CN105790724B - A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell - Google Patents
A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell Download PDFInfo
- Publication number
- CN105790724B CN105790724B CN201610280164.3A CN201610280164A CN105790724B CN 105790724 B CN105790724 B CN 105790724B CN 201610280164 A CN201610280164 A CN 201610280164A CN 105790724 B CN105790724 B CN 105790724B
- Authority
- CN
- China
- Prior art keywords
- mrow
- mfrac
- msub
- msup
- capacitance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H5/00—One-port networks comprising only passive electrical elements as network components
Landscapes
- Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
- Networks Using Active Elements (AREA)
Abstract
The invention discloses a kind of preparation method of 0 to 1 rank power stage fractional order capacity cell, this method obtains Foster I types RC one-port networks topological structure corresponding with the transmission function and parameter using point anti-method design S domains transmission function approached using the method for circuit synthesis.In preparation process, it is contemplated that the voltage and current stress that fractional order capacity cell is born, chooses the resistance and capacity cell of different size.The fractional order capacitance constructed according to the present invention can be used in actual power stage circuit.
Description
Technical field
The present invention relates to the construction field of fractional order electronic component, refers in particular to a kind of 0 to 1 rank power stage fractional order capacitance
The preparation method of element.
Background technology
At present, 0 to 1 rank fractional order capacity cell remains in the Theoretical Design stage.Except according to electrochemical principle in reality
Test (" Sivarama Krishna M., the Das S. of bibliography 1 beyond room manufacture fractional order element；Biswas K.,Goswami
B.“Fabrication of a Fractional Order Capacitor With Desired Specifications:A
Study on Process Identification and Characterization.”IEEE Trans.on Electron
Devices, vol.58, no.11, pp.4067-4073, Oct.2011. ", " Mondal D., the Biswas K. of bibliography 2
“Packaging of Single-Component Fractional Order Element.”IEEE Trans.on Device
And Materials Reliability, vol.13, no.1, pp.73-80, Mar.2013. "), existing main resolving ideas
It is to form circuit using various active, passive devices, preferable fractional order element is approached under certain precision, that is to say selected
Some frequency band in, being configured to embody the circuit of the electrology characteristic of idealized score rank element, (" Yuan Xiao points anti-to force bibliography 3
Mathematical principle Beijing of nearly circuit:Science Press, 2015. ").
The anti-design for approaching circuit is divided to trace back to research of the 1960s on 1/n rank condenser network models earliest
(" Carlson G.E., Halijak C.A. " the Approximation of fractional capacitors of bibliography 4
(1/s)1/n by a regular Newton process.”IEEE Trans.on Circuit Theory,vol.11,
No.2, pp.210-213,1964. "), also have some improvement projects propose in succession (bibliography 5 " A.Charef, H.H.Sun,
Y.Y.Tsao,and B.Onaral.“Fractal System as Represented by Singularity
Function. " IEEE Trans.on Automatic Control, vol.37, no.9, pp.1465-1470,1992. ", ginseng
Examine " Elwakil, A.S. " the Fractional-Order Circuits and Systems of document 6:An Emerging
Interdisciplinary Research Area.”IEEE Circuits and Systems Magazine.vol.10,
No.4, pp.40-50, Nov.2010. ", " Juraj Valsa and Jiri Vlach. " the RC models of a of bibliography 7
Constant phase element. " Int.J.Circ.Theor.Appl., vol.41, pp.59-67,2013. "), it is existing
The fractional order element of construction is usually combined with amplifier, used in Fractional Order PID Controller, fractional calculus circuit, fractional order
(" the Ivo Petras.Fractional- of bibliography 8 in the low-power circuits such as wave filter, fractional order oscillation signal generator
Order Nonlinear Systems.Berlin:Springer-Verlag, 2011 ", " the Madhab Chandra of bibliography 9
Tripathy,Debasmita Mondal,Karabi Biswas and Siddhartha Sen.“Experimental
studies on realization of fractional inductors and fractional-order bandpass
filters.”Int.J.Circ.Theor.Appl.,vol.43,pp.1183-1196,2015.”).Although it has been related at present
Research (" Martinez, R., the et al. of bibliography 10 of power inverter working characteristics comprising fractional order element
“Fractional DC/DC converter in solar-powered electrical generation systems.”
2009IEEE 14th International Conference on Emerging Technologies&Factory
Automation (ETFA 2009), vol.3, pp.1-6, Sept.2009. ", " Wang Faqiang, Ma Xikui the inductance of bibliography 11
The fractional order modeling and simulation analysis Acta Physica Sinicas of Boost under continuous current mode, vol.60, no.7,
Pp.070506, Jul.2011. ", " Yang Ning-Ning, the Liu Chong-Xin and Wu Chao- of bibliography 12
Jun.Modeling and dynamics analysis of the fractional-order Buck Boost
Converter in continuous conduction mode.Chin.Phys.B, Vol.21, No.8,080503,2012 ",
" Chaojun Wu, Gangquan Si, Yanbin Zhang, Ningning Yang. " the The fractional- of bibliography 13
order state-space averaging modeling of the Buck-Boost DC/DC converter in
discontinuous conduction mode and the performance analysis.”Nonlinear
Dynamics,vol.79,no.1,pp.689-703,Jan.2015.”)。
It can be seen from the above that it is badly in need of a kind of fractional order capacity cell that can be used in power inverter at present, however, due to reality
The power limit of the presence of parasitic parameter and element in electronic component, yet there are no applicable fractional order electricity in existing document
Hold element to be reported.
The content of the invention
It is an object of the invention to the design principle according to fractional order element, there is provided a kind of to can be used in power inverter
The preparation method of 0 to 1 rank power stage fractional order capacity cell.
It is to achieve the above object, provided by the present invention that the technical scheme comprises the following steps：
1) impedance function equation is write according to idealized score rank condensance characteristic, row：
In formula, β represents the order of fractional order capacitance, and ω is the work angular frequency of capacitance, and C represents the appearance of fractional order capacitance
Value；
2) the s domains transmission function of idealized score rank capacitance is write by impedance function, row：
3) by designing ziAnd pi, approached using following rational approximations function pair s domains transmission function：
Wherein：
Y is error of the approximating function with former transmission function on amplitude-versus-frequency curve, and β is the order of fractional order capacitance,
ωminFor the lower limit of the frequency range of involved approximating function；In addition, in transmission function N be by order β, approximate error y and
Design approaches frequency band (ωmin, ωmax) determine, expression is：
4) according to the integrated approach of passive one-port RC network, first with zp2tf functions in matlab by obtained by step 3)
Zero pole point form rational approximations function be converted to the form of rational fraction, then will have using residue functions in matlab
The approximating function for managing Fractional form carries out residue, is converted into the transmission function of following form：
Wherein KiAnd σiProvided by the zp2tf functions in matlab and residue functions；
5) according to residue expression formula obtained by step 4), obtain designed fractional order capacity cell and approach circuit and be
The Foster I type single port RC networks of topological structure, i.e. RiWith CiParallel connection forms RiCiUnit, then with Ri+1Ci+1Unit is mutually gone here and there
Connection, wherein value standard are：
6) the fractional order capacitance that step 5) obtains approaches circuit, since RC element circuits parameter differs, for power
When in converter, different voltage will be born, the power grade born according to each RC units, and existing capacitance resistance device
The characteristics of, select actual polypropylene film capacitance and power resistor to be welded, 0 to 1 required rank power stage is finally made
Fractional order capacity cell.
Compared with prior art, the present invention having the following advantages that and beneficial effect：
By fractional order capacitance provided by the present invention, in selected frequency band, possess the electrology characteristic of idealized score rank element,
Due to consideration that the power grade that element can be born, therefore can be used in power stage converter；Further, since in topology
Polypropylene film capacitance is employed in structure, under switching frequency, the fractional order capacity cell of construction from parasitic parameter shadow
Ring.
Brief description of the drawings
Fig. 1 is to include fractional order capacitance C in embodiment 1βDC-DC Boosts circuit diagram.
Fig. 2 is 0.9 rank, 10 μ F capacitance principle figures in embodiment 1.
Fig. 3 is 0.9 rank, 10 μ F capacitance practical circuit diagrams in embodiment 1.
Fig. 4 is 0.8 rank, 10 μ F capacitance principle figures in embodiment 2.
Fig. 5 is 0.8 rank, 10 μ F capacitance practical circuit diagrams in embodiment 2.
Fig. 6 a are to calculate 0.9 rank capacitance voltage oscillogram of gained DC-DC Boosts using predictor-corrector method.
Fig. 6 b are to calculate 0.8 rank capacitance voltage oscillogram of gained DC-DC Boosts using predictor-corrector method.
Fig. 7 a are to emulate 0.9 rank capacitance voltage oscillogram using the PSIM of present invention construction fractional order capacitance.
Fig. 7 b are to emulate 0.8 rank capacitance voltage oscillogram using the PSIM of present invention construction fractional order capacitance.
Fig. 8 a 0.9 rank capacitance voltage oscillograms of DC-DC Boosts obtained by Experiment of Electrical Circuits.
Fig. 8 b 0.8 rank capacitance voltage oscillograms of DC-DC Boosts obtained by Experiment of Electrical Circuits.
Embodiment
With reference to specific embodiment, the invention will be further described.
Embodiment 1
Fig. 1 is referred to, Fig. 1 is the schematic diagram of the DC-DC Boosts of the present embodiment 1, and wherein Boost is defeated
Enter voltage E=12V, switching frequency fs=25kHz, duty cycle 0.4, inductance L=477 μ H, load R=40 Ω, fractional order capacitance
For 0.9 rank, 10 μ F capacitances.Method specific implementation step provided by the invention is as follows：
S1, the anti-approach method of one kind point carried using document 5, under current switch frequency, when approximate error 2dB with
When interior, 0.9 rank, 10 μ F capacitances are designed, concrete condition is as follows：
S11, according to idealized score rank condensance characteristic, row write impedance function equation：
S12, by impedance function, the s domains transmission function for writing idealized score rank capacitance can be arranged：
S13, take and approach frequency band as (10-2, 107) rad/s, N=6 can be obtained, rational approximations function is：
Wherein：
Y is error of the approximating function with former transmission function on amplitude-versus-frequency curve, and β is the order of fractional order capacitance,
ωminFor the lower limit of the frequency range of involved approximating function；In addition, in transmission function N be by order β, approximate error y and
Design approaches frequency band (ωmin, ωmax) determine, expression is：
S2, the fractional order capacitor topological structure are Foster I type single port RC networks, specific configuration process and relevant parameter
Selection standard is：
S21, the integrated approach according to passive one-port RC network, first with zp2tf functions in matlab by obtained by S1
Zero pole point form rational approximations function is converted to the form of rational fraction, then will be reasonable using residue functions in matlab
The approximating function of Fractional form carries out residue, is converted into the transmission function of following form：
Wherein KiAnd σiProvided by the zp2tf functions in matlab and residue functions, numerical value is as shown in table 1 below；
K obtained by table 1- programsiAnd σiValue
| 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, the residue expression formula according to obtained by S21, can obtain designed fractional order capacity cell and approach circuit
For the Foster I type single port RC networks of topological structure, i.e. RiWith CiParallel connection forms RiCiUnit, then with Ri+1Ci+1Unit is mutual
Series connection, structure chart is as shown in Fig. 2, wherein value standard is：
Value standard is as shown in table 2 below.
R in table 2-0.9 rank capacitance one-port networksiAnd CiTheoretical values
S3, the fractional order capacitance using construction, carry out circuit simulation in PSIM simulation softwares, it is known that F points of 0.9 rank, 10 μ
Number rank capacitances are by the voltage for bearing highest 29.6V and the peak point current of 2.2A, and the voltage that each RC units are born in circuit
Current stress also observes acquisition, calculates the power grade that each RC units are born, and selects actual polypropylene film capacitance and work(
Rate resistive element specification is as shown in table 3 below.Finally constitute and meet that 0.9 rank, the 10 μ F capacitances of this implementation requirements form, actual circuit
As shown in Figure 3.
R in table 3-0.9 rank capacitance one-port networksiAnd CiPower grade and select device
| i | Power grade/W | Ri/Ω | Ci/μF |
| 1 | It is minimum negligible | E24 metalfilmresistors | Polypropylene film capacitance |
| 2 | 0.68 | 3W fixed carbon resisters | Ibid |
| 3 | 3 | 5W is noninductive cement resistor | Ibid |
| 4 | 0.5 | E24 metalfilmresistors | Ibid |
| 5 | It is minimum negligible | E24 metalfilmresistors | Ibid |
| 6 | It is minimum negligible | E24 metalfilmresistors | Ibid |
Embodiment 2
The present embodiment still uses the DC-DC Boosts in embodiment 1, and it is 0.8 to change wherein fractional order capacitance
10 μ F capacitances of rank.As shown in FIG., using Boost input voltage E=12V, switching frequency fs=25kHz, duty cycle
0.4, inductance L=477 μ H, load R=40 Ω.Method specific implementation step provided by the invention is as follows：
S1, the anti-approach method of one kind point carried using document 5, under current switch frequency, when approximate error 2dB with
When interior, 0.8 rank, 10 μ F capacitances are designed, concrete condition is as follows：
S11, according to idealized score rank condensance characteristic, row write impedance function equation：
S12, by impedance function, the s domains transmission function for writing idealized score rank capacitance can be arranged：
S13, take and approach frequency band as (10-2, 107) rad/s, N=9 can be obtained, rational approximations function is：
Wherein：
Y is error of the approximating function with former transmission function on amplitude-versus-frequency curve, and β is the order of fractional order capacitance,
ωminFor the lower limit of the frequency range of involved approximating function；In addition, in transmission function N be by order β, approximate error y and
Design approaches frequency band (ωmin, ωmax) determine, expression is：
S2, the fractional order capacitor topological structure are Foster I type single port RC networks, specific configuration process and relevant parameter
Selection standard is：
S21, the integrated approach according to passive one-port RC network, first with zp2tf functions in matlab by obtained by S1
Zero pole point form rational approximations function is converted to the form of rational fraction, then will be reasonable using residue functions in matlab
The approximating function of Fractional form carries out residue, is converted into the transmission function of following form：
Wherein KiAnd σiProvided by the zp2tf functions in matlab and residue functions, numerical value is as shown in table 4 below；
K obtained by table 4- programsiAnd σiValue
| 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, the residue expression formula according to obtained by S21, can obtain designed fractional order capacity cell and approach circuit
For the Foster I type single port RC networks of topological structure, i.e. RiWith CiParallel connection forms RiCiUnit, then with Ri+1Ci+1Unit is mutual
Series connection, structure chart is as shown in figure 4, wherein value standard is：
Value standard is as shown in table 5 below.
R in table 5-0.8 rank capacitance one-port networksiAnd CiTheoretical 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 |
S3, the fractional order capacitance using construction, carry out circuit simulation in PSIM simulation softwares, it is known that F points of 0.8 rank, 10 μ
Number rank capacitance is by the voltage for bearing highest 25V and the peak point current of 1.4A, and the voltage electricity that each RC units are born in circuit
Stream stress also observes acquisition, calculates the power grade that each RC units are born, selects actual polypropylene film capacitance and power
Resistive element specification is as shown in table 6 below.Finally constitute and meet that 0.8 rank, the 10 μ F capacitances of this implementation requirements form, actual circuit is such as
Shown in Fig. 5.
R in table 6-0.8 rank capacitance one-port networksiAnd CiPower grade and select device
According to Fig. 6 a, 6b, 7a, 7b, 8a, 8b, due to be respectively adopted in Boost IRF640B and
MUR16200TG is as switching tube and power diode, it is contemplated that the conduction voltage drop and dead resistance resistance value of device, theoretical calculation
As a result it is fitted very well with PSIM simulation results, actual circuit experimental result, illustrates by fractional order capacitance provided by the present invention,
Possess the electrology characteristic of idealized score rank element, can be used in power stage converter.
Embodiment described above is only the preferred embodiments of the invention, and but not intended to limit the scope of the present invention, therefore
The change that all shape, principles according to the present invention are made, should all cover within the scope of the present invention.
Claims (1)
1. a kind of preparation method of 0 to 1 rank power stage fractional order capacity cell, it is characterised in that comprise the following steps：
1) impedance function equation is write according to idealized score rank condensance characteristic, row：
<mrow>
<msub>
<mi>Z</mi>
<mi>C</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mi>&beta;</mi>
</msup>
<mi>C</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, β represents the order of fractional order capacitance, and ω is the work angular frequency of capacitance, and C represents the capacitance of fractional order capacitance；
2) the s domains transmission function of idealized score rank capacitance is write by impedance function, row：
<mrow>
<msub>
<mi>Z</mi>
<mi>C</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mi>s</mi>
<mi>&beta;</mi>
</msup>
<mi>C</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
3) by designing ziAnd pi, approached using following rational approximations function pair s domains transmission function：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>Z</mi>
<mi>C</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mi>s</mi>
<mi>m</mi>
</msup>
<mi>C</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&ap;</mo>
<mfrac>
<mn>1</mn>
<mi>C</mi>
</mfrac>
<munder>
<mi>lim</mi>
<mrow>
<mi>N</mi>
<mo>&RightArrow;</mo>
<mi>&infin;</mi>
</mrow>
</munder>
<mfrac>
<mrow>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>N</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</munderover>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mi>s</mi>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mi>s</mi>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msup>
<mn>10</mn>
<mrow>
<mfrac>
<mi>y</mi>
<mn>10</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mi>i</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&beta;</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mi>i</mi>
<mi>&beta;</mi>
</mfrac>
<mo>+</mo>
<mn>0.5</mn>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<msub>
<mi>&omega;</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msup>
<mn>10</mn>
<mfrac>
<mi>y</mi>
<mrow>
<mn>10</mn>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&beta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</msup>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
The error that y is approximating function with former transmission function on amplitude-versus-frequency curve, β are the orders of fractional order capacitance, ωminFor
The lower limit of the frequency range of involved approximating function；In addition, N is by order β, approximate error y and design in transmission function
Approach frequency band (ωmin, ωmax) determine, expression is：
<mrow>
<mi>N</mi>
<mo>=</mo>
<mn>1</mn>
<mo>+</mo>
<mi>I</mi>
<mi>n</mi>
<mi>t</mi>
<mi>e</mi>
<mi>g</mi>
<mi>e</mi>
<mi>r</mi>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<mi>lg</mi>
<mrow>
<mo>(</mo>
<mfrac>
<msub>
<mi>&omega;</mi>
<mi>max</mi>
</msub>
<msub>
<mi>&omega;</mi>
<mi>min</mi>
</msub>
</mfrac>
<msup>
<mn>10</mn>
<mfrac>
<mrow>
<mn>20</mn>
<mi>&beta;</mi>
</mrow>
<mi>y</mi>
</mfrac>
</msup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>lg</mi>
<mrow>
<mo>(</mo>
<msup>
<mn>10</mn>
<mrow>
<mfrac>
<mi>y</mi>
<mn>10</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>&beta;</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mi>&beta;</mi>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
4) according to the integrated approach of passive one-port RC network, first with zp2tf functions in matlab by zero obtained by step 3)
Limit form rational approximations function is converted to the form of rational fraction, then using residue functions in matlab by reasonable point
The approximating function of formula form carries out residue, is converted into the transmission function of following form：
<mrow>
<msub>
<mi>Z</mi>
<mi>C</mi>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>N</mi>
</munderover>
<mfrac>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
<mrow>
<mi>s</mi>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein KiAnd σiProvided by the zp2tf functions in matlab and residue functions；
5) the residue expression formula according to obtained by step 4), obtains designed fractional order capacity cell and approaches circuit as topology
The Foster I type single port RC networks of structure, i.e. RiWith CiParallel connection forms RiCiUnit, then with Ri+1Ci+1Unit is serially connected,
Wherein value standard is：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&sigma;</mi>
<mi>i</mi>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
6) the fractional order capacitance that step 5) obtains approaches circuit, since RC element circuits parameter differs, for power conversion
When in device, different voltage will be born, the power grade born according to each RC units, and the spy of existing capacitance resistance device
Point, selects actual polypropylene film capacitance and power resistor to be welded, and 0 to 1 required rank power stage fraction is finally made
Rank capacity cell.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610280164.3A CN105790724B (en) | 2016-04-28 | 2016-04-28 | A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610280164.3A CN105790724B (en) | 2016-04-28 | 2016-04-28 | A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105790724A CN105790724A (en) | 2016-07-20 |
| CN105790724B true CN105790724B (en) | 2018-04-13 |
Family
ID=56399164
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610280164.3A Active CN105790724B (en) | 2016-04-28 | 2016-04-28 | A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105790724B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106411291B (en) | 2016-07-31 | 2023-04-07 | 华南理工大学 | High-power adjustable high-frequency fractional order capacitor with order greater than 1 and control method thereof |
| CN109308387B (en) * | 2018-09-12 | 2023-01-31 | 成都师范学院 | Voltage fractional order integral control type memory container |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5889486A (en) * | 1997-09-18 | 1999-03-30 | National Semiconductor Corporation | Split capacitor array for digital-to-analog signal conversion |
| CN103915915A (en) * | 2014-03-31 | 2014-07-09 | 华南理工大学 | Fractional order series resonance wireless power transmission system |
| CN103915910A (en) * | 2014-03-31 | 2014-07-09 | 华南理工大学 | Wireless power transmission system with integral-order parts and fractional-order parts realizing series-parallel resonance |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2014158970A1 (en) * | 2013-03-14 | 2014-10-02 | Saudi Basic Industries Corporation | Fractional order capacitor based on dielectric polymer doped with conductive nano-fillers |
-
2016
- 2016-04-28 CN CN201610280164.3A patent/CN105790724B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5889486A (en) * | 1997-09-18 | 1999-03-30 | National Semiconductor Corporation | Split capacitor array for digital-to-analog signal conversion |
| CN103915915A (en) * | 2014-03-31 | 2014-07-09 | 华南理工大学 | Fractional order series resonance wireless power transmission system |
| CN103915910A (en) * | 2014-03-31 | 2014-07-09 | 华南理工大学 | Wireless power transmission system with integral-order parts and fractional-order parts realizing series-parallel resonance |
Non-Patent Citations (4)
| Title |
|---|
| Power Factor Correction Using Fractional Capacitors;Wajdi Ahmad;《International Symposium on Circuits & Systems》;20031231;第1-3页 * |
| 分数阶并联RLαCβ电路;刁利杰等;《物理学报》;20141231;第1-13 * |
| 含分数阶电抗元件网络的灵敏度分析;马龙等;《华北电力大学学报》;20130531;第1-5页 * |
| 电感电流伪连续模式下Boost变换器的分数阶建模与分析;谭程等;《物理学报》;20141231;第1-10页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105790724A (en) | 2016-07-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Qin et al. | Generalized average modeling of dual active bridge DC–DC converter | |
| Jamil et al. | Analysis, Design and Implementation of Zero-Current-Switching Resonant Converter DC-DC Buck Converter | |
| CN110518801B (en) | Small signal modeling method for double-active full-bridge converter under double phase-shift modulation | |
| CN105119322B (en) | A kind of control method for improving grid-connected voltage source type inverter system stability | |
| CN206962700U (en) | Buck converter load current detection circuits without external sampling resistance | |
| CN105790724B (en) | A kind of preparation method of 0 to 1 rank power stage fractional order capacity cell | |
| Ayachit et al. | Steady-state and small-signal analysis of a-source converter | |
| CN204333898U (en) | A kind of convertible frequency air-conditioner and Intelligent Power Module overcurrent protection Circuit tuning thereof | |
| Krismer et al. | Accurate small-signal model for an automotive bidirectional dual active bridge converter | |
| Zhu et al. | Dynamic modeling of a hybrid switched-capacitor-based converter with phase-shift control | |
| Bahravar et al. | Mathematical modeling and transient analysis of dc-dc buck-boost converter in CCM | |
| CN106026650A (en) | Offset voltage eliminating circuit | |
| CN103701464B (en) | Fractional order element converter | |
| CN109672212A (en) | LCL gird-connected inverter current inner loop full-order sliding mode dummy control method | |
| CN106301038A (en) | The control circuit of a kind of Switching Power Supply fixed frequency and control method | |
| Ragusa et al. | High frequency modelling method of EMI filters for hybrid Si-SiC matrix converters in aerospace applications | |
| Akbarabadi et al. | Numerical average value modeling of second order flyback converter in both operational modes | |
| Wang et al. | Stability evaluation of power hardware-in-the-loop simulation for dc system | |
| Seo et al. | Small-signal analysis of S-hybrid step-down DC-DC converter | |
| CN110543703B (en) | Quasi-resonant converter modeling analysis method considering different time scales | |
| Vosters et al. | Energy and impedance space modeling of power electronic converters | |
| Zhang et al. | Using RC type damping to eliminate right-half-plane zeros in high step-up DC-DC converter with diode-capacitor network | |
| Arena et al. | A Cost-Effective Hardware in the Loop Implementation of Dual Active Bridge for Fast Prototyping of Electric Vehicles Charging Controls | |
| Lin et al. | Impact of the cascaded dc-dc converter on the dq impedance of a pfc converter | |
| Khan et al. | Model order reduction of power electronic circuits |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |