CN105790724A - Manufacturing method of 0 to 1 order power level fraction order capacitance component - Google Patents

Abstract

The invention discloses a manufacturing method of a 0 to 1 order power level fraction order capacitance component. In the method, a fractance approximation method is used to design an S domain transfer function. A circuit integration method is used to acquire a Forster I type RC single port network topology structure and a parameter corresponding to the transfer function. During a manufacturing process, a voltage current stress borne by the fraction order capacitance component is considered and resistance and capacitance components with different specifications are selected. A fraction order capacitor constructed in the invention can be used for an actual power level circuit.

Description

A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell

Technical field

The present invention relates to the structure field of fractional order electronic component, the preparation method referring in particular to a kind of 0 to 1 rank power stage fractional order capacity cell.

Background technology

At present, 0 to 1 rank fractional order capacity cell remains in the Design Theory stage.(list of references 1 " SivaramaKrishnaM., DasS. beyond fractional order element is manufactured at laboratory except that according to electrochemical principle；nullBiswasK.,GoswamiB.“FabricationofaFractionalOrderCapacitorWithDesiredSpecifications:AStudyonProcessIdentificationandCharacterization.”IEEETrans.onElectronDevices,vol.58,no.11,pp.4067-4073,Oct.2011.”，List of references 2 " MondalD.,BiswasK.“PackagingofSingle-ComponentFractionalOrderElement.”IEEETrans.onDeviceandMaterialsReliability,vol.13,no.1,pp.73-80,Mar.2013.”)，Existing main resolving ideas be utilize various active、Passive device constitutes circuit，Desirable fractional order element is approached under certain precision，That is to say in certain selected frequency band，Be configured to embody the electrology characteristic of idealized score rank elements circuit (list of references 3 " and Yuan Xiao. point anti-mathematical principle approaching circuit. Beijing: Science Press,2015.”).

nullDivide the anti-design approaching circuit can trace back to the sixties in 20th century of the research (list of references 4 " CarlsonG.E. about 1/n rank condenser network model the earliest,HalijakC.A.“Approximationoffractionalcapacitors(1/s)1/nbyaregularNewtonprocess.”IEEETrans.onCircuitTheory,vol.11,no.2,pp.210-213,1964.”)，Some improvement projects are also had in succession to propose (list of references 5 " A.Charef,H.H.Sun,Y.Y.Tsao,andB.Onaral.“FractalSystemasRepresentedbySingularityFunction.”IEEETrans.onAutomaticControl,vol.37,no.9,pp.1465-1470,1992.”，List of references 6 " Elwakil,A.S.“Fractional-OrderCircuitsandSystems:AnEmergingInterdisciplinaryResearchArea.”IEEECircuitsandSystemsMagazine.vol.10,no.4,pp.40-50,Nov.2010.”，List of references 7 " JurajValsaandJiriVlach. " RCmodelsofaconstantphaseelement. " Int.J.Circ.Theor.Appl.,vol.41,pp.59-67,2013.”)，The fractional order element of existing structure generally combines with amplifier，It is used in Fractional Order PID Controller、Fractional calculus circuit、Fractional order wave filter、(list of references 8 " IvoPetras.Fractional-OrderNonlinearSystems.Berlin:Spring er-Verlag in the low-power circuits such as fractional order oscillation signal generator,2011”，List of references 9 " MadhabChandraTripathy,DebasmitaMondal,KarabiBiswasandSiddharthaSen.“Experimentalstudiesonrealizationoffractionalinductorsandfractional-orderbandpassfilters.”Int.J.Circ.Theor.Appl.,vol.43,pp.1183-1196,2015.”).nullAlthough the existing research (list of references 10 " Martinez about the power inverter operating characteristic comprising fractional order element at present,R.,etal.“FractionalDC/DCconverterinsolar-poweredelectricalgenerationsystems.”2009IEEE14thInternationalConferenceonEmergingTechnologies&FactoryAutomation(ETFA2009),vol.3,pp.1-6,Sept.2009.”，List of references 11 " Wang Faqiang,Ma Xikui. under continuous current mode pattern, the fractional order modeling and simulation of Boost is analyzed. Acta Physica Sinica,vol.60,no.7,pp.070506,Jul.2011.”，List of references 12 " YangNing-Ning,LiuChong-XinandWuChao-Jun.Modelinganddynamicsanalysisofthefractional-orderBuckBoostconverterincontinuousconductionmode.Chin.Phys.B,Vol.21,No.8,080503,2012”，List of references 13 " ChaojunWu,GangquanSi,YanbinZhang,NingningYang.“Thefractional-orderstate-spaceaveragingmodelingoftheBuck-BoostDC/DCconverterindiscontinuousconductionmodeandtheperformanceanalysis.”NonlinearDynamics,vol.79,no.1,pp.689-703,Jan.2015.”).

As can be seen here, it is badly in need of at present a kind of fractional order capacity cell that can be used in power inverter, but, due to the Power Limitation of the existence of parasitic parameter and element in actual electronic component, existing document yet there are no applicable fractional order capacity cell and be in the news.

Summary of the invention

It is an object of the invention to the design principle according to fractional order element, it is provided that the preparation method of a kind of 0 to 1 rank power stage fractional order capacity cell that can be used in power inverter.

For achieving the above object, technical scheme provided by the present invention comprises the following steps:

1) according to idealized score rank condensance characteristic, row write impedance function equation:

$Z_C=\frac{1}{{\left(j\mathrm{\ω}\right)}^{\mathrm{\β}}C}---\left(1\right)$

In formula, β represents the order of fractional order electric capacity, and ω is the operating angle frequency of electric capacity, and C represents the capacitance of fractional order electric capacity；

2) by impedance function, row write the s territory transmission function of idealized score rank electric capacity:

$Z_C\left(s\right)=\frac{1}{s^{\mathrm{\β}}C}---\left(2\right)$

3) by designing z_iAnd p_i, utilize following rational approximations function that s territory is transferred function by and approach:

$\begin{array}{c}{Z}_C\left(s\right)=\frac{1}{s^{m}C}\\ \≈\frac{1}{C}\underset{N\→\mathrm{\∞}}{\lim }\frac{\underset{i=0}{\overset{N-1}{\Π}}(1+\frac{s}{z_i})}{\underset{i=0}{\overset{N-1}{\Π}}(1+\frac{s}{p_i})}\end{array}---\left(3\right)$

Wherein:

$\left\{\begin{array}{c}{p}_i={10}^{\frac{y}{10}(\frac{1+n}{1-\mathrm{\β}}+\frac{n}{\mathrm{\β}}+0.5)}{\mathrm{\ω}}_{\min }\\ z_i={10}^{\frac{y}{10(1-\mathrm{\β})}}{p}_i\end{array}\right.---\left(4\right)$

Y is approximating function and former transmission function error on amplitude-versus-frequency curve, and β is the order of fractional order electric capacity, ω_minLower limit for the frequency band range of involved approximating function；Additionally, N is approached frequency band (ω by order β, approximate error y and design in transmission function_min, ω_max) determine, expression is:

$N=1+Integer\[\frac{\lg \left(\frac{{\mathrm{\ω}}_{\max }}{{\mathrm{\ω}}_{\min }}{10}^{\frac{20\mathrm{\β}}{y}}\right)}{\lg \left({10}^{\frac{y}{10}(\frac{1}{1-\mathrm{\β}}+\frac{1}{\mathrm{\β}})}\right)}\]---\left(5\right)$

4) integrated approach according to passive one-port RC network, first with zp2tf function in matlab by step 3) the zero pole point form rational approximations function of gained is converted to the form of rational fraction, then utilize residue function in matlab that the approximating function of rational fraction form is carried out residue, be converted into the transmission function of following form:

$Z_C=\underset{i=0}{\overset{N}{\Σ}}\frac{K_i}{s+{\mathrm{\σ}}_i}---\left(6\right)$

Wherein K_iAnd σ_iProvided by the zp2tf function in matlab and residue function；

5) according to step 4) gained residue expression formula, obtaining designed fractional order capacity cell, to approach circuit be topological structure be Foster I type single port RC network, i.e. R_iWith C_iComposition R in parallel_iC_iUnit, then with R_i+1C_i+1Unit is serially connected, and wherein value standard is:

$\left\{\begin{array}{c}{R}_i=\frac{K_i}{{\mathrm{\σ}}_i}\\ C_i=\frac{1}{K_i}\end{array}\right.---\left(7\right)$

6) step 5) obtain fractional order electric capacity approach circuit, due to RC element circuit parameter not etc., time in for power inverter, different voltage will be born, according to the power grade that each RC unit bears, and the feature of existing capacitance resistance device, select actual polypropylene film electric capacity and power resistor to weld, final prepare 0 to 1 required rank power stage fractional order capacity cell.

The present invention compared with prior art, has the advantage that and beneficial effect:

By fractional order electric capacity provided by the present invention, in selected frequency band, possess the electrology characteristic of idealized score rank element, it is contemplated that the power grade that element can bear, be therefore usable in power stage changer；Additionally, due to have employed polypropylene film electric capacity in topological structure, under switching frequency, the fractional order capacity cell of structure is not by the impact of parasitic parameter.

Accompanying drawing explanation

Fig. 1 includes fractional order electric capacity C in embodiment 1^βThe circuit theory diagrams of DC-DCBoost changer.

Fig. 2 is 0.9 rank 10 μ F capacitance principle figure in embodiment 1.

Fig. 3 is 0.9 rank 10 μ F electric capacity practical circuit diagram in embodiment 1.

Fig. 4 is 0.8 rank 10 μ F capacitance principle figure in embodiment 2.

Fig. 5 is 0.8 rank 10 μ F electric capacity practical circuit diagram in embodiment 2.

Fig. 6 a calculates gained DC-DCBoost changer 0.9 rank capacitance voltage oscillogram for utilizing predictor-corrector method.

Fig. 6 b calculates gained DC-DCBoost changer 0.8 rank capacitance voltage oscillogram for utilizing predictor-corrector method.

Fig. 7 a adopts the PSIM that the present invention constructs fractional order electric capacity to emulate 0.9 rank capacitance voltage oscillogram.

Fig. 7 b adopts the PSIM that the present invention constructs fractional order electric capacity to emulate 0.8 rank capacitance voltage oscillogram.

Fig. 8 a is Experiment of Electrical Circuits gained DC-DCBoost changer 0.9 rank capacitance voltage oscillograms.

Fig. 8 b is Experiment of Electrical Circuits gained DC-DCBoost changer 0.8 rank capacitance voltage oscillograms.

Detailed description of the invention

Below in conjunction with specific embodiment, the invention will be further described.

Embodiment 1

Refer to the schematic diagram of the DC-DCBoost changer that Fig. 1, Fig. 1 are the present embodiment 1, wherein Boost input voltage E=12V, switching frequency fs=25kHz, dutycycle 0.4, inductance L=477 μ H, load R=40 Ω, fractional order electric capacity is 0.9 rank 10 μ F electric capacity.It is as follows that method provided by the invention is embodied as step:

S1, utilizing the one that document 5 carries to divide anti-approach method, under current switch frequency, when approximate error is within 2dB, design 0.9 rank 10 μ F electric capacity, concrete condition is as follows:

S11, according to idealized score rank condensance characteristic, row write impedance function equation:

$Z_C=\frac{{10}^5}{{(j\×7.8540\×{10}^4)}^{0.9}}---\left(1\right)$

S12, by impedance function, it is possible to row write idealized score rank electric capacity s territory transmission function:

$Z_C\left(s\right)=\frac{{10}^5}{s^{0.9}}---\left(2\right)$

S13, take that to approach frequency band be (10^-2, 10⁷) rad/s, N=6 can be obtained, rational approximations function is:

$Z_C\left(s\right)=\frac{9.675e5\×\underset{i=1}{\overset{5}{\Π}}(1+\frac{s}{z_i})}{\underset{i=1}{\overset{6}{\Π}}(1+\frac{s}{p_i})}---\left(3\right)$

Wherein:

$\left\{\begin{array}{c}{p}_i={10}^{\frac{y}{10}(\frac{1+n}{1-\mathrm{\β}}+\frac{n}{\mathrm{\β}}+0.5)}{\mathrm{\ω}}_{min}\\ z_i={10}^{\frac{y}{10(1-\mathrm{\β})}}{p}_i\end{array}\right.---\left(4\right)$

Y is approximating function and former transmission function error on amplitude-versus-frequency curve, and β is the order of fractional order electric capacity, ω_minLower limit for the frequency band range of involved approximating function；Additionally, N is approached frequency band (ω by order β, approximate error y and design in transmission function_min, ω_max) determine, expression is:

$N=1+Integer\[\frac{\lg \left(\frac{{\mathrm{\ω}}_{\max }}{{\mathrm{\ω}}_{\min }}{10}^{\frac{20\mathrm{\β}}{y}}\right)}{\lg \left({10}^{\frac{y}{10}(\frac{1}{1-\mathrm{\β}}+\frac{1}{\mathrm{\β}})}\right)}\]---\left(5\right)$

S2, described fractional order capacitor topological structure are Foster I type single port RC network, and specific configuration process and relevant parameter selection standard be:

S21, integrated approach according to passive one-port RC network, first with zp2tf function in matlab, the zero pole point form rational approximations function of S1 gained is converted to the form of rational fraction, then utilize residue function in matlab that the approximating function of rational fraction form is carried out residue, be converted into the transmission function of following form:

$Z_C=\underset{i=0}{\overset{N}{\Σ}}\frac{K_i}{s+{\mathrm{\σ}}_i}---\left(6\right)$

Wherein K_iAnd σ_iBeing provided by the zp2tf function in matlab and residue function, numerical value is as shown in table 1 below；

Table 1-program gained K_iAnd σ_iValue

i	Ki	σi
			1	3.8844e+005	1.6681e+009
2	2.3193e+005	1.0000e+007
			3	1.3903e+005	5.9948e+004
4	8.3350e+004	359.3814
			5	5.0145e+004	2.1544
6	7.4606e+004	0.0129

S22, according to S21 gained residue expression formula, can obtaining designed fractional order capacity cell, to approach circuit be topological structure be Foster I type single port RC network, i.e. R_iWith C_iComposition R in parallel_iC_iUnit, then with R_i+1C_i+1Unit is serially connected, structure chart as in figure 2 it is shown, wherein value standard be:

$\left\{\begin{array}{c}{R}_i=\frac{K_i}{{\mathrm{\σ}}_i}\\ C_i=\frac{1}{K_i}\end{array}\right.---\left(7\right)$

Value standard is as shown in table 2 below.

R in the electric capacity one-port network of table 2-0.9 rank_iAnd C_iTheoretical values

The fractional order electric capacity that S3, utilization construct, PSIM simulation software carries out circuit simulation, known 0.9 rank 10 μ F fractional order electric capacity is by the peak point current of the voltage and 2.2A that bear the highest 29.6V, and the voltage x current stress that in circuit, each RC unit bears also observes acquisition, calculate the power grade that each RC unit bears, select actual polypropylene film electric capacity and power resistive elements specification as shown in table 3 below.Finally constituting the 0.9 rank 10 μ F electric capacity meeting this implementation requirements to form, side circuit is as shown in Figure 3.

R in the electric capacity one-port network of table 3-0.9 rank_iAnd C_iPower grade and select device

i	Power grade/W	Ri/Ω	Ci/μF
				1	Minimum ignore	E24 metalfilmresistor	Polypropylene film electric capacity
2	0.68	3W fixed carbon resister	Ibid
				3	3	5W is noninductive cement resistor	Ibid
4	0.5	E24 metalfilmresistor	Ibid
				5	Minimum ignore	E24 metalfilmresistor	Ibid
6	Minimum ignore	E24 metalfilmresistor	Ibid

Embodiment 2

The present embodiment still adopts the DC-DCBoost changer in embodiment 1, and changing wherein fractional order electric capacity is 0.8 rank 10 μ F electric capacity.As shown in FIG., Boost input voltage E=12V, switching frequency fs=25kHz, dutycycle 0.4, inductance L=477 μ H, load R=40 Ω are adopted.It is as follows that method provided by the invention is embodied as step:

S1, utilizing the one that document 5 carries to divide anti-approach method, under current switch frequency, when approximate error is within 2dB, design 0.8 rank 10 μ F electric capacity, concrete condition is as follows:

S11, according to idealized score rank condensance characteristic, row write impedance function equation:

$Z_C=\frac{{10}^5}{{(j\×7.8540\×{10}^4)}^{0.8}}---\left(1\right)$

S12, by impedance function, it is possible to row write idealized score rank electric capacity s territory transmission function:

$Z_C\left(s\right)=\frac{{10}^5}{s^{0.8}}---\left(2\right)$

S13, take that to approach frequency band be (10^-2, 10⁷) rad/s, N=9 can be obtained, rational approximations function is:

$Z_C\left(s\right)=\frac{5.5054e6\×\underset{i=1}{\overset{8}{\Π}}(1+\frac{s}{z_i})}{\underset{i=1}{\overset{9}{\Π}}(1+\frac{s}{p_i})}---\left(3\right)$

Wherein:

$\left\{\begin{array}{c}{p}_i={10}^{\frac{y}{10}(\frac{1+n}{1-\mathrm{\β}}+\frac{n}{\mathrm{\β}}+0.5)}{\mathrm{\ω}}_{min}\\ z_i={10}^{\frac{y}{10(1-\mathrm{\β})}}{p}_i\end{array}\right.---\left(4\right)$

Y is approximating function and former transmission function error on amplitude-versus-frequency curve, and β is the order of fractional order electric capacity, ω_minLower limit for the frequency band range of involved approximating function；Additionally, N is approached frequency band (ω by order β, approximate error y and design in transmission function_min, ω_max) determine, expression is:

$N=1+Integer\[\frac{\lg \left(\frac{{\mathrm{\ω}}_{\max }}{{\mathrm{\ω}}_{\min }}{10}^{\frac{20\mathrm{\β}}{y}}\right)}{\lg \left({10}^{\frac{y}{10}(\frac{1}{1-\mathrm{\β}}+\frac{1}{\mathrm{\β}})}\right)}\]---\left(5\right)$

S2, described fractional order capacitor topological structure are Foster I type single port RC network, and specific configuration process and relevant parameter selection standard be:

S21, integrated approach according to passive one-port RC network, first with zp2tf function in matlab, the zero pole point form rational approximations function of S1 gained is converted to the form of rational fraction, then utilize residue function in matlab that the approximating function of rational fraction form is carried out residue, be converted into the transmission function of following form:

$Z_C=\underset{i=0}{\overset{N}{\Σ}}\frac{K_i}{s+{\mathrm{\σ}}_i}---\left(6\right)$

Wherein K_iAnd σ_iBeing provided by the zp2tf function in matlab and residue function, numerical value is as shown in table 4 below；

Table 4-program gained K_iAnd σ_iValue

i	Ki	σi
			1	2.4759e+006	1.3335e+008
2	1.3278e+006	7.4989e+006
			3	7.4481e+005	4.2170e+005
4	4.1878e+005	2.3714e+004
			5	2.3550e+005	1.3335e+003
6	1.3244e+005	74.9894
			7	7.4597e+004	4.2170
8	4.3182e+004	0.2371
			9	5.2363e+004	0.0133

S22, according to S21 gained residue expression formula, can obtaining designed fractional order capacity cell, to approach circuit be topological structure be Foster I type single port RC network, i.e. R_iWith C_iComposition R in parallel_iC_iUnit, then with R_i+1C_i+1Unit is serially connected, and as shown in Figure 4, wherein value standard is structure chart:

$\left\{\begin{array}{c}{R}_i=\frac{K_i}{{\mathrm{\σ}}_i}\\ C_i=\frac{1}{K_i}\end{array}\right.---\left(7\right)$

Value standard is as shown in table 5 below.

R in the electric capacity one-port network of table 5-0.8 rank_iAnd C_iTheoretical values

i	Ri/Ω	Ci/μF
			1	18.6m	0.4039
2	177.1m	0.7532
			3	1.7662	1.3426
4	17.6598	2.3879
			5	176.5976	4.2463
6	1.7661k	7.5505
			7	17.69k	13.405
8	182.1k	23.158
			9	3.9267M	19.097

The fractional order electric capacity that S3, utilization construct, PSIM simulation software carries out circuit simulation, known 0.8 rank 10 μ F fractional order electric capacity is by the peak point current of the voltage and 1.4A that bear the highest 25V, and the voltage x current stress that in circuit, each RC unit bears also observes acquisition, calculate the power grade that each RC unit bears, select actual polypropylene film electric capacity and power resistive elements specification as shown in table 6 below.Finally constituting the 0.8 rank 10 μ F electric capacity meeting this implementation requirements to form, side circuit is as shown in Figure 5.

R in the electric capacity one-port network of table 6-0.8 rank_iAnd C_iPower grade and select device

According to Fig. 6 a, 6b, 7a, 7b, 8a, 8b, owing to being respectively adopted IRF640B and MUR16200TG in Boost as switching tube and power diode, consider conduction voltage drop and the dead resistance resistance of device, the calculated results and PSIM simulation result, side circuit experimental result matching obtain very well, illustrate by fractional order electric capacity provided by the present invention, possesses the electrology characteristic of idealized score rank element, it is possible to be used in power stage changer.

Embodiment described above is only the preferred embodiments of the invention, not limits the practical range of the present invention with this, therefore all changes made according to the shape of the present invention, principle, all should be encompassed in protection scope of the present invention.

Claims (1)

1. the preparation method of a rank power stage fractional order capacity cell, it is characterised in that comprise the following steps:

1) according to idealized score rank condensance characteristic, row write impedance function equation:

$Z_C=\frac{1}{{\left(j\mathrm{\ω}\right)}^{\mathrm{\β}}C}---\left(1\right)$

In formula, β represents the order of fractional order electric capacity, and ω is the operating angle frequency of electric capacity, and C represents the capacitance of fractional order electric capacity；

2) by impedance function, row write the s territory transmission function of idealized score rank electric capacity:

$Z_C\left(s\right)=\frac{1}{s^{\mathrm{\β}}C}---\left(2\right)$

3) by designing z_iAnd p_i, utilize following rational approximations function that s territory is transferred function by and approach:

$\begin{array}{c}{Z}_C\left(s\right)=\frac{1}{s^{m}C}\\ \≈\frac{1}{C}\underset{N\→\mathrm{\∞}}{\lim }\frac{\underset{i=0}{\overset{N-1}{\Π}}(1+\frac{s}{z_i})}{\underset{i=0}{\overset{N}{\Π}}(1+\frac{s}{p_i})}\end{array}---\left(3\right)$

Wherein:

$\left\{\begin{array}{c}{p}_i={10}^{\frac{y}{10}\left(\frac{1+n}{1-\mathrm{\β}}+\frac{n}{\mathrm{\β}}+0.5\right)}{\mathrm{\ω}}_{\min }\\ z_i={10}^{\frac{y}{10\left(1-\mathrm{\β}\right)}}{p}_i\end{array}\right.---\left(4\right)$

Y is approximating function and former transmission function error on amplitude-versus-frequency curve, and β is the order of fractional order electric capacity, ω_minLower limit for the frequency band range of involved approximating function；Additionally, N is approached frequency band (ω by order β, approximate error y and design in transmission function_min, ω_max) determine, expression is:

$N=1+Integer\[\frac{\lg \left(\frac{{\mathrm{\ω}}_{max}}{{\mathrm{\ω}}_{\min }}{10}^{\frac{20\mathrm{\β}}{y}}\right)}{\lg \left({10}^{\frac{y}{10}\left(\frac{1}{1-\mathrm{\β}}+\frac{1}{\mathrm{\β}}\right)}\right)}\]---\left(5\right)$

4) integrated approach according to passive one-port RC network, first with zp2tf function in matlab by step 3) the zero pole point form rational approximations function of gained is converted to the form of rational fraction, then utilize residue function in matlab that the approximating function of rational fraction form is carried out residue, be converted into the transmission function of following form:

$Z_C=\underset{i=0}{\overset{N}{\Σ}}\frac{K_i}{s+{\mathrm{\σ}}_i}---\left(6\right)$

Wherein K_iAnd σ_iProvided by the zp2tf function in matlab and residue function；

5) according to step 4) gained residue expression formula, obtaining designed fractional order capacity cell, to approach circuit be topological structure be Foster I type single port RC network, i.e. R_iWith C_iComposition R in parallel_iC_iUnit, then with R_i+1C_i+1Unit is serially connected, and wherein value standard is:

$\left\{\begin{array}{c}{R}_i=\frac{K_i}{{\mathrm{\σ}}_i}\\ C_i=\frac{1}{K_i}\end{array}\right.---\left(7\right)$

6) step 5) obtain fractional order electric capacity approach circuit, due to RC element circuit parameter not etc., time in for power inverter, different voltage will be born, according to the power grade that each RC unit bears, and the feature of existing capacitance resistance device, select actual polypropylene film electric capacity and power resistor to weld, final prepare 0 to 1 required rank power stage fractional order capacity cell.