Patent Application
20180131068
The present disclosure generally relates to high dielectric constant materials for microwave applications.
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.
In some implementations, the present disclosure relates to a composition including a material with a formula Ba4+xSm(2/3)(14−x+0.5y)Ti18−yAlyO54, 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 Ba4+xSm(2/3)(14−x+0.5y)Ti18−yAlyO54, 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 Ba4+xSm(2/3)(14−x+0.5y)Ti18−yAlyO54, 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]10Ti18−yAlyO54. 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 (τf) 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.
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
Ba6−3xLn8+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 (τf) values. The other lanthanides Nd, Pr, Ce and La series all yield positive τf values. In the context of dielectric resonators, temperature coefficient of resonant frequency (τf) 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 (Ba6−3xLn8+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 τf 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]10Ti18−yAlyO54, (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
Ba6−3xLn8+2x+(y/3)Ti18−yAlyO54, (4A)
Ba6−3x+(y/2)Ln8+2xTi18−yAlyO54, and (4B)
Ba6−3x−yLn8+2x+yTi18−yAlyO54, (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 Ba4Ln9.667Ti17AlO54, 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 (Bamax) is equal to 2−(aluminum percent)/50. The barium percent (in the A1 site) can then be expressed as (NBa−4)/Bamax, where NBa is the total number of formula units of Ba. Equivalently, barium percent can be expressed as
barium percent=(NBa−4)/(2−(aluminum percent)/50), (6)
where NBa 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 Ba4Ln9.667Ti17AlO54 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 Ba4Ln9.667Ti17AlO54. 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
Ba4+x′Ln8+2x+y−(2/3)x′Ti18−yAlyO54, (7)
where x′ represents the additional formula units of barium. Equivalently, x′ can be expressed as x′=NBa−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
Ba4+x′Ln(2/3)[14+0.5y−x]Ti18−yAlyO54, (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
Ba4+x′Sm(2/3)[14+0.5y−x′]Ti18−yAlyO54. (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 (Ba6-3xLn8+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 τf values can be introduced to compensate for the negative τf 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 (Ba4+x′Sm(2/3)[14+0.5y−x′]Ti18−yAlyO54), 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 (τf) 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.
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.
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 (τf) are not listed. Among the samples whose τf values are listed, all of them are negative, mainly due to the Sm being the primary lanthanide. As described herein, such negative values of τf can be compensated by introduction of other lanthanides (e.g., Nd, Pr, Ce and La) having positive τf 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 τf 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 (τf) can be adjusted by different combinations of Sm and Nd, and/or different substitutions of Ti with Al.
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 (Ba4+x′Sm(2/3)[14+0.5y−x′]Ti18−yAlyO54). In the example context of some of Sm being replaced with neodymium (Nd), such a formula can be expressed as
Ba4(Nd1-xSmX)28/3+y/3Ti18−yAlyO54. (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 (τf) 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.
For the samples listed in Table 6, their values of τf 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 τf 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 τf=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 τf 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 Ba4Nd6.16Sm3.4Ti17.32Al0.68O54. 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 Ge0.1 for Ti0.1 yields a relatively high Qf value of approximately 12300 (at 1 GHz).
FIGS. June 2010 show examples of how dielectric materials and/or devices having one or more features as described herein can be fabricated.
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.
In some implementations, powder prepared in the powder preparation step (block 21) of
In some implementations, formed objects fabricated as described herein can be sintered to yield desirable physical properties as ceramic devices.
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
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.
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.
| Number | Date | Country | |
|---|---|---|---|
| 61912463 | Dec 2013 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 14561182 | Dec 2014 | US |
| Child | 15695342 | US |
