described above, but the present disclosure is not limited by the contents of the embodiments. Constituent elements described above include those that can be easily assumed by a person skilled in the art, those that are substantially identical to the constituent elements, and those within a so-called range of equivalency. The constituent elements described above can be combined as appropriate. Various omissions, substitutions, or modifications of the constituent elements can be made without departing from the spirit of the above-described embodiments.