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WO2018193403A1 - Procédé de modélisation d'une conception de condensateur d'ordre fractionnel - Google Patents

Procédé de modélisation d'une conception de condensateur d'ordre fractionnel Download PDF

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Publication number
WO2018193403A1
WO2018193403A1 PCT/IB2018/052734 IB2018052734W WO2018193403A1 WO 2018193403 A1 WO2018193403 A1 WO 2018193403A1 IB 2018052734 W IB2018052734 W IB 2018052734W WO 2018193403 A1 WO2018193403 A1 WO 2018193403A1
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Prior art keywords
fractional order
frequencies
order capacitor
permittivity
determining
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English (en)
Inventor
Khaled Nabil Salama
Agamyrat AGAMBAYEV
Mohamed Farhat
Hakan BAGCI
Karam H. RAJAB
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SABIC Global Technologies BV
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SABIC Global Technologies BV
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Definitions

  • C is a constant that represents a capacitance
  • a is a number in the range 0 ⁇ a ⁇ 1.
  • Conventional capacitors have an a-value that is approximately 1 .
  • Such conventional capacitors may be referred to as "integer order" capacitors. It is understood, notwithstanding, that such conventional capacitors commonly exhibit an a -value of less than 1 , but even low- quality conventional capacitors commonly exhibit an a-value > 0.95. As such, conventional capacitors are often modeled as ideal integer order devices.
  • the a -value of a capacitor may be sensitive to an operating frequency. Said in other words, FOCs may exhibit an a-value of approximately integer order, except in a predefined frequency band.
  • FOCs have applications in a variety of different fields that may be said to provide solutions to fractional order calculus problems. Some of these applications include solving nonlinear problems in such real-world domains as pattern recognition, automated control, signal processing, and modeling various processes. As one specific example, FOCs have application in proportional-integral-differential (PID) controllers. While fractional order calculus and FOCs have been studied theoretically, in practice it has been difficult to realize practical FOCs. Previous FOC realization approaches have involved liquid-electrode based (LEB) type FOCs, fractal-type (FT) FOCs, and ladder network approximation FOCs composed of conventional resistors and capacitors (e.g., integer order capacitors).
  • LEB liquid-electrode based
  • FT fractal-type
  • ladder network approximation FOCs composed of conventional resistors and capacitors (e.g., integer order capacitors).
  • a method of producing a fractional order capacitor comprises designing a fractional order capacitor based on a performance criteria by a design application executing on a computer, where the designing produces a design specification comprising an identity of a dielectric matrix material, identities of a plurality of filler materials, and a fill fraction of each of the filler materials and determining an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies by a modeling application executing on the computer based on the design specification, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials.
  • the method further comprises determining a phase angle of the fractional order capacitor at each of the plurality of frequencies by the modeling application based on the effective permittivity of the composite dielectric determined at each of the plurality of frequencies, determining a frequency bandwidth of the fractional order capacitor by the modeling application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies, and determining a phase angle of the fractional order capacitor in the frequency bandwidth by the modeling application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies within the frequency bandwidth.
  • the method further comprises determining that the frequency bandwidth of the fractional order capacitor and the phase angle of the fractional order capacitor in the frequency bandwidth satisfy the performance criteria and producing a fractional order capacitor in accordance with the design specification.
  • a method of modeling a fractional order capacitor comprises providing a design specification of a fractional order capacitor, where the design specification comprises an identity of a dielectric matrix material, identities of a plurality of filler materials, a dopant number of each of the filler materials, and a fill fraction of each of the filler materials, determining a conductivity of each of the filler materials by an application executing on a computer based on the dopant number of the filler materials, and determining a permittivity of each of the filler materials at each of a plurality of frequencies by the application based on the conductivity of the filler material.
  • the design specification comprises an identity of a dielectric matrix material, identities of a plurality of filler materials, a dopant number of each of the filler materials, and a fill fraction of each of the filler materials, determining a conductivity of each of the filler materials by an application executing on a computer based on the dopant number of the filler materials, and determining a permittivity of each of
  • the method further comprises determining an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies by the application based on the design specification and based on the permittivity of the filler materials at each of the plurality of frequencies, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials, determining a phase angle of the fractional order capacitor at each of the plurality of frequencies by the application based on the effective permittivity of the composite dielectric determined at each of the plurality of frequencies, determining a frequency bandwidth of the fractional order capacitor by the application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies, and determining a phase angle of the fractional order capacitor in the frequency bandwidth by the application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies within the frequency bandwidth.
  • a method of modeling a fractional order capacitor comprises providing a design specification of a fractional order capacitor having a composite dielectric layer comprised of a first layer of a first dielectric material and a second layer of a second dielectric material, where the design specification comprises an identity of the first dielectric material, an identity of the second dielectric material, a thickness of the first layer, and a thickness of the second layer, determining an effective permittivity of the composite dielectric layer of the fractional order capacitor at each of a plurality of frequencies by an application executing on a computer based on the design specification, and determining a phase angle of the fractional order capacitor at each of the plurality of frequencies by the application based on the effective permittivity of the composite dielectric layer determined at each of the plurality of frequencies.
  • the method further comprises determining a frequency bandwidth of the fractional order capacitor by the application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies and determining a phase angle of the fractional order capacitor in the frequency bandwidth by the application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies within the frequency bandwidth.
  • FIG. 1 is an illustration of a fractional order capacitor having a composite dielectric according to an embodiment of the disclosure.
  • FIG. 2 is an illustration of a fractional order capacitor having a layered dielectric according to another embodiment of the disclosure.
  • FIG. 3 is an illustration of a fractional order capacitor having a layered dielectric according to yet another embodiment of the disclosure.
  • FIG. 4 is a flow chart of a method according to an embodiment of the disclosure.
  • FIG. 5 is a flow chart of another method according to an embodiment of the disclosure.
  • FIG. 6 is a flow chart of yet another method according to an embodiment of the disclosure.
  • FIG. 7 is a block diagram of a computer system according to an embodiment of the disclosure.
  • the present disclosure teaches a system and methods for modeling a fractional order capacitor (FOC) based on a design specification of the FOC.
  • the design specification may comprise information about a composite dielectric of the FOC.
  • the design specification may comprise a list of materials used to make the dielectric and the volume fraction of the composite dielectric associated with each different material (a volume fraction may be the fraction of the volume of the composite dielectric that the volume of a single material represents).
  • the design specification may identify a dielectric matrix material and a plurality of different filler materials.
  • the design specification may identify a dopant concentration or dopant number associated with at least some of the filler materials (e.g., those filler materials that have been doped).
  • the design specification may identify an aspect ratio describing the geometric shape of one or more of the filler materials (which may be provided as small particles that are suspended in the dielectric matrix material to form the composite dielectric).
  • a modeling application executing on a computer may model the FOC at a plurality of different frequencies and determine the performance characteristics or operational parameters of the FOC based on modeling the FOC design specification.
  • a workstation communicatively coupled to the computer may input the design specification to the application.
  • the application may read the design specification out of a file such as a data file or configuration file.
  • a design application executing on the computer may design the FOC in response to input FOC operational parameters, and the modeling application may model one or more of the FOC designs produced by the design application.
  • the modeling application may be considered to be encapsulated within the design application.
  • the modeling application may be invoked via an application programming interface (API) by the design application, for example to determine a fitness metric of a given FOC design based on operational parameters of the given FOC design determined by the modeling application.
  • API application programming interface
  • the design application invokes the API of the modeling application, providing the given FOC design as an input or argument to the API; and the modeling application returns operational parameters of the given FOC design based on modeling of the given FOC design to the design application.
  • the modeling application models a given FOC design, in part, by determining an effective permittivity of the FOC at each of a plurality of frequencies across a broad frequency range, for example from 10 Hz to 100 GHz, from 1 KHz to 10 GHz, or some other frequency range.
  • the frequencies may be chosen from this range in a linear fashion (e.g., 1000 frequencies each separated by about 10 MHz) or in a logarithmic fashion (e.g., 1000 frequencies where each successive frequency is about 1.0209 times the previous frequency).
  • the operational frequency bandwidth of the FOC may not be known, so a very broad range of frequencies may be analyzed.
  • a workstation may input a frequency range for use in analyzing the performance of the FOC.
  • the effective permittivity of the composite dielectric can be modeled and/or determined based on the frequency-dependent permittivity of the dielectric matrix material, based on the frequency-dependent permittivities of the filler materials, and based on the volume fractions of the materials in the composite dielectric.
  • a phase angle of the FOC may be modeled for the FOC at each of the frequencies based on the effective permittivity at each of the frequencies. By modeling the phase angles for the FOC across the complete range of frequencies (e.g., 10 Hz to 10 GHz) it can be determined where the phase angle is at a minimum value - the desired "sweet spot" for the operational frequency of the FOC.
  • the operational frequency of the FOC may be defined as the frequency band at which the associated phase angle of the FOC is within some predefined value of the minimum phase angle.
  • the operational frequency of the FOC may be defined as the frequency band at which the phase angle of the FOC is within 3 degrees of the minimum phase angle or within some other predefined value of the minimum phase angle.
  • the nominal phase angle of the FOC may then be defined as the midpoint between the minimum phase angle of the FOC and the maximum phase angle. So for example, if the minimum phase angle is 69.8 degrees, the maximum phase angle may be 72.8 degrees and the nominal phase angle may be deemed 71 .3 degrees. It is understood that other definitions of the allowable variation of the phase angle within the operational frequency band are contemplated by the present disclosure.
  • a ripple amplitude for the FOC can be calculated by identifying maximum and minimum phase angles at different frequencies across the frequency operating range (i.e., identify local maxima and local minima of phase angle).
  • a composite dielectric of an FOC may comprise two or more layers of different dielectric materials.
  • the design specification may identify the dielectric materials and the thickness of each of the layers.
  • the design specification may identify a spatial orientation among the layers of the composite dielectric.
  • the effective permittivity of the composite dielectric may be modeled and/or determined at each of the different frequencies based on the permittivities of each dielectric layer at the frequencies and based on the thickness of the layers, as described further hereinafter.
  • the FOC design may use dielectric matrix material that may be selected from high-k dielectric materials (e.g.
  • a material with a high dielectric constant such as hafnium dioxide (Hf02), hafnium silicate (HfSi0 4 ), zirconium dioxide (Zr02), or zirconium silicate (ZrSi0 4 ).
  • the FOC design may use dielectric matrix material that comprises polyvinylidene fluoride (PVDF) or PVDF based material.
  • the filler materials may be selected from transition metal dichalcogenide semiconductor materials such as molybdenum disulfide (M0S 2 ), molybdenum ditelluride (MoTe 2 ), tungsten disulfide (WS2), and/or tungsten diselenide (WSe 2 ).
  • transition metal dichalcogenide semiconductor materials such as molybdenum disulfide (M0S 2 ), molybdenum ditelluride (MoTe 2 ), tungsten disulfide (WS2), and/or tungsten diselenide (WSe 2 ).
  • M0S 2 molybdenum disulfide
  • MoTe 2 molybdenum ditelluride
  • WS2 tungsten disulfide
  • WSe 2 tungsten diselenide
  • single walled carbon nanotubes which exhibit semiconductor-like behavior, may also be used as filler materials.
  • Each filler material for example M0S 2
  • M0S 2 incorporated in the composite dielectric may comprise a plurality of different filler materials differentiated by different doping levels.
  • an FOC design can be determined for an input desired phase angle and an input desired frequency band.
  • Adding more filler materials, for example different versions of the same base filler material each having different dopant levels, is a technique that can broaden the frequency bandwidth in which the phase angle of the FOC satisfies the input desired phase angle.
  • Adapting or tuning the conductivity of filler material versions by adapting dopant levels can adjust a ripple or variation of the phase angle in the specified frequency bandwidth. Adjusting the volume fraction or fill fraction of filler materials can adjust the amplitude of the phase angle.
  • the designed FOC can be tuned or designed to both achieve a predefined or target phase angle and achieve a predefined frequency bandwidth.
  • an aspect ratio of filler materials may be selected to further adapt the characteristic behavior of the composite dielectric. For example, the shape of filler materials can be varied between oblate to spherical to prolate.
  • the modeling of the fractional order capacitor taught herein can be used to predict the behavior of a proposed FOC design before physical realization and testing in the laboratory. This approach can reduce waste of valuable dielectric materials and time in fabrication and testing. It can permit the FOC designer to anticipate the expected performance of a prospective FOC design and determine whether to invest further time in fabricating and testing that design.
  • modeling conventional capacitors is quite different from the methods of modeling fractional order capacitors as summarized above and described in further detail hereinafter.
  • the modeling of conventional capacitors typically assume the capacitor behavior is frequency independent.
  • the conventional capacitor model assumes the permittivity of the dielectric is constant and frequency independent.
  • the only figure of merit associated with the capacitor is a capacitance value alone which may be determined by rules of thumb without any actual modeling of the components of the subject conventional capacitor.
  • This simplified model is not feasible for modeling fractional order capacitors, however, which do exhibit frequency-dependent behavior.
  • the fractional order capacitor modeling taught herein is further complicated by modeling different permittivities of materials at different dopant levels.
  • the model of the conventional capacitor may be analogized to a one dimensional model (e.g., the capacitance number), while the modelling of the fractional order capacitors taught herein may be analogized to a three dimensional model: a first dimension associated with frequency, a second dimension associated with a given material, and a third dimension associated with different dopant levels associated with the same given material.
  • This analogy it is understood, is suggestive and poetic rather than explicit, but it serves to contrast the complexity and computational intensity of the modeling of fractional order capacitors taught herein versus conventional integer order capacitors.
  • frequencies over a broad range may be selected to determine the operational frequency bandwidth of a given FOC design where the frequencies are selected at a constant logarithmic offset from each other (e.g., each subsequent frequency is selected as about 2.15 times the previous frequency [3 samples per decade], as about 1.47 times the previous frequency [6 samples per decade], as about 1 .26 times the previous frequency [10 samples per decade], or some other logarithmic offset).
  • the FOC 100 comprises a first plate 102 connected to a first terminal 104, a second plate 106 connected to a second terminal 108, and a composite dielectric 1 10. It is understood that the illustration of the FOC 100 is not intended to represent a relative scale or a particular realization form.
  • an FOC may be realized as two extended metal ribbons sandwiching an extended composite dielectric ribbon, which are then rolled up tightly to form a cylindrical shape.
  • the FOC may be built as a component of a semiconductor chip, for example deposited on a semiconductor die using semiconductor manufacturing processes, or as a component of a system on a chip (SOC).
  • the composite dielectric 1 10 comprises a dielectric matrix 1 12 and a plurality of filler particles 1 14.
  • the shapes and orientations of the filler particles 1 14 are depicted in FIG. 1 to suggest that they may be disposed with random orientations within the dielectric matrix 1 12.
  • the filler particles 1 14 are illustrated as elongated (either oblate or prolate, depending on the reference axis of the particles) in FIG. 1
  • the filler particles 1 14 may have a different aspect ratio (e.g., spherical).
  • the composite dielectric 1 10 may comprise a mix of filler particles 1 14 of different aspect ratios.
  • the filler particles 1 14 may be very small, for example less than 100 ⁇ in length, less than 10 ⁇ in length, less than 1 ⁇ in length, less than 100 nm in length, or some other size.
  • Part of the design of a capacitor may involve designing a separation between the plates 102, 106 and a surface area of the plates 102, 106. While the separation and area of the plates 102, 106 may be designed to realize the FOC 100, this may be deemed a conventional design parameter. While it is understood that the design specification or instructions for building or manufacturing an FOC may include such plate separation and area details, they may not have a direct effect on the fractional order behavior of the capacitor which is more affected by the properties of the composite dielectric 1 10 than by geometry. [0033] The phase angle of an FOC at a given frequency is a function of an effective permittivity of the composite dielectric 1 10:
  • ⁇ is the phase angle and 8 e ⁇ is the effective permittivity of the composite dielectric 1 10 at the given frequency.
  • the effective permittivity can be thought of as the aggregate permittivity of the composite dielectric 1 10.
  • Permittivity is a fundamental physical property of matter generally, and of dielectrics in specific, that is a measure of how an electric field affects and is affected by the material.
  • the effective permittivity of the composite dielectric 1 10 can be modeled, estimated, and/or determined using an effective medium approximation model, for example using the Bruggeman's model, the Maxwell Garnett mixing rule, or using another approximation model or equation.
  • an application e.g., a modeling application
  • a computer performs methods of modeling and/or determining the phase angle of the FOC 100 at each of the analyzed frequencies and determines summary performance characteristics such as an operational frequency bandwidth (a.k.a., constant phase zone (CPZ)), a constant phase angle (CPA) (a.k.a., nominal phase angle), and a phase angle ripple amplitude.
  • the effective permittivity of the composite dielectric 1 10 at a given frequency can be modeled by a function of a permittivity of the dielectric matrix material 1 12 at the given frequency, the permittivity of each of the different filler materials 1 14 at the given frequency, as well as the volume fractions (the fraction of the volume of the composite dielectric) occupied by each of the filler materials 1 14:
  • the effective permittivity of the composite dielectric 1 10 may also be a function of an aspect ratio (quantification of shape) of filler materials.
  • the permittivities may be independent of operational frequency, for example the permittivity of the dielectric matrix 1 12 may be independent of operational frequency for some materials, but in general at least some of the permittivities of the components of the composite dielectric 1 10 (e.g., some of the filler particles 1 14) may be different at different frequencies.
  • the permittivity of a dielectric matrix material 1 12 may be a known physical property and may be provided as a frequency-dependent function or as a frequency independent constant for use by the application executing on the computer, for example provided as a table or list of data or embedded among a list of defined constant values within the application code.
  • the permittivity of undoped filler materials may be known physical properties and provided as a frequency-dependent function or as a frequency independent constant for use by the application.
  • the permittivity of doped filler material may a function of the permittivity of the undoped filler material, of the conductivity of the doped filler material, and of the frequency:
  • sc the permittivity of the un-doped filler material ('sc' stands for semiconductor)
  • ⁇ the conductivity of the doped filler material
  • ⁇ 0 the permittivity of free space
  • q the charge of the charge carrier in the doped filler material
  • u the mobility of the charge carriers in the doped filler material
  • 71 is the number of dopant concentration.
  • different models or equations may be used to model and/or determine the permittivity of doped filler material.
  • a plurality of values of permittivity for a doped filler material at different dopant levels may be determined and provided in a look-up table or list of constants for the application, and doped filler materials that have intermediate dopant levels may be determined by interpolating between permittivity values of neighboring doped filler materials read from the look-up table or list of constants.
  • a multiphase Maxwell-Garnett mixing rule may be used to model the effective permittivity.
  • the multiphase Maxwell-Garnett mixing rule for purposes of this disclosure may be given:
  • Equations EQ 1 , EQ2, EQ3, EQ4, and EQ 5 may be used to develop algorithms in the application to model, estimate, and/or determine the phase angle of the FOC 100 at each of a plurality of different frequencies. It is understood that the equations may be simplified and/or mathematically transformed to make computer solution of the equations more tractable and/or efficient. In some circumstances, some of the terms of the equations may be simplified. For example, when the filler materials
  • depolarization factors N may all be equal and EQ 5 may be further simplified. For example, if the effect of depolarization factors N may be considered of negligible importance, EQ 5 may be further simplified. Additionally, some other technique than the Maxwell-Garnett mixing rule may be used to find the effective permittivity at different frequencies.
  • the application may model, estimate, and/or determine the phase angle of the FOC 100 at each of a plurality of frequencies in a predefined range of frequencies which may be supposed to be a practical range of interest. It is understood this range can be defined differently in different embodiments.
  • the frequency range may extend from 10 Hz to 100 GHz.
  • the frequency range may extend from 1 KHz to 50 Ghz.
  • the frequency range may extend from 1 MHz to 5 GHz.
  • the frequency range may extend over some other range.
  • the frequency range may be relatively broad because it may not be known in advance at what frequency an FOC 100 of a given design specification may exhibit the desirable fractional order behavior.
  • the frequency range of interest may be input by a user of the application to model the subject candidate FOC design (e.g. , via a workstation communicatively coupled to the computer on which the application executes).
  • the application may select a predefined number of frequencies distributed linearly across the frequency range at which to determine the phase angle of the FOC 100.
  • the application may select a predefined number of frequencies distributed logarithmically across the frequency range at which to determine the phase angle of the FOC 100.
  • Each subsequent frequency may be selected as a fixed ratio to the previous frequency. For example, each subsequent frequency may be selected as about 2.15 times the previous frequency (e.g., 3 samples per frequency decade), as about 1 .47 times the previous frequency (e.g. , 6 samples per decade), as about 1 .26 times the previous frequency (e.g., 10 samples per decade), or using some other logarithmic offset.
  • the modeling application may remodel the subject FOC design, restricting its modeling to frequencies in the operating frequency bandwidth and using a more fine grained approach to selecting frequencies for modeling. This second modeling may be useful to confirm the initial modeling and also to determine a ripple amplitude of the FOC design with more precision.
  • phase angle ⁇ can be modeled and/or determined by:
  • a fractional order capacitor as described herein may have an a in the CPZ such that a is in a range defined by: 0 ⁇ a ⁇ 0.95 (i.e., 0 > ⁇ > -85.5°), 0 ⁇ a ⁇ 0.90 (i.e.,.
  • a ripple amplitude for a candidate FOC design can be calculated by identifying the maximum and the minimum phase angles at different frequencies across the operational frequency bandwidth.
  • the FOC design may be translated into a set of manufacturing instructions or a "recipe" for making the FOC 100.
  • the manufacturing instructions may restrict themselves to defining the composition of the composite dielectric 1 10, for example by identifying the dielectric matrix material 1 12, defining the filler material 1 14 or filler materials, and defining a volume fraction of the one or more filler materials 1 14.
  • the manufacturing instructions may define a dopant level of one or more of the filler materials 1 14.
  • the manufacturing instructions may further define a thickness of the composite dielectric 1 10 (e.g., define a separation of the plates 102, 106 from each other) and define an area of the plates 102, 106.
  • the definition of the area of the plates 102, 106 may be provided as a length and a width of the plates 102, 106. It may be understood that the composite dielectric 1 10 may have a length and a width substantially equal to that defined for the plates 102, 106, for example some small increment less wide and some small increment less long than the plates 102, 106 or possibly a small increment wider and longer than the plates 102, 106.
  • the FOC 100 may be built in accordance with the manufacturing instructions. It is understood that some aspects of the manufacturing of the FOC 100 may be determined separately. For example, the length, cross-sectional area, and material of the terminals 104, 108 may be independently determined or defined. A packaging of the FOC 100 may be determined separately.
  • the FOC capacitor 130 comprises the first plate 102, the first electrical terminal 104, the second plate 106, and the second terminal 108, and a composite dielectric 132.
  • the composite dielectric 132 comprises a first dielectric layer 134 of thickness Ti and a second dielectric layer 136 of thickness T 2 .
  • the first dielectric layer 134 comprises a first dielectric material having a first frequency-dependent permittivity.
  • the second dielectric layer 136 comprises a second different dielectric material having a second different frequency-dependent permittivity.
  • the effective permittivity of the composite dielectric 132, and hence the phase angle ⁇ of the FOC 130, is an intermediate value between the first frequency-dependent permittivity of the first dielectric layer 134 and the second frequency-dependent permittivity of the second dielectric layer 136.
  • the effective permittivity of the composite dielectric 132 may be modeled and/or determined at a given frequency a
  • the application that executes on the computer can model a candidate design of the FOC 130 based on a design specification and model, estimate, and/or project a performance of the FOC 130, for example estimate an operational frequency bandwidth based on the proximity of the phase angle to a minimum phase angle determined over the entire range of analyzed frequencies, estimate a nominal phase angle of the FOC 100 within the operational frequency bandwidth, and estimate a phase angle ripple amplitude in the operational frequency bandwidth.
  • Estimating the performance of the FOC 100 based on modeling the FOC design may be referred to as determining the performance envelope of the FOC based on the design.
  • the application may have a list of available dielectric materials for composing the dielectric layers 134, 136.
  • the application may be provided with a function or formula for determining the frequency-dependent permittivity of the different available dielectric materials.
  • the application may have a function for determining the effective permittivity of the composite dielectric 132 at a given frequency based on the permittivity of each dielectric layer 134, 136 at the given frequency, based on T-i , and based on T 2 .
  • the FOC capacitor 130 comprises the first plate 102, the first electrical terminal 104, the second plate 106, and the second terminal 108, and a composite dielectric 152.
  • the composite dielectric 152 comprises a third dielectric layer 154 of thickness T 3 , a fourth dielectric layer 156 of thickness T 4: and a fifth dielectric layer 158 of thickness T 5 .
  • the third dielectric layer 154 comprises a third dielectric material having a third frequency-dependent permittivity.
  • the fourth dielectric layer 156 comprises a fourth different dielectric material having a fourth different frequency- dependent permittivity.
  • the fifth dielectric layer 158 comprises a fifth different dielectric material having a fifth different frequency-dependent permittivity.
  • the width of the third dielectric layer 154 is an intermediate value between extremes of the third frequency-dependent permittivity of the third dielectric layer 154, the fourth frequency-dependent permittivity of the fourth dielectric layer 156, and the fifth frequency-dependent permittivity of the fifth dielectric layer 158.
  • a sensitivity of the design of the FOC 150 to manufacturing variances in building the layers 154, 156, 158 may be reduced.
  • the effective permittivity of the composite dielectric 152 may be determined by applying EQ 8 twice. For example, EQ 8 may be used to find the effective permittivity of the third dielectric layer 154 and the fourth dielectric layer 156.
  • this effective permittivity may be substituted for the first permittivity and the sum of the thicknesses T 3 and T 4 substituted for the first thickness in EQ 8 and the permittivity of the fifth dielectric layer 158 substituted for the second permittivity and the thickness T 5 substituted for the second thickness used in EQ 8.
  • Method 200 may be performed to design, model, and produce a fractional order capacitor (FOC).
  • a fractional order capacitor is designed by a design application executing on a computer based on a performance criteria, where the designing produces a design specification comprising an identity of a dielectric matrix material, identities of a plurality of filler materials, and a fill fraction of each of the filler materials.
  • the design application may execute on a computer system such as that described with reference to FIG. 7 below.
  • the design specification may comprise specifications of aspect ratios of the filler materials.
  • the performance criteria may be provided to the design application as input from a workstation or read from a configuration file.
  • the performance criteria may comprise a desired operational frequency bandwidth and nominal phase angle of the fractional order capacitor.
  • the performance criteria may further define a maximum phase angle ripple value.
  • a modeling application executing on the computer models and/or determines an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies based on the design specification, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials.
  • the modeling application may execute on a computer system such as that described with reference to FIG. 7 below.
  • the modeling application models and/or determines a phase angle of the fractional order capacitor at each of the plurality of frequencies based on the effective permittivity of the composite dielectric modeled and/or determined at each of the plurality of frequencies.
  • the application may execute a computer algorithm that effects the calculation set forth in EQ 5 above (the multiphase Maxwell-Garnett mixing rule). It is understood that the form of the computer algorithm may differ from EQ 5 to achieve computing efficiencies or to simplify the expression to make computer solution more rapid. Alternatively, a different algorithm than the multiphase Maxwell-Garnett mixing rule may be used.
  • the modeling application determines a frequency bandwidth of the fractional order capacitor based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies. For example, the modeling application may deem the operational frequency bandwidth of the FOC as the range of frequencies at which the phase angle remains less than a threshold amount more than the minimum phase angle.
  • the threshold may be coded into the modeling application, or the threshold may be input to the modeling application via a workstation.
  • the modeling application determines a phase angle of the fractional order capacitor in the frequency bandwidth based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies within the frequency bandwidth (e.g., within the frequency bandwidth of the fractional order capacitor determined in block 208).
  • the phase angle of the fractional order capacitor in the frequency bandwidth may be referred to as the nominal phase angle of the fractional order capacitor in the frequency bandwidth or simply the nominal phase angle of the fractional order capacitor.
  • the nominal phase angle of the fractional order capacitor may be the average value of the phase angle of the fractional order capacitor determined at each of the frequencies within the frequency bandwidth of the fractional order capacitor.
  • the method 200 may further comprise determining a ripple amplitude of the phase angle within the operational frequency bandwidth. It is understood that the processing of blocks 204, 206, 208, and 210 may be performed repeatedly by the modeling application, for example in response to iterative invocations of the modeling application to evaluate a plurality of different FOC designs.
  • the design application may perform the processing of block 212.
  • the modeling application may perform the processing of block 212.
  • the functionality of designing and modeling the fractional order capacitor may be integrated in a single application.
  • produce a fractional order capacitor in accordance with the design specification Producing the fractional order capacitor can comprise producing a plurality of fractional order capacitors such as thousands, tens of thousands, hundreds of thousands or some other number. Producing the fractional order capacitor can comprise manufacturing the fractional order capacitor.
  • the processing of block 214 may be conducted based on the design specification determined in block 202, evaluated in blocks 204 through block 210, and confirmed in compliance with the performance criteria in block 212.
  • the method 200 may further comprise a block of converting the design specification into a set of instructions or a "recipe" for building the fractional order capacitor of the determined design.
  • the method 230 may be performed to model a fractional order capacitor (FOC), for example to model the FOC to determine its performance envelope.
  • FOC fractional order capacitor
  • a design specification of a fractional order capacitor is provided, where the design specification comprises an identity of a dielectric matrix material, identities of a plurality of filler materials, a dopant number of each of the filler materials, and a volume fraction or fill fraction of each of the filler materials.
  • the design specification may comprise specifications of aspect ratios of the filler materials.
  • the design specification may be provided to an application executing on a computer system as input from a workstation or read from a configuration file.
  • an application e.g.
  • the modeling application executing on a computer models and/or determines a conductivity of each of the filler materials based on the dopant number of the filler materials.
  • the application may execute on a computer system such as that described with reference to FIG. 7 below.
  • the application models and/or determines a permittivity of each of the filler materials at each of a plurality of frequencies based on the conductivity of the filler material.
  • the application models and/or determines an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies based on the design specification and based on the permittivity of the filler materials at each of the plurality of frequencies, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials.
  • the application may execute a computer algorithm that effects the calculation set forth in EQ 5 above (the multiphase Maxwell-Garnett mixing rule). It is understood that the form of the computer algorithm may differ from EQ 5 to achieve computing efficiencies or to simplify the expression to make computer solution more rapid. Alternatively, a different algorithm than the multiphase Maxwell-Garnett mixing rule may be used.
  • the application models and/or determines a phase angle of the fractional order capacitor at each of the plurality of frequencies based on the effective permittivity of the composite dielectric determined at each of the plurality of frequencies.
  • the application determines a frequency bandwidth of the fractional order capacitor based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies. For example, the application may deem the operational frequency bandwidth of the FOC as the range of frequencies at which the phase angle remains less than a threshold amount more than the minimum phase angle.
  • the threshold may be coded into the application, or the threshold may be input to the application via a workstation.
  • the application determines a phase angle of the fractional order capacitor in the frequency bandwidth based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies within the frequency bandwidth.
  • the phase angle of the fractional order capacitor in the frequency bandwidth may be referred to as the nominal phase angle of the fractional order capacitor in the frequency bandwidth or simply the nominal phase angle of the fractional order capacitor.
  • the nominal phase angle of the fractional order capacitor may be the average value of the phase angle of the fractional order capacitor determined at each of the frequencies within the frequency bandwidth of the fractional order capacitor.
  • the method 230 may further comprise determining a ripple amplitude of the phase angle within the operational frequency bandwidth. [0055] Turning now to FIG. 6, a method 260 is described. The method 260 may be performed to model a fractional order capacitor (FOC), for example to model the FOC to determine its performance envelope.
  • FOC fractional order capacitor
  • a design specification of a fractional order capacitor having a composite dielectric layer comprised of a first layer of a first dielectric material and a second layer of a second dielectric material is provided, where the design specification comprises an identity of the first dielectric material, an identity of the second dielectric material, a thickness of the first layer, and a thickness of the second layer.
  • the design specification may be provided to an application executing on a computer system as input from a workstation or read from a configuration file.
  • an application e.g., the modeling application
  • the application may execute on a computer system such as that described with reference to FIG. 7 below.
  • the application models and/or determines a phase angle of the fractional order capacitor at each of the plurality of frequencies based on the effective permittivity of the composite dielectric layer determined at each of the plurality of frequencies.
  • the application determines a frequency bandwidth of the fractional order capacitor based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies. For example, the application may deem the operational frequency bandwidth of the FOC as the range of frequencies at which the phase angle remains less than a threshold amount more than the minimum phase angle.
  • the threshold may be coded into the application, or the threshold may be input to the application via a workstation.
  • the application determines a phase angle of the fractional order capacitor in the frequency bandwidth based on the phase angle of the fractional order capacitor modeled and/or determined at each of the plurality of frequencies within the frequency bandwidth.
  • the phase angle of the fractional order capacitor in the frequency bandwidth may be referred to as the nominal phase angle of the fractional order capacitor in the frequency bandwidth or simply the nominal phase angle of the fractional order capacitor.
  • the nominal phase angle of the fractional order capacitor may be the average value of the phase angle of the fractional order capacitor determined at each of the frequencies within the frequency bandwidth of the fractional order capacitor.
  • the method 260 may further comprise determining a ripple amplitude of the phase angle within the operational frequency bandwidth.
  • FIG. 7 illustrates a computer system 380 suitable for implementing one or more embodiments disclosed herein.
  • the computer system 380 includes a processor 382 (which may be referred to as a central processor unit or CPU) that is in communication with memory devices including secondary storage 384, read only memory (ROM) 386, random access memory (RAM) 388, input/output (I/O) devices 390, and network connectivity devices 392.
  • the processor 382 may be implemented as one or more CPU chips.
  • a design that is still subject to frequent change may be preferred to be implemented in software, because re-spinning a hardware implementation is more expensive than re-spinning a software design.
  • a design that is stable that will be produced in large volume may be preferred to be implemented in hardware, for example in an application specific integrated circuit (ASIC), because for large production runs the hardware implementation may be less expensive than the software implementation.
  • ASIC application specific integrated circuit
  • a design may be developed and tested in a software form and later transformed, by well-known design rules, to an equivalent hardware implementation in an application specific integrated circuit that hardwires the instructions of the software.
  • a machine controlled by a new ASIC is a particular machine or apparatus, likewise a computer that has been programmed and/or loaded with executable instructions may be viewed as a particular machine or apparatus.
  • the CPU 382 may execute a computer program or application.
  • the CPU 382 may execute software or firmware stored in the ROM 386 or stored in the RAM 388.
  • the CPU 382 may copy the application or portions of the application from the secondary storage 384 to the RAM 388 or to memory space within the CPU 382 itself, and the CPU 382 may then execute instructions that the application is comprised of.
  • the CPU 382 may copy the application or portions of the application from memory accessed via the network connectivity devices 392 or via the I/O devices 390 to the RAM 388 or to memory space within the CPU 382, and the CPU 382 may then execute instructions that the application is comprised of.
  • an application may load instructions into the CPU 382, for example load some of the instructions of the application into a cache of the CPU 382.
  • an application that is executed may be said to configure the CPU 382 to do something, e.g. , to configure the CPU 382 to perform the function or functions promoted by the subject application.
  • the CPU 382 becomes a specific purpose computer or a specific purpose machine.
  • the secondary storage 384 is typically comprised of one or more disk drives or tape drives and is used for non-volatile storage of data and as an over-flow data storage device if RAM 388 is not large enough to hold all working data. Secondary storage 384 may be used to store programs which are loaded into RAM 388 when such programs are selected for execution.
  • the ROM 386 is used to store instructions and perhaps data which are read during program execution. ROM 386 is a non-volatile memory device which typically has a small memory capacity relative to the larger memory capacity of secondary storage 384.
  • the RAM 388 is used to store volatile data and perhaps to store instructions. Access to both ROM 386 and RAM 388 is typically faster than to secondary storage 384.
  • the secondary storage 384, the RAM 388, and/or the ROM 386 may be referred to in some contexts as computer readable storage media and/or non-transitory computer readable media.
  • I/O devices 390 may include printers, video monitors, liquid crystal displays (LCDs), touch screen displays, keyboards, keypads, switches, dials, mice, track balls, voice recognizers, card readers, paper tape readers, or other well-known input devices.
  • LCDs liquid crystal displays
  • touch screen displays keyboards, keypads, switches, dials, mice, track balls, voice recognizers, card readers, paper tape readers, or other well-known input devices.
  • the network connectivity devices 392 may take the form of modems, modem banks, Ethernet cards, universal serial bus (USB) interface cards, serial interfaces, token ring cards, fiber distributed data interface (FDDI) cards, wireless local area network (WLAN) cards, radio transceiver cards that promote radio communications using protocols such as code division multiple access (CDMA), global system for mobile communications (GSM), long-term evolution (LTE), worldwide interoperability for microwave access (WiMAX), near field communications (NFC), radio frequency identity (RFID), and/or other air interface protocol radio transceiver cards, and other well-known network devices. These network connectivity devices 392 may enable the processor 382 to communicate with the Internet or one or more intranets.
  • CDMA code division multiple access
  • GSM global system for mobile communications
  • LTE long-term evolution
  • WiMAX worldwide interoperability for microwave access
  • NFC near field communications
  • RFID radio frequency identity
  • RFID radio frequency identity
  • the processor 382 might receive information from the network, or might output information to the network in the course of performing the above-described method steps. Such information, which is often represented as a sequence of instructions to be executed using processor 382, may be received from and outputted to the network, for example, in the form of a computer data signal embodied in a carrier wave.
  • Such information may be received from and outputted to the network, for example, in the form of a computer data baseband signal or signal embodied in a carrier wave.
  • the baseband signal or signal embedded in the carrier wave may be generated according to several methods well-known to one skilled in the art.
  • the baseband signal and/or signal embedded in the carrier wave may be referred to in some contexts as a transitory signal.
  • the processor 382 executes instructions, codes, computer programs, scripts which it accesses from hard disk, floppy disk, optical disk (these various disk based systems may all be considered secondary storage 384), flash drive, ROM 386, RAM 388, or the network connectivity devices 392. While only one processor 382 is shown, multiple processors may be present. Thus, while instructions may be discussed as executed by a processor, the instructions may be executed simultaneously, serially, or otherwise executed by one or multiple processors.
  • the computer system 380 may comprise two or more computers in communication with each other that collaborate to perform a task.
  • an application may be partitioned in such a way as to permit concurrent and/or parallel processing of the instructions of the application.
  • the data processed by the application may be partitioned in such a way as to permit concurrent and/or parallel processing of different portions of a data set by the two or more computers.
  • virtualization software may be employed by the computer system 380 to provide the functionality of a number of servers that is not directly bound to the number of computers in the computer system 380.
  • virtualization software may provide twenty virtual servers on four physical computers.
  • Cloud computing may comprise providing computing services via a network connection using dynamically scalable computing resources.
  • Cloud computing may be supported, at least in part, by virtualization software.
  • a cloud computing environment may be established by an enterprise and/or may be hired on an as-needed basis from a third party provider.
  • Some cloud computing environments may comprise cloud computing resources owned and operated by the enterprise as well as cloud computing resources hired and/or leased from a third party provider.
  • the computer program product may comprise one or more computer readable storage medium having computer usable program code embodied therein to implement the functionality disclosed above.
  • the computer program product may comprise data structures, executable instructions, and other computer usable program code.
  • the computer program product may be embodied in removable computer storage media and/or non-removable computer storage media.
  • the removable computer readable storage medium may comprise, without limitation, a paper tape, a magnetic tape, magnetic disk, an optical disk, a solid state memory chip, for example analog magnetic tape, compact disk read only memory (CD-ROM) disks, floppy disks, jump drives, digital cards, multimedia cards, and others.
  • the computer program product may be suitable for loading, by the computer system 380, at least portions of the contents of the computer program product to the secondary storage 384, to the ROM 386, to the RAM 388, and/or to other non-volatile memory and volatile memory of the computer system 380.
  • the processor 382 may process the executable instructions and/or data structures in part by directly accessing the computer program product, for example by reading from a CD-ROM disk inserted into a disk drive peripheral of the computer system 380.
  • the processor 382 may process the executable instructions and/or data structures by remotely accessing the computer program product, for example by downloading the executable instructions and/or data structures from a remote server through the network connectivity devices 392.
  • the computer program product may comprise instructions that promote the loading and/or copying of data, data structures, files, and/or executable instructions to the secondary storage 384, to the ROM 386, to the RAM 388, and/or to other non-volatile memory and volatile memory of the computer system 380.
  • the secondary storage 384, the ROM 386, and the RAM 388 may be referred to as a non-transitory computer readable medium or a computer readable storage media.
  • a dynamic RAM embodiment of the RAM 388 likewise, may be referred to as a non-transitory computer readable medium in that while the dynamic RAM receives electrical power and is operated in accordance with its design, for example during a period of time during which the computer system 380 is turned on and operational, the dynamic RAM stores information that is written to it.
  • the processor 382 may comprise an internal RAM, an internal ROM, a cache memory, and/or other internal non-transitory storage blocks, sections, or components that may be referred to in some contexts as non-transitory computer readable media or computer readable storage media.
  • a method of producing a fractional order capacitor comprises: designing a fractional order capacitor based on a performance criteria by a design application executing on a computer, where the designing produces a design specification comprising an identity of a dielectric matrix material, identities of a plurality of filler materials, and a fill fraction of each of the filler materials; determining an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies by a modeling application executing on the computer based on the design specification, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials; determining a phase angle of the fractional order capacitor at each of the plurality of frequencies by the modeling application based on the effective permittivity of the composite dielectric determined at each of the plurality of frequencies; determining a frequency bandwidth of the fractional order capacitor by the modeling application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies; determining a design specification comprising an identity of a dielectric matrix material
  • a second aspect can include the method of the first aspect, further comprising providing a list of filler materials and data on their permittivity and conductivity, where the list comprises molybdenum disulfide (M0S 2 ), molybdenum ditelluride (MoTe 2 ), tungsten disulfide (WS2), tungsten diselenide (WSe 2 ), and single walled carbon nanotubes, where determining the effective permittivity of the composite dielectric of the fractional order capacitor is further based on the data on the permittivity and conductivity of the filler materials.
  • M0S 2 molybdenum disulfide
  • MoTe 2 molybdenum ditelluride
  • WS2 tungsten disulfide
  • WSe 2 tungsten diselenide
  • single walled carbon nanotubes where determining the effective permittivity of the composite dielectric of the fractional order capacitor is further based on the data on the permittivity and conductivity of the filler materials.
  • a third aspect can include the method of the second aspect, wherein the data on the permittivity of the filler materials is an undoped permittivity of the filler materials and the data on the conductivity of the filler materials is data on an electric charge of a charge carrier in the doped filler material and a mobility of the charge carriers in the doped filler material.
  • a fourth aspect can include the method of the third aspect, wherein the design specification further comprises a dopant number expressing a concentration of dopants in at least some of the filler materials.
  • a fifth aspect can include the method of the fourth aspect, further comprising determining a conductivity of at least some of the filler materials as the product of the electric charge with the mobility of the charge carrier with the dopant number of the filler materials.
  • a sixth aspect can include the method of any of the first to fifth aspects, further comprising providing a list of dielectric matrix materials and data on their permittivity, where the list comprises hafnium dioxide (Hf02), hafnium silicate (HfSi0 4 ), zirconium dioxide (Zr02), zirconium silicate (ZrSi0 4 ), and polyvinylidene (PVDF) and data on their permittivity, wherein determining the effective permittivity of the composite dielectric at the plurality of frequencies is based at least in part on the data on the permittivity of the dielectric matrix identified in the design specification.
  • Hf02 hafnium silicate
  • Zr02 zirconium silicate
  • PVDF polyvinylidene
  • a seventh aspect can include the method of any of the first to sixth aspects, wherein the frequency bandwidth of the fractional order capacitor is identified as the range of the plurality of frequencies at which the determined phase angle is within a predefined threshold of the minimum phase angle determined over the plurality of frequencies.
  • An eighth aspect can include the method of any of the first to seventh aspects, wherein the phase angle of the fractional order capacitor in the frequency bandwidth is identified as the mean of the phase angles determined within the frequency bandwidth of the fractional order capacitor.
  • a ninth aspect can include the method of any of the first to eighth aspects, wherein the design specification further identifies an aspect ratio of particles of the filler materials.
  • a method of modeling a fractional order capacitor comprises: providing a design specification of a fractional order capacitor, where the design specification comprises an identity of a dielectric matrix material, identities of a plurality of filler materials, a dopant number of each of the filler materials, and a fill fraction of each of the filler materials; determining a conductivity of each of the filler materials by an application executing on a computer based on the dopant number of the filler materials; determining a permittivity of each of the filler materials at each of a plurality of frequencies by the application based on the conductivity of the filler material; determining an effective permittivity of a composite dielectric of the fractional order capacitor at each of a plurality of frequencies by the application based on the design specification and based on the permittivity of the filler materials at each of the plurality of frequencies, where the composite dielectric comprises a mixture of the dielectric matrix material and the plurality of filler materials; determining
  • An eleventh aspect can include the method of the tenth aspect, further comprising providing a list of filler materials, where the list of filler materials comprises identities of transition metal dichalcogenide semiconductor materials and data on their permittivity and conductivity, where determining the effective permittivity of the composite dielectric of the fractional order capacitor is further based on the data on the permittivity and conductivity of the filler materials.
  • a twelfth aspect can include the method of the eleventh aspect, wherein the list of filler materials comprise molybdenum disulfide (M0S 2 ), molybdenum ditelluride (MoTe 2 ), tungsten disulfide (WS 2 ), tungsten diselenide (WSe 2 ).
  • M0S 2 molybdenum disulfide
  • MoTe 2 molybdenum ditelluride
  • WS 2 tungsten disulfide
  • WSe 2 tungsten diselenide
  • a thirteenth aspect can include the method of any of the tenth to twelfth aspects, further comprising providing a list of dielectric matrix materials, wherein the list of dielectric matrix materials comprises identities of high-k dielectric materials and data on their permittivity, where determining the effective permittivity of the composite dielectric of the fractional order capacitor is further based on the data on the permittivity of the dielectric matrix materials.
  • a fourteenth aspect can include the method of the thirteenth aspect, wherein the high-k dielectric materials comprise hafnium dioxide (Hf0 2 ), hafnium silicate (HfSi0 4 ), zirconium dioxide (Zr0 2 ), and zirconium silicate (ZrSi0 4 ).
  • the high-k dielectric materials comprise hafnium dioxide (Hf0 2 ), hafnium silicate (HfSi0 4 ), zirconium dioxide (Zr0 2 ), and zirconium silicate (ZrSi0 4 ).
  • a fifteenth aspect can include the method of any of the tenth to fourteenth aspects, further comprising determining a ripple amplitude of the determined phase angle of the fractional order capacitor within the frequency bandwidth of the fractional order capacitor.
  • a sixteenth aspect can include the method of any of the tenth to fifteenth aspects, wherein the phase angle of the fractional order capacitor in the frequency bandwidth is identified as the mean of the phase angles determined within the frequency bandwidth of the fractional order capacitor.
  • a seventeenth aspect can include the method of any of the tenth to sixteenth aspects, wherein the design specification further identifies an aspect ratio of particles of the filler materials.
  • a method of modeling a fractional order capacitor comprises: providing a design specification of a fractional order capacitor having a composite dielectric layer comprised of a first layer of a first dielectric material and a second layer of a second dielectric material, where the design specification comprises an identity of the first dielectric material, an identity of the second dielectric material, a thickness of the first layer, and a thickness of the second layer; determining an effective permittivity of the composite dielectric layer of the fractional order capacitor at each of a plurality of frequencies by an application executing on a computer based on the design specification; determining a phase angle of the fractional order capacitor at each of the plurality of frequencies by the application based on the effective permittivity of the composite dielectric layer determined at each of the plurality of frequencies; determining a frequency bandwidth of the fractional order capacitor by the application based on the phase angle of the fractional order capacitor determined at each of the plurality of frequencies; and determining a phase angle of the fractional order
  • a nineteenth aspect can include the method of the eighteenth aspect, further comprising: determining a permittivity of the first dielectric material at each of the plurality of frequencies by the application; determining a permittivity of the second dielectric material at each of the plurality of frequencies by the application, and wherein determining the effective permittivity of the composite dielectric layer of the fractional order capacitor at each of the plurality of frequencies is further based on the permittivity of the first dielectric material determined at each of the plurality of frequencies and on the permittivity of the second dielectric material determined at each of the plurality of frequencies.
  • a twentieth aspect can include the method of any of the eighteen to nineteenth aspects, wherein the composite dielectric layer further comprises a third layer of a third dielectric material and the design specification of the fractional order capacitor further comprises an identity of the third dielectric material and a thickness of the third layer and further comprising determining a permittivity of the third dielectric material at each of the plurality of frequencies by the application, wherein determining the effective permittivity of the composite dielectric layer of the fractional order capacitor at each of the plurality of frequencies is further based on the permittivity of the third dielectric material determined at each of the plurality of frequencies.

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Abstract

L'invention concerne un procédé de production d'un condensateur d'ordre fractionnel (FOC). Le procédé consiste à déterminer une permittivité effective d'un diélectrique composite du FOC à chaque fréquence d'une pluralité de fréquences par une application s'exécutant sur un ordinateur sur la base d'une spécification de conception de FOC, le diélectrique composite comprenant un mélange d'un matériau de matrice diélectrique et d'une pluralité de matériaux de charge, à déterminer un angle de phase du FOC à chacune des fréquences sur la base de la permittivité effective du diélectrique composite déterminée à chacune des fréquences, à déterminer une bande passante de fréquence du FOC sur la base de l'angle de phase du condensateur d'ordre fractionnel déterminé à chacune des fréquences, à déterminer un angle de phase du FOC dans la bande passante de fréquence sur la base de l'angle de phase du FOC déterminé à chacune des fréquences à l'intérieur de la bande passante de fréquence, et à construire le FOC conformément à la spécification de conception.
PCT/IB2018/052734 2017-04-19 2018-04-19 Procédé de modélisation d'une conception de condensateur d'ordre fractionnel Ceased WO2018193403A1 (fr)

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CN119514170A (zh) * 2024-11-01 2025-02-25 吉林化工学院 一种基于联合多新息梯度的柔性机械臂分数阶建模方法

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CN109921072A (zh) * 2019-03-20 2019-06-21 南京理工大学 一种质子交换膜燃料电池输出功率的预测控制方法
CN109921072B (zh) * 2019-03-20 2022-04-01 南京理工大学 一种质子交换膜燃料电池输出功率的预测控制方法
CN113408126A (zh) * 2021-06-17 2021-09-17 华南理工大学 一种求分数阶甚高频谐振变换器瞬态解的解耦方法
CN119514170A (zh) * 2024-11-01 2025-02-25 吉林化工学院 一种基于联合多新息梯度的柔性机械臂分数阶建模方法
CN119514170B (zh) * 2024-11-01 2025-07-08 吉林化工学院 一种基于联合多新息梯度的柔性机械臂分数阶建模方法

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