JP3475555B2 - TM mode dielectric resonator, TM mode dielectric resonator device, and high frequency bandpass filter device - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a TM mode dielectric resonator, a TM mode dielectric resonator device and a high frequency band pass filter device used in a microwave, quasi-millimeter wave or millimeter wave high frequency band.

[0002]

2. Description of the Related Art With the development of mobile communication, high-frequency resonators and high-frequency filters are required to be smaller, thinner, and have lower loss. As a resonator that can meet these demands, there is a circular TM mode dielectric resonator formed by forming a circular conductor on the upper surface of a dielectric substrate having a ground conductor formed on the lower surface.

The resonance frequency of the circular TM mode dielectric resonator is equal to the diameter of the circular conductor when the thickness of the dielectric substrate is sufficiently larger than the skin depth of the circular conductor at the resonance frequency. It is determined by setting the dielectric constant of the dielectric substrate to a predetermined value. The unloaded Q of the circular TM mode dielectric resonator is the conductor loss of the circular conductor, the dielectric loss of the dielectric substrate, the radiation loss that is lost by passing through the circular conductor, and the loss around the circular conductor. It is determined by the radiation loss due to exposure and the thickness of the dielectric substrate. Here, the unloaded Q of the circular TM mode dielectric resonator increases substantially in proportion to the thickness of the dielectric substrate.

As a dielectric material in recent years, a material having a high dielectric constant and a low loss characteristic has been developed and put into practical use, and in a high frequency band, a high frequency current is concentrated on a conductor surface due to a skin effect. , The surface resistance (also referred to as skin resistance) increases as the position approaches the conductor surface, and the conductor loss (Joule loss) increases. Therefore, comparing the dielectric loss with the conductor loss, the conductor loss is more dominant than the dielectric loss in the unloaded Q. Here, the skin effect means that inside the conductor, the distance from the surface of the conductor increases,
This is a phenomenon peculiar to the transmission of high-frequency signals, in which the high-frequency current decays exponentially.

From the above, in the conventional circular TM mode dielectric resonator, a metal having a high conductivity such as Cu or Ag is used, and in order to avoid the radiation loss which is lost through the circular conductor, the skin The circular conductor and the ground conductor are formed in a film thickness sufficiently thicker than the depth, and the size and the no-load Q are automatically determined from the design center frequency.

[0006]

However, in the conventional circular TM mode dielectric resonator, when the design center frequency is determined, the dimensions of the dielectric resonator are automatically determined, and it is possible to meet the demand for thinning. There was a problem that it could not be done.

A first object of the present invention is to solve the above problems and provide a TM mode dielectric resonator and a TM mode dielectric resonator device which are thinner than conventional examples and have a high unloaded Q. Especially.

A second object of the present invention is to solve the above problems and provide a high-frequency bandpass filter device which is thinner than the conventional example, has a small loss in the pass band and a large attenuation in the stop band. Especially.

[0009]

A TM mode dielectric resonator according to a first aspect of the present invention comprises a dielectric substrate sandwiched by a pair of electrodes having a predetermined shape, and has a predetermined resonance frequency. In the TM mode dielectric resonator having, one electrode of the pair of electrodes is a thin film laminated electrode formed by alternately laminating thin film conductors and thin film dielectrics, and the thin film laminated electrode is , At least one sub-TM mode resonator constituted by a pair of the thin film conductors sandwiching the thin film dielectric is laminated, and by the thin film conductor formed in contact with the dielectric substrate and the other electrode. An electromagnetic field generated when the main TM mode resonator constituted by sandwiching the dielectric substrate is excited at the same resonance frequency as the resonance frequency, and the sub TM.
The film thickness and the dielectric constant of each of the thin film dielectrics are set so that the electromagnetic field generated when the mode resonator is excited at the same resonance frequency as the resonance frequency is substantially in phase with each other. Of the thin film conductors other than the thin film conductor formed farthest from the dielectric substrate to have a thickness smaller than the skin depth of the resonance frequency, and the electromagnetic field of the main TM mode resonator and the sub TM mode resonator. And the electromagnetic fields of the sub-TM mode resonators adjacent to each other are coupled to each other.

According to another aspect of the present invention, there is provided a TM mode dielectric resonator having a dielectric substrate sandwiched by a pair of electrodes having a predetermined shape, and having a predetermined resonance frequency. Both of the pair of electrodes are
A thin film laminated electrode constituted by alternately laminating a thin film conductor and a thin film dielectric, wherein each thin film laminated electrode is constituted by at least a pair of the thin film conductors sandwiching the thin film dielectric. One sub-TM mode resonator is laminated, and the dielectric substrate is sandwiched by two thin film conductors formed in contact with the dielectric substrate among the thin film conductors of each thin film laminated electrode. The electromagnetic field generated when the main TM mode resonator is excited at the same resonance frequency as the resonance frequency, and the sub TM mode resonance of the first thin film laminated electrode formed on one surface of the dielectric substrate. An electromagnetic field generated when the resonator is excited at the same resonance frequency as the resonance frequency thereof is substantially in phase with each other, and the electromagnetic field of the main TM mode resonator,
An electromagnetic field generated when the sub-TM mode resonator of the second thin film laminated electrode formed on the other surface of the dielectric substrate is excited at the same resonance frequency as its resonance frequency is substantially in phase with each other. The film thickness and the dielectric constant of each thin film dielectric are set so that the thickness of the thin film conductor other than the thin film conductor formed farthest from the dielectric substrate in the first thin film laminated electrode is set to the resonance. The electromagnetic field of the main TM-mode resonator and the electromagnetic field of the sub-TM-mode resonator of the first thin-film laminated electrode are coupled to each other by making the thickness thinner than the skin depth of frequency, and the electromagnetic fields of the first thin-film laminated electrode are mutually connected. The thickness of a thin film conductor other than the thin film conductor formed so as to couple the electromagnetic fields of the adjacent sub-TM mode resonators and formed farthest from the dielectric substrate in the second thin film laminated electrode is set to the resonance. Lap The main T and thinner than the skin depth of a few
The electromagnetic field of the M-mode resonator and the electromagnetic field of the sub-TM mode resonator of the second thin film laminated electrode are coupled to each other, and the electromagnetic fields of adjacent sub-TM mode resonators of the second thin film laminated electrode are adjacent to each other. Is set so that they are combined.

A TM mode dielectric resonator according to a third aspect is the TM mode dielectric resonator according to the first or second aspect, wherein the film thickness of the thin film conductor formed farthest from the dielectric substrate is the above. Π / 2 of skin depth at resonance frequency
It is characterized by being set to double.

A TM mode dielectric resonator according to a fourth aspect is the TM mode dielectric resonator according to any one of the first to third aspects, wherein the thin film conductor is formed in contact with the dielectric substrate. The film thickness of each thin film conductor from the dielectric substrate to the thin film conductor formed farthest away is made thicker as the film thickness of the thin film conductor formed farther from the dielectric substrate.

According to a fifth aspect of the present invention, there is provided a TM mode dielectric resonator device comprising the TM mode dielectric resonator according to any one of the first to fourth aspects and the TM mode dielectric resonator at the resonance frequency. And a cavity for confining an electromagnetic field generated when excited in the cavity.

According to a sixth aspect of the present invention, in the high frequency band pass filter device, at least one TM according to any one of the first to fourth aspects, wherein two TM mode dielectric resonators adjacent to each other are electromagnetically coupled. Mode dielectric resonator and the above-mentioned T
The M mode dielectric resonator is provided with an input terminal for inputting a high frequency signal and an output terminal for outputting a high frequency signal output from the TM mode dielectric resonator.

[0015]

In the TM mode dielectric resonator according to claim 1 of the present invention, the TM mode dielectric resonator is formed in contact with the dielectric substrate when the TM mode dielectric resonator is excited by a high frequency signal having the resonance frequency. The thin film conductor that transmits a part of the resonance energy of the TM mode dielectric resonator to the thin film conductor formed apart from the dielectric substrate via the thin film dielectric. As a result, a high frequency current flows through each of the thin film conductors, effectively increasing the skin depth. Thereby, the conductor loss and the surface resistance can be reduced as compared with the conventional one, and the TM mode dielectric resonator has a relatively large unloaded Q.

Further, in the TM mode dielectric resonator according to claim 1, a thin film conductor formed in contact with the dielectric substrate when the main TM mode resonator is excited by a high frequency signal having the resonance frequency. Transmits a part of the resonance energy of the main TM mode resonator to the sub TM mode resonator. Each of the thin film conductors transmits a part of the resonance energy to the sub-TM mode resonator formed further away from the dielectric substrate. As a result, the sub TM mode resonator resonates at the same frequency as the main TM mode resonator, and the conductive thin films in the vicinity of the surface near the dielectric substrate and in the vicinity of the surface apart from the dielectric substrate are in opposite directions. Two high-frequency currents facing each other (hereinafter, facing two
Two high-frequency currents. ) Is flowing. That is, since the film thickness of each thin film conductor other than the thin film conductor formed farthest from the dielectric substrate is thinner than the skin depth δ0, the two high frequency currents facing each other interfere with each other,
They are partially offset by each other. On the other hand, in each thin film dielectric, a displacement current is generated by the electromagnetic field, and a high frequency current is generated on the surface of the adjacent thin film conductor. Further, the film thickness of each of the thin film dielectrics is set to be the same as that of the main TM mode resonator and each of the sub Ts.
Since the electromagnetic fields of the M-mode resonator are set to have substantially the same phase, the high frequency currents flowing through the thin film conductors have substantially the same phase. As a result, the high frequency currents flowing in the same phase in each of the thin film conductors effectively increase the skin depth. As a result, the conductor loss and the surface resistance can be significantly reduced as compared with the conventional one, and the TM mode dielectric resonator has a relatively large unloaded Q.

In the TM mode dielectric resonator according to claim 2 of the present invention, the TM mode dielectric resonator has a high frequency signal having the resonance frequency, like the TM mode dielectric resonator according to claim 1. When excited by, the thin film conductor formed in contact with the dielectric substrate forms part of the resonance energy of the TM mode dielectric resonator away from the dielectric substrate via the thin film dielectric. Permeate through thin film conductors. As a result, a high frequency current flows through each of the thin film conductors, effectively increasing the skin depth. Thereby, the conductor loss and the surface resistance can be reduced as compared with the conventional one, and the TM mode dielectric resonator has a relatively large unloaded Q.

Further, in the TM mode dielectric resonator according to claim 2, when the main TM mode resonator is excited by a high frequency signal having the resonance frequency, the sub TM mode resonance of the first thin film laminated electrode is generated. And the sub TM mode resonator of the second thin film laminated electrode resonates at the same frequency as that of the main TM mode resonator, respectively, near the surface of each conductor thin film close to the dielectric substrate and away from the dielectric substrate. In the vicinity of the surface, two high-frequency currents facing each other in the opposite directions (hereinafter referred to as two high-frequency currents facing each other) flow, and the two high-frequency currents facing each other interfere with each other and are partially offset from each other. Then, the high frequency currents flowing through the respective thin film conductors are substantially in phase with each other. As a result, the high frequency currents flowing in the same phase in each of the thin film conductors effectively increase the skin depth. As a result, the first and second
Both the conductor loss and the surface resistance of the thin film laminated electrode can be greatly reduced compared to the conventional one, and the TM mode dielectric resonator has a relatively large unloaded Q.

In the TM mode dielectric resonator according to claim 3, the film thickness of the thin film conductor formed farthest from the dielectric substrate is π / 2 of the skin depth at the resonance frequency.
It is set to double. As a result, the skin effect is mitigated also in the thin film conductor itself, and the surface resistance of the thin film conductor itself is reduced. Further, since the thin film conductor is set to be larger than the skin depth of the resonance frequency, the radiation loss is suppressed to be small.

In the TM mode dielectric resonator according to claim 4, the film of each thin film conductor from the thin film conductor formed in contact with the dielectric substrate to the thin film conductor formed farthest from the dielectric substrate. Since the thickness is made thicker as the film thickness of the thin film conductor formed apart from the dielectric substrate, the amplitude of the high frequency current increases as the thin film conductor formed farther from the dielectric substrate. Thereby, the skin depth can be substantially increased most, and the TM mode dielectric resonator has a relatively large unloaded Q.

In the TM mode dielectric resonator device according to the fifth aspect, an electromagnetic field generated when the TM mode dielectric resonator is excited at the resonance frequency is confined in the cavity. As a result, the radiation loss can be reduced as compared with the TM mode dielectric resonator having no cavity.

A high frequency band pass filter device according to a sixth aspect of the present invention comprises the above TM mode dielectric resonator, and constitutes a band pass filter having a relatively small loss in the pass band and a relatively large attenuation amount in the stop band.

[0023]

Embodiments of the present invention will be described below with reference to the drawings. In the attached drawings, the same components are designated by the same reference numerals. <First Embodiment> FIG. 1 is a partially cutaway perspective view of a TM mode dielectric resonator device according to a first embodiment of the present invention.
FIG. 2 shows the TM of the first embodiment taken along the line AA 'in FIG.
It is sectional drawing of a mode dielectric resonator apparatus. Here, FIG.
Although not a cross-sectional view, the thin film conductors 1 to 5 are shown with hatching in order to distinguish them from the thin film dielectric.

The TM mode dielectric resonator device according to the first embodiment includes a thin film laminated electrode 6 having a structure in which thin film conductors 1 to 5 and thin film dielectrics 30-1 to 30-4 are alternately laminated. , Thin film conductors E1 to E5 and thin film dielectric E30-1
To E30-4 and a thin film laminated electrode E6 having a structure in which the dielectric substrate 10 is sandwiched between the TM mode dielectric resonator R1 and the TM mode dielectric resonator R1. It is characterized by comprising a cylindrical case 40 for confining an electromagnetic field generated when excited at the resonance frequency inside the case 40.

In the TM mode dielectric resonator, the thin film laminated electrode 6 has circular thin film conductors 1 to 5 each having a predetermined radius r on the upper surface of the dielectric substrate 10 and the same radius as the thin film conductors 1 to 5. Circular thin film dielectric 3 with r
0-1 to 30-4 are formed by alternately laminating the thin film conductors 5 so as to be in contact with the upper surface of the dielectric substrate 10. The dielectric substrate 10 is a circular sapphire substrate whose upper and lower surfaces are cut into R surfaces and whose upper and lower surfaces are mirror-polished, and a part of the circumference is cut to show the plane orientation. The orientation flat 101 is formed. Here, the R plane is the plane orientation (1/102) of the sapphire single crystal.
That is. / In parentheses represents a bar (-) added above the second number "1", and
The same applies. In addition to these, there are A-side (11/20) and C-side (0001). As a result, four TMs, one thin film dielectric is sandwiched between a pair of thin film conductors, respectively.
Mode dielectric resonators (hereinafter referred to as sub-TM mode resonators) 201 to 204 are stacked. In FIGS. 1 and 2, the reference symbols of the sub-TM mode resonators indicate the thin film dielectrics 30-1 to 30-4 of the sub-TM mode resonators.
Is attached in parentheses. Here, the resonance frequencies of the sub-TM mode resonators 201 to 204 are all set to be equal.

Further, the thin film laminated electrode E6 is the dielectric substrate 1
0 thin film conductors E1 each having a predetermined radius r
To E5 and thin film dielectrics E30-1 to E30-4 having the same radius r as the thin film conductors E1 to E5 face the thin film conductor 5 such that the thin film conductor E5 is in contact with the lower surface of the dielectric substrate 10. As described above, they are alternately laminated. As a result, four sub-TM mode resonators 211 to 214 each having one thin film dielectric sandwiched by a pair of thin film conductors are stacked. Where vice T
The resonance frequencies of the M-mode resonators 211 to 214 are all equal and the sub-TM-mode resonators 201 to 2 are used.
04 and the sub-TM mode resonators 211 to 21.
It is set to be equal to the resonance frequency of 4.

Further, the dielectric substrate 10 is sandwiched by the thin film conductor 5 and the thin film conductor E5 to form a TM mode resonator (hereinafter referred to as a main TM mode resonator) 210. Here, the resonance frequency of the main TM mode resonator 210 is set to be equal to the resonance frequencies of the sub TM mode resonators 201 to 204 and the sub TM mode resonators 211 to 214. In addition, the main TM mode resonator 210 is
The circumferential condition inside the dielectric substrate 10 that connects the outer circumference circle of the thin film conductor 5 and the outer circumference circle of the thin film conductor E5 in the thickness direction satisfies the opening condition. That is, the circumferential surface is a magnetic wall. In addition, Vice T
Thin film dielectric 30-1 of the M-mode resonators 201 to 204
To 30-4 and the circumferential surfaces of the thin film dielectrics E30-1 to 30-4 of the sub-TM mode resonators 211 to 214 are magnetic walls that satisfy the opening conditions.

Here, especially in the TM mode dielectric resonator device of the first embodiment, as will be described later in detail, the main T
An electromagnetic field generated when the M-mode resonator 210 is excited at the above resonance frequency and each sub-TM-mode resonator 201 to 20.
4 so that the electromagnetic field generated when the 4 is excited at the resonance frequency is substantially in phase with each other.
Dielectric film thickness x _{a1 to} x _a4 and dielectric constant ε _{s of} 1 to 30-4
And the electromagnetic fields of the main TM mode resonator 210 and the electromagnetic fields generated when the sub TM mode resonators 211 to 214 are excited at the resonance frequency are substantially in phase with each other. Dielectrics E30-1 to E30-4
The dielectric film thicknesses x _{ae1 to} x _ae4 and the dielectric constant ε _s are set. In addition, the conductor film thicknesses ξa _{2 to} ξa ₅ of the thin film conductors 2 to 5 are set to be smaller than the skin depth δ ₀ of the resonance frequency and set to a predetermined film thickness such that the upper layers are thicker, Adjacent main TM mode resonator 210 and sub TM mode resonator 204, sub TM mode resonator 204 and sub TM mode resonator 203, sub TM mode resonator 203 and sub TM mode resonator 202, sub TM mode resonator 202 And the electromagnetic fields between the sub TM mode resonator 201 are coupled to each other. Accordingly, the resonance energy of the main TM mode resonator 210 is transferred to the sub TM mode resonator 204,
A part is moved to 203, 202, and 201, and as shown in FIG. 4B, a high-frequency current flows in each of the thin film conductors 1 to 5, so that the skin effect due to a high frequency is significantly suppressed. Here, FIG. 4B is a graph showing the amplitude of the current in the thickness direction in the thin film laminated electrode 6 of FIG. 1, and FIG. 4A shows the skin depth of the used frequency used for comparison. It is a graph which shows the amplitude of the electric current of the thickness direction in a thick 1-layer conductor.

Similarly, by setting the conductor film thicknesses ξa _{e2 to} ξa _e5 of the thin film conductors E2 to E5, the main TM
Part of the resonance energy of the mode resonator 210 is transferred to the sub-TM mode resonators 214, 213, 212 and 211,
The thin-film conductors E1 to E5 are configured so that a high-frequency current flows through them, thereby significantly suppressing the skin effect due to high frequencies. That is, the thin film laminated electrodes 6 and E6 are high frequency electromagnetic field coupling type thin film laminated electrodes.

Further, each conductor film thickness ξa of the thin film conductors 1, E1
₁ and ξa _e1 are set to be π / 2 times the skin depth δ ₀ of the resonance frequency, which is the film thickness at which the total loss of the conductor loss and the radiation loss of the thin film conductors 1, E1 is minimized. , E1
To form.

Then, the TM mode dielectric resonator R1
Is a cylindrical case 4 having upper and lower end surfaces facing each other and having the same inner diameter as the outer circumference circle of the dielectric substrate 10.
0, the side surface of the dielectric substrate 10 and the inner peripheral surface of the case 40 are in contact with each other, and the upper surface of the thin film laminated electrode 6 is separated from the upper end surface of the case 40 by a predetermined distance. The lower surface of E6 and the lower end surface of the case 40 are fixed in contact with each other so as to be electrically conductive. The TM mode dielectric resonator device of the first embodiment is constructed as described above.

Next, the conductor film thickness ξa of each thin film conductor 1 to 5
_The method of setting _{1 to} ξ a ₅ and the dielectric film thicknesses x _{a1 to} x _a4 of the thin film dielectrics 30-1 to 30-4 will be described in detail.

FIG. 8A shows the electric field distribution in the cross section of the dielectric substrate 10 sandwiched by the thin film conductor 5 and the thin film conductor E5 when the TM mode dielectric resonator R1 resonates in the TM ₁₁₀ mode. FIG. 9 is a sectional view showing FIG.
[FIG. 8] A sectional view showing a magnetic field distribution in the transverse section when the TM mode dielectric resonator R1 resonates in a TM ₁₁₀ mode. Further, FIG. 9A shows a dielectric substrate 10 sandwiched by the thin film conductor 5 and the thin film conductor E5 when the TM mode dielectric resonator R1 resonates in the TM ₂₁₀ mode.
9 is a cross-sectional view showing an electric field distribution in a cross section of FIG.
(B) shows that the TM mode dielectric resonator R1 has a TM ₂₁₀
It is sectional drawing which shows the magnetic field distribution in the said cross section when resonating in mode. Further, FIG. 10 (a) shows the above TM
FIG. 10B is a sectional view showing an electric field distribution in a transverse section of the dielectric substrate 10 sandwiched by the thin film conductor 5 and the thin film conductor E5 when the mode dielectric resonator R1 resonates in the TM ₀₁₀ mode. , The TM mode dielectric resonator R1
FIG. 6 is a cross-sectional view showing a magnetic field distribution in the transverse section when the element resonates in the TM ₀₁₀ mode. Above TM ₁₁₀ mode, T
The electromagnetic fields in the thin film dielectrics 30-1 to 30-4 when resonating in the M ₂₁₀ mode and the TM ₀₁₀ mode are distributed similarly to the inside of the dielectric substrate 10.

As shown in FIGS. 8 to 10, the resonance modes of the main TM mode resonator 210 and the sub TM mode resonators 201 to 4 of the first embodiment are different in the thickness of the thin film conductors 1 to 5, respectively. Electric field 51 parallel to the vertical direction and the thin film conductor 1
Magnetic field 61 which is orthogonal to the thickness direction. That is, the rectangular minute regions 81, 82, 83 sandwiched by the thin film conductor 5 and the thin film conductor E5 can be regarded as TEM transmission lines (hereinafter referred to as the main transmission line LN10). Here, the minute regions 81, 82 and 83 are
It has its longitudinal direction perpendicular to the magnetic field 61 when resonating in the M mode. Similarly, the minute regions 81, 82, 83
And a rectangular minute region (not shown) of the thin film dielectric 30-k which is opposed to the thickness direction and is sandwiched by the thin film conductors k and k + 1 is a TEM transmission line (hereinafter referred to as a sub transmission line). Can be regarded as Here, the sub-transmission line LNk is attached to the sub-transmission line in association with the thin film dielectric 30-k in order to distinguish the sub-transmission line from each other in the specification.
In this specification, an electromagnetic field mode having an electric field 51 parallel to the thin film conductors 1 to 5 in the thickness direction and a magnetic field 61 orthogonal to the thickness direction of the thin film conductors 1 to 5 is called a parallel propagation mode. The TM ₁₁₀ mode, the TM ₂₁₀ mode, the TM ₀₁₀ mode and the TEM mode are parallel propagation modes, respectively. From the above, the conductor film thicknesses ξa _{1 to} ξa ₅ of the thin film conductors 1 to ₅ and the dielectric film thicknesses x _{a1 to} x of the thin film dielectrics 30-1 to 30-4 that minimize the surface resistance of the thin film laminated electrode 6 are obtained. _a4 can be set as follows.

First, the conductor film thickness ξa _{1 at} which the surface resistance RAs ₁ of the thin film conductor ₁ is minimized is obtained. FIG. 14A is a circuit diagram of a distributed constant type equivalent circuit in the thickness direction of the thin film conductor 1 including an air layer, and the equivalent circuit has a distribution including loss resistance as shown in FIG. 14A. It consists of a constant circuit. 14
The distributed constant type equivalent circuit of (a) is composed of two terminals T1-3 and T1-4 virtually provided on the lower first surface of the thin film conductor 1 in the minute region, and the thin film conductor in the minute region. It is provided between two terminals T1-1 and T1-2 that are virtually provided on the second surface on the upper side of 1. Each unit circuit of the distributed constant type equivalent circuit has a unit inductance ldx provided in a direction parallel to the thickness direction.
And a parallel circuit of a unit capacitance cdx and a unit conductance gdx provided in a direction perpendicular to the thickness direction, respectively, and the parallel circuit and the unit inductance ldx are connected in an inverted L shape. And
The distributed constant type equivalent circuit is configured by connecting a plurality of the unit circuits in cascade in the thickness direction, and two terminals T1-1 and T1-2 on the air layer side of the equivalent circuit are connected to the air layer. Impedance ZA _L is connected. Here, the unit inductance ldx, the unit capacitance cdx, and the unit conductance gdx are expressed by the following equations 1, 2, and 3, respectively. In Equations 1, 2 and 3, σ is the thin film conductor 1
The conductivity of, epsilon ₀ is the dielectric constant in vacuum, mu ₀ is the permeability, dx is the thin-film conductors 1 thickness direction of the minute length in vacuum, ZA _L is the impedance of the air layer, y _a sub transmission line Is the track width. Further, β ₀ is the main transmission line LN at the resonance frequency
It is a phase constant of 10 and is expressed by the following equation 4 using the angular frequency ω ₀ corresponding to the resonance frequency and the dielectric constant ε _m of the dielectric substrate 10.

[0036]

## EQU00001 ## ldx = (μ ₀ / y _a β ₀ ) dx

(2) cdx = ε ₀ y _a β ₀ dx

Gdx = σy _a β ₀ dx

[Formula 4] β ₀ = ω ₀ √ (μ ₀ ε _m ).

Further, the equivalent circuit of FIG.
It can be converted into the lumped constant type equivalent circuit of (b).
In the lumped constant type equivalent circuit, two complex impedances ZA ₁ provided in a direction parallel to the thickness direction and a complex admittance YA ₁ provided in a direction perpendicular to the thickness direction are connected in a T-shape. Composed. Here, the complex impedance ZA ₁ , the complex admittance YA ₁ , and the impedance ZA _{L of the} air layer are expressed by Equations 6, 7, and 8, respectively. Further, a value obtained by dividing the skin depth [delta] ₀ represented the conductor thickness Kushiei ₁ of the thin-film conductor 1 by the number 5 is defined as the normalized conductor film thickness xi] ₁ of the thin-film conductor 1, the table as numbers 9 did.

[0038]

(5) δ ₀ = √ (2 / ω ₀ μ ₀ σ)

ZA ₁ = [(1 + j) / (σδ ₀ y _a β ₀ )] tanh
_{[(1 + j) ξ 1} /2]

YA ₁ = [σδ ₀ y _a β ₀ / (1 + j)] · sinh [(1 + j) ξ ₁ ]

ZA _L = (1 / y _a ) (1 / β ₀ ) √ (μ ₀ / ε ₀ )

[Formula 9] ξ ₁ ≡ ξa ₁ / δ ₀

Further, the surface impedance ZAs ₁ when the equivalent circuit of FIG. 14B is viewed from the terminals T1-3 and T1-4 at the left end is expressed by equation 10. Here, as shown in Expression 11, the impedance ZA _{L of the} air layer is sufficiently larger than the complex impedance ZA ₁ and the complex admittance YA ₁ , so that the terminal T of the equivalent circuit of FIG.
The approximation that 1-1 and T1-2 are open ends can be used, and the surface impedance ZAs ₁ is expressed by
It is represented by.

[0040]

ZAs ₁ = ZA ₁ + [YA ₁ + (ZA ₁ + Z _L ) ^-1 ]
^-1

ZA _L σδ ₀ y _a β ₀ = σδ ₀ √ (μ ₀ / ε ₀ ) ≈∞

[Formula 12] ZAs ₁ = ZA ₁ + 1 / YA ₁

Further, the surface impedance ZAs ₁ expressed by the equation 12 is added to the complex impedance ZA expressed by the equation 6.
Substituting ₁ and the complex admittance YA ₁ for rearranging, the surface impedance ZAs ₁ is expressed as shown in Expression 13.

[0042]

ZAs ₁ = [(1 + j) / (σδ ₀ y _a β ₀ )] / [ta
nh {(1 + j) ξ ₁ }]

Further, the surface impedance ZAs ₁ is calculated by using the surface resistance RAs ₁ and the surface reactance XAs ₁ ,
Can be expressed as

[0044]

[Formula 14] ZAs ₁ = RAs ₁ + jXAs ₁

When the surface impedance ZAs ₁ expressed by the equation 13 is divided into the real part and the imaginary part, the surface resistance RAs ₁ and the surface reactance XAs ₁ are expressed by the equations 15 and 16, respectively. You can

[0046]

## EQU15 ## RA _S1 = {sinh (2ξ ₁ ) + sin (2ξ ₁ )} / [σδ
₀ y _a β ₀ {cosh (2ξ ₁ ) −cos (2ξ ₁ )}]

XA _S1 = {sinh (2ξ ₁ ) −sin (2ξ ₁ )} / [σδ
₀ y _a β ₀ {cosh (2ξ ₁ ) −cos (2ξ ₁ )}]

FIG. 15 shows a normalized surface resistance Rs ₁ obtained by multiplying the surface resistance RAs ₁ obtained by using Equation 15 by σδ ₀ y _a β _0.
3 is a graph showing the relationship between the standardized conductor film thickness ξ ₁ and. As is clear from FIG. 15, the normalized conductor film thickness ξ ₁ is 1 and 2
The standardized surface resistance Rs ₁ has a minimum value which is an extreme value. In standardized thickness xi] ₁ normalized surface resistance Rs ₁ is minimized, the partial derivative ∂Rs ₁ / ∂ξ ₁ for normalized conductor film thickness xi] ₁ normalized surface resistance Rs ₁ shown in Formula 17 0 become. Therefore, in order to find the standardized film thickness ξ ₁ that minimizes the standardized surface resistance Rs ₁ , it is sufficient to find the standardized conductor film thickness ξ ₁ that satisfies Eq.

[0048]

[Expression 17] ∂Rs ₁ / ∂ξ ₁ =-{2sinh (2ξ ₁ ) ・ sin (2ξ
₁ )} / {cosh (2ξ ₁ ) −cos (2ξ ₁ )} ² = 0

Partial differential coefficient ∂Rs ₁ / ∂ξ expressed by equation 17
_The normalized film thickness ξ ₁ when ₁ becomes 0 is represented by Expression 18 where n is a positive integer. In particular, the normalized film thickness ξ ₁ when n = 1 is expressed by Equation 19, and the normalized surface resistance Rs ₁
Is the minimum value Rs ₁ min expressed by the equation 20.

[0050]

## EQU1 ## ξ ₁ = (nπ) / 2, n = 1, 2, 3, ...

[Formula 19] ξ ₁ = π / 2

## EQU20 ## Rs ₁ min = tanh (π / 2) ≈0.917

Here, the thin film conductor 1 as defined by the equation 9
Since the normalized film thickness ξ _{1 of} is a value normalized by the skin depth δ ₀ , the conductor film thickness ξa ₁ of the thin film conductor 1 having the dimension of the physical length is given by Expression 21.

[0052]

Ξa ₁ = (π / 2) δ ₀ = (π / 2) √ [2 / (ω ₀ μ ₀ σ)]]

As is clear from the above results, when the normalized conductor film thickness ξ ₁ is π / 2, that is, when the conductor film thickness ξa ₁ of the thin film conductor ₁ is π / 2 times the skin depth δ _0. , surface resistance RAs _1, the conductor thickness Kushiei ₁ of the thin-film conductor 1 is the surface resistivity RAs ₁ when sufficiently thick compared to the skin depth δ ₀ 1 / (σδ ₀
y _a beta ₀₎ becomes a minimum value smaller _{0.917 / (σδ 0 y a β} 0). Further, as is clear from FIG. 15, when the standardized conductor film thickness ξ ₁ is set to a value within the range of 1.14 ≦ ξ ₁ ≦ 2.75, the standardized surface resistance Rs ₁ becomes smaller than 1. That is, when the normalized conductor film thickness ξ ₁ is set to a value within the range of 1.14 ≦ ξ ₁ ≦ 2.75, the surface resistance RAs at that time is set.
₁ is smaller than the surface resistivity RAs ₁ when sufficiently thick compared conductor thickness Kushiei ₁ of the thin-film conductor 1 to the skin depth [delta] _0.

Next, the conductor film thicknesses ξa _{2 to} ξa ₅ of the thin film conductors 2 to ₅ and the dielectrics of the thin film dielectrics 30-1 to 30-4 such that the surface resistance Rs of the thin film laminated electrode 6 is minimized. A method of setting the film thickness x _{a1 to} x _a4 will be described. FIG.
(A) shows thin film conductors 1 to 5 (hereinafter, representatively thin film conductor k
Called. 16) is a distributed constant type equivalent circuit in the thickness direction, and is a distributed constant circuit including a loss resistance as shown in FIG. Here, the same symbols are attached to the same components as those in FIG. The distributed constant type equivalent circuit of FIG. 16A has two terminals Tk-3 and Tk-4 virtually provided on the first surface of the thin-film conductor k and a virtual terminal on the second surface of the thin-film conductor 1. Two terminals T provided on
It is provided between k-1 and Tk-2. Each unit circuit of the distributed constant type equivalent circuit is provided in the same manner as the unit circuit of the thin film conductor 1 of FIG. 14 with a unit inductance ldx provided in a direction parallel to the thickness direction and in a direction perpendicular to the thickness direction. A parallel circuit including the unit capacitance cdx and the unit conductance gdx is provided, and the parallel circuit and the unit inductance ldx are connected in an inverted L shape. The distributed constant type equivalent circuit is configured by connecting a plurality of the unit circuits in cascade in the thickness direction. Here, the unit inductance ldx, the unit capacitance cdx, and the unit conductance gdx are expressed by the equations 1, 2, and 3, respectively. Ξ a _k is the thin film conductor k
A film thickness, y _a is set to a line width of the thin-film conductors k equal to the line width of the thin-film conductors 1. Furthermore, β ₀ is the main transmission line LN at the resonance frequency described above.
The phase constant of 10 is given by the equation 4, and σ is the conductivity of the thin film conductor k (k = 2, 3, 4, 5) and is the thin film conductor 1.
Is set to the same value as. The skin depth δ ₀ of each thin film conductor has the same value.

The equivalent circuit of FIG. 16 (a) is shown in FIG.
It can be converted into the lumped constant type equivalent circuit of (b).
In the lumped constant type equivalent circuit, two complex impedances ZA _k provided in a direction parallel to the thickness direction and a complex admittance YA _k provided in a direction perpendicular to the thickness direction are connected in a T type. Composed. Here, the complex impedance ZA _k and the complex admittance YA _k is a normalized conductor film thickness xi] _k thin film conductor k which is defined a conductor thickness Kushiei _k of thin-film conductors k by the number 22 divided by the skin depth [delta] ₀ It is expressed by the following equations 23 and 24, respectively.

[0056]

## EQU22 ## ξ _k ≡ξ a _k / δ ₀

ZA _k = [(1 + j) / (σδ ₀ y _a β ₀ )] tanh
[(1 + j) ξ _k / 2]

YA _k = [σδ ₀ y _a β ₀ / (1 + j)] · sinh [(1 + j) ξ _k ]

Since the dielectric loss of the thin film dielectric 30-k is sufficiently smaller than the conductor loss of the thin film conductor k, the dielectric loss can be set to 0, and the complex impedance of the thin film dielectric 30-k is Reactance W expressed by equation 27
It can be represented only by A _k . Here, in Equation 27,
The dielectric film thicknesses x _a of the thin film dielectrics 30-1 to 30-4 (hereinafter, the thin film conductor 30-k is representatively represented) are respectively defined as dielectric film thicknesses x _{a1 to} x _a4 (hereinafter, represented as x. _{Add ak} .)
And the inductance Lk expressed by the equation 25 and the equation 26
The capacitance Ck represented by here,
In Equation 26, ε _s is the dielectric constant of the thin film dielectric 30-k, and the thin film dielectrics 30-1 to 30-4 are set to have the same value. As described above, the thin film laminated electrode 6
The equivalent circuit of can be expressed as shown in FIG. In FIG. 3, it is assumed that an ideal conductor, that is, a conductor having no conductor loss is formed on the lower surface of the dielectric substrate 10. In FIG. 3, ZAs _{1 to} ZAs ₅ are surface impedances when the direction of the upper air layer from the terminals T1-3 to T5-3 and T1-4 to T5-4 of the thin film conductors 1 to ₅ is viewed. Te, subjecting the ZAs _k when you call on behalf of the following.

[0058]

Lk = μ ₀ (x _ak / y _a ) (1 / β ₀ )

[Number 26] _{Ck = ε S (y a /} x ak) (1 / β 0)

-JWA _k = jω ₀ Lk + 1 / (jω ₀ Ck)

WA _k = (1 / σδ ₀ ) (1 / y _a ) (2x _ak
/ Δ ₀ ) (ε _m / ε _s -1)

Equation 28 is _obtained by further modifying the reactance WA _k of Equation 27 using Equations 25, 26 and 4. Also, the numbers 23, 24, and 2 obtained as described above
Recurrence formula regarding surface impedance ZAs _k With 8 is given by the following equation 29 as the number 30. Where number 29 is k
Is an expression that holds when = 1 and Equation 30 is an expression that holds when k ≧ 2.

[0060]

ZAs ₁ = ZA ₁ + [YA ₁ + (ZA ₁ + ZA _L ) ^-1 ] ^-1

[Number 30] _{ZAs k = ZA k + [YA} k + (ZA k -jWA k-1
+ ZAs _k-1 ) ^-1 ] ^-1

The surface resistance RAs ₀ per ₁ rad at the angular frequency ω ₀ is expressed by the _equation 31. Here, if the surface resistance RAs ₀ is selected as the normalization factor, the standardized surface impedance Zs _k can be expressed as in the following Expressions 32 and 33 by normalizing Expressions 29 and 30. Further, the standardized complex impedance Z _k , the standardized complex admittance Y _k , the standardized reactance W _k, and the standardized impedance Z _L of the air layer are
Equations 23, 24, 28 and 8 can be standardized and expressed as equation 34, equation 35, equation 36 and equation 37, respectively.

[0062]

RAs ₀ = 1 / (σδ ₀ y _a β ₀ )

Zs ₁ = Z ₁ + [Y ₁ + (Z ₁ + Z _L ) ⁻¹ ] ⁻¹

Equation 33] _{Zs k = Z k + [Y} k + (Z k -jW k-1 + Zs k-1) -1] -1

Z _k = (1 + j) · tanh [(1 + j) ξ _k / 2]

[Equation 35] Y _k = [1 / (1 + j)] · sinh [(1 + j) ξ _k ]

W _k = 2x _k (ε _m / ε _s -1)

Z _L = σδ ₀ √ (μ ₀ / ε ₀ ) = √ {2σ / (ω ₀ ε ₀ )}

Here, x _k is a standardized dielectric film thickness of the thin film dielectric 30-k, and is defined by the following formula 38. Further, the standardized surface impedance Zs _k can be expressed as in Equation 39 using the standardized surface resistance Rs _k and the standardized reactance Xs _k .

[0064]

X _k = x _ak / δ ₀

(39) Zs _k = Rs _k + jXs _k

Equations 32 and 33, which are recurrence formulas of the normalized surface impedance Zs _k normalized as above, were obtained.
Next, using the recurrence formula of the normalized surface impedance Zs _k expressed by the above equation 33, the normalized conductor film thickness ξ _k-1 of the thin film conductor _k-1 and the thin film dielectric 30- (k-2) are used. When the standardized dielectric film thickness x _k-2 is given, the standardized conductor film thickness ξ _k and the standardized dielectric film thickness x _k-1 for minimizing the standardized surface resistance Rs _k are _obtained. . Now, the normalized surface impedance Zs _k-1 of the thin film conductor k-1 is, as is clear from the equation 39, the equation 40
Can be expressed as Using this formula 40, formula 33 is expressed as formula 41.

[0066]

Zs _k-1 = Rs _k-1 + jXs _k-1

[Expression 41] Zs _k = Z _k + [Y _k + {Z _k + Rs _k-1 -j (W _k-1-
Xs _k-1 )} ^-1 ] ^-1

Now, let us consider the conditions for minimizing the normalized surface resistance Rs _k for the equation 41 which holds when k ≧ 2.

Since the standardized conductor film thickness ξ _k-1 and the standardized dielectric film thickness x _k-1 are given as described above, the standardized surface impedance Zs _k of the thin film conductor k expressed by the equation 41 is given. The variables in can be considered to be the normalized conductor film thickness ξ _k and the reactance W _k-1 of the thin film dielectric k-1. Therefore, by obtaining the normalized conductor film thicknesses ξ _k and W _k−1 that minimize the normalized surface resistance Rs _k , which is the real part of the surface impedance Zs _k , the normalized surface resistance Rs _k is minimized. The conductor film thickness ξ _k and the normalized dielectric film thickness x _k-1 can be obtained.

[0069] normalized surface resistance Rs _k is a real part of the normalized surface impedance Zs _k becomes a minimum normalized conductor film thickness xi] _k
And W _k−1 are _obtained by transforming the standardized complex impedance Z _k represented by the equation 34 and the standardized complex admittance Y _k represented by the equation 35 by using a known hyperbolic function theorem, The complex impedance Z _k and the standardized complex admittance Y _k are represented by the following equations 42 and 43, respectively. For convenience of calculation, the normalized surface impedance Zs _k expressed by the equation 41 is _defined as Xs _k−1 −W _k−1 as the reactance X, and the normalized complex impedance Z expressed by the equation 42. _By substituting the standardized complex admittance Y _k represented by _k and Formula 43 into Formula 41, and organizing the standardized surface impedance Zs _k into the form of the sum of the real part Rs _k and the imaginary part Xs _k , It can be seen that the normalized surface resistance Rs _k and the normalized surface reactance Xs _k are expressed by the equations 45 and 46, respectively.

[0070]

[Number 42] _{Z k = (1 + j)} (sinhξ k + jsinξ k) / (coshξ k + cosξ k)

[Number 43] _{Y k = [1 / (1} + j)] (sinhξ k · cosξ k + jcos
hξ _k · sinξ _k)

X = Xs _k-1 −W _k-1

[Formula 45] Rs _k = (2 · cosh ² ξ _k · Rs _k-1 + 2 · cosh ² ξ _k · X
+ coshξ _k・ sinhξ _k・ Rs _k-1 ² + coshξ _k・ sinhξ _k・ X ² + 2
・ Coshξ _k・ sinh ξ _k + 2 ・ cos ² ξ _k・ Rs _k-1 -2 ・ cos ² ξ _k・ X +
_{cosξ k · sinξ k · Rs k} -1 2 + cosξ k · sinξ k · X 2 - 2 · cos
_{ξ k · sinξ k - 2 ·} Rs k-1) / (cosh 2 ξ k · Rs k-1 2 + cosh 2 ξ
^{_{k · X 2 + 2 · cosh}} 2 ξ k + 2 · coshξ k · sinhξ k · Rs k-1 + 2 · co
_{shξ k · sinhξ k · X -} cos 2 ξ k · Rs k-1 2 -cos 2 ξ k · X 2 + 2 ·
_{^{cos 2 ξ k + 2 · cosξ}} k · sinξ k · Rs k-1 - 2 · cosξ k · sinξ k
・ X-2)

[Equation 46] Xs _k = (2 · cosh ² ξ _k · Rs _k-1 + 2 · cosh ² ξ _k · X
+ coshξ _k・ sinhξ _k・ Rs _k-1 ² + coshξ _k・ sinhξ _k・ X ² + 2
_{· Coshξ k · sinhξ k - 2} · cos 2 ξ k · Rs k-1 +2 · cos 2 ξ k · X -
_{cosξ k · sinξ k · Rs k} -1 2 - cosξ k · sinξ k · X 2 + 2 · cos
_{ξ k · sinξ k - 2 ·} X) / (cosh 2 ξ k · Rs k-1 2 + cosh 2 ξ k · X 2
_{^{+ 2 · cosh 2 ξ k +}} 2 · coshξ k · sinhξ k · Rs k-1 + 2 · coshξ k
・ Sinhξ _k・ X-cos ² ξ _k・ Rs _k-1 ² -cos ² ξ _k・ X ² + 2 ・ cos ²
_{ξ k + 2 · cosξ k ·} sinξ k · Rs k-1 - 2 · cosξ k · sinξ k · X -
2)

Next, the normalized surface resistance Rs _{k is set} to the reactance X.
When partial differentiation is carried out with, the partial differential coefficient ∂Rs _k / ∂X is
And partial differentiation of the standardized surface resistance Rs _k by ξ _k ,
The partial differential coefficient ∂Rs _k / ∂ξ is expressed by the following equations 47 and 48, respectively.

[0072]

[Expression 47] ∂R s _k / ∂X =-{2 ・ (2 ・ cosh ² ξ _k・ cos ² ξ _k・
Rs _k-1 ² -2 ・ cosh ² ξ _k・ cos ² ξ _k・ X ² -4 ・ cosh ² ξ _k・ cos ξ _{k
· Sinξ k · Rs k-1} - 4 · cosh 2 ξ k · cosξ k · sinξ k · X - cosh
² ξ _k・ Rs _k-1 ² + cosh ² ξ _k・ X ² + 4 ・ cosh ξ _k・ cos ² ξ _k・ sinh
_{ξ k · Rs k-1 -} 4 · coshξ k · cos 2 ξ k · sinhξ k · X - 4 · cosh
_{ξ k · cosξ k · sinhξ k} · sinξ k · Rs k-1 · X - 4 · coshξ k · cos
_{ξ k · sinhξ k · sinξ k} - 2 · coshξ k · sinhξ k · Rs k-1 + 2 ·
coshξ _k・ sinh ξ _k・ X-cos ² ξ _k・ Rs _k-1 ² + cos ² ξ _k・ X ² +
2 ・ cosξ _k・ sin ξ _k・ Rs _k-1 + 2 ・ cos ξ _k・ sin ξ _k・ X)} / (cosh
⁴ ξ _k · Rs _k-1 ⁴ + 2 · cosh ⁴ ξ _k · Rs _k-1 ² · X ² + 8 · cosh ⁴ ξ _k ·
Rs _k-1 ² + 8 ・ cosh ⁴ ξ _k・ Rs _k-1・ X + cosh ⁴ ξ _k・ X ⁴ + 8 ・ co
sh ⁴ ξ _k・ X ² + 4 ・ cosh ⁴ ξ _k + 4 ・ cosh ³ ξ _k・ sinh ξ _k・ Rs _{k-1
^{3 + 4 · cosh 3 ξ k}} · sinhξ k · Rs k-1 2 · X + 4 · cosh 3 ξ k · sinh
ξ _k・ Rs _k-1・ X ² + 8 ・ cosh ³ ξ _k・ sinh ξ _k・ Rs _k-1 + 4 ・ cosh
^{_{3 ξ k · sinhξ k · X}} 3 + 8 · cosh 3 ξ k · sinhξ k · X - 2 · cosh 2 ξ
^{_{k · cos 2 ξ k · Rs}} k-1 4 - 4 · cosh 2 ξ k · cos 2 ξ k · Rs k-1 2 · X 2
-2 ・ cosh ² ξ _k・ cos ² ξ _k・ X ⁴ + 8 ・ cosh ² ξ _k・ cos ² ξ _k + 4 ・ c
^{_{osh 2 ξ k · cosξ k ·}} sinξ k · Rs k-1 3 - 4 · cosh 2 ξ k · cosξ k ·
^{_{sinξ k · Rs k-1 2}} · X + 4 · cosh 2 ξ k · cosξ k · sinξ k · Rs k-1
^{· X 2 + 8 · cosh 2} ξ k · cosξ k · sinξ k · Rs k-1 - 4 · cosh 2 ξ k
_{· Cosξ k · sinξ k · X} 3 -8 · cosh 2 ξ k · cosξ k · sinξ k · X - 8 ·
^{_{cosh 2 ξ k · Rs k-}} 1 2 - 8 · cosh 2 ξ k · Rs k-1 · X -8 · cosh 2 ξ k
・ X ² -8 ・ cosh ² ξ _k -4 ・ cosh ξ _k・ cos ² ξ _k・ sinh ξ _k・ Rs
^{_{k-1 3 - 4 · coshξ}} k · cos 2 ξ k · sinhξ k · Rs k-1 2 · X - 4 · cos
^{_{hξ k · cos 2 ξ k ·}} sinhξ k · Rs k-1 · X 2 + 8 · coshξ k · cos 2 ξ k
_{· Sinhξ k · Rs k-1} - 4 · coshξ k · cos 2 ξ k · sinhξ k · X 3 + 8
^{_{· Coshξ k · cos 2 ξ k}} · sinhξ k · X + 8 · coshξ k · cosξ k · sinh
_{ξ k · sinξ k · Rs k} -1 2 - 8 · coshξ k · cosξ k · sinhξ k · sin
^{_{ξ k · X 2 - 8 ·}} coshξ k · sinhξ k · Rs k-1 - 8 · coshξ k · sinh
^{_{ξ k · X + cos 4 ξ}} k · Rs k-1 4 + 2 · cos 4 ξ k · Rs k-1 2 · X 2 - 8
・ Cos ⁴ ξ _k・ Rs _k-1 ² + 8 ・ cos ⁴ ξ _k・ Rs _k-1・ X + cos ⁴ ξ _k・ X ⁴
-8 ・ cos ⁴ ξ _k・ X ² + 4 ・ cos ⁴ ξ _k -4 ・ cos ³ ξ _k・ sin ξ _k・ Rs
_k-1 ³ + 4 ・ cos ³ ξ _k・ sin ξ _k・ Rs _k-1 ²・ X -4 ・ cos ³ ξ _k・ sin
ξ _k・ Rs _k-1・ X ² + 8 ・ cos ³ ξ _k・ sin ξ _k・ Rs _k-1 + 4 ・ cos ³ ξ
^{_{k · sinξ k · X 3 -}} 8 · cos 3 ξ k · sinξ k · X + 8 · cos 2 ξ k · Rs
^{_{k-1 2 - 8 · cos}} 2 ξ k · Rs k-1 · X + 8 · cos 2 ξ k · X 2 - 8 · cos 2
_{ξ k - 8 · cosξ k ·} sinξ k · Rs k-1 + 8 · cosξ k · sinξ k · X +
Four)

[Expression 48] ∂R s _k / ∂ξ _k ＝-{4 ・ (4 ・ cosh ² ξ _k・ cos ² ξ _k・
Rs _k-1 ^2-4・ cosh ² ξ _k・ cos ² ξ _k・ X ² + 2 ・ cosh ² ξ _k・ cos ξ _{k
· Sinξ k · Rs k-1} 3 + 2 · cosh 2 ξ k · cosξ k · sinξ k · Rs k-1 2
^{· X + 2 · cosh 2 ξ} k · cosξ k · sinξ k · Rs k-1 · X 2 - 4 · cosh 2 ξ
_{k · cosξ k · sinξ k ·} Rs k-1 +2 · cosh 2 ξ k · cosξ k · sinξ k · X
_{^{3 - 4 · cosh 2 ξ k}} · cosξ k · sinξ k · X - 2 · cosh 2 ξ k · Rs k-1
_{^{2 + 2 · cosh 2 ξ k}} · X 2 + 2 · coshξ k · cos 2 ξ k · sinhξ k · Rs
^{_{k-1 3 - 2 · coshξ}} k · cos 2 ξ k · sinhξ k · Rs k-1 2 · X + 2 · cos
^{_{hξ k · cos 2 ξ k ·}} sinhξ k · Rs k-1 · X 2 + 4 · coshξ k · cos 2 ξ k
_{· Sinhξ k · Rs k-1} - 2 · coshξ k · cos 2 ξ k · sinhξ k · X 3 - 4
^{_{· Coshξ k · cos 2 ξ k}} · sinhξ k · X + coshξ k · cosξ k · sinhξ
_k・ sinξ _k・ Rs _k-1 ⁴ + 2 ・ coshξ _k・ cosξ _k・ sinhξ _k・ sinξ _{k
^{· Rs k-1 2 · X}} 2 + coshξ k · cosξ k · sinhξ k · sinξ k · X 4 - 4
・ Coshξ _k・ cosξ _k・ sinhξ _k・ sinξ _k -coshξ _k・ sinhξ _k・
Rs _k-1 ³ + coshξ _k・ sinh ξ _k・ Rs _k-1 ²・ X-coshξ _k・ sinh
ξ _k・ Rs _k-1・ X ² -2 ・ cosh ξ _k・ sinh ξ _k・ Rs _k-1 + cosh ξ _{k
^{· Sinhξ k · X 3 + 2}} · coshξ k · sinhξ k · X - 2 · cos 2 ξ k · Rs
^{_{k-1 2 + 2 · cos}} 2 ξ k · X 2 - cosξ k · sinξ k · Rs k-1 3 - cos
_{ξ k · sinξ k · Rs k} -1 2 · X - cosξ k · sinξ k · Rs k-1 · X 2 +2 ·
_{cosξ k · sinξ k · Rs k} -1 - cosξ k · sinξ k · X 3 + 2 · cosξ k
・ Sin ξ _k・ X + Rs _k-1 ² -X ² )} / (cosh ⁴ ξ _k・ Rs _k-1 ⁴ + 2 ・ co
sh ⁴ ξ _k・ Rs _k-1 ²・ X ² + 8 ・ cosh ⁴ ξ _k・ Rs _k-1 ² +8 ・ cosh ⁴ ξ _k
・ Rs _k-1・ X + cosh ⁴ ξ _k・ X ⁴ + 8 ・ cosh ⁴ ξ _k・ X ² + 4 ・ cosh ^{4
_{ξ k + 4 · cosh 3 ξ}} k · sinhξ k · Rs k-1 3 + 4 · cosh 3 ξ k · sinh
ξ _k・ Rs _k-1 ²・ X + 4 ・ cosh ³ ξ _k・ sinh ξ _k・ Rs _k-1・ X ² + 8 ・ c
^{_{osh 3 ξ k · sinhξ k ·}} Rs k-1 + 4 · cosh 3 ξ k · sinhξ k · X 3 + 8
^{_{· Cosh 3 ξ k · sinhξ k}} · X - 2 · cosh 2 ξ k · cos 2 ξ k · Rs k-1 4 -
_{^{4 · cosh 2 ξ k · cos}} 2 ξ k Rs k-1 2 · X 2 - 2 · cosh 2 ξ k · cos 2 ξ k
^{· X 4 + 8 · cosh 2} ξ k · cos 2 ξ k + 4 · cosh 2 ξ k · cosξ k · sinξ
^{_{k · Rs k-1 3 -}} 4 · cosh 2 ξ k · cosξ k · sinξ k · Rs k-1 2 · X + 4
^{_{· Cosh 2 ξ k · cosξ k}} · sinξ k · Rs k-1 · X 2 + 8 · cosh 2 ξ k · cos
_{ξ k · sinξ k · Rs k} -1 - 4 · cosh 2 ξ k · cosξ k · sinξ k · X 3 -
_{^{8 · cosh 2 ξ k · cosξ}} k · sinξ k · X - 8 · cosh 2 ξ k · Rs k-1 2 -
_{^{8 · cosh 2 ξ k · Rs}} k-1 · X - 8 · cosh 2 ξ k · X 2 - 8 · cosh 2 ξ k -
^{_{4 · coshξ k · cos 2 ξ}} k · sinhξ k · Rs k-1 3 - 4 · coshξ k · cos
^{_{2 ξ k · sinhξ k · Rs}} k-1 2 · X - 4 · coshξ k · cos 2 ξ k · sinhξ k
^{_{· Rs k-1 · X 2}} + 8 · coshξ k · cos 2 ξ k · sinhξ k · Rs k-1 - 4 · c
^{_{oshξ k · cos 2 ξ k ·}} sinhξ k · X 3 + 8 · coshξ k · cos 2 ξ k · sinh
_{ξ k · X + 8 · coshξ} k · cosξ k · sinhξ k · sinξ k · Rs k-1 2 -
_{8 · coshξ k · cosξ k ·} sinhξ k · sinξ k · X 2 - 8 · coshξ k · sin
_{hξ k · Rs k-1 -} 8 · coshξ k · sinhξ k · X + cos 4 ξ k · Rs k-1
_{^{4 + 2 · cos 4 ξ k}} · Rs k-1 2 · X 2 - 8 · cos 4 ξ k · Rs k-1 2 +8 · co
^{_{s 4 ξ k · Rs k-}} 1 · X + cos 4 ξ k · X 4 - 8 · cos 4 ξ k · X 2 + 4 · cos
^{_{4 ξ k - 4 · cos 3}} ξ k · sinξ k · Rs k-1 3 + 4 · cos 3 ξ k · sinξ k
・ Rs _k-1 ²・ X -4 ・ cos ³ ξ _k・ sin ξ _k・ Rs _k-1・ X ² + 8 ・ cos ³ ξ _{k
· Sinξ k · Rs k-1} + 4 · cos 3 ξ k · sinξ k · X 3 - 8 · cos 3 ξ k · s
_{inξ k · X + 8 · cos} 2 ξ k · Rs k-1 2 - 8 · cos 2 ξ k · Rs k-1 · X +
8 ・ cos ² ξ _k・ X ² -8 ・ cos ² ξ _k- 8 ・ cos ξ _k・ s
inξ _k・ Rs _k-1 + 8 ・ cos ξ _k・ sin ξ _k・ X + 4)

Here, the partial differential coefficient ∂R expressed by the equation 47
s _k / ∂X and partial differential coefficient ∂R s _k / ∂ξ _k
Substituting Rs _k-1 = tan ξ _k and X = −tan ξ _k into, the partial differential coefficient ∂Rs _k / ∂X and the partial differential coefficient ∂Rs _k / ∂ξ _k are both zero. That is, when Rs _k-1 = tan ξ _k and X = −tan ξ _k , the normalized surface resistance Rs _k takes an extreme value. On the other hand, FIG.
, Define a Q increase rate RQ with the inverse of the normalized surface resistance Rs _k, the Q increasing rate RQ for the height direction, the corresponding values of Q increase rate RQ the normalized conductor film thickness xi] _k and reactance X _W It is the three-dimensional graph which was made to represent. Where reactance X _W
Is defined as X _W = −X for convenience of calculation. As can be seen from FIG. 17, ξ _k = tan
^-1 (Rs _k-1 ), when X _W = Rs _k-1 , that is, Rs _k-1 = t
When an ξ _k and X = −tan ξ _k, the Q increase rate RQ takes a maximum value and the normalized surface resistance Rs _k takes a minimum value which is a minimum value.

From the above, the conditions for minimizing the normalized surface resistance Rs _k are given by the following equations 49 and 50.

[0075]

Ξ _k = tan ^-1 (Rs _k-1 )

(50) W _k-1 = Rs _k-1 + Xs _k-1

Here, the formula 49 is rewritten as the following formula 51 for convenience of later.

[0077]

[Expression 51] Rs _k-1 = tan ξ _k

Equation 5 which is the minimum condition of the normalized surface resistance Rs _k
Substituting 0 and the equation 51 into the equation 41 and rearranging the equation gives the recurrence formula as the following equation 52.

[0079]

[Expression 52] Zs _k = Z _k + [Y _k + {Z _k + (1-j) tan ξ _k } ^-1 ] ^-1

Further, the standardized complex impedance Z _k expressed by the equation 34 and the standardized complex admittance Y _k expressed by the equation 35 are modified by using the known formulas given by the following equations 53 and 54. If the equation 52 is rearranged by substituting it into the equation 52 later, the standardized surface impedance Zs _k can be expressed by a simple equation such as the following equation 55.

[0081]

[Equation 53] tanh [(1 + j) ξ _k / 2] = (sinh ξ _k + jsin ξ _k )
/ (Cosh ξ _k + cos ξ _k )

Equation 54] sinh {(1 + j) ξ k} = sinhξ k cosξ k + jcoshξ k sinξ k

[Expression 55] Zs _k = (1 + j) tanhξ _k

At this time, as is apparent from the equation 55, the normalized surface resistance Rs _k and the normalized surface reactance Xs _k are
In agreement, it is expressed by the following equation 56.

[0083]

(56) Rs _k = Xs _k = tanh ξ _k

Looking at equation 56 for the thin film conductor k-1,
When the normalized conductor film thickness ξ _k-1 is set so that the normalized surface resistance Rs _k-1 is minimized, the following equation 57 is satisfied. By using the equations 57, 50 and 51, the relationship between the normalized conductor film thickness ξ _k and the normalized conductor film thickness ξ _k-1 can be expressed by a simple equation such as the equation 58. Further, the normalized reactance W _k can be expressed as in Equation 59 by using Equation 56. Therefore, the conditions for minimizing the normalized surface resistance Rs _k can be expressed by the following equations 58 and 59.

[0085]

Rs _k-1 = Xs _k-1 = tanh ξ _k-1

(58) ξ _k = tan ^-1 (tanh ξ _k-1 )

(59) W _k = 2 tanh ξ _k

Further, by combining the equations 36 and 59, the normalized dielectric film thickness x _k when the normalized surface resistance Rs _k becomes the minimum can be expressed by the following equation 60.

[0087]

X _k = (ε _m / ε _s -1) ^-1 tanhξ _k

As described in detail above, when k ≧ 2,
The standardized conductor film thickness ξ _k for minimizing the standardized surface resistance Rs _k can be easily obtained by using Expression 51 or Expression 58.

Next, the phase velocity v _{m of the} TEM wave having the same frequency as the resonance frequency f ₀ propagating through the main transmission line LN10.
And the phase velocity v _s of the TEM wave having the same frequency as the resonance frequency f ₀ propagating in the sub transmission line LNk will be described. First, the dielectric loss of the dielectric substrate 10 is
Since it is sufficiently smaller than the conductor loss of, the dielectric loss can be set to 0, and the equivalent circuit of the dielectric substrate 10 has an inductance L10 represented by the following equation 61 as shown in FIG.
Can be expressed using only the capacitance C10 expressed by

[0090]

Equation 61] _{L10 = μ 0 (H / y} a) (1 / β 0)

C10 = ε _m (y _a / H) (1 / β ₀ ).

Therefore, if the inductance L10 and the capacitance C10 are used, the main transmission line LN10
The characteristic impedance Z _0m of can be expressed as in Equation 63. Further, the phase velocity v _m is defined as in Equation 64 by using the angular frequency ω ₀ corresponding to the resonance frequency f ₀ and the phase velocity β ₀ , and the angular frequency ω ₀ is represented by Equation 65. Therefore, the phase velocity v _m can be expressed by the equation 66 using the inductance L10 and the capacitance C10.

[0092]

Equation 63] _{Z 0m = √ (L10 / C10} ) = (H / y a)
√ (μ ₀ / ε _m )

V _m = ω ₀ / β ₀

Ω ₀ = 1 / √ (L10 · C10)

[Expression 66] v _m = 1 / √ (L10 · C10) (1 / β ₀ ).
= 1 / √ (μ ₀ ε _m )

Next, if the normalized conductor film thickness ξ _k <1, the complex impedance ZA _k expressed by the equation 23 is expressed by the equation 23
The right side of can be transformed using the approximate expression represented by the equation 67. Therefore, the complex impedance ZA _k is
It can be expressed as 8. Also, (1 + j) × (1+
Since j) = 2j, Expression 68 can be transformed into Expression 69. Further, if the right side of the equation 69 is transformed using the relational expression represented by the equation 70, the complex impedance Z
A _k can be expressed as in Equation 71.

[0094]

Equation 67] tanh [(1 + j) ξ k / 2] ≒ {(1 + j) / 2} tanhξ k

ZA _k ≈ [(1 + j) / (σδ ₀ y _a β ₀ )] {(1
+ J) / 2} tanhξ _k

ZA _k ≈ [j / (σδ ₀ y _a β ₀ )] tanhξ _k

Equation 70] _{1 / σδ 0 = √ {ω} 0 μ 0 / (2σ)} = (ω 0 μ 0/2) √ {2 / (ω 0 μ 0 σ)} = ω 0 μ 0 δ 0/2

ZA _k ≈ [jω ₀ μ ₀ δ ₀ / (2y _a β ₀ )] tanh ξ _k

When the normalized conductor film thickness ξ _k <1, the complex admittance YA _k expressed by the equation 24 is calculated by the equation 7
The complex admittance YA _k can be expressed by the following equation 73, which can be transformed by using the approximate expression represented by 2.

[0096]

(72) sinh [(1 + j) ξ _k ] ≈ (1 + j) sinh ξ _k

YA _k ≈σδ ₀ y _a β ₀ sinhξ _k

As is clear from the equation (71), the complex impedance ZA _k has only a positive reactance component when the conductor film thickness ξa _k is smaller than the skin depth δ ₀ . That is, when the conductor film thickness ξa _k is smaller than the skin depth δ ₀ , the complex impedance ZA _k behaves as an inductance. Further, as is clear from the equation (73), the complex admittance Y _k has only a real part, that is, a conductance component.

Next, the phase velocity of the sub transmission line LNk constituted by the thin film dielectric 30-k sandwiched by the thin film conductor k and the thin film conductor k + 1 will be described.

First, the characteristic impedance Z _0k of the sub transmission line LNk is expressed by the following equation 74. Here, Lk is the inductance represented by the equation 25, and Ck is the equation 26
Is the capacitance represented by. Lrk is a complex impedance Z having only a positive reactance component.
Thin film conductor k and thin film conductor k + 1 obtained by summing A _k and complex impedance ZA _{k + 1} having only positive reactance component
Due to the inductance. Therefore, the inductance Lrk can be expressed as in Equation 75.

[0100]

Z _0k = √ {(Lk + Lrk) / Ck}

Equation 75] _{Lrk = (1/2) (μ 0} δ 0 / y a) (1 /
β ₀ ) (tanhξ _k + tanhξ _{k + 1} )

[0101] In addition, when ξ _k <1 is, tanhξ _k ≒ tanh
The approximate expression of ξ _{k + 1} is established, and by using the approximate expression, Expression 75 can be expressed as Expression 76.

[0102]

[Number 76] _{Lrk ≒ (μ 0 δ 0 /} y a) (1 / β 0) tanhξ k

Further, on the right side of the equation 74, L represented by the equation 25
k, Ck expressed by Expression 26 and Lrk expressed by Expression 75
By substituting, the characteristic impedance Z _0k can be expressed as in _Expression 77, and further by deforming the right side thereof, it can be expressed as in Expression 78.

[0104]

Equation 77] _{Z 0k = √ [{(μ} 0 x ak / y a) + (μ 0 δ 0 / y a) t
anhξ _k } / (ε _S y _a / x _ak )]

Equation 78] _{Z 0k = √ (μ 0 /} ε S) (x ak / y a) √ {1+ (1
/ X _k ) tanh ξ _k }

Furthermore, the phase velocity v _s of the sub transmission line LNk
Can be expressed by the following Expression 79, and Lk expressed by Expression 25, Ck expressed by Expression 26, and Expression 75 on the right side of Expression 79.
In Substituting Lrk represented, the phase velocity v _s is the number 8
It can be expressed as 0, and by transforming its right side, it can be expressed as in Equation 81.

[0106]

V _s = 1 / √ {(Lk + Lrk) Ck} (1 / β ₀ ).

(80) v _s = 1 / √ [{(μ ₀ x _ak / y _a ) + (μ ₀ δ ₀ / y
_a ) tanh ξ _k } (ε _S y _a / x _ak )]

V _s = {1 / √ (μ ₀ ε _s )} [1 / √ {1+ (1
/ X _k ) tanhξ _k }]

Next, the main transmission line LN1 represented by the equation 66
The ratio of the phase velocity v _{m of} 0 and the phase velocity v _s expressed by the equation 81 can be expressed by the equation 82.

[0108]

V _m / v _s = √ (ε _s / ε _m ) √ {1+ (1 / x _k ) tanhξ _k }

Next, by modifying the equation 36 representing the normalized reactance W _k , the ratio of the dielectric constant ε _m of the dielectric substrate 10 and the dielectric constant ε _s of the thin film dielectric 30-k is
It can be expressed as in equation (83).

[0110]

(83) ε _m / ε _s = 1 + W _k / (2x _k )

Here, by substituting the expression 83 into the expression 82, the ratio of the phase speed v _m and the phase speed v _s can be expressed by the following expression 84.

[0112]

[Expression 84] v _m / v _s = √ {1+ (1 / x _k ) tanhξ _k } / √
{1 + W _k / (2x _k )}

As is clear from the equation 84 obtained as described above, the phase velocity v _m of the main transmission line LN10 and the phase velocity v _s of the sub transmission line LNk are equal to each other, v _m / v _s =
When 1, that is, when W _k = 2 tanh ξ _k . Here, the normalized reactance W _k is the thin film dielectric 30-k.
It is the calculated by the normalized dielectric film thickness x _k and the dielectric constant epsilon _s, the phase velocity v _s of the sub-transmission line LNk consisting a thin-film dielectric 30-k which is sandwiched set by the thin-film conductor k and the thin-film conductors k + 1 is , Is calculated from the normalized reactance W _k .

Further, by substituting W _k = 2 tanh ξ _k into Equation 83 and transforming it, the dielectric constant ε _s of the thin film dielectric 30-k is changed.
Can be expressed as in the following Equation 85. Therefore,
By setting the dielectric film thickness ξ a _k of the thin film dielectric 30-k and the dielectric constant ε _s of the thin film dielectric so as to satisfy Expression 85, the phase velocity v _m of the main transmission line LN10 and the sub transmission line L
The Nk phase velocities v _s can be matched. Further, considering Expression 85, the dielectric constant ε _s of the thin film dielectric that matches the phase velocity v _m of the main transmission line LN10 and the phase velocity v _s of the sub transmission line LNk is always the dielectric constant ε _m of the dielectric substrate 10. Set smaller. As a result, the effective permittivity of the thin film dielectric 30-k sandwiched between the thin film conductors k and k + 1 is set equal to the effective permittivity of the dielectric substrate 10.

[0115]

Ε _s = ε _m / (1 + tanh ξ _k / x _k ) = ε _m / (1 + δ ₀ tanh ξ _k / x _ak )

As described above in detail, when the conductor film thickness ξ _k of the thin film conductor k is set to be smaller than the skin depth δ ₀ , the phase velocity v _m of the main transmission line LN10 and the phase velocity of the sub transmission line LNk are set. W _k = 2 tanhξ which is a conditional expression for matching v _s
k matches the equation 59. Here, as described above, Expression 59 is the dielectric film thickness x of the thin film dielectric 30-k so that the standardized surface resistance Rs _{k + 1} is minimized when the standardized conductor film thickness ξ _k is given. _This is a conditional expression for setting _ak . That is, the phase velocity v _m of the main transmission line LN10 and the sub-transmission line L
In order to match the Nk phase velocity v _s , the thin film dielectric 3
The normalized surface resistance Rs _{k + 1} can be minimized by setting the dielectric film thickness ξa _k of 0-k.

As described above, by setting the dielectric film thicknesses x _{a1 to} x _a4 and the dielectric constant ε _s of the thin film dielectrics 30-1 to 30-4, the main transmission line LN10 and the transmission lines L are set.
The phase velocities of the TEM waves propagating through N1 to LN5 are substantially matched with each other. Then, by setting the conductor film thicknesses ξa _{2 to} ξa ₅ of the respective thin film conductors 2 to ₅ to a predetermined film thickness smaller than the skin depth δ ₀ of the resonance frequency, the main transmission line LN10 and the sub transmission line LN4 and The electromagnetic fields of the sub transmission lines LN1, LN2, LN3 and LN4 adjacent to each other are coupled to each other. As a result, the electromagnetic field of the main transmission line LN10 and the sub-transmission lines LN1, LN2, LN
The electromagnetic fields of L3 and LN4 are substantially in phase with each other.

Here, the TM mode dielectric resonator R1 is used.
When the resonance occurs in the TM ₁₁₀ mode, as described above, the main transmission line LN10 and the sub transmission lines LN1 and LN are
2, LN3 and LN4 are the micro region 81 of the main TM mode resonator 210 and the sub TM mode resonator 20 respectively.
Each of the minute regions 1 to 204. Therefore, when the TM-mode dielectric resonator R1 resonates in the TM ₁₁₀ mode, the electromagnetic fields in the micro-region 81 of the main TM-mode resonator 210 and the micro-regions of the sub-TM-mode resonators 201 to 204 are mutually different. Since they are substantially in phase, the main TM mode resonator 21 which is an assembly of the main transmission lines LN10.
The electromagnetic field of 0 and the electromagnetic fields of the sub TM mode resonators 201 to 204, which are an assembly of the sub transmission lines LN1 to LN4, are substantially in phase. The same applies when the TM mode dielectric resonator R1 resonates in the TM ₂₁₀ mode or the TM ₀₁₀ mode. In other words, when the TM mode dielectric resonator R1 resonates in the TM ₁₁₀ mode, TM ₂₁₀ mode or TM ₀₁₀ mode, the electromagnetic field of the main TM mode resonator 210 and the electromagnetic waves of the sub TM mode resonators 201 to 204. by setting the dielectric film thickness Kushiei _k of the thin-film dielectric 30-k so as to be substantially in phase the field Prefecture, it can be normalized surface resistance Rs _{k + 1} to a minimum.
Further, as described above, the effective permittivity of the thin film dielectric 30-k and the effective permittivity of the dielectric substrate 10 are set to be equal, and the thin film conductors 1 to 5 are formed to have the same radius. Therefore, the TM mode resonator 21 is
0 and the resonance frequencies of the sub-TM mode resonators 201 to 204 match each other.

In the above description, the TM mode dielectric resonator R1 is TM ₁₁₀ mode, TM ₂₁₀ mode or T mode.
Although it was performed when resonating in the M ₀₁₀ mode, the principle described above is valid in all TM modes generally represented by TM _mnp , as shown _below . here,
The letters m, n, and p displayed after the letters TM are defined by how many times π the phase changes in the φ, r, and z directions of the cylindrical coordinate system. First, in the case of p = 0, that is, in the TM mode generally represented by TM _mn0 , the main TM mode resonator 210 and the sub TM mode resonators 201 to 4 are _arranged in the thickness direction of the thin film conductors 1 to 5. Is a parallel propagation mode having an electric field parallel to and a magnetic field orthogonal to the thickness direction of the thin film conductors 1 to 5, and the above-described principle can be applied as it is. In the TM mode when p is not 0, the electromagnetic fields of the sub TM mode resonators 201 to 204 are parallel propagation modes, and the main TM mode resonator 210 is in the dielectric substrate in the vicinity of the thin film conductor 5. Then, it has an electric field parallel to the thickness direction of the thin film conductor 5 and a magnetic field orthogonal to the thickness direction of the thin film conductor 5. That is, as far as the vicinity of the thin film conductor 5 is concerned, the TM mode when p is not 0 can be regarded as a parallel propagation mode.
Therefore, also in this mode, the normalized surface resistance Rs _{k + 1} can be reduced by setting the film thickness x _ak and the dielectric constant ε _s of the thin film dielectric 30-k as in the parallel propagation mode.

Next, the standardized surface impedance Zs ₁ when k = ₁ will be described in detail. The normalized surface impedance Zs ₁ when the normalized conductor film thickness ξ ₁ of the thin film conductor 1 is sufficiently larger than ₁ can be expressed by the following formula 85 using formula 34. Here, when the normalized conductor film thickness ξ ₁ is sufficiently larger than 1, it means that the normalized conductor film thickness ξ ₁ ≧ 3.

[0121]

[Equation 86] Z ₁ = 1 + j

As is clear from the equation (86), both the normalized surface resistance Rs ₁ and the normalized reactance Xs ₁ of the thin film conductor 1 are 1 and coincide with each other. When the normalized conductor film thickness ξ ₁ of the thin film conductor 1 is sufficiently larger than ₁ , that is, the normalized conductor film thickness ξ ₁ ≧
When 3, the number 5 for all k when k ≧ 1
The numbers 5 to 60 hold. Therefore, by giving a normalized conductor film thickness ξ ₁ larger than 3 as an initial value,
From Equation 60, the standardized conductor film thickness ξ _k and the standardized dielectric film thickness x _k that minimize the standardized surface resistance Rs _k can be obtained for all k.

When the normalized conductor film thickness ξ ₁ is not sufficiently larger than 1, that is, when the normalized conductor film thickness ξ ₁ <3,
The normalized surface resistance Rs ₁ and the normalized surface reactance Xs ₁ are obtained from the real and imaginary parts of the normalized surface impedance Zs _k obtained by substituting the equations 34 and 35 into the equation 32, respectively.
Further, the normalized dielectric film thickness x ₁ of the thin film dielectric 30-1 is obtained by using the equation 50 when k = 2 and the equation 36 when k = 1.

[0124] Table 1 is determined to stacking number 30 normalized conductor film thickness xi] _k for normalizing surface resistance Rs _k is minimized when the normalized conductor film thickness xi] ₁ of the thin conductor 1 was ∞, its together with the results and is Tanhkushi _k and Q increase rate RQ is normalized surface resistance Rs _k of 1 / tanhξ _k calculation result is obtained by the table.

[0125]

[Table 1] ────────────────────────────────── k ξ _k Rs _k ＝ tanh ξ _k RQ = 1 / tanhξ _k ────────────────────────────────── 1 ∞ 1.0000 1.000 002 2 0.78539 0. 65579 1.524486 3 0.58043 0.552298 1.91210 4 0.448186 0.447773 2.23345 5 0.42096 0.393774 2.551416 6 0.37856 0.336145 2.76656 7 0.34684 0. 33357 2.99782 8 0.32196 0.31128 3.212248 9 0.30177 0.229293 3.41367 10 0.28496 0.27749 3.60366 11 0.27068 0.264326 3.78412 12 0.25835 0.38. 25 275 3.953636 13 0.24757 0.224263 4.12142 14 0.23803 0.233363 4.28011 15 0.222952 0.222557 4.43313 16 0.222186 0.221829 0.458103 17 0.21491. 21167 4.72432 18 0.20859 0.20561 4.86338 19 0.20279 0.20005 4.99858 20 0.17945 0.19492 5.123021 21 0.19250 0.191016 5.25855 22.0.18792 0.021. 18574 5.38383 23 0.18364 0.18161 5.50627 24 0.17965 0.177774 5.660425 25.17590 0.17411 5.74331 26 0.17238 0.17069 5.85823 27.0.1690 6747 5.97095 28 0.16593 0.16443 6.08157 29 0.16297 0.16154 6.19022 30 0.161016 0.18880 6.29700 ───────────────── ──────────────────

[0126] Further, Table 2 normalized conductor film thickness several stacked xi] _k 30 for normalizing the surface resistance Rs _k is minimized when the normalized conductor film thickness xi] ₁ of the thin-film conductor 1 and [pi / 2 Up to
The results are shown in the table together with the calculated results of the normalized surface resistance Rs _k tanh ξ _k and the Q increase rate RQ 1 / tanh ξ _k .

[0127]

[Table 2] ────────────────────────────────── k ξ _k Rs _k ＝ tanh ξ _k RQ = 1 / _{tanhξ k ────────────────────────────────── 1 π / 2 0.91715} 1.09033 2 0.74221 0.63047 1.58609 3 0.562552 0.50985 1.96135 4 0.47149 0.43940 2.27578 5 0.41401 0.39187 2.555184 6 0.373348 0.35703 2.800867 0.334292. 0.33008 3.02949 8 0.31882 0.30844 3.24206 9 0.29918 0.209056 3.4453 10 0.228278 0.227547 3.63006 11 0.26881 0.26251 380927 12 0.25672. 0. 5122 3.98042 13 0.24613 0.24128 4.14452 14 0.267575 0.232443 4.236336 15 0.22837 0.222448 4.45461 16 0.02208 0.221730 460183 17 0.213397 0. 21077 4.744448 18 0.20773 0.20479 4.88297 19 0.20200 0.199929 5.01764 20 0.19671 0.194422 5.14879 21 0.1919183 0.18951 5.27666822 0.18729. 18513 540154 23 0.18305 0.18104 5.52358 24 0.17910 0.177721 5.64298 25 0.17539 0.173361 5.7591 26 0.117190 0.170222 5.87451 27 0.16861. 0.16703 5.998692 28 0.165550 0.16400 6.09725 29 0.16256 0.161614 6.20563 30 0.15977 0.15842 6.31214 ─────────────── ────────────────────

The following can be seen from Tables 1 and 2. (A) The normalized conductor film thickness ξ _k for minimizing the normalized surface resistance Rs _k is smaller than 1 when k ≧ 2, and the larger _k is, the smaller the normalized conductor film thickness ξ _k is. (B) The larger k is, the smaller the minimum value of the normalized surface resistance Rs _k can be. (C) The larger k is, the larger the Q increase rate RQ can be.

As described above, the conductor film thicknesses ξa _{1 to} ξa ₅ of the thin film conductors 1 to ₅ and the dielectrics of the thin film dielectrics 30-1 to 30-4 are set so that the surface resistance of the thin film laminated electrode 6 is minimized. The body thickness x _{a1 to} x _a4 can be set.

Similarly, the conductor film thicknesses ξa _{e1 to} ξa _e5 of the thin film conductors E1 to E5 and the thin film dielectrics 30-1 to 30 are set so that the surface resistance of the thin film laminated electrode E6 is minimized.
Dielectric thickness x _ae1 to x _AE4 -4 can be set.

T of the first embodiment constructed as described above
The operation of the M-mode dielectric resonator device will be described below.

When the main TM mode resonator 210 is excited by a high frequency signal having a resonance frequency, the thin film conductor 5 in the lowermost layer transfers a part of the resonance energy of the main TM mode resonator 210 to the upper thin film conductor 4. To Penetrate. Each of the thin film conductors 1 to 4 transmits a part of the resonance energy incident through the lower thin film dielectric to the upper thin film conductor. Accordingly, the sub TM mode resonator 201 is provided.
Nos. 4 to 4 resonate at the same frequency as the main TM mode resonator 210, and two high-frequency currents facing each other (hereinafter, facing each other) in the vicinity of the upper surface and the lower surface of the conductor thin films 1 to 5 are opposite to each other. Two high-frequency currents) are flowing. That is, since the film thickness of each of the thin film conductors 2 to 5 is thinner than the skin depth δ ₀ , the two high-frequency currents that face each other interfere with each other and are partially canceled by each other. On the other hand, in each of the thin film dielectrics 30-1 to 30-4, a displacement current is generated by the electromagnetic field, and a high frequency current is generated on the surface of the adjacent thin film conductor. Furthermore, each of the thin film dielectrics 30-1 to 30-3
Each dielectric thickness x _a1 to x _a4 0-4, the electromagnetic field of the main TM-mode resonator 210 and the respective sub-TM mode resonators 201 to 204 are configured to be substantially in phase Therefore, the high frequency currents flowing through the thin film conductors 1 to 5 are substantially in phase with each other. As a result, the high frequency currents flowing in the same phase in each of the thin film conductors 1 to 5 are
Effectively increases the skin depth.

FIG. 11 is a plan view showing the current distribution on the surface of the thin film conductor 5 when the TM mode dielectric resonator R1 resonates in the TM ₁₁₀ mode. As shown in FIG. 11, the current 71 when the TM-mode dielectric resonator R1 resonates in the TM ₁₁₀ mode is the point 10 on the outer periphery of the thin-film conductor 5.
1 to a point 102 on the outer circumference of the thin film conductor 5 facing the point 101. Here, among the currents 71, the currents 71 other than the current 71 passing through the center of the outer circumference circle flow outwardly as shown in FIG.

FIG. 12 is a plan view showing a current distribution on the surface of the thin film conductor 5 when the TM mode dielectric resonator R1 resonates in the TM ₂₁₀ mode. As shown in FIG. 12, the current 71 when the TM mode dielectric resonator R1 resonates in the TM ₂₁₀ mode is calculated from two points 105 and 106 on the outer circumference of the thin film conductor 5 which face each other.
05, 106 and points 103, 104 on the outer circumference circle separated by 90 degrees from the center of the outer circumference circle,
Each bends inward and flows.

FIG. 13 is a plan view showing the current distribution on the surface of the thin film conductor 5 when the TM mode dielectric resonator R1 resonates in the TM ₀₁₀ mode. As shown in FIG. 13, the current 71 when the TM mode dielectric resonator R1 resonates in the TM ₀₁₀ mode flows in the radial direction of the outer circumference circle of the thin film conductor 5. Here, in any of the above modes, the direction of the current 71 is reversed according to the electric field and the magnetic field that oscillate due to resonance.

Further, in any of the above TM modes, when the TM mode dielectric resonator R1 resonates, the main TM mode resonator and each sub TM mode resonator 201.
To 204 resonate in the same mode, and thin film conductors 1 to 4
Also has a similar current distribution. And the above main T
M-mode resonator 210 and each sub-TM-mode resonator 20 described above
Since the electromagnetic fields 1 to 204 are configured to be substantially in phase, the thin film conductor 1 can be used in each mode.
Currents flow in the same directions on the upper surfaces of the thin film conductors 1 to 4, and currents flow in the same directions on the lower surfaces of the thin film conductors 1 to 4. Then, as described above, two high-frequency currents facing each other in opposite directions flow near the upper surface and the lower surface of each of the conductor thin films 1 to 5.

Further, in the present embodiment, the conductor film thickness is set to be thicker in the upper layer thin film conductor, and the amplitude of the high frequency current increases as it goes to the upper layer thin film conductor. This effectively operates to maximize the skin depth. Furthermore, since the uppermost thin-film conductor 1 is set to be π / 2 times the skin depth thicker than the skin depth, it operates so as to effectively increase the skin depth of the thin-film conductor itself. The resonance energy is shielded so as not to be radiated into free space.

The present inventor prototyped and evaluated the following circular TM ₀₁₀ mode dielectric resonator in order to confirm the effect of the present invention. The number of laminated layers n represented by the number of layers of the thin film conductor k is 2 when both the thin film laminated electrodes 6 and E6 are two layers.
Two types of E6 each having 5 layers were experimentally manufactured and evaluated. Further, as a comparison, a circular TM ₀₁₀ mode dielectric resonator of a conventional example in which a conductor having a thickness of 8 μm is formed on both surfaces was prototyped and evaluated. Table 3 shows the set values of the film thickness of the thin film laminated electrodes 6 and E6 of the prototype circular _TM010 mode dielectric resonator and the film thickness of the thin film dielectric. Further, Table 3 also shows the effective conductivity and the effective conductivity increase rate when the film thickness is set. Table 4 shows measured values of the no-load Q, the effective conductivity, and the effective conductivity increase rate of the circular TM ₀₁₀ mode dielectric resonator when the film thicknesses shown in Table 3 are set. Here, in the circular TM ₀₁₀ mode dielectric resonator, the film thickness of each thin film conductor is set to be equal to each other, and the film thickness of each thin film dielectric is set to be equal to each other. Also, the dielectric substrate 10 has a diameter of 50.8 cut so that the upper surface and the lower surface become R surfaces.
A single crystal sapphire having a thickness of 0.3 mm and a thickness of 0.33 mm was used. In addition, the thin-film dielectric has an S with a relative dielectric constant of 4.3.
The conductivity of TiO ₂ in the thin film conductor is 4.93 × 10 ⁷ S /
Copper that is m was used. The resonance frequency of the circular _TM010 mode dielectric resonator was set to 3.0 GHz.

[0139]

[Table 3] ─────────────────────────────────── Number of laminated layers Conductor film thickness ξa Dielectric film thickness x _a Effective conductivity Increase in effective conductivity n (μm) (μm) (× 10 ⁷ S / m) (times) ──────────────────────── ──────────── Single layer 8.0 ─ 4.93 1.00 2 layers 0.97 0.92 12.40 2.52 5 layers 0.69 0.56 29.385 .96 ───────────────────────────────────

[0140]

[Table 4] ─────────────────────────────────── Number of layers No load Q Effective conductivity Effective conductivity Rate of increase n (× 10 ⁷ S / m) (times) ─────────────────────────────────── Single Layer 302 4.93 1.00 2 layer 453 11.07 2.25 5 layer 678 24.81 5.03 ──────────────────────── ───────────

The measured values of the unloaded Q of the TM ₀₁₀ mode dielectric resonator were 95% and 92% of the theoretical values for the two-layer and five-layer structures, respectively. Further, as is clear from Table 4, the effective rate of increase in conductivity is 2.25 times in the case of the two layers and is 5.25 in the case of the five layers as compared with the case of the conventional single layer. It is found that the effective conductivity is increased by a factor of 03, which is approximately proportional to the number of stacked layers n.

According to the TM mode dielectric resonator R1 of the first embodiment described above, since the thin film laminated electrodes 6 and E6 are provided, the skin depth is effectively increased, and the conductor loss and the surface resistance are reduced. It can be significantly reduced as compared with the conventional one. As a result, a very large unloaded Q dielectric resonator can be realized. Further, since the no-load Q can be increased, the dielectric substrate 1 for obtaining a desired no-load Q
The thickness of 0 can be reduced as compared with the conventional example.

Since the TM mode dielectric resonator device of the first embodiment described above is provided with the TM mode dielectric resonator R1, the unloaded Q can be increased and the cavity 40 is provided. Since the radiation loss can be reduced and the unloaded Q can be further increased, it is possible to prevent the electromagnetic field of the TM mode dielectric resonator from coupling with the electromagnetic field of an external circuit, and stabilize the resonance frequency. You can

<Second Embodiment> FIG. 5 is a perspective view of a high frequency band pass filter device according to a second embodiment of the present invention. The high-frequency bandpass filter device according to the second embodiment has four TM-mode dielectric resonators R1a, R1b, and R having the same structure as the TM-mode dielectric resonator R1 shown in FIG.
1c, R1d and the TM mode dielectric resonator R at one end
1a and a microstripline M21 having the other end serving as an input terminal 22a, and a microstripline M21 having one end capacitively coupled with the TM mode dielectric resonator R1d and the other end serving as an output terminal 21a. Two adjacent TM mode dielectric resonators R1a, R1b,
It is characterized in that R1c and R1d are configured to be electromagnetically coupled.

The configuration of the high frequency bandpass filter device of the second embodiment will be described in detail below with reference to the drawings. As shown in FIG. 5, on the upper surface of the dielectric substrate 20, four thin film laminated electrodes 6a, 6b, 6c, 6d which have the same structure as the thin film laminated electrode 6 of FIG.
Are formed at predetermined intervals in the longitudinal direction. Further, as shown in FIG. 6, thin film laminated electrodes E6a, E6b, E6c, E6d are formed on the lower surface of the dielectric substrate 20 so as to face the thin film laminated electrodes 6a, 6b, 6c, 6d, respectively. Thereby, the thin film laminated electrodes 6a, 6b, 6
c, 6d and thin film laminated electrodes E6a, E6b, E6c, E6
TM mode dielectric resonators R each having a predetermined resonance frequency by the dielectric substrate 20 sandwiched by d and
1a, R1b, R1c, R1d are configured. And
The TM mode dielectric resonator R1a and the TM mode dielectric resonator R1b adjacent to each other are electromagnetically coupled, and the TM mode dielectric resonator R1b and the TM mode dielectric resonator R1c adjacent to each other are electromagnetically coupled, TM mode dielectric resonator R1c and TM mode dielectric resonator R1 which are adjacent to each other
d is electromagnetically coupled.

A strip conductor 22 is formed on the upper surface of the dielectric substrate 20 at a predetermined distance from the thin film laminated electrode 6a, and a strip conductor 21 is formed at a predetermined distance from the thin film laminated electrode 6d. It is formed. Further, the thin film laminated electrode E is formed on the lower surface of the dielectric substrate 20.
The ground conductor 23 is formed on the entire surface including the side surfaces and the lower surfaces of 6a, E6b, E6c, and E6d. Here, as shown in FIG. 6, the thin film conductors E2, E3, E4, E5 and the ground conductor 2 are provided on the side surfaces of the thin film laminated electrodes E6a, E6b, E6c, E6d.
3 so that they are not electrically connected to each other.
The ground conductor 23 is formed via 23a, 123b, 123c, and 123d. Thereby, the dielectric substrate 2
0 is sandwiched by the strip conductor 22 and the ground conductor 23 to form a microstrip line M22. One end of the microstrip line M22 is capacitively coupled with the TM mode dielectric resonator R1a, and the other end serves as an input terminal 22a. The dielectric substrate 20 is sandwiched by the strip conductor 21 and the ground conductor 23 to form a microstrip line M21.
One end of the microstrip line M21 has the TM
It is capacitively coupled to the mode dielectric resonator R1d, and the other end becomes the output terminal 21a.

In the high frequency band pass filter device of the second embodiment constructed as described above, the input terminal 22
When a high frequency signal having a predetermined frequency is input from a,
The high frequency signal is the microstrip line M22.
Is transmitted and capacitively coupled to the TM mode dielectric resonator R1a to excite and resonate the TM mode dielectric resonator R1a. The resonance energy of the TM-mode dielectric resonator R1a is electromagnetically coupled to the TM-mode dielectric resonator R1b to excite and resonate the TM-mode dielectric resonator R1b. The TM mode dielectric resonator R1b
Of the TM mode dielectric resonator R1.
The TM mode dielectric resonator R1 electromagnetically coupled to c
Excit c to resonate. The resonance energy of the TM mode dielectric resonator R1c is electromagnetically coupled to the TM mode dielectric resonator R1d to excite and resonate the TM mode dielectric resonator R1d. The resonance energy of the TM mode dielectric resonator R1d is capacitively coupled to one end of the microstrip line M21 to excite a high frequency signal having the same frequency as the high frequency signal input to the microstrip line M21. The microstrip line M21 transmits the high frequency signal and outputs the high frequency signal from the output terminal 21a.

The high-frequency bandpass filter device according to the second embodiment described above has the TM mode dielectric resonators R1a, R1b, R1 capable of increasing the unloaded Q as compared with the conventional example.
Since c and R1d are used, the loss in the pass band can be reduced and the attenuation in the stop band can be increased. Further, when a predetermined pass band loss and a predetermined stop band attenuation characteristic are given, the thickness of the dielectric substrate 20 can be made thinner than in the conventional example, so that the high frequency band pass filter device is made thin. can do.

<Modification> FIG. 7 is a sectional view of a high frequency band pass filter device according to a modification of the invention. The high-frequency bandpass filter device according to the above modification has a thin film laminated electrode E6 as compared with the high-frequency bandpass filter device according to the second embodiment.
A thin film laminated electrode E6e is formed on the entire lower surface of the dielectric substrate 20 in place of a, E6b, E6c, E6d and the ground conductors 23, 24.

The thin film laminated electrode E6e is similar to the thin film laminated electrode 6 in the thin film conductors E1e, E2e, E3e and E.
4e, E5e and thin film dielectrics E30-1e, E30-2
e, E30-3e, and E30-4e are alternately laminated.

The high-frequency bandpass filter device of the modified example configured as described above operates in the same manner as the high-frequency bandpass filter device of the second embodiment and has the same effect. E6a, E6b, E6
Since c, E6d and the ground conductors 23, 24 are not formed individually, they can be formed by a simple process.

In the above-described first and second embodiments and modifications, the film thicknesses ξa ₁ and ξae ₁ of the thin film conductors 1 and E1 are formed to be π / 2 times the skin depth δ ₀ of the resonance frequency. However,
The present invention is not limited to this, and the preferable range of 1.14 ≦
It may be formed to have an arbitrary value in the range of ξ ₁ ≦ 2.75. As a result, the standardized surface resistance Rs ₁ can be made smaller than 1. That is, the normalized conductor film thickness ξ ₁
Is set to a value within the range of 1.14 ≦ ξ ₁ ≦ 2.75, the surface resistance RAs ₁ of the thin film laminated electrodes 6 and E6 at that time is set to the conductor film thickness ξa ₁ of the thin film conductors 1 and E1, ξa
It can be made smaller than the surface resistance when e ₁ is sufficiently thicker than the skin depth δ ₀ . Further, the present invention is not limited to this, and the conductor film thicknesses ξa ₁ and ξae ₁ may be set to arbitrary values sufficiently larger than the skin depth δ ₀ . In this case, the same effect as that of this embodiment can be obtained by increasing the number of laminated layers.

In the first and second embodiments and the modifications described above, the thin film laminated electrodes 6 and E6 are composed of five layers of thin film conductors and four layers of thin film dielectrics, but the present invention is not limited to this. It is not limited to this, and more layers may be laminated or fewer layers may be formed. If the number of layers is increased, the surface resistance is reduced, and if the number of layers is reduced, the size and cost can be reduced.

In the first and second embodiments and the modifications described above, the thin film laminated electrodes 6 and E6 are both formed of laminated electrodes, but the present invention is not limited to this, and one of them is formed of a thin film laminated electrode. You may do it.

[0155] The above first and the second embodiments and modifications, the conductor thickness Kushiei _k other than the top layer has been set to be as thick as the upper layer, of the present invention is the frequency used is not limited to this skin If it is thinner than the depth, the film thickness other than the uppermost layer may be made equal, or thick thin film conductors and thin thin film conductors may be laminated irregularly.

In the above-mentioned first and second embodiments and modifications, the thin film laminated electrodes 6, E6, 6a, 6b, 6c, 6 are formed.
Although d, E6a, E6b, E6c, and E6d are formed to have a circular shape, the present invention is not limited to this and may have other shapes such as an elliptical shape and a square shape. In the first embodiment described above, the orientation flat 101 is provided on the side surface of the dielectric substrate 10, but the present invention is not limited to this, and a dielectric substrate without the orientation flat 101 may be used. .

[0157]

In the TM mode dielectric resonator according to claim 1 of the present invention, at least one of the pair of electrodes sandwiching the dielectric substrate has a thin film conductor and a thin film dielectric. It is a thin film laminated electrode formed by alternately laminating. Thereby, it is possible to reduce the conductor loss and the surface resistance of the one electrode as compared with the conventional one,
It is possible to provide a TM mode dielectric resonator having a high unloaded Q as compared with the conventional example. Further, since the no-load Q can be made higher than that of the conventional example, the thickness of the dielectric substrate when obtaining a desired no-load Q can be made thinner than that of the conventional example. Thin TM compared to
A mode dielectric resonator can be provided.

A TM mode dielectric resonator according to a second aspect is the TM mode dielectric resonator according to the first aspect,
One of the pair of electrodes is the thin film laminated electrode, and the thin film laminated electrode is at least one sub-TM.
The mode resonators are laminated. Then, the film thickness and the dielectric constant of each thin film dielectric are set so that the electromagnetic field of the main TM mode resonator and the electromagnetic field of the sub TM mode resonator are substantially in phase with each other. Of these, the film thickness of each thin film conductor other than the thin film conductor formed farthest from the dielectric substrate is set to be thinner than the skin depth of the resonance frequency. As a result, the high frequency currents flowing in the same phase in each of the thin film conductors effectively increase the skin depth. Therefore, the conductor loss and the surface resistance of the one electrode can be significantly reduced as compared with the conventional one, and a TM mode dielectric resonator having a large unloaded Q can be provided. Further, since the no-load Q can be increased, the thickness of the dielectric substrate when obtaining a desired no-load Q can be made thinner than that of the conventional example, and can be made thinner than that of the conventional example. A TM mode dielectric resonator can be provided.

A TM mode dielectric resonator according to a third aspect is the TM mode dielectric resonator according to the first aspect.
Both of the pair of electrodes are the thin film laminated electrodes, and each of the thin film laminated electrodes is composed of at least one pair of the thin film conductors sandwiching the thin film dielectric.
One sub TM mode resonator is laminated. The electromagnetic field of the main TM mode resonator and the electromagnetic field of the sub TM mode resonator of the first thin film laminated electrode formed on one surface of the dielectric substrate are substantially in phase with each other, The electromagnetic field of the main TM mode resonator and the sub-T of the second thin film laminated electrode formed on the other surface of the dielectric substrate.
The film thickness and the dielectric constant of each of the thin film dielectrics are set so that the electromagnetic field of the M-mode resonator is substantially in phase with each other, and the thin film dielectrics are formed farthest from the dielectric substrate in the first thin film laminated electrode. Of the thin film conductors other than the thin film conductor other than the thin film conductor that is formed farthest from the dielectric substrate in the second thin film laminated electrode. The film thickness is set to be thinner than the skin depth of the resonance frequency. Thereby, both the conductor loss and the surface resistance of the pair of electrodes can be significantly reduced as compared with the conventional one.
A TM mode dielectric resonator having an unloaded Q larger than that of the mode dielectric resonator can be provided. Further, since the unloaded Q can be increased, the thickness of the dielectric substrate when obtaining a desired unloaded Q can be reduced as compared with the TM mode dielectric resonator according to claim 2. .

A TM mode dielectric resonator according to claim 4 is the TM mode dielectric resonator according to any one of claims 1 to 3, wherein the thin film conductor is formed farthest from the dielectric substrate. Is set to π / 2 times the skin depth at the resonance frequency. As a result, the film thickness of the thin film conductor formed farthest from the dielectric substrate is larger than that of the TM mode dielectric resonator in which the film thickness is set to a film thickness other than π / 2 times the skin depth at the resonance frequency. A TM mode dielectric resonator having a load Q can be provided. In addition, the thickness of the dielectric substrate for obtaining a desired no-load Q is set to the thickness of the thin film conductor formed farthest from the dielectric substrate other than π / 2 times the skin depth at the resonance frequency. Since the thickness can be made thinner than that of the TM mode dielectric resonator set to the film thickness of, the TM mode dielectric resonator can be made thin.

The TM mode dielectric resonator according to claim 5 is the TM mode dielectric resonator according to any one of claims 1 to 4, wherein the thin film conductor is formed in contact with the dielectric substrate. The film thickness of each thin film conductor from the dielectric substrate to the thin film conductor formed farthest away is set thicker as the film thickness of the thin film conductor formed farther from the dielectric substrate. As a result, a TM mode dielectric resonator having a high unloaded Q is provided as compared with a TM mode dielectric resonator that is not set to be as thick as the thickness of the thin film conductor formed apart from the dielectric substrate. can do. Further, the thickness of the dielectric substrate for obtaining a desired no-load Q is not set to be as thick as the thickness of the thin film conductor formed apart from the dielectric substrate. Since it can be made thinner than
The M-mode dielectric resonator can be made thin.

A TM mode dielectric resonator device according to a sixth aspect of the present invention is the TM mode dielectric resonator according to any one of the first to fifth aspects, and the TM mode dielectric resonator at the resonance frequency. A cavity for confining an electromagnetic field generated when excited in the cavity. As a result, the electromagnetic field of the TM mode dielectric resonator is confined in the cavity, so that the radiation loss can be reduced, and no load is applied as compared with the TM mode dielectric resonator having no cavity. A TM mode dielectric resonator device having a large Q can be provided.

According to a seventh aspect of the high frequency band pass filter device, at least one TM according to any one of the first to sixth aspects, wherein two TM mode dielectric resonators adjacent to each other are electromagnetically coupled. Mode dielectric resonator and the above-mentioned T
The M-mode dielectric resonator has an input terminal for inputting a high-frequency signal and an output terminal for outputting a high-frequency signal output from the TM-mode dielectric resonator. As a result, it is possible to provide a high-frequency bandpass filter device having a small loss in the passband and a large attenuation in the stopband. Further, when a predetermined pass band loss and a predetermined stop band attenuation characteristic are given, the thickness of the dielectric substrate can be made smaller than that of the conventional example, so that the high frequency band pass filter device is made thin. can do.

[Brief description of drawings]

FIG. 1 is a partially cutaway perspective view of a TM mode dielectric resonator device according to a first embodiment of the present invention.

2 is an A- of the TM mode dielectric resonator device of FIG.
It is sectional drawing about A '.

FIG. 3 is a diagram showing a thin film laminated electrode 6 and a dielectric substrate 1 in FIG.
It is a circuit diagram which shows the equivalent circuit of 0.

4 (a) is a graph showing the amplitude of the current in the thickness direction in a single-layer conductor thicker than the skin depth at the operating frequency, and FIG. 4 (b) is a graph showing the current in the thickness direction in the thin film laminated electrode 6 of FIG. It is a graph which shows an amplitude.

FIG. 5 is a perspective view of a high frequency bandpass filter device according to a second embodiment of the present invention.

6 is a B- of the high frequency band pass filter device of FIG.
It is sectional drawing about B '.

FIG. 7 is a cross-sectional view of a modified high frequency band pass filter device according to the present invention.

FIG. 8 (a) shows that the TM mode dielectric resonator R1 has T
Thin film conductor 5 and thin film conductor E when resonating in M ₁₁₀ mode
5B is a cross-sectional view showing an electric field distribution in the cross section of the dielectric substrate 10 sandwiched by 5 and FIG. 6B is a magnetic field distribution in the cross section when the TM mode dielectric resonator R1 resonates in the TM ₁₁₀ mode. FIG.

FIG. 9 (a) shows that the TM mode dielectric resonator R1 has T
Thin film conductor 5 and thin film conductor E when resonating in M ₂₁₀ mode
5B is a cross-sectional view showing an electric field distribution in a cross section of the dielectric substrate 10 sandwiched by 5 and FIG. 6B is a magnetic field distribution in the cross section when the TM mode dielectric resonator R1 resonates in the TM ₂₁₀ mode. FIG.

FIG. 10A is a cross-sectional view showing an electric field distribution in a cross section of a dielectric substrate 10 sandwiched by a thin film conductor 5 and a thin film conductor E5 when a TM mode dielectric resonator R1 resonates in a TM ₀₁₀ mode. It is a figure and (b) is sectional drawing which shows the magnetic field distribution in the said cross section when TM mode dielectric resonator R1 resonates in _TM010 mode.

11 is a TM mode dielectric resonator R1 of FIG.
₁₁ is a plan view showing a current distribution on the surface of the thin film conductor 5 when resonating in the ₀₁₁ mode.

FIG. 12 is a TM mode dielectric resonator R1 of FIG.
FIG. 8 is a plan view showing a current distribution on the surface of the thin film conductor 5 when resonating in ₂₁₀ mode.

FIG. 13 is a TM mode dielectric resonator R1 of FIG.
FIG. 6 is a plan view showing a current distribution on the surface of the thin film conductor 5 when resonating in the ₀₁₀ mode.

14 (a) is a thin film conductor 1 including the air layer of FIG.
Is a circuit diagram of a distributed constant type equivalent circuit in the thickness direction of
FIG. 6B is a circuit diagram of a lumped constant type equivalent circuit obtained by converting the distributed constant type equivalent circuit of FIG.

15 is a graph showing the relationship between the normalized surface resistance Rs ₁ and the normalized conductor film thickness xi] ₁ of the thin-film conductor 1 of FIG.

16A is a circuit diagram of a distributed constant type equivalent circuit in the thickness direction of the thin film conductor k in the thin film laminated electrode of FIG. 1, and FIG. 16B is a distributed constant type equivalent circuit of FIG. It is a circuit diagram of a lumped constant type equivalent circuit converted into a lumped constant type.

17 is a three-dimensional graph showing the Q increase rate RQ of the thin film laminated electrode 6 of FIG. 1 by the normalized conductor film thickness ξ _k and the reactance Xw.

[Explanation of symbols]

R1, R1a, R1b, R1c, R1d, R10a, R
10b, R10c, R10d ... TM mode dielectric resonator, 1, 2, 3, 4, 5, E1, E2, E3, E4, E5
E1e, E2e, E3e, E4e, E5e ... Thin film conductor, 6, E6, 6a, 6b, 6c, 6d, E6a, E6b,
E6c, E6d, E6e ... Thin film laminated electrode, 10, 20 ... Dielectric substrate, 21, 22 ... Strip conductor, 23 ... Ground conductor, 30-1, 30-2, 30-3, 30-4, E30-
1, E30-2, E30-3, E30-4, E30-1
e, E30-2e, E30-3e, E30-4e ... Thin film dielectric, 40 ... Case, 201, 202, 203, 204, 211, 212, 2
13, 214 ... Sub TM mode resonator, 210 ... Main TM mode resonator.

─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Norifumi Matsui No. 26-10 Tenjin Tenjin, Nagaokakyo City, Kyoto Prefecture Murata Manufacturing Co., Ltd. (56) Reference JP-A-8-167804 (JP, A) (58) Fields surveyed (Int.Cl. ⁷ , DB name) H01P 7/10 H01P 1/20 H01P 3/18

Claims (6)

(57) [Claims] 1. A TM mode dielectric resonator having a dielectric substrate sandwiched by a pair of electrodes having a predetermined shape, and having a predetermined resonance frequency, wherein one electrode of the pair of electrodes is A thin film laminated electrode constituted by alternately laminating a thin film conductor and a thin film dielectric, wherein the thin film laminated electrode comprises at least one thin film conductor sandwiching the thin film dielectric. Vice T
A main TM mode resonator, which is formed by stacking M-mode resonators and in which the dielectric substrate is sandwiched by the thin film conductor formed in contact with the dielectric substrate and the other electrode, An electromagnetic field generated when excited at the same resonance frequency and an electromagnetic field generated when excited at the same resonance frequency as the resonance frequency of the sub-TM mode resonator are substantially in phase with each other. By setting the film thickness and the permittivity of each thin film dielectric, the film thickness of each thin film conductor other than the thin film conductor formed farthest from the dielectric substrate among the above thin film conductors is made thinner than the skin depth of the resonance frequency. The electromagnetic field of the main TM mode resonator and the electromagnetic field of the sub TM mode resonator are coupled to each other, and the electromagnetic fields of the sub TM mode resonators adjacent to each other are coupled to each other. TM mode dielectric resonator according to symptoms. 2. A TM mode dielectric resonator having a dielectric substrate sandwiched by a pair of electrodes having a predetermined shape and having a predetermined resonance frequency, wherein the pair of electrodes are both a thin film conductor and a thin film. A thin film laminated electrode constituted by alternately laminating dielectrics, wherein each thin film laminated electrode is at least one sub-TM composed of a pair of the thin film conductors sandwiching the thin film dielectric. A main TM mode in which mode resonators are stacked, and the dielectric substrate is sandwiched by two thin film conductors formed in contact with the dielectric substrate among the thin film conductors of the thin film laminated electrodes. An electromagnetic field generated when the resonator is excited at the same resonance frequency as the resonance frequency, and the sub-TM module of the first thin film laminated electrode formed on one surface of the dielectric substrate. And the electromagnetic field generated when the resonator is excited at the same resonance frequency as the resonance frequency, and the main T
This occurs when the electromagnetic field of the M-mode resonator and the sub-TM-mode resonator of the second thin film laminated electrode formed on the other surface of the dielectric substrate are excited at the same resonance frequency as the resonance frequency. The film thickness and the dielectric constant of each of the thin film dielectrics are set so that the electromagnetic field is substantially in phase with each other, except for the thin film conductor formed farthest from the dielectric substrate in the first thin film laminated electrode. The thickness of the thin film conductor is made thinner than the skin depth of the resonance frequency, and the electromagnetic field of the main TM mode resonator and the sub TM of the first thin film laminated electrode are
The electromagnetic fields of the mode resonators are coupled to each other and the electromagnetic fields of the sub-TM mode resonators adjacent to each other in the first thin film laminated electrode are set to be coupled to each other, and the dielectric constant is set in the second thin film laminated electrode. The film thickness of the thin film conductors other than the thin film conductor formed farthest from the body substrate is made thinner than the skin depth of the resonance frequency, and the electromagnetic field of the main TM mode resonator and the sub TM of the second thin film laminated electrode are set. A TM mode dielectric resonator, wherein the electromagnetic fields of the mode resonator are coupled to each other and the electromagnetic fields of the sub TM mode resonators adjacent to each other in the second thin film laminated electrode are coupled to each other. 3. The film thickness of the thin film conductor formed farthest from the dielectric substrate is set to π / 2 times the skin depth at the resonance frequency, according to claim 1 or 2. TM mode dielectric resonator. 4. The film thickness of each thin film conductor from the thin film conductor formed in contact with the dielectric substrate to the thin film conductor formed farthest from the dielectric substrate is formed apart from the dielectric substrate. The TM mode dielectric resonator according to any one of claims 1 to 3, wherein the film thickness of the thin film conductor is increased. 5. T according to one of claims 1 to 4.
A TM mode dielectric having an M mode dielectric resonator and a cavity for confining an electromagnetic field generated when the TM mode dielectric resonator is excited at the resonance frequency in the cavity. Resonator device. 6. One of claims 1 to 4, wherein two TM mode dielectric resonators adjacent to each other are electromagnetically coupled.
And at least one TM mode dielectric resonator, an input terminal for inputting a high frequency signal to the TM mode dielectric resonator, and an output terminal for outputting a high frequency signal output from the TM mode dielectric resonator. A high-frequency bandpass filter device comprising: