CERAMIC MATERIALS, DEVICES, AND METHODS FOR MICROWAVE APPLICATIONS

Description

CROSS-REFERENCE TO RELATED APPLICATION(S)

Any and all applications for which a foreign or domestic priority claim is identified in the Application Data Sheet as filed with the present application are hereby incorporated by reference under 37 CFR 1.57. This application is a continuation of U.S. application Ser. No. 14/561,182 filed Dec. 4, 2014, entitled ENHANCED Q HIGH DIELECTRIC CONSTANT MATERIAL FOR MICROWAVE APPLICATIONS, which claims priority to and the benefit of the filing date of U.S. Provisional Application No. 61/912,463 filed Dec. 5, 2013, entitled ENHANCED Q HIGH DIELECTRIC CONSTANT MATERIAL FOR MICROWAVE APPLICATIONS, the benefits of the filing dates of which are hereby claimed and the disclosures of which are hereby expressly incorporated by reference herein in their respective entirety.

BACKGROUND

Field

The present disclosure generally relates to high dielectric constant materials for microwave applications.

Description of the Related Art

In some radio-frequency (RF) applications such as microwave applications, ceramic materials are often utilized as, for example, dielectric resonators. Such dielectric resonators can be implemented in devices such as narrowband filters.

SUMMARY

In some implementations, the present disclosure relates to a composition including a material with a formula Ba_4+xSm_{(2/3)(14−x+0.5y)}Ti_18−yAl_yO₅₄, with the quantity y being in a range 0<y<2, and the quantity x being in a range 0<x<2−y.

In some embodiments, the quantity x can be in a range 0<x<1−0.5y corresponding to barium content being in a range of 0% to 50%. In some embodiments, the quantity y can be approximately 0.5 and the quantity x can be in a range from approximately 0.01 to approximately 1.0. In some embodiments, the quantity y can be approximately 1.0 and the quantity x can be in a range from approximately 0.01 to approximately 0.5. In some embodiments, the quantity y can be approximately 1.4 and the quantity x can be in a range from approximately 0.01 to approximately 0.3.

In some embodiments, at least some of Sm can be substituted by another lanthanide including La, Ce, Pr, Nd or Gd. In some embodiments, the other lanthanide such as La or Nd can substitute up to approximately 50 atomic percent of Sm.

In some embodiments, at least some of Ba can be substituted by Sr. Sr can substitute up to approximately 30 atomic percent of Ba.

In some embodiments, the composition can further include a minor additive including manganese oxide, manganese carbonate, cerium oxide, copper oxide, germanium oxide, silica or gallium oxide. The minor additive can constitute less than approximately 2 percent by weight. The minor additive can be cerium oxide or manganese oxide; and such a minor additive can constitutes less than 0.5 percent by weight.

In some embodiments, a composition having one or more of the foregoing features can further include a high Q second phase material. The high Q second phase material can include TiO₂, BaTi₄O₉ or Ba₂Ti₉O₂₀.

According to a number of implementations, the present disclosure relates to a dielectric resonator having a ceramic device configured as a microwave resonator. The ceramic device includes a material with a formula Ba_4+xSm_{(2/3)(14−x+0.5y)}Ti_18−yAl_yO₅₄, with the quantity y being in a range 0<y<2, and the quantity x being in a range 0<x<2−y.

In some embodiments, the material can have a dielectric constant value that is greater than 60 for frequencies less than or equal to 1 GHz. Such a dielectric constant value can be in a frequency range that is greater than or equal to 700 MHz and less than or equal to 1 GHz. In some embodiments, the material can have a Qf value that is greater than 10,000, with the quantity Q being a quality factor, and the quantity f being a frequency expressed in GHz.

In accordance with some teachings, the present disclosure relates to a narrowband radio-frequency (RF) filter having an input port and an output port, and one or more dielectric resonators implemented between the input port and the output port. Each of the one or more dielectric resonators includes a ceramic device. The ceramic device includes a material with a formula Ba_4+xSm_{(2/3)(14−x+0.5y)}Ti_18−yAl_yO₅₄, with the quantity y being in a range 0<y<2, and the quantity x being in a range 0<x<2−y.

In a number of implementations, the present disclosure relates to a method for fabricating a tungsten bronze material having titanium (Ti) in a plurality of octahedral sites. The method includes substituting aluminum (Al) for at least some of the titanium (Ti) in the octahedral sites to yield a dielectric constant value greater than 60 and a Qf value greater than 10,000 at a frequency (f) at or less than 1 GHz. The method further includes adjusting contents of A1 and A2 sites to compensate for charge imbalance resulting from the aluminum substitution of titanium.

In some embodiments, the tungsten bronze material can be represented by a formula [A2]₄[A1]₁₀Ti_18−yAl_yO₅₄. In some embodiments, substantially all of the A2 sites can be occupied by barium (Ba) and at least some of the A1 sites can be occupied by samarium (Sm), such that the adjusting includes adding x formula unit of Ba and (2/3)x formula unit of Sm to the A1 sites. In some embodiments, the method can further include substituting at least some of the samarium with another lanthanide (Ln) to yield a temperature coefficient of resonant frequency (τ_f) that is less negative.

For purposes of summarizing the disclosure, certain aspects, advantages and novel features of the inventions have been described herein. It is to be understood that not necessarily all such advantages may be achieved in accordance with any particular embodiment of the invention. Thus, the invention may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other advantages as may be taught or suggested herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows that in some embodiments, a ceramic device such as a puck can include a material having one or more features as described herein.

FIG. 2 shows that in some embodiments, a ceramic puck having one or more features as described herein can include a center aperture dimensioned to allow, for example, tuning of the ceramic puck when utilized as a microwave resonator.

FIG. 3 shows an example of a tunable microwave resonator configuration.

FIG. 4 shows an example of a cavity filter having a plurality of cavities arranged between radio-frequency (RF) ports.

FIG. 5 shows an example of an RF system that can utilize one or more of the filter device of FIG. 4.

FIG. 6 shows a process that can be implemented to fabricate a ceramic material having one or more features as described herein.

FIG. 7 shows a process that can be implemented to press-form a shaped object from a powder material prepared as described herein.

FIG. 8 shows example stages associated with the process of FIG. 7.

FIG. 9 shows a process that can be implemented to sinter formed objects having one or more features as described herein.

FIG. 10 shows example stages associated with the process of FIG. 9.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

The headings provided herein, if any, are for convenience only and do not necessarily affect the scope or meaning of the claimed invention.

Disclosed are compositions that can include materials having relatively high dielectric constant values and enhanced Q values. Examples of such materials are described herein in greater detail. Also described herein are examples of how such materials can be manufactured. Also described herein are examples of devices and applications in which such materials can be utilized.

In some radio-frequency (RF) applications such as microwave applications (e.g., low-frequency (700 MHz-1 GHz) applications), materials with a dielectric constant greater than 60 and having a desired or optimized quality factor Q can be desirable. For example, a Qf (product of Q and frequency f) value greater than 10,000 in the foregoing frequency range (700 MHz to 1 GHz range) can be desirable. Further, such a material preferably has a temperature coefficient of resonant frequency that is near zero. Conventional high-dielectric-constant materials typically do not have sufficient Q and/or require expensive raw materials such as Ga or Ge.

Disclosed are various examples of materials that can meet desired Q specifications or requirements without the expensive raw materials in their respective compositions. Also disclosed are examples of how such materials can be implemented in low-frequency microwave applications. Although described in such low-frequency context, it will be understood that one or more features of the present disclosure can also be implemented in other RF applications.

Various examples of dielectric materials and associated methods are described in U.S. Pat. No. 8,318,623 which is expressly incorporated by reference in its entirely and to be considered part of the specification of the present application.

Some compounds with an orthorhombic tungsten bronze structure can be represented by a general formula

Ba_6−3xLn_8+2xTi₁₈O₅₄,  (1)

where Ln can be a lanthanide such as lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), samarium (Sm) or gadolinium (Gd). Such a structure can be implemented for microwave dielectric applications due to their high dielectric constants (e.g., 60-100) and their ability to be tuned to a near zero temperature coefficient of resonant frequency.

In some applications, it is additionally desirable to minimize or reduce the dielectric loss tangent (tan δ) or to maximize or increase the quality factor Q (an inverse of dielectric loss tangent, 1/tan δ) of a dielectric material used for microwave applications, since such a property typically yields sharper resonances and sharper transitions for filter applications.

From a crystallographic perspective, the foregoing materials can be represented as

[A2]₄[A1]₁₀Ti₁₈O₅₄.  (2)

Typically, the 10 available A1 sites are rhombic while the 4 available A2 sites are pentagonal. The Ti atoms typically occupy octahedral sites. The A1 sites may be occupied by Ba atoms, Ln atoms, or may be vacant. The A2 sites may be occupied by Ba or Ln atoms. Although described in the context of rhombic sites, it will be understood that one or more features of the present disclosure can also be implemented in other types of sites.

For the orthorhombic tungsten bronze structure represented by Formula 1, it is generally understood that the value of Q can be optimal when the quantity x has a value of 2/3 (0.667), where substantially all of the Ba atoms reside in the pentagonal A2 sites and substantially all of the lanthanide (Ln) atoms reside in the rhombic A1 sites. A number of studies have shown that the value of Q is typically maximum when the lanthanide (Ln) chosen is Sm, and decreases with increasing lanthanide size in the order of, for example, Nd, Pr, Ce and La. The Gd material shows a very limited solid solution range and typically yields a relatively low Q as well.

Among the foregoing lanthanide examples, Sm and Gd are lanthanides that yield negative temperature coefficient of resonant frequency (τ_f) values. The other lanthanides Nd, Pr, Ce and La series all yield positive τ_f values. In the context of dielectric resonators, temperature coefficient of resonant frequency (τ_f) is typically a combination of temperature coefficient of dielectric constant of a resonator, temperature coefficient of the resonator cavity, and the coefficient of thermal expansion of the resonator.

Based on the foregoing properties of the example lanthanides, a typical design strategy can involve blends of two lanthanides such as Sm and Nd or Sm and La to achieve temperature compensated ceramic bodies. Aside from such design considerations based on physical properties, availability and/or cost of raw materials can also impact designs of ceramic devices. For example, there is a demand for ceramic solutions for microwave materials that do not contain scarce and/or costly elements such as neodymium (Nd), gallium (Ga) or germanium (Ge). Samarium (Sm) and lanthanum (La) are significantly less scarce for rare earth elements.

As described in U.S. Pat. No. 8,318,623, as well as in, for example, U.S. Pat. Nos. 5,182,240, 5,185,304 and 5,310,710, at least some of the titanium in tungsten bronze material can be substituted by, for example, aluminum. The resulting charge imbalance can be compensated by adding Ln material (e.g., Nd, a mixture of Nd and Sm, a mixture of Nd and Y, or a mixture of Sm and non-lanthanide Bi) into the vacant A1 lattice site(s) (e.g., in Formula 2). It is also noted that in the tungsten bronze material of Formula 1 (Ba_6−3xLn_8+2xTi₁₈O₅₄), for x values less than or equal to 2/3 where Ln=Nd (in the BaO—Nd₂O₃—TiO₂ ternary system), the resulting phase is chemically compatible with the high Q rutile form of TiO₂ (with τ_f being greater than approximately 500 ppm/° C.).

In some embodiments, aluminum (Al) can be substituted for titanium (Ti) in the octahedral site to yield, contrary to published findings, highest or enhanced Q material at approximately 1 GHz for x values less than or equal to 2/3. In the context of Formula 2, the foregoing substitution of Ti by Al can be represented as

[A2]₄[A1]₁₀Ti_18−yAl_yO₅₄,  (3)

where y unit of Ti is substituted by y unit of Al.

As described herein, charge imbalance resulting from substitution of Ti⁺⁴ with Al⁺³ can be compensated by appropriate occupations of the A1 and/or A2 sites by, for example, Ln⁺³ and/or Ba⁺², respectively. In the context of such Ln and Ba, Formula 3 can be expressed as a modified form of Formula 1, as one of the following example formulas

Ba_6−3xLn_8+2x+(y/3)Ti_18−yAl_yO₅₄,  (4A)

Ba_6−3x+(y/2)Ln_8+2xTi_18−yAl_yO₅₄, and  (4B)

Ba_6−3x−yLn_8+2x+yTi_18−yAl_yO₅₄,  (4C)

where the charge imbalance of y (+4 of Ti to +3 of Al) can be compensated by adding an appropriate amount of Ba (+2), Ln (+3), or a mixture of the two. For example, in Formula 4A, charge balancing can be achieved by adding Ln³⁺, with the formula unit of y/3 to account for the +3 charge. In Formula 4B, charge balancing can be achieved by adding Ba²⁺, with the formula unit of y/2 to account for the +2 charge. In Formula 4C, charge balancing can be achieved by subtracting y formula unit of Ba (+2) and adding y formula unit of Ln (+3). It is noted that Formulas 4A and 4B are extreme cases involving only one type of addition (of Ln or Ba), and that the charge imbalance may also be compensated with a mixture of Ln³⁺ and Ba²⁺ (such as the example of Formula 4C). Previous studies have taught that the Q is optimal only if all of the barium remains on the A2 site and the lanthanide remains on the A1 site. However, the present disclosure shows that such is not necessarily true.

It is noted that in Formula 4, there are 10 available rhombic A1 sites. Accordingly, and in the context of the example of Formula 4A, a limit can be imposed, where formula unit of 8+2x+(y/3) has a maximum value of 10. In such a configuration, the maximum value for y is 2 when x=2/3. In terms of Al substitution of Ti, the maximum amount of aluminum which may be substituted for titanium is 2 formula units (y=2).

Based on the foregoing limit of 2 formula units of aluminum substitution of titanium, aluminum content can be expressed as

aluminum percent=100(y/2),  (5)

where y represents the formula units of aluminum in the composition of Formula 4A. For example, when y=2 in which Formula 4A becomes Ba₄Ln₁₀Ti₁₆Al₂O₅₄ (with x=2/3), aluminum percent is 100%. In another example, when y=1 and x has a value of 2/3 based on the formula units for barium (6−3x) being equal to 4, Formula 4A becomes Ba₄Ln_9.667Ti₁₇AlO₅₄, with aluminum percent being 50%. Note that in both cases (of aluminum percent of 100% and 50%), all of the charge compensation for the aluminum substitution comes from adding additional Ln³⁺ to the A1 site.

In some embodiments, where the compensation of the aluminum substitution at least partially occurs by adding Ba²⁺ to the A1 site, the maximum amount of barium which can fit into the A1 site can depend on the foregoing aluminum percent, due to charge balance considerations. The maximum amount of barium which can be placed in the A1 site (Ba_max) is equal to 2−(aluminum percent)/50. The barium percent (in the A1 site) can then be expressed as (N_Ba−4)/Ba_max, where N_Ba is the total number of formula units of Ba. Equivalently, barium percent can be expressed as

barium percent=(N_Ba−4)/(2−(aluminum percent)/50),  (6)

where N_Ba is the number of barium atoms in the formula (e.g., 6−3x−y in Formula 4). For example, in the case of aluminum percent being 100 (yielding a zero denominator), barium percent is zero, with no barium in the A1 sites and all of the Ba atoms occupying the A2 sites. In another example, the 50%-aluminum configuration that yields the example formula Ba₄Ln_9.667Ti₁₇AlO₅₄ also results in barium percent of zero, since all of the available aluminum is compensated by additional Ln³⁺ in the A1 site. Examples of non-zero barium percent configurations are described herein in greater detail.

As described herein in reference to the example of Formula 4C, an aluminum substitution of titanium by an amount of y formula units can be charge-compensated by an addition of lanthanide (by y formula units) and a subtraction of barium (by y formula units). In the context of zero barium percent configurations, a 100%-aluminum configuration can yield Ba₄Ln₁₀Ti₁₆Al₂O₅₄, and a 50%-aluminum configuration can yield Ba₄Ln_9.667Ti₁₇AlO₅₄. In the context of non-zero barium percent configurations, at least some of the barium can occupy the A1 sites.

In configurations where more than four formula units of barium are present, Formula 4C can be expressed as

Ba_4+x′Ln_{8+2x+y−(2/3)x′}Ti_18−yAl_yO₅₄,  (7)

where x′ represents the additional formula units of barium. Equivalently, x′ can be expressed as x′=N_Ba−4. Such an increase in Ba (+2) can be charge balanced by a decrease of (2/3)x′ formula units of Ln(+3). In Formula 7, the aluminum substitution formula unit quantity y can be greater than zero and less than or equal to 2 as described herein, such that 0<y≤2. The extra-barium formula unit x′ can be greater than or equal to zero, and less than or equal to a maximum value of 2−y, such that 0≤x′≤2−y. Such a maximum value of 2−y can be calculated by, for example, assuming that the Ln formula unit of 8+2x+y−(2/3)x′ (of Formula 7) and the additional Ba formula unit of x′ sum to the maximum A1 occupation number of 10 (e.g., 8+2x+y−(2/3)x′+x′=10). The quantity x′ can be solved to yield x′=2−y.

In some embodiments, all four A2 sites can be occupied by barium and the additional x′ formula units of barium can occupy A1 sites. In such embodiments, since all four of the A2 sites are occupied by 6−3x−y formula units (barium number in Formula 4C), 6−3x−y can be set to equal 4, which yields an expression x=(2/3)−(1/3)y. Substituting such an expression of x into the subscript of Ln in Formula 7, the subscript becomes 8+2[(2/3)−(1/3)y]+y−(2/3)x′, which in turn can be expressed as (2/3)[14+(1/2)y−x′]. Accordingly, Formula 7 can be expressed as

Ba_4+x′Ln_{(2/3)[14+0.5y−x]}Ti_18−yAl_yO₅₄,  (8)

where the aluminum substitution formula unit quantity y can be greater than zero and less than or equal to 2, such that 0<y≤2. The extra-barium formula unit x′ can be greater than or equal to zero, and less than or equal to a maximum value of 1−0.5x, such that 0≤x′≤1−0.5y. Such a maximum value of 1−0.5y can be calculated by, for example, assuming that the Ln formula unit of (2/3)[14+0.5y−x′] (of Formula 8) and the additional Ba formula unit of x′ sum to the maximum A1 occupation number of 10 (e.g., (2/3)[14+0.5y−x′]+x′=10). The quantity x′ can be solved to yield x′=1−0.5y. It is noted that in Formula 8, the four formula units of Ba occupy all of the four A2 sites; and such occupation is reflected in the Ln formula unit of (2/3)[14+0.5y−x′].

In embodiments where lanthanide is samarium (Ln=Sm), Formula 8 can be expressed as

Ba_4+x′Sm_{(2/3)[14+0.5y−x′]}Ti_18−yAl_yO₅₄.  (9)

In such a system, the substitution of aluminum (Al) for titanium (Ti) as described herein can yield high Q rutile form of TiO₂ being chemically compatible with Formula 1 (Ba_6-3xLn_8+3xTi₁₈O₅₄) when the value of x is less than or equal to 2/3, similar to the foregoing neodymium (Nd) system (Ln=Nd). In some embodiments of the Sm system, one or more lanthanides having positive τ_f values can be introduced to compensate for the negative τ_f value associated with Sm. For example, some of Sm can be substituted by another lanthanide such as La, Ce, Pr, Nd or Gd. In some embodiments, the other lanthanide can be La or Nd, and such lanthanide can substitute up to approximately 50 percent (e.g., mole %) of Sm.

Although various examples are described in the context of barium, it will be understood that one or more of other alkaline earth metals can replace at least some of the barium content. For example, strontium (Sr) can be included, and its content percent can be calculated in the same manner as the barium percent described herein in reference to Equation 6.

In some embodiments having x values <0.667 in, for example Formula 4, there may be conditions where rutile TiO₂ can be added as a second crystallographic phase. Examples of such additions are described herein in greater detail. Further, some embodiments can include small amounts of acceptor dopants such as MnO₂ or CeO₂ added to the composition to, for example, prevent or reduce thermal reduction of the titanium from Ti⁴⁺ to Ti³⁺.

Table 1 lists various samples having various combinations of aluminum percent (Al %, as described in Equation 5), barium percent (Ba %, as described in Equation 6), strontium percent (Sr %, similar to the barium percent), lanthanum percent (La %, mole percent), cerium oxide weight percent (CeO₂ w %), and titanium oxide or rutile weight percent (TiO₂ w %). Table 1 also lists density values of selected ones of the samples. Empty cells, if any, correspond to values that are either not applicable or not available. It will be understood that each of the samples listed in Table 1 is based on Formula 9 (Ba_4+x′Sm_{(2/3)[14+0.5y−x′]}Ti_18−yAl_yO₅₄), with the various percent values corresponding to substitutions of Ba or Sm, or introduction of second phase materials (e.g., TiO₂).

Table 2 lists Q values for the same samples of Table 1, at or near f=1 GHz. Corresponding Qf values are also listed. Table 2 also lists dielectric constant values (∈′) corresponding to the listed approximately 1 GHz frequency values for selected ones of the samples. Table 2 also lists values of temperature coefficient of resonant frequency (τ_f) for selected ones of the samples. Empty cells, if any, correspond to values that are either not applicable or not available.

Table 3 lists Q values for some of the samples of Table 1, at or near f=3 GHz. Corresponding Qf values are also listed. Table 3 also lists dielectric constant values (∈′) corresponding to the listed approximately 3 GHz frequency values. Empty cells, if any, correspond to values that are either not applicable or not available.

TABLE 1
							Den-
Sam-							sity
ple	Al	Ba	Sr	La	CeO2	TiO2	(g/
No.	%	%	%	%	w %	w %	cm3)

1	100	0	0	2.75	0	0
2	100	0	0	2.75	0	0
3	100	0	0	2.75	0	0
4	100	0	0	2.75	0	0
5	100	0	0	2.75	0	0
6	100	0	0	2.75	0	0
7	100	0	0	2.75	0	0
8	75	0	0	0	0	0
9	75.1	24.8	0	0	0	0
10	50	0	0	0	0	0
11	50	25	0	0	0	0
12	25	0	0	0	0	0
13	24.9	24.9	0	0	0	0
14	0	0	0	0	0	25
15	0	25.1	0	0	0	25
16	75	25	0	0	0	25
17	50	0	0	0	0	25
18	50	25	0	0	0	25
19	25	0	0	0	0	25
20	25	25	0	0	0	25
21	25	0	0	0	0	12.5
22	25	25	0	0	0	12.5
23	75.1	24.8	0	0	0.25	0	5.453
24	50	25	0	0	0.5	0
25	24.9	24.9	0	0	0.75	0
26	0	25.1	0	0	0.75	25
27	0	25.1	0	0	0.875	12.5
28	24.9	24.9	0	0	0.558	25
29	24.9	24.9	0	0	0.658	12.5
30	74.2	48.06	0	2.8	0.25	0	5.896
31	49.85	25.09	0	5.78	0.5	0
32	24.98	24.91	0	8.89	0.75	0
33	0	24.92	0	12.14	0.875	0
34	24.98	24.91	0	8.89	0.75	25
35	24.98	24.91	0	8.89	0.75	12.5
36	74.75	25.34	0	2.84	0	0	5.916
37	49.68	24.91	0	5.82	0	0
38	24.67	24.8	0	8.92	0	0
39	0	24.92	0	12.14	0	25
40	0	24.92	0	12.14	0	12.5
41	24.67	24.8	0	8.92	0	25
42	24.67	24.8	0	8.92	0	12.5
43	9.93	24.9	0	5	0	0
44	9.93	25.1	0	10	0	0
45	31.28	24.88	0	5	0	0
46	31.28	24.88	0	10	0	0
47	50.02	24.84	0	5	0	0
48	50.02	24.84	0	10	0	0
49	70.07	25	0	5	0	0	5.74
50	70.07	25	0	10	0	0
51	89.95	25.87	0	5	0	0
52	89.95	25.87	0	10	0	0
53	9.93	24.9	0	2.5	0	0
54	31.28	24.88	0	2.5	0	0
55	50.02	24.84	0	2.5	0	0	5.76
56	70.07	25	0	2.5	0	0	5.74
57	89.95	25.87	0	2.5	0	0
58	10	31.99	0	5	0	0
59	10	31.99	0	10	0	0
60	29.8	33.8	0	5	0	0
61	29.8	33.8	0	10	0	0
62	49.6	37.06	0	5	0	0
63	49.6	37.06	0	10	0	0
64	69.4	45.02	0	5	0	0	5.7
65	69.4	45.02	0	10	0	0	5.7
66	89.23	82.2	0	5	0	0	5.64
67	89.23	82.2	0	10	0	0	5.66
68	10	31.99	0	2.5	0	0
69	29.8	33.8	0	2.5	0	0
70	49.6	37.06	0	2.5	0	0
71	69.4	45.02	0	2.5	0	0	5.75
72	89.23	82.2	0	2.5	0	0	5.67
73	74.2	48	0	10	0	0	5.77
74	74.2	48	0	10	0	10
75	74.2	0	48	10	0	0	5.81
76	74.2	48	0	20	0	0	5.78
77	74.2	48	0	30	0	0	5.77
78	74.2	48	0	40	0	0	5.67
79	74.75	25.35	0	10	0	0	5.8
80	74.75	25.35	0	10	0	10
81	74.75	0	25.35	10	0	0	5.8
82	74.75	25.35	0	20	0	0	5.79
83	74.75	25.35	0	30	0	0	5.77
84	74.75	25.35	0	40	0	0	5.71
85	70.06	25	0	10	0	0	5.76
86	70.06	25	0	10	0	10
87	70.06	0	25	10	0	0	5.82
88	70.06	25	0	20	0	0	5.66
89	70.06	25	0	30	0	0	5.73
90	70.06	25	0	40	0	0	5.73
91	89.25	82.3	0	10	0	0
92	89.25	82.3	0	10	0	10
93	89.25	0	82.3	10	0	0
94	89.25	82.3	0	20	0	0
95	89.25	82.3	0	30	0	0
96	89.25	82.3	0	40	0	0
97	69.35	45	0	10	0	0	5.76
98	69.35	45	0	10	0	10
99	69.35	0	45	10	0	0	5.79
100	69.35	45	0	20	0	0	5.73
101	69.35	45	0	30	0	0	5.76
102	69.35	45	0	40	0	0	5.64
103	50	0	0	5	0	0
104	50	0	0	5	0	10
105	50	12.5	0	5	0	0
106	50	12.5	0	5	0	10
107	50	25	0	5	0	0
108	50	25	0	5	0	10
109	50	37.5	0	5	0	0
110	50	37.5	0	5	0	10
111	50	50	0	5	0	0
112	50	50	0	5	0	10
113	50	75	0	5	0	0
114	50	75	0	5	0	10
115	50	100	0	5	0	0
116	50	100	0	5	0	10
117	66.67	0	0	5	0	0
118	66.67	0	0	5	0	10
119	66.67	25	0	5	0	0
120	66.67	25	0	5	0	10
121	66.67	50	0	5	0	0
122	66.67	50	0	5	0	10
123	66.67	75	0	5	0	0
124	66.67	75	0	5	0	10
125	66.67	100	0	5	0	0
126	66.67	100	0	5	0	10
127	83.33	50	0	5	0	10
128	83.33	100	0	5	0	0
129	83.33	100	0	5	0	10
130	70.06	25	0	40	0	0
131	70.06	25	0	40	0.067	0
132	70.06	25	0	40	0.033	0
133	70.06	25	0	40	0.067	0
134	70.06	25	0	40	0	0
135	70.06	25	0	40	0.133	0
136	50	20	0	0	0	8.333
137	50	20	0	0	0.067	8.333
138	50	20	0	0	0.067	8.333
139	25	25	0	0	0	8.333
140	25	25	0	0	0.067	8.333	5.61
141	25	25	0	0	0.033	8.333	5.61
142	25	25	0	0	0.067	8.333
143	25	25	0	10	0	8.333
144	25	25	0	10	0.067	8.333
145	25	25	0	10	0.033	8.333
146	25	25	0	10	0.067	8.333
147	50	27	0	0	0.067	10
148	50	29	0	0	0.067	10
149	50	31	0	0	0.067	10
150	50	33	0	0	0.067	10
151	50	35	0	0	0.067	10
152	50	37	0	0	0.067	10
153	50	39	0	0	0.067	10
154	50	41	0	0	0.067	10
155	50	43	0	0	0.067	10
156	50	45	0	0	0.067	10
157	70.06	25	.3GeO2	0	.067MnO2	0
158	70.06	25	.3GeO2	0	0.067	0
159	70.06	25	.3GeO2	40	.067MnO2	0
160	70.06	25	.3GeO2	40	0.067	0
161	70.06	25	0	50Nd2O3	0.067	0
162	70.06	25	0	50Nd2O3	.067MnO2	0
163	70.06	25	.3GeO2	50Nd2O3	0.067	0
164	70.06	25	.3GeO2	50Nd2O3	.067MnO2	0
165	25	25	.3GeO2	0	0.067	10
166	25	25	.3GeO2	10	0.067	10
167	25	25	0	10Nd2O3	0.067	0
168	25	25	.3GeO2	10Nd2O3	0.067	0
169	25	25	0	50Nd2O3	0.067	0
170	25	25	.3GeO2	50Nd2O3	0.067	0

TABLE 2
Sample No.	Q (1 GHz)	f	Qf (1 GHz)	ε′ (1 GHz)	τF

1	2170	1.156	2508.52
2	3170	1.172	3715.24
3	3420	1.111	3799.62
4	6580	1.089	7165.62
5	4770	1.045	4984.65
6	7300	1.013	7394.9
7	7830	0.949	7430.67
8	2620	1.092	2861.04
9	9510	1.104	10499.04
10	3600	1.054	3794.4
11	6720	1.052	7069.44
12	4410	1.016	4480.56
13	3600	1.0528	3790.08	81.8
14
15
16	1000	0.98	980	82
17	1500	0.9543	1431.45	81.9
18	4780	0.974	4655.72
19	1400	0.9484	1327.76	84.2
20	1500	0.9805	1470.75	79.7
21	1000	0.9929	992.9	78.4
22	1400	1.026	1436.4	73.8
23	9700	1.1895	11538.15		−41.61
24	8000	1.0859	8687.2	68.3
25	2500	1.0306	2576.5	76.6
26	3900	1.0723	4181.97	76.7
27
28	1000	0.9966	996.6	77.1
29
30	12000	1.0818	12981.6	63.1	−62.53
31	9400	1.0363	9741.22
32	9900	1.0109	10007.91
33	5200	1.0903	5669.56
34	5000	1.2524	6262
35	3800	1.3473	5119.74
36	11000	1.0839	11922.9	66	−61.19
37	9600	1.0446	10028.16
38	8000	0.9915	7932
39	6000	1.0312	6187.2
40	6300	1.0055	6334.65
41	8000	1.1036	8828.8
42	8000	1.0685	8548
43	7680	0.9718	7463.424
44	7668	0.9669	7414.1892
45	8742	1.0128	8853.8976
46	8734	1.0081	8804.7454
47	9910	1.0601	10505.591
48	9696	1.0502	10182.739
49	10923	1.0876	11879.855		−55.32
50	10580	1.0904	11536.432		−48.21
51	4352	1.1621	5057.4592
52	7031	1.2009	8443.5279
53	7079	1.0114	7159.7006
54	7885	1.1273	8888.7605
55	10224	1.0482	10716.797		−46.15
56	10780	1.1261	12139.358		−57.93
57	3674	1.1532	4236.8568
58	3556	0.9687	3444.6972
59	4647	0.9609	4465.3023
60	7770	1.0052	7810.404
61	7948	1.0043	7982.1764
62	9417	1.0411	9804.0387
63	9302	1.0517	9782.9134
64	10341	1.0823	11192.064		−54.1
65	10018	1.0909	10928.636		−46.83
66	10860	1.1288	12258.768		−62.16
67	10445	1.1151	11647.22		−55.87
68	2653	0.9673	2566.2469
69	6935	1.0049	6968.9815
70	9223	1.0384	9577.1632
71	10003	1.1293	11296.388		−58.02
72	11197	1.1336	12692.919		−65.23
73	9700	1.0987	10657.39	65.5	−50.34
74	4500	1.1571	5206.95	69.8
75	9300	1.0991	10221.63	66.3	−51.46
76	9400	1.1015	10354.1	67.8	−32.96
77	8200	1.0835	8884.7	69.5	−12.82
78	6600	1.1135	7349.1	70.5	15.09
79	10600	1.1003	11663.18	66	−52.13
80	3600	1.0643	3831.48	67.1
81	8800	1.1149	9811.12	65.8	−53.34
82	9800	1.09	10682	67.5	−36.93
83	8800	1.0905	9596.4	68.8	−16.24
84	7400	1.0616	7855.84	69.9	7.33
85	10300	1.1232	11568.96	65.8	−48.71
86	4300	1.0486	4508.98	69.3
87	8700	1.1725	10200.75	67	−51.36
88	10400	1.0536	10957.44	65.5	−32.12
89	9000	1.045	9405	68.9	−14.01
90	7600	1.0537	8008.12	71.9	9.81
91	9200	1.2902	11869.84	61.2
92	2600	1.088	2828.8	64.1
93	8000	1.1366	9092.8	61.5
94	9200	1.1044	10160.48	61.9
95	7500	1.1018	8263.5	62.8
96	6000	1.1165	6699	62.8
97	10000	1.0912	10912	66.9	−47.17
98	4800	1.0472	5026.56	71.9
99	9400	1.0952	10294.88	67.8	−49.31
100	9500	1.0742	10204.9	68.1	−29.03
101	8400	1.0607	8909.88	70.9	−8.75
102	6800	1.0476	7123.68	71.2	20.57
103	4300	1.0483	4507.69	70.8
104	2500	1.0174	2543.5	73.9
105	10300	1.0656	10975.68	68.7
106	2700	1.0132	2735.64	75.6
107	9850	1.0651	10491.235	69.2
108	7000	1.0099	7069.3	75.7
109	9000	1.0788	9709.2	70.1
110	6800	1.0302	7005.36	73.6
111	2000	1.0491	2098.2	71.9
112	4800	1.1632	5583.36	55
113
114	5700	1.0687	6091.59	66
115
116
117	4200	1.0897	4576.74	67.4
118	5600	1.0445	5849.2	67.3
119	10600	1.102	11681.2	65.5
120	1600	1.0285	1645.6	71.4
121	9700	1.102	10689.4	66.5
122	3200	1.0222	3271.04	72.5
123	1000	1.0881	1088.1	68.4
124	5100	1.0373	5290.23	68.2
125
126	4900	1.0799	5291.51	63.4
127	1600	1.0603	1696.48	66.7
128	1600	1.1628	1860.48	61.7
129	3700	1.0604	3923.48	67.4
130	6600	1.0502	6931.32	71.1
131	6900	1.0722	7398.18	71.1
132	6900	1.0661	7356.09	71.2
133	6800	1.0789	7336.52	71.4
134	6100	1.0704	6529.44	71.5
135	7000	1.0816	7571.2	69.6
136	6900	1.0419	7189.11	73.4
137	7300	1.037	7570.1	73.4
138	6900	1.0293	7102.17	72.9
139	8800	1.0313	9075.44	72.9
140	9900	1.0287	10184.13	72.9	−2.6
141	9900	1.0244	10141.56	73	−1.86
142	9600	1.0327	9913.92	72.7
143	8000	1.0281	8224.8	74.6
144	8600	1.0266	8828.76	74.4
145	8200	1.0362	8496.84	74.4
146	7900	1.0366	8189.14	74.4
147	1700	1.1102	1887.34	63.9
148	2000	1.1221	2244.2	64
149	2600	1.1132	2894.32	64.2
150	3000	1.1339	3401.7	62.8
151	3500	1.0861	3801.35	65.4
152	4300	1.0872	4674.96	64.3
153	5600	1.0834	6067.04	65.2
154	5800	1.0893	6317.94	65.5
155	5800	1.0991	6374.78	63.6
156	5000	1.0901	5450.5	63.3
157	9000	1.1791	10611.9	64.3
158	9200	1.1796	10852.32	63.8
159	6200	1.1302	7007.24	71.2
160	6200	1.1229	6961.98	71.1
161	10200	1.1065	11286.3	64
162	10300	1.1121	11454.63	65.3
163	10400	1.1118	11562.72	64.3
164	9500	1.124	10678	67
165	3800	1.1339	4308.82	63.8
166	6000	1.1159	6695.4	60.3
167	5600	1.0165	5692.4	77.6
168	6700	1.0823	7251.41	75.2
169	8800	1.0029	8825.52	80.4
170	8500	1.0377	8820.45	79.5

TABLE 3
Sample No.	Q (3 GHz)	f	Qf (3 GHz)	ε′ (3 GHz)

23	3669	3.5075	12869.018	54.69
30	4104	3.301	13547.304	65.06
36	4080	3.283	13394.64	65.81
49	3981	3.3071	13165.565	64.3
50	3952	3.2981	13034.091
55	3619	3.1984	11575.01	68.8
56	3988	3.315	13220.22	63.97
64	3808	3.3186	12637.229	63.85
65	3746	3.2934	12337.076	64.86
66	4175	3.4485	14397.488	59.07
67	3986	3.4196	13630.526	60.08
71	3807	3.3019	12570.333	64.52
72	4161	3.4473	14344.215	59.19
73	3726	3.2956	12279.406	64.89
75	4055	3.273	13272.015	65.84
76	3784	3.2418	12266.971	67.04
77	3548	3.1944	11333.731	69.1
78	3106	3.1836	9888.2616	69.64
79	4152	3.2889	13655.513	65.19
81	3890	3.2922	12806.658	65.06
82	3915	3.243	12696.345	67.01
83	3725	3.2149	11975.503	68.29
84	3319	3.1924	10595.576	69.25
85	4121	3.2855	13539.546	65.33
87	3941	3.2575	12837.808	66.46
88	3864	3.2943	12729.175	65.08
89	3594	3.2154	11556.148	68.36
90	3279	3.158	10355.082	70.9
97	3973	3.2739	13007.205	65.89
99	3955	3.2538	12868.779	66.7
100	3635	3.239	11773.765	67.35
101	3520	3.1777	11185.504	70.03
102	2975	3.1723	9437.5925	70.27
140	3776	3.1235	11794.336	72.7
141	3793	3.1231	11845.918	72.66

As described herein, in some radio-frequency (RF) applications such as low-frequency (700 MHz-1 GHz) microwave applications, materials with dielectric constant values greater than 60 and having Qf (product of Q and frequency f) values greater than 10,000 can be desirable. Among the non-limiting examples listed in Tables 1-3, a number of configurations can include such a combination of relatively high dielectric constant (e.g., greater than 60) and relatively high Qf (e.g., greater than 10,000) at or near such a low-frequency range of 700 MHz-1 GHz. Table 4 lists such configurations selected from the list of Tables 1-3.

TABLE 4
Sample	Al	Ba	Sr	La	CeO2	TiO2	Qf
No.	%	%	%	%	w %	w %	(1 GHz)	ε′	τF

9	75.1	24.8	0	0	0	0	10499
23	75.1	24.8	0	0	0.25	0	11538		−41.61
30	74.2	48.06	0	2.8	0.25	0	12982	63.1	−62.53
32	24.98	24.91	0	8.89	0.75	0	10008
36	74.75	25.34	0	2.84	0	0	11923	66	−61.19
37	49.68	24.91	0	5.82	0	0	10028
47	50.02	24.84	0	5	0	0	10506
48	50.02	24.84	0	10	0	0	10183
49	70.07	25	0	5	0	0	11880		−55.32
50	70.07	25	0	10	0	0	11536		−48.21
55	50.02	24.84	0	2.5	0	0	10717		−46.15
56	70.07	25	0	2.5	0	0	12139		−57.93
64	69.4	45.02	0	5	0	0	11192		−54.1
65	69.4	45.02	0	10	0	0	10929		−46.83
66	89.23	82.2	0	5	0	0	12259		−62.16
67	89.23	82.2	0	10	0	0	11647		−55.87
71	69.4	45.02	0	2.5	0	0	11296		−58.02
72	89.23	82.2	0	2.5	0	0	12693		−65.23
73	74.2	48	0	10	0	0	10657	65.5	−50.34
75	74.2	0	48	10	0	0	10222	66.3	−51.46
76	74.2	48	0	20	0	0	10354	67.8	−32.96
79	74.75	25.35	0	10	0	0	11663	66	−52.13
82	74.75	25.35	0	20	0	0	10682	67.5	−36.93
85	70.06	25	0	10	0	0	11569	65.8	−48.71
87	70.06	0	25	10	0	0	10201	67	−51.36
88	70.06	25	0	20	0	0	10957	65.5	−32.12
91	89.25	82.3	0	10	0	0	11870	61.2
94	89.25	82.3	0	20	0	0	10160	61.9
97	69.35	45	0	10	0	0	10912	66.9	−47.17
99	69.35	0	45	10	0	0	10295	67.8	−49.31
100	69.35	45	0	20	0	0	10205	68.1	−29.03
105	50	12.5	0	5	0	0	10976	68.7
107	50	25	0	5	0	0	10491	69.2
119	66.67	25	0	5	0	0	11681	65.5
121	66.67	50	0	5	0	0	10689	66.5
140	25	25	0	0	0.067	8.333	10184	72.9	−2.6
141	25	25	0	0	0.033	8.333	10142	73	−1.86
157	70.06	25	.3GeO2	0	.067MnO2	0	10612	64.3
158	70.06	25	.3GeO2	0	0.067	0	10852	63.8
161	70.06	25	0	50Nd2O3	0.067	0	11286	64
162	70.06	25	0	50Nd2O3	.067MnO2	0	11455	65.3
163	70.06	25	.3GeO2	50Nd2O3	0.067	0	11563	64.3
164	70.06	25	.3GeO2	50Nd2O3	.067MnO2	0	10678	67

In Table 4, some of the listed samples do not have measured dielectric constant (∈′) values. However, and as described herein in reference to Formula 1, tungsten bronze based materials, including the samples of Table 4, will tend to have dielectric constant values that are greater than 50.

Also in Table 4, some of the measured values of temperature coefficient of resonant frequency (τ_f) are not listed. Among the samples whose τ_f values are listed, all of them are negative, mainly due to the Sm being the primary lanthanide. As described herein, such negative values of τ_f can be compensated by introduction of other lanthanides (e.g., Nd, Pr, Ce and La) having positive τ_f values.

For example, in Table 4, samples 56, 49, 50 and 88 all have the same 70% aluminum percent value and 25% barium percent value, but have increasing lanthanum content (La %) of 2.5%, 5%, 10% and 20%, respectively. For the same samples in the same order, one can see that the τ_f values (−57.93, −55.32, −48.21 and −32.12) become less negative as La % value increases.

In some embodiments, materials having one or more features as described herein can be implemented as microwave dielectric materials. As described herein, such microwave dielectric materials can be configured to have dielectric constant values greater than 60. When combined with improved Q performance and temperature compensation capability, such microwave dielectric materials can be desirable for RF applications such as LTE applications in which filters can benefit from reduced sizes.

As described herein, substituting aluminum (Al) for at least some of the titanium (Ti) in the octahedral sites of a tungsten bronze material can yield some or all the foregoing desirable properties. Such substitutions can be effectuated in cost-effective manner.

As also described herein, lanthanides such as Sm and/or Nd can be utilized to achieve temperature compensated ceramic bodies. Table 5 lists additional examples of compositions that show, among others, how temperature coefficient of resonant frequency (τ_f) can be adjusted by different combinations of Sm and Nd, and/or different substitutions of Ti with Al.

TABLE 5
Sample	Density (g/cm3)	Dielectric Constant	τF	Qf (at 3 GHz)

Ba4Sm9.6Ti17.2Al.8O54	5.62	66.33	−50.38	11641
Ba4Nd9.46667Ti17.6Al.4O54	5.69	79.5	48.17	16073
Ba4Nd9.6Ti17.2Al.8O54	5.67	75.12	32.07	15298
Ba4Nd9.7333Ti16.8Al1.2O54	5.70	70.07	13.76	14635
Ba4Nd9.8666Ti16.4Al1.6O54	5.35	60.22	8.5	16028
Ba4Nd9.0667Y.4Ti17.6Al.4O54	5.63	78.42	26.36	13936
Ba4Nd8.8Y.8Ti17.2Al.8O54	5.57	72.3	5.85	14673
Ba4Sm7.5733Nd1.8933Ti17.6Al.4O54	5.77	80.27	20.23	15653
Ba4Sm5.76Nd3.84Y.8Ti17.2Al.8O54	5.81	74.65	−7.26	16534

At least some of the compositions listed in Table 5 are more specific examples of the samarium (Sm) based compositions described herein in reference to Formula 9 (Ba_4+x′Sm_{(2/3)[14+0.5y−x′]}Ti_18−yAl_yO₅₄). In the example context of some of Sm being replaced with neodymium (Nd), such a formula can be expressed as

Ba₄(Nd_1-xSm_X)_28/3+y/3Ti_18−yAl_yO₅₄.  (10)

In Formula 10, x can be referred to as Sm content, and y can be referred to as Al content.

As described in reference to Table 5, temperature coefficient of resonant frequency (τ_f) can be tuned by different combinations of Sm and Nd, and/or different substitutions of Ti with Al. Table 6 lists various examples of combinations of the Sm content (x) and the A1 content (y) in reference to Formula 10.

TABLE 6
Sample	Qf (at 1 GHz)	Qf (at 3 GHz)	ε′

x = 0.2, y = 1.6	9796	15907	65.61
x = 0.4, y = 1.2	10210	14448	70.02
x = 0.6, y = 0.8	9436	13107	73.07
x = 0.8, y = 0.4	7688	12021	76.46
x = 0.6, y = 0.4	8824	13247	77.81
x = 0.4, y = 0.8	10302	15395	73.96
x = 0.2, y = 1.2	10151	15638	71.22
x = 0.4, y = 0.4	9068	15593	70.38
x = 0.2, y = 0.8	9154	14851	75.38
x = 0.355, y = 0.68	10500	15321	75.2

For the samples listed in Table 6, their values of τ_f are generally in a range of −50 to 0 or 0 to 50. Accordingly, such samples can be utilized to estimate a plane in which τ_f is zero or close to zero, if such tuning is desired. For the example described in reference to Formula 10 and Table 6, such a τ_f=0 plane can be along an approximate line between points (y≈0, x≈0.77) and (y≈1.8, x≈2) when y (Al content) is on the horizontal axis and x (Sm content) is on the vertical axis. In such a system, one can see that the example configuration of (x=0.355, y=0.68) (last example in Table 6) yields relatively high values of dielectric constant (75.2) and Qf (10500 at 1 GHz), while having τ_f that is tuned to a value close to zero. It will be understood that other systems having one or more features as described herein can also be tuned in a similar manner.

In some embodiments, Q value of a system can be adjusted (e.g., enhanced) by adjusting the Sm content (in the example context of the system of Formula 10), adding elements/compounds, and/or substituting elements/compounds. In the context of the example system of Formula 10, a more specific example can be represented by Ba₄Nd_6.16Sm_3.4Ti_17.32Al_0.68O₅₄. Examples of adjustments to such a system, and the resulting values of Qf, are listed in Table 7. If a Qf value greater than 10000 is desired, one can see that, for example, substituting Ge_0.1 for Ti_0.1 yields a relatively high Qf value of approximately 12300 (at 1 GHz).

TABLE 7
Ba4Nd6.16Sm3.4Ti17.32Al0.68O54

	x = 0.6	Qf = 8467 (1 GHz)
	x = 0.75	Qf = 8993 (1 GHz)
	1% Na2O added	Qf = 9943 (1 GHz)
	1% K2O added	Qf = 7597 (1 GHz)
	+2% Ba2Ti9O20	Qf = 9982 (1 GHz)
	Sn.05 for Ti.05	Qf = 10040 (1 GHz)
	(Ba3.6Sr0.4)	Qf = 8958 (1 GHz)
	Mg.34Ti.34 for Al.68	Qf = 8101 (1 GHz)
	Zn.34Ti.34 for Al.68	Qf = 6396 (1 GHz)
	Ge.1 for Ti.1	Qf = 12300 (1 GHz)
	Fe.68 for Al.68	Qf = 4610
	Mn.68 for Al.68	Qf = 8045
	Mg.34Ge.34 for Al.68	Qf = 8509
	Zn.34Ge.34 for Al.68	Qf = 10044

FIGS. 1 and 2 show examples of microwave devices that can be formed from materials having one or more features as described herein. FIG. 1 shows that in some embodiments, a ceramic puck 100 can include a material as described herein so as to yield desirable properties such as a high dielectric constant (e.g., greater than 60) and a high Qf value (e.g., greater than 10,000) at relatively low frequencies (e.g., 700 MHz-1 GHz). Such a puck 100 can be implemented in a cylindrical shape having a diameter D_r and a height L_r. Such a puck 100 can be utilized as a microwave resonator.

FIG. 2 shows that in some embodiments, a ceramic puck 100 having one or more features as described herein can include a center aperture dimensioned to allow, for example, tuning of the ceramic puck when utilized as a microwave resonator. The aperture is shown to have a diameter of d_r. The overall diameter D_r and the height L_r may or may not be the same as the solid ceramic puck counterpart.

FIG. 3 shows a tunable microwave resonator configuration 110. A ceramic puck 100 similar to the example of FIG. 2 is shown to be supported by a support structure. A ceramic tuning element can be dimensioned to fit within the aperture of the ceramic puck 100; and tuning can be achieved by the extent of insertion of the tuning element into the aperture.

FIG. 4 shows an example of a cavity filter 120 having a plurality of cavities 122 arranged between RF ports 124, 126. Each cavity 122 can be dimensioned to receive a resonator puck (e.g., 100 in FIGS. 1 and 2). Such a resonator puck may or may not be tunable. The resonators in their respective cavities can pass successively filtered RF signal through slots formed between neighboring cavities.

FIG. 5 shows an example of an RF system that can utilize one or more of the filter device 120 of FIG. 4. For example, the filter device of FIG. 4 can be implemented as a dielectric narrowband filter 120 between an antenna and a diplexer. The diplexer can be configured to provide a filtered signal to a low-noise amplifier (LNA) to be further processed by an Rx portion of a baseband subsystem. The diplexer can also be configured to route an amplified RF signal from a power amplifier (PA) to the antenna for transmission.

FIGS. June 2010 show examples of how dielectric materials and/or devices having one or more features as described herein can be fabricated. FIG. 6 shows a process 20 that can be implemented to fabricate a ceramic material having one or more of the foregoing properties. In block 21, powder having one or more features as described herein can be prepared. In block 22, a shaped object can be formed from the prepared powder. In block 23, the formed object can be sintered. In block 24, the sintered object can be finished to yield a finished ceramic object having one or more desirable properties.

In implementations where the finished ceramic object is part of a device, the device can be assembled in block 25. In implementations where the device or the finished ceramic object is part of a product, the product can be assembled in block 26.

FIG. 6 further shows that some or all of the steps of the example process 20 can be based on a design, specification, etc. Similarly, some or all of the steps can include or be subjected to testing, quality control, etc.

In some implementations, powder prepared in the powder preparation step (block 21) of FIG. 6 can be formed into different shapes by different forming techniques. By way of an example, FIG. 7 shows a process 50 that can be implemented to press-form a shaped object from a powder material prepared as described herein. In block 52, a shaped die can be filled with a desired amount of the powder. In FIG. 8, configuration 60 shows the shaped die as 61 that defines a volume 62 dimensioned to receive the powder 63 and allow such power to be pressed. In block 53, the powder in the die can be compressed to form a shaped object. Configuration 64 shows the powder in an intermediate compacted form 67 as a piston 65 is pressed (arrow 66) into the volume 62 defined by the die 61. In block 54, pressure can be removed from the die. In block 55, the piston (65) can be removed from the die (61) so as to open the volume (62). Configuration 68 shows the opened volume (62) of the die (61) thereby allowing the formed object 69 to be removed from the die. In block 56, the formed object (69) can be removed from the die (61). In block 57, the formed object can be stored for further processing.

In some implementations, formed objects fabricated as described herein can be sintered to yield desirable physical properties as ceramic devices. FIG. 9 shows a process 70 that can be implemented to sinter such formed objects. In block 71, formed objects can be provided. In block 72, the formed objects can be introduced into a kiln. In FIG. 10, a plurality of formed objects 69 are shown to be loaded into a sintering tray 80. The example tray 80 is shown to define a recess 81 dimensioned to hold the formed objects 69 on a surface 82 so that the upper edge of the tray is higher than the upper portions of the formed objects 69. Such a configuration allows the loaded trays to be stacked during the sintering process. The example tray 80 is further shown to define cutouts 83 at the side walls to allow improved circulation of hot gas at within the recess 81, even when the trays are stacked together. FIG. 10 further shows a stack 84 of a plurality of loaded trays 80. A top cover 85 can be provided so that the objects loaded in the top tray generally experience similar sintering condition as those in lower trays.

In block 73, heat can be applied to the formed objects so as to yield sintered objects. Such application of heat can be achieved by use of a kiln. In block 74, the sintered objects can be removed from the kiln. In FIG. 10, the stack 84 having a plurality of loaded trays is depicted as being introduced into a kiln 87 (stage 86a). Such a stack can be moved through the kiln (stages 86b, 86c) based on a desired time and temperature profile. In stage 86d, the stack 84 is depicted as being removed from the kiln so as to be cooled.

In block 75, the sintered objects can be cooled. Such cooling can be based on a desired time and temperature profile. In block 76, the cooled objects can undergo one or more finishing operations. In block 77, one or more tests can be performed.

Heat treatment of various forms of powder and various forms of shaped objects are described herein as calcining, firing, annealing, and/or sintering. It will be understood that such terms may be used interchangeably in some appropriate situations, in context-specific manners, or some combination thereof.

Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise,” “comprising,” and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to.” The word “coupled”, as generally used herein, refers to two or more elements that may be either directly connected, or connected by way of one or more intermediate elements. Additionally, the words “herein,” “above,” “below,” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the above Detailed Description using the singular or plural number may also include the plural or singular number respectively. The word “or” in reference to a list of two or more items, that word covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list.

The above detailed description of embodiments of the invention is not intended to be exhaustive or to limit the invention to the precise form disclosed above. While specific embodiments of, and examples for, the invention are described above for illustrative purposes, various equivalent modifications are possible within the scope of the invention, as those skilled in the relevant art will recognize. For example, while processes or blocks are presented in a given order, alternative embodiments may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, or may be performed at different times.

The teachings of the invention provided herein can be applied to other systems, not necessarily the system described above. The elements and acts of the various embodiments described above can be combined to provide further embodiments.

While some embodiments of the inventions have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the disclosure. Indeed, the novel methods and systems described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the spirit of the disclosure. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the disclosure.