CN101029914A - Method for measuring iron-core parameter, designing transformer iron-core parameter and coil parameter by frequency impedance - Google Patents
Method for measuring iron-core parameter, designing transformer iron-core parameter and coil parameter by frequency impedance Download PDFInfo
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Abstract
A method of utilizing resistance-frequency relation to measure parameter of iron core includes using five parameters to express parameters of iron core and three parameters as coil parameters, utilizing mathematical relation to link iron core parameters and coil parameters as well as electric parameters together to form resistance-frequency relation of transformer no-load to transformer on-load and making energy converted resistance expressed by resistance-frequency relation be in according with ohm law.
Description
Technical field
Electricity
Technical background
Existing design of transformer method is based on traditional Theory of Electromagnetic Field, with magnetic field intensity as the iron core parameter, with the coil total number of turns as coil parameter, form computing formula with iron core parameter, coil parameter and voltage, but, the method for designing computational accuracy of existing transformer is low, the design transformer mainly relies on experiment to carry out, not only the design cycle grows up to this height in the product design of being undertaken by experiment, and design level accumulates the product design of carrying out by technical experience and is difficult to make the parameter of product design to reach best mainly by the accumulation of technical experience.
The list of references of relevant existing transformer technology has: " electronic transformer handbook, " power transformer handbook.The design of transformer handbook is the authoritative reference book of existing design of transformer technology.
The difference of the inventive method and traditional transformer method for designing is: this method no longer adopts traditional Theory of Electromagnetic Field, the energy conversion that transformer carried out is defined as the conversion of energy of a charge between coil and the iron core, and the conversion of energy of a charge is defined as the electrical phenomena that meets Ohm law.Among the present invention, is the iron core parameter-definition five parameters, coil parameter is defined as three parameters, the coil of coiling in the same way is divided into two different coefficients with the coil of oppositely coiling with a function region, iron core parameter and coil parameter are connected the frequency impedance that forms resistance and frequency by mathematical relation, the energy conversion resistance of expressing with frequency impedance meets Ohm law, the power of the relationship expression energy conversion of the voltage in the usefulness Ohm law, electric current, resistance.Design according to the power relation of the expressed energy conversion of Ohm law iron core parameter and coil parameter transformer.
List of references related to the present invention has " design and production method that reduces transformer loss and volume ", number of patent application: 2003101166612
Technical advance
This method is compared its technical advance with traditional design of transformer method: the method that five iron core parameters that define among the present invention can enough Physical Experiments is measured exactly, and the material of iron core is identical, physical form, five parameters of iron core were identical when physical size was identical.Unloaded frequency impedance and the load frequency impedance set up by iron core parameter, coil parameter and electrical quantity meet Ohm law.Frequency impedance during according to unloaded and load, can enough mathematical methods directly carry out high-precision transformer parameters designing, utilize computing machine can design thousands of kinds of schemes in a short period of time and optimize preferred plan, remove a large amount of experiments that traditional transformer when design institute must carry out from, surmounted the highest level that technical experience accumulates in the existing design of transformer technology.
Goal of the invention
The objective of the invention is: a plurality of parameters of definition iron core, set up the method and parameter computing method of measuring the iron core parameter, set up the frequency impedance of the energy conversion that meets Ohm law of iron core parameter and coil parameter co expression, set up the method for designing of transformer core parameter and coil parameter again with frequency impedance.
Technical scheme
The inventive method no longer designs transformer with magnetic field theory, it is characterized in that: the energy conversion that transformer carried out is defined as the conversion of energy of a charge between coil and the iron core, the energy conversion of carrying out between coil and the iron core is expressed with energy conversion resistance, use Rk, A, B, K, five parameters of N0 are as the iron core parameter, use N, S, three parameters of M are as coil parameter, coil to coiling in the same way is distinguished into two different coefficients with the coil of oppositely coiling with function F (α), the LC that the main coil shnt capacitor forms during with zero load relation in parallel is as basic model, iron core parameter and coil parameter are connected by mathematical relation, form the energy conversion resistance and the frequency impedance of frequency of operation when unloaded, the frequency impedance during zero load is 4 * C * f * Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1 can not form the AC transformer of LC relation in parallel frequency impedance when unloaded and be Rk/R0 * { K+A * Cos[B/ (4 * R0 * f)] } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1, the expressed energy conversion resistance of frequency impedance when frequency impedance when unloaded and load meets Ohm law, the iron core parameter can be measured and calculate to unloaded frequency impedance according to LC relation in parallel, frequency impedance during according to zero load can calculate the minimum output resistance of secondary coil, energy conversion resistance when frequency impedance can calculate idling frequency during according to zero load, energy conversion resistance and energy exchange electric current and voltage conforms Ohm law.Frequency impedance during with load is set up frequency impedance the getting in touch between the two when unloaded, and the frequency impedance of the transformer of shnt capacitor when load has the frequency impedance of the unidirectional accelerating potential of complete period load, the frequency impedance of the two-way accelerating potential of complete period load, the frequency impedance of the unidirectional accelerating potential of semiperiod load, the frequency impedance of the two-way accelerating potential of semiperiod load.A frequency impedance is arranged during the AC transformer load.The frequency impedance design of frequency impedance during according to load when unloaded LC is in parallel when concerning the transformer fixed frequency iron core parameter and coil parameter, design process is that the Frequency point of transformer rated power is decided to be changeless Frequency point, idling frequency point all departs from the fixed rate Frequency point with the maximum load Frequency point, equivalent resistance according to energy conversion resistance and pull-up resistor is selected Frequency point, or select the equivalent resistance of energy conversion resistance and pull-up resistor according to Frequency point, by energy conversion resistance and equivalent resistance iron core parameter and coil parameter are designed; Concern that by the LC of fixed frequency point design transformer can realize with dynamic frequency work by circuit; Iron core parameter and coil parameter when the frequency impedance of the frequency impedance during according to load when unloaded can be to the AC transformer fixed frequency design; Frequency impedance when frequency impedance during according to load and zero load can design the iron core parameter and the coil parameter of electronic transformer.
Be more convenient for understanding for instructions, technical scheme is divided into inventive principle and two parts of method for designing are write.
Inventive principle
One, definition energy conversion impedance
Energy conversion device by coil and iron core are formed just forms LC relation in parallel at the coil port shnt capacitor.Apply back-lash voltage at the main coil port, just can form an oscillating voltage, oscillating voltage can form maximum voltage resonance point at some Frequency points, and the resistance of tuning-points is energy conversion resistance.
(1) capacitor and iron core carried out the process of energy conversion mutually during the LC parallel connection concerned:
(1) starts acceleration.
When back-lash voltage is applied to the main coil port, electric current passes through main coil, electric current by main coil quickens the moving charge in the iron core, to be energy be transformed into process in the iron core by coil to the process of quickening, if: the interior accelerating potential of coil this moment is a forward voltage, and the direction of motion of the electric charge that is accelerated in the iron core is the A direction.Have only coil when the energy of iron core internal conversion surpasses the ultimate value that can hold energy in the iron core, just can't quicken the energy in the iron core again.When the back-lash voltage that do not break during the value of reaching capacity of the accelerated charge energy in the iron core stops the electric charge in the iron core is quickened, and the energy in the capacitor continues by coil the moving charge in the iron core to be quickened, and stops the moving charge in the iron core is quickened when the forward voltage of main coil port is zero.
(2) electric charge by the motion of A direction quickens the moving charge in the coil in the iron core.
When the forward voltage in the capacitor is zero, the electric charge of pressing the motion of A direction in the iron core quickens the moving charge in the coil, the energy of a charge that is accelerated in the coil is transferred to store in the capacitor and is got up to form the reciprocal capacitance voltage opposite with the forward voltage direction, the energy of a charge that moves by the A direction in iron core stops when being zero the electric charge in the coil is quickened, and the amplitude of the interior reverse voltage of capacitor this moment is a maximum.
(3) reverse voltage in the capacitor quickens the moving charge in the iron core.
When the electric charge in the iron core does not have energy, reverse voltage in the capacitor quickens the moving charge in the iron core by coil again, the charge movement direction that is accelerated in the iron core is opposite with the A direction, if: the direction of motion of the moving charge in the iron core is the B direction, stops the moving charge in the iron core is quickened when then the reverse voltage of accelerator in capacitor is zero.
(4) electric charge by the motion of B direction quickens the electric charge in the coil in the iron core.
When the reverse voltage of capacitor is zero, the electric charge of pressing the motion of B direction in the iron core quickens the moving charge in the coil, the energy of a charge that is accelerated in the coil is transferred to store in the capacitor and is got up to form forward voltage, the energy of a charge that moves by the B direction in iron core stops when being zero the electric charge in the coil is quickened, and the amplitude of the interior forward voltage of capacitor this moment is a maximum.In this process, can apply the impressed voltage makeup energy to the main coil port.
(5) forward voltage of capacitor quickens the moving charge in the iron core.
When the energy of a charge that moves by the B direction in the iron core is zero, the forward voltage of capacitor quickens the moving charge in the iron core, acceleration direction is A, and the direction of motion of electric charge is A in the iron core, quickens by the electric charge of A direction motion in stopping iron core when the forward voltage of capacitor is zero.
(6) in the LC relation in parallel, energy in the capacitor quickens by the moving charge of coil in iron core, moving charge in the iron core quickens the moving charge in the coil, repeating above-mentioned (2), (3), (4), (5) described process repeatedly, such circulation has repeatedly just formed the LC oscillating voltage.
Above-mentioned four conversion process of energy have formed a work period, and per two conversion process of energy form the work period half.In the iron core by the electric charge of A direction motion to the moving charge in the coil quicken with capacitor in reverse voltage two negative half periods that process is a waveform that the moving charge in the iron core is quickened, be the positive half cycle of a waveform to the forward voltage that the electric charge in the coil quickens with capacitor to two processes that the moving charge in the iron core quickens by the electric charge of B direction motion in the iron core.
Four conversion process of energy of an above-mentioned work period have two assumed conditions.Assumed condition one is that iron core and capacitor self do not have energy loss, thereby the transformer of iron core and coil composition can not have energy output.Assumed condition two is that capacitor equals iron core to the energy of moving charge acceleration in the coil and the time of acceleration by coil to the energy of the acceleration of the moving charge in the iron core and the time of acceleration.
(2) definition energy conversion impedance
When zero load, there are two conversion process of energy per half work period, and two energy conversion resistance are arranged in two conversion process of energy, and two energy conversion resistance can be unequal, when two energy conversion resistance all are minimum value and when equal, be defined as the energy conversion resistance of coil and iron core.Because energy conversion resistance be that the energy of hour conversion is for maximum, so the energy conversion voltage that is formed by energy conversion resistance is maximum.Because what iron core and coil were used when carrying out a conversion process of energy is that energy is expressed, the energy of unit interval is exactly a power, thereby can express its voltage, electric current, the relation of resistance with Ohm law, must relate to frequency of operation when expressing with Ohm law, therefore, the energy conversion relation of iron core and coil is exactly a frequency impedance in the transformer.
In the conversion process of energy of transformer, the frequency impedance mathematics of the frequency impedance during load when unloaded is relevant, and the frequency impedance during zero load is the basic frequency impedance of transformer.
The definition of energy conversion resistance: when the no-load transformer work of LC relation in parallel, per half work period inner capacitor and iron core carry out the primary energy conversion mutually by main coil, capacitor energy converts iron core energy and iron core energy to by main coil, and to convert capacitor energy to by main coil be two conversion process of energy, two conversion process of energy have two energy conversion resistance, two energy conversion resistance all is minimum value and is the resistance that iron core and coil carry out energy conversion when equal, energy conversion resistance is that the condition of definite value is and frequency dependence, for the energy conversion resistance of definite value meets Ohm law.
If: when the energy in the coil when iron core is changed, the electric current by coil is I, the voltage of formation is U, the resistance of energy conversion is R0, is known by Ohm law: U=I * R0
In like manner, when the energy in the iron core when coil is changed, the voltage that forms on coil is U, transimpedence is R, then the electric current in the coil is I, has: U=I * R0
Two, the current relationship in the conversion process of energy
Capacitor in the LC relation in parallel and iron core whenever carry out an energy conversion cycle will be through four conversion process of energy, and each conversion process of energy equals the four/one-period in an oscillating voltage cycle.
If: the capacitor volume value is C, and the quantity of electric charge of acceleration is Q, and the peak value of oscillating voltage is U, has
Q＝C×U
Q/dt＝C×U/dt
I＝C×U/dt
As dt=1/4 * T, during T=1/f, have:
I＝4×C×U×f
...............(1)
Electric current in the following formula is the electric current that carries out energy exchange mutually between capacitor and the iron core in the LC relation in parallel.
Three, the frequency impedance of energy conversion in the LC relation in parallel
(1) any one iron core can both be used a plurality of parameter-definitions, and after physical property, physical form, the physical size of iron core were determined, the iron core parameter of definition was an invariant parameter.Therefore, different iron cores, when the material character of iron core, physical form, when physical size is identical, the parameter of iron core is identical; When the material character of iron core, physical form, when physical size is inequality, iron core parameter inequality.
The definition of iron core parameter: Rk, A, B, K, N0 are five parameters of iron core.Wherein, Rk is the resistance coefficient of single-turn circular coil energy conversion, the intensity when A expresses energy conversion, and B expresses the ratio of electric capacity (or electric current) in mathematical relation, and K expresses the curve location of A, the formation of B parameter, and N0 expresses the number of turn coefficient of every layer line circle.
(2) quantity of the number of plies of the number of turn of every layer line circle, coil, bridging coil is three parameters of coil, is made of the frequency impedance of energy conversion jointly three coil parameters and iron core parameter.
The coil parameter definition: N, S, M are three parameters of coil, and wherein, N is the equivalent number of turn of every layer line circle, and S is the coil number of plies, and M is the quantity of bridging coil.
(3) mathematical relation of energy conversion resistance
Energy conversion resistance and iron core parameter correlation in the LC relation in parallel are relevant with coil parameter.If: R0 is the all-in resistance of energy conversion, and its funtcional relationship is:
R0＝F(K，A，B，C，Rk，N0，N，S，M)
...............(2)
R0 be expressed as Rk and function F (K, A, B, C) and function (N, S, M, product N0) has:
R0＝Rk×F(K，A，B，C)×F(N，S，M，N0)
...............(3)
Know by (1) formula: 4 * C * f=1/R0
Have: 4 * C * f * Rk * F (K, A, B, C) * F (N, S, M, N0)=1
...............(4)
The mathematical relation F of four iron core parameters (K, A, B, C)
Empirical formula is:
F(K，A，B，C)＝K+A×Cos(B×C)
...............(5)
(5) formula substitution (4) formula has:
4×C×f×Rk×[K+A×Cos(B×C)]×F(N，S，M，N0)＝1
...............(6)
(5) formula substitution (3) formula gets:
R0＝Rk×[K+A×Cos(B×C)]×F(N，S，M，N0)
...............(7)
The mathematical relation of five coil parameters
F (N, S, M, N0) quantity, the number of plies with the coiling mode of coil and bridging coil is relevant, and different coiling modes have different mathematical expressions.
(1) single layer coil
The empirical formula of single layer coil is:
F(N，S，M，N0)＝N±M
1/M×(N/N0)
1.5×M
...............(8)
(8) formula substitution (6) has:
4×C×f×Rk×[K+A×Cos(B×C)]×[N±M
1/M×(N/N0)
1.5×M]＝1
...............(9)
(9) in the formula, when N＞N0, get positive sign, have:
4×C×f×Rk×[K+A×Cos(B×C)]×[N+M
1/M×(N/N0)
1.5×M]＝1
...............(10)
(9) in the formula, when N≤N0, get negative sign, have:
4×C×f×Rk×[K+A×Cos(B×C)]×[N-M
1/M×(N/N0)
1.5×M]＝1
...............(11)
(2) multilayer coiling in the same way
Be coiling in the same way when the coil winding direction of adjacent layer is identical.For example: the starting point of ground floor coil is b for a terminal point, folds to a point from the b point with shortest path, and the starting point of second layer coil still is a, and terminal point still is b, and the like, the starting point of each layer line circle is a, and terminal point is b, and the Origin And Destination of each layer line circle is all identical.In the same way during coiling, the coil in the different coil layer is identical at the lip-deep projecting direction of iron core at lattice coil.
When coil had the S layer, the number of turn of every layer line circle was respectively N1, N2, and N3...Ni...Ns, the equivalent number of turn of every layer line circle is N, empirical formula is:
N＝(N1×N2×N3×...Ni...×Ns)
1/s
F(N，S，M，N0)＝[N±M
1/M×(Ns/N0)
1.5×M]×S
...............(12)
(12) formula substitution (6) has:
N＝(N1×N2×N3×...Ni...×Ns)
1/s
4×C×f×Rk×[K+A×Cos(B×C)]×[N±M
1/M×(Ns/N0)
1.5×M]×S＝1
...............(13)
(3) the reverse coiling of multilayer
The coil winding direction of adjacent layer is reverse coiling when opposite.For example: the starting point of ground floor coil is b for a terminal point, and the starting point of second layer coil is a for the b terminal point, and the 3rd layer starting point is b for a terminal point, and the like, the terminal point of two adjacent layer coil last layer coils is the starting point of next layer line circle.
The reverse coiling of lattice coil is with the difference of coiling in the same way, in the same way during coiling between layer and the layer coil move towards identical, oppositely during coiling layer with layer between coil move towards to have an angle.Since during the reverse coiling of coil between layer and the layer coil move towards to have angle, so the adjacent layer coil has angle in the lip-deep projected angle trend of iron core, the adjacent layer coil is inequality to the acceleration direction of moving charge in the iron core, the direction of motion that is accelerated electric charge in the iron core is the direction of closing of all coils layer acceleration direction, obviously, project to the lip-deep angle that moves towards of iron core between coil layer and the layer and affect energy conversion resistance between iron core and coil, and projected angle is determined by coil diameter and coil quantity.
If: the width of coil layer is L1, and it is L2 that every circle coil projects to the lip-deep length of iron core, and its empirical formula is:
F(α)＝1/[1-N
1/2÷M×L1/N/L2]
＝1/[1-L1÷(M×N
1/2×L2)]
...............(14)
4×C×f×Rk×[K+A×Cos(B×C)]×[N±M
1/M×(Ns/N0)
1.5×M]×S/[1-L1÷(M×N
1/2×L2)]＝1
...............(15)
The general formula of frequency impedance during six zero loads
4×C×f×Rk×[K+A×Cos(B×C)]×[N±M
1/M×(Ns/N0)
1.5×M]×S×F(α)＝1
...............(16)
(16) formula substitution (3) formula:
R0＝Rk×[K+A×Cos(B×C)]×[N±M
1/M×(Ns/N0)
1.5×M]×S×F(α)
...............(17)
The scope and the condition of parameter in the resistance frequency general formula:
(1) in general formula, as coil F (α)=1 during, F when coil is reverse coiling (α)=1/[1-L1 ÷ (M * N for coiling in the same way
1/2* L2)]
(2) in N＞N0 up-to-date style ± symbol gets positive sign, in N≤N0 up-to-date style ± symbol gets negative sign.
(3) parallel connection in the coil only refers to the parallel connection of lead in same layer line circle, when coil is individual layer, the coiling in parallel of M root lead is arranged that is:; When coil has the S layer, in each layer the parallel connection of M root lead is arranged all; Has only lead situation in parallel that just is suitable in the above-mentioned formula in parallel in layer.To not produce effect in parallel if carry out layer with layer is in parallel, thereby also just can not calculate by parallel connection, for example, ground floor is with a lead coiling N circle, and the second layer, the 3rd layer are when the S layer all carries out identical coiling with ground floor, and the effect of M layer parallel connection is identical with the effect of one deck coil, can only be by non-in parallel calculating of single layer coil, and when identical S layer line circle carried out layer parallel connection, effect in parallel between random layer was identical with the effect of any one deck.
(4) when with M root lead parallel connection coiling, when impressed voltage is connected to the main coil port, all connect identical with its effect of a part of lead that connects wherein by parallel way.For example, by the coil of parallel way coiling, it is identical all to connect three a leads and connection lead or the effect of two leads wherein with three leads.
(5) be zero load when secondary coil does not have power output, the quantity of secondary coil and the number of turn of secondary coil do not exert an influence to the main coil calculation of parameter when unloaded.
(6) B * C is an angle value, and the scope of B * C is: π/4＜B * C＜π goes beyond the scope and can not calculate with above-mentioned general formula.
B * C should be in π/4 between the π and will approach π.As B * C during greater than π, duty is a state of saturation, and except special transformer need use the state of saturation, general transformer should not use state of saturation work.As B * C during less than π/4, the utilization ratio of iron core and coil is low.
(7) revisal o'clock can be calculated in B * C＜π/4.(B * C) is a cosine curve to K+A * Cos, and cosine curve has a flex point and tangent line value that variation has taken place in the time of 45 °, and as B * C during less than 45 °, curve gives revisal by experiment.
Carry out the method for revisal.With A * Ctg (B * C) replace A * Cos (B * C), with straight line y (x) to A * Ctg (B * C) carry out curvilinear translation, formula is: F (K, A, B, C)=K+y (x)+A * Ctg (B * C)
Being X-axis, be in the plane coordinate system of Y-axis among the y (x) with modified value y (x) with B * C.Y (x) method by experiment can be determined.
(8) when B * C＞π F (B C) is an asymptotic line for K, A, and the physical form of every kind of core material determines that its asymptotic line of back is unique, can method by experiment determine the value of the approximate Calculation of Asymptotes F of replacement of straight line (C).
Experiment and subordinate list explanation when seven LC relation in parallel is unloaded
Experimental technique: secondary coil does not have load, main coil with transformer is in parallel with electric capacity, apply square wave with signal source to main coil, use oscilloscope measurement, some when power taking pressure amplitude degree is maximum is a data point, the frequency values f of image data point and capacitance C, wherein, as long as the driving force of signal source satisfies the requirement of vibration, the square wave amplitude size that signal source applies is to not influence of experimental result.If the driving force of signal source can not satisfy the requirement of vibration, should adopt switching tube that square wave is carried out power amplification.
When utilizing frequency impedance to measure the iron core parameter, the back-lash voltage that applies to main coil must be a square-wave voltage, and the definition square wave is for measuring the reference waveform of iron core parameter.
The mathematics calculation method: to a kind of core material, K, A, B are constant value.When the shape of iron core and physical size were constant, the value of Rk, N0 also was a constant value.Mathematical solution resolves above-mentioned five constant values at last.
Know by (6) formula, 4 * C * f * Rk * [K+A * Cos (B * C)] * F (N, S, M, N0)=1, when the coil parameter of same iron core is constant, change capacitance after frequency values will change, and F (M N0) but can not change for N, S, has:
C1/C2×f1/f2×[K+A×Cos(B×C1)]/[K+A×Cos(B×C2)]＝1
C1/C3×f1/f3×[K+A×Cos(B×C1)]/[K+A×Cos(B×C3)]＝1
C2/C3×f2/f3×[K+A×Cos(B×C2)]/[K+A×Cos(B×C3)]＝1
Order: a11=C1/C2 * f1/f2 * [K+A * Cos (B * C1)]/[K+A * Cos (B * C2)]
a13＝C1/C3×f1/f3×[K+A×Cos(B×C1)]/[K+A×Cos(B×C3)]
a23＝C2/C3×f2/f3×[K+A×Cos(B×C2)]/[K+A×Cos(B×C3)]
By finding the solution a11
2+ a13
2+ a23
2Minimum value can obtain the mathematical solution of K, A, B.After K, A, B obtained, N0, Rk just can directly resolve out.
Experimental data and result of calculation are listed with the form of form, and in the tables of data, M is the quantity of the parallel conducting wire of coil, N is an individual layer equivalent coil quantity, and S is the coil number of plies, and D is a diameter of wire, C is the capacitor volume value, and f is a survey frequency, and Rk is a calculation result data.
(1) iron core is a Ferrite Material, and core configuration is an annular, annular external diameter Φ=43mm.
In the table one, experimental data and result of calculation: K=1 A=0.340857 B=10.22761 * 10
6N0=27.6
The 1st to the 63rd, the mean value of Rk is: Rk=7.763274, the middle error relative value of Rk is: MM/Rk=7.3/1000
The value of B * C is less than π/4 in the 64th 65, and needing by experiment, curve gives revisal.
Attached: table one
| Sequence number | M | N | D | C(μF) | f(Hz) | R0(Ω) | Average |
| 1 | 1 | 65 | 0.64 | 0.325 | 2064 | 8.078613 | 7.819529 |
| 2 | 1 | 65 | 0.64 | 0.208 | 2709 | 7.812372 | |
| 3 | 1 | 65 | 0.64 | 0.095 | 4222 | 7.567602 | |
| 4 | 1 | 62 | 0.64 | 0.325 | 2220 | 7.885432 | 7.8787 |
| 5 | 1 | 62 | 0.64 | 0.208 | 2781 | 7.98956 | |
| 6 | 1 | 62 | 0.64 | 0.095 | 4322 | 7.761107 | |
| 7 | 1 | 57 | 0.64 | 0.325 | 2328 | 8.199082 | 7.926961 |
| 8 | 1 | 57 | 0.64 | 0.208 | 3047 | 7.950989 | |
| 9 | 1 | 57 | 0.64 | 0.095 | 4793 | 7.630812 | |
| 10 | 1 | 54 | 0.64 | 0.325 | 2647 | 7.623084 | 7.505781 |
| 11 | 1 | 54 | 0.64 | 0.208 | 3397 | 7.539361 | |
| 12 | 1 | 54 | 0.64 | 0.095 | 5257 | 7.354898 | |
| 13 | 1 | 51 | 0.64 | 0.325 | 2661 | 8.041521 | 8.014266 |
| 14 | 1 | 51 | 0.64 | 0.208 | 3403 | 7.978825 | |
| 15 | 1 | 51 | 0.64 | 0.095 | 5111 | 8.022453 | |
| 16 | 1 | 46 | 0.64 | 0.325 | 3111 | 7.6466 | 7.683593 |
| 17 | 1 | 46 | 0.64 | 0.208 | 3954 | 7.636197 | |
| 18 | 1 | 46 | 0.64 | 0.095 | 5868 | 7.767982 | |
| 19 | 1 | 41 | 0.64 | 0.325 | 3376 | 7.928335 | 7.864943 |
| 20 | 1 | 41 | 0.64 | 0.208 | 4356 | 7.799055 | |
| 21 | 1 | 41 | 0.64 | 0.095 | 6519 | 7.86744 | |
| 22 | 1 | 37 | 0.64 | 0.325 | 3890 | 7.643092 | 7.695257 |
| 23 | 1 | 37 | 0.64 | 0.208 | 4875 | 7.740864 | |
| 24 | 1 | 37 | 0.64 | 0.095 | 7397 | 7.701844 | |
| 25 | 1 | 33 | 0.64 | 0.325 | 4388 | 7.616464 | 7.573 |
| 26 | 1 | 33 | 0.64 | 0.208 | 5614 | 7.556017 | |
| 27 | 1 | 33 | 0.64 | 0.095 | 8486 | 7.546523 |
| 28 | 1 | 28 | 0.64 | 0.325 | 5056 | 7.817446 | 7.883013 |
| 29 | 1 | 28 | 0.64 | 0.208 | 6302 | 7.960474 | |
| 30 | 1 | 28 | 0.64 | 0.095 | 9622 | 7.817446 | |
| 31 | 1 | 23 | 0.64 | 0.325 | 6534 | 7.392065 | 7.392065 |
| 32 | 1 | 23 | 0.64 | 0.208 | 8020 | 7.643917 | |
| 33 | 1 | 23 | 0.64 | 0.095 | 12222 | 7.572383 | |
| 34 | 1 | 18 | 0.64 | 0.325 | 8162 | 8.12275 | 8.102578 |
| 35 | 1 | 18 | 0.64 | 0.208 | 10256 | 8.204782 | |
| 36 | 1 | 18 | 0.64 | 0.095 | 15919 | 7.980202 | |
| 37 | 1 | 13 | 0.64 | 0.325 | 11800 | 7.738918 | 7.69043 |
| 38 | 1 | 13 | 0.64 | 0.208 | 15083 | 7.684577 | |
| 39 | 1 | 13 | 0.64 | 0.095 | 22880 | 7.647795 | |
| 40 | 1 | 9 | 0.64 | 0.325 | 17435 | 7.52055 | 7.59205 |
| 41 | 1 | 9 | 0.64 | 0.208 | 21800 | 7.642027 | |
| 42 | 1 | 9 | 0.64 | 0.095 | 33034 | 7.613573 | |
| 43 | 1 | 4 | 0.64 | 0.325 | 40559 | 7.222679 | 7.69043 |
| 44 | 1 | 4 | 0.64 | 0.208 | 51428 | 7.229884 | |
| 45 | 1 | 4 | 0.64 | 0.095 | 80203 | 6.998821 | |
| 46 | 1 | 29 | 0.34 | 0.325 | 4834 | 7.888885 | 7.710336 |
| 47 | 1 | 29 | 0.34 | 0.208 | 6218 | 7.784253 | |
| 48 | 1 | 29 | 0.34 | 0.095 | 9798 | 7.45787 | |
| 49 | 1 | 19 | 0.34 | 0.325 | 7630 | 8.239654 | 8.240059 |
| 50 | 1 | 19 | 0.34 | 0.208 | 9587 | 8.323312 | |
| 51 | 1 | 19 | 0.34 | 0.095 | 14786 | 8.157212 | |
| 52 | 1 | 9 | 0.34 | 0.325 | 17379 | 7.552572 | 7.504393 |
| 53 | 1 | 9 | 0.34 | 0.208 | 22095 | 7.539996 | |
| 54 | 1 | 9 | 0.34 | 0.095 | 33893 | 7.420611 | |
| 55 | 2 | 30 | 0.64 | 0.327 | 4650 | 7.87035 | 7.855779 |
| 56 | 2 | 30 | 0.64 | 0.21 | 5899 | 7.847794 | |
| 57 | 2 | 30 | 0.64 | 0.0962 | 8878 | 7.848739 | |
| 58 | 3 | 10 | 0.64 | 0.325 | 15597 | 7.420021 | 7.391339 |
| 59 | 3 | 10 | 0.64 | 0.208 | 19897 | 7.38251 | |
| 60 | 3 | 10 | 0.64 | 0.095 | 30083 | 7.37148 | |
| 61 | 4 | 15 | 0.34 | 0.325 | 10114 | 7.626508 | |
| 62 | 4 | 15 | 0.34 | 0.208 | 12864 | 7.610585 |
| 63 | 4 | 15 | 0.34 | 0.095 | 19405 | 7.616668 | 7.61692 |
| 64 | 4 | 30 | 0.64 | 0.0457 | 14939 | 9.032027 | |
| 65 | 4 | 30 | 0.64 | 0.0211 | 21921 | 13.04643 |
(2) iron core is a Ferrite Material, is shaped as a jar shape, magnetic jar external diameter Φ=43mm.Coil is a multilayer in the same way in the coiling table two, experimental data and result of calculation: K=1 A=0.356 B=10.22761 * 10
6The mean value of N0=17Rk: middle relatively error: the M/Rk=3.33/1000 of Rk=9.762154 Rk
Attached: table two
| Sequence number | M | N | S | The line footpath | C(μF) | f(Hz) | R0(Ω) | Mean value | Remarks |
| 1 | 3 | 9 | 1 | 0.36 | 0.325 | 13650 | 9.673676 | 9.733415 | |
| 2 | 3 | 9 | 1 | 0.36 | 0.208 | 16919 | 9.816835 | ||
| 3 | 3 | 9 | 1 | 0.36 | 0.095 | 25230 | 9.736651 | ||
| 4 | 3 | 10 | 2 | 0.36 | 0.325 | 6563 | 9.652624 | 9.763415 | |
| 5 | 3 | 10 | 2 | 0.36 | 0.208 | 8206 | 9.647513 | ||
| 6 | 3 | 10 | 2 | 0.36 | 0.095 | 12091 | 9.684236 | ||
| 7 | 3 | 9 | 3 | 0.36 | 0.325 | 4398 | 9.722537 | 9.753206 | |
| 8 | 3 | 9 | 3 | 0.36 | 0.208 | 5487 | 9.738654 | ||
| 9 | 3 | 9 | 3 | 0.36 | 0.095 | 8066 | 9.798428 | ||
| 10 | 3 | 9 | 4 | 0.36 | 0.325 | 3377 | 9.581013 | 9.624511 | |
| 11 | 3 | 9 | 4 | 0.36 | 0.208 | 4216 | 9.590514 | ||
| 12 | 3 | 9 | 4 | 0.36 | 0.095 | 6164 | 9.701983 | ||
| 13 | 3 | 8 | 5 | 0.36 | 0.325 | 2678 | 9.912949 | 10.00036 | |
| 14 | 3 | 8 | 5 | 0.36 | 0.208 | 3332 | 9.956519 | ||
| 15 | 3 | 8 | 5 | 0.36 | 0.095 | 4943 | 10.13162 | ||
| 16 | 3 | 9 | 6 | 0.36 | 0.325 | 2283 | 9.722937 | 9.856355 | |
| 17 | 3 | 9 | 6 | 0.36 | 0.208 | 2832 | 9.795107 | ||
| 18 | 3 | 9 | 6 | 0.36 | 0.095 | 4082 | 10.05102 | ||
| 19 | 3 | 9 | 7 | 0.36 | 0.325 | 1953 | 9.739231 | 9.952647 | |
| 20 | 3 | 9 | 7 | 0.36 | 0.208 | 2410 | 9.862998 | ||
| 21 | 3 | 9 | 7 | 0.36 | 0.095 | 3428 | 10.25571 | ||
| 22 | 3 | 8 | 8 | 0.36 | 0.325 | 1724 | 9.758395 | 9.999507 | |
| 23 | 3 | 8 | 8 | 0.36 | 0.208 | 2135 | 9.847294 | ||
| 24 | 3 | 8 | 8 | 0.36 | 0.095 | 2992 | 10.39283 | ||
| 25 | 2 | 9 | 4 | 0.64 | 0.325 | 3373 | 9.993566 | 9.98648 | |
| 26 | 2 | 9 | 4 | 0.64 | 0.208 | 4217 | 9.989236 | ||
| 27 | 2 | 9 | 4 | 0.64 | 0.095 | 6245 | 9.976636 | ||
| 28 | 2 | 9 | 3 | 0.64 | 0.325 | 4729 | 9.460446 | 9.523126 | |
| 29 | 2 | 9 | 3 | 0.64 | 0.208 | 5923 | 9.510502 | ||
| 30 | 2 | 9 | 3 | 0.64 | 0.095 | 8669 | 9.582664 | ||
| 31 | 1 | 17 | 3 | 0.64 | 0.325 | 2320 | 9.460446 | ||
| 32 | 1 | 17 | 3 | 0.64 | 0.208 | 2884 | 9.510502 |
| 33 | 1 | 17 | 3 | 0.64 | 0.095 | 4150 | 9.775327 | 9.582091 | |
| 34 | 1 | 16 | 4 | 0.64 | 0.325 | 1980 | 9.592615 | 9.505218 | |
| 35 | 1 | 16 | 4 | 0.64 | 0.208 | 2444 | 9.719232 | ||
| 36 | 1 | 16 | 4 | 0.64 | 0.095 | 3821 | 9.203804 | ||
| 37 | 1 | 16 | 3 | 0.64 | 0.325 | 2630 | 9.723668 | 9.838913 | |
| 38 | 1 | 16 | 3 | 0.64 | 0.208 | 3268 | 9.795725 | ||
| 39 | 1 | 16 | 3 | 0.64 | 0.095 | 4745 | 9.988347 | ||
| 40 | 1 | 16 | 2 | 0.64 | 0.325 | 3969 | 9.72573 | 9.782565 | |
| 41 | 1 | 16 | 2 | 0.64 | 0.208 | 4948 | 9.756737 | ||
| 42 | 1 | 16 | 2 | 0.64 | 0.095 | 7245 | 9.865229 | ||
| 43 | 1 | 16 | 1 | 0.64 | 0.325 | 7973 | 9.714189 | 9.737164 | Four coils are stacked, the ground floor test |
| 44 | 1 | 16 | 1 | 0.64 | 0.208 | 9954 | 9.731092 | ||
| 45 | 1 | 16 | 1 | 0.64 | 0.095 | 14684 | 9.766212 | ||
| 46 | 1 | 16 | 1 | 0.64 | 0.325 | 7975 | 9.732574 | 9.753688 | Four coils are stacked, second layer test |
| 47 | 1 | 16 | 1 | 0.64 | 0.208 | 9956 | 9.749996 | ||
| 48 | 1 | 16 | 1 | 0.64 | 0.095 | 14697 | 9.778493 | ||
| 49 | 1 | 16 | 1 | 0.64 | 0.325 | 7972 | 9.751143 | 9.769871 | Four coils are stacked, the 3rd layer of test |
| 50 | 1 | 16 | 1 | 0.64 | 0.208 | 9960 | 9.761003 | ||
| 51 | 1 | 16 | 1 | 0.64 | 0.095 | 14691 | 9.797464 | ||
| 52 | 1 | 16 | 2 | 0.64 | 0.325 | 4109 | 9.470111 | 9.528629 | Four coils are stacked, and three, four layers in parallel in the same way |
| 53 | 1 | 16 | 2 | 0.64 | 0.208 | 5124 | 9.497581 | ||
| 54 | 1 | 16 | 2 | 0.64 | 0.095 | 7491 | 9.618196 | ||
| 55 | 1 | 16 | 3 | 0.64 | 0.325 | 2701 | 9.61309 | 9.754888 | Four coils are stacked, and two, three, four is in parallel in the same way |
| 56 | 1 | 16 | 3 | 0.64 | 0.208 | 3347 | 9.702035 | ||
| 57 | 1 | 16 | 3 | 0.64 | 0.095 | 4832 | 9.949537 | ||
| 58 | 1 | 16 | 1 | 0.64 | 0.325 | 7946 | 9.826108 | 9.844728 | Four coils are stacked, and one, two layer in parallel in the same way |
| 59 | 1 | 16 | 1 | 0.64 | 0.208 | 9923 | 9.835323 | ||
| 60 | 1 | 16 | 1 | 0.64 | 0.095 | 14628 | 9.872872 | ||
| 61 | 1 | 16 | 1 | 0.64 | 0.325 | 7933 | 9.815765 | 9.839498 | Four coils are stacked, and one, three layer in parallel in the same way |
| 62 | 1 | 16 | 1 | 0.64 | 0.208 | 9912 | 9.830163 | ||
| 63 | 1 | 16 | 1 | 0.64 | 0.095 | 14619 | 9.876524 |
(3) iron core is a Ferrite Material, is shaped as a jar shape, and magnetic jar external diameter Φ=43mm, coil are the reverse coiling of multilayer
In the table three, experimental data and result of calculation: K=1 A=0.356 B=10.22761 * 10
6N0=17 L1=13.8mm L2=54.97787mm
The mean value of Rk: middle relatively error: the M/Rk=5.15/1000 of Rk=9.848085 Rk
Subordinate list three
| Sequence number | M | N | S | The line footpath | C(μF) | f(Hz) | R0(Ω) | Mean value | Remarks |
| 1 | 1 | 17 | 2 | 0.64 | 0.325 | 3558 | 9.776175 | 9.784623 | |
| 2 | 1 | 17 | 2 | 0.64 | 0.208 | 4442 | 9.785652 | ||
| 3 | 1 | 17 | 2 | 0.64 | 0.965 | 6488 | 9.792044 |
| 4 | 1 | 17 | 3 | 0.64 | 0.523 | 2307 | 10.05162 | 10.17093 | |
| 5 | 1 | 17 | 3 | 0.64 | 0.208 | 2874 | 10.08301 | ||
| 6 | 1 | 17 | 3 | 0.64 | 0.965 | 4221 | 10.03408 | ||
| 7 | 1 | 17 | 4 | 0.64 | 0.325 | 1796 | 9.683639 | 9.862679 | |
| 8 | 1 | 17 | 4 | 0.64 | 0.208 | 2219 | 9.794473 | ||
| 9 | 1 | 17 | 4 | 0.64 | 0.965 | 3142 | 10.10993 | ||
| 10 | 1 | 17 | 5 | 0.64 | 0.325 | 1403 | 9.912629 | 10.17093 | |
| 11 | 1 | 17 | 5 | 0.64 | 0.208 | 1757 | 9.895929 | ||
| 12 | 1 | 17 | 5 | 0.64 | 0.965 | 2375 | 10.69992 | ||
| 13 | 2 | 8 | 7 | 0.64 | 0.325 | 2163 | 9.526265 | 9.649356 | |
| 14 | 2 | 8 | 7 | 0.64 | 0.208 | 2680 | 9.608107 | ||
| 15 | 2 | 8 | 7 | 0.64 | 0.096 | 3850 | 9.813694 | ||
| 16 | 2 | 8 | 7 | 0.64 | 0.096 | 2163 | 9.493785 | 9.596092 | Two leads in parallel only connect one |
| 17 | 2 | 8 | 7 | 0.64 | 0.096 | 2689 | 9.547711 | ||
| 18 | 2 | 8 | 7 | 0.64 | 0.096 | 3865 | 9.746781 | ||
| 19 | 2 | 8 | 6 | 0.64 | 0.325 | 2471 | 9.728664 | 9.810707 | |
| 20 | 2 | 8 | 6 | 0.64 | 0.208 | 3071 | 9.782269 | ||
| 21 | 2 | 8 | 6 | 0.64 | 0.096 | 4443 | 9.921189 | ||
| 22 | 2 | 8 | 6 | 0.64 | 0.325 | 2484 | 9.649212 | 9.800792 | Two leads in parallel only connect one |
| 23 | 2 | 8 | 6 | 0.64 | 0.208 | 3069 | 9.759779 | ||
| 24 | 2 | 8 | 6 | 0.64 | 0.096 | 4433 | 9.993383 | ||
| 25 | 2 | 8 | 5 | 0.64 | 0.325 | 2985 | 9.664133 | 9.678458 | |
| 26 | 2 | 8 | 5 | 0.64 | 0.208 | 3729 | 9.667368 | ||
| 27 | 2 | 8 | 5 | 0.64 | 0.096 | 5451 | 9.703873 | ||
| 28 | 2 | 8 | 4 | 0.64 | 0.325 | 3723 | 9.685548 | 9.688756 | |
| 29 | 2 | 8 | 4 | 0.64 | 0.208 | 4649 | 9.692842 | ||
| 30 | 2 | 8 | 4 | 0.64 | 0.096 | 6825 | 9.687878 | ||
| 31 | 2 | 8 | 3 | 0.64 | 0.325 | 4871 | 9.870470 | 9.861558 | |
| 32 | 2 | 8 | 3 | 0.64 | 0.208 | 6083 | 9.877149 | ||
| 33 | 2 | 8 | 3 | 0.64 | 0.096 | 8962 | 9.837054 | ||
| 34 | 2 | 8 | 2 | 0.64 | 0.325 | 7338 | 9.828099 | 9.773063 | |
| 35 | 2 | 8 | 2 | 0.64 | 0.208 | 9188 | 9.808886 | ||
| 36 | 2 | 8 | 2 | 0.64 | 0.096 | 13658 | 9.682203 | ||
| 37 | 3 | 9 | 4 | 0.34 | 0.095 | 3154 | 10.1713 | 10.22677 | |
| 38 | 3 | 9 | 4 | 0.34 | 0.208 | 3937 | 10.18277 | ||
| 39 | 3 | 9 | 4 | 0.34 | 0.095 | 5742 | 10.32623 | ||
| 40 | 3 | 9 | 3 | 0.34 | 0.325 | 4818 | 9.832217 | 9.735881 | |
| 41 | 3 | 9 | 3 | 0.34 | 0.208 | 5264 | 10.1554 | ||
| 42 | 3 | 9 | 3 | 0.34 | 0.095 | 7708 | 10.17535 |
The minimum output resistance of eight secondary coils and the equivalent resistance of pull-up resistor on main coil
(1) computing formula of the minimum output resistance of secondary coil
The computing formula of the minimum output resistance of secondary coil is identical with the computing formula of main coil energy conversion resistance, calculates according to formula (17).If the secondary coil minimum resistance is R2, has:
R2＝Rk×[K+A×Cos(B×C)]×[N±M
1/M×(Ns/N0)
1.5×M]×S×F(α)
..............(18)
In the formula (18), when secondary coil during for coiling in the same way, F (α)=1, when secondary coil is reverse coiling, F (α)=1/[1-L1 ÷ (M * N
1/2* L2)], B * C is determined by main coil.L1 is the width of by-pass ring layer, and L2 is that the every circle coil of secondary coil projects to the lip-deep length of iron core.On an iron core, the L1 of main coil and secondary coil and L2 can be inequality.
(2) the minimum output resistance of secondary coil and the relation of pull-up resistor
When secondary coil had load, pull-up resistor must be established greater than the minimum resistance of secondary coil, and pull-up resistor is R3, has:
R3＞R2
..............(19)
If R3＜R2 can cause the output of secondary coil overload, the secondary coil overload can increase core loss and cause thermal value to increase.
(3) relation of the energy exchange power of main coil and secondary coil peak power output
The energy exchange power of main coil is greater than the peak power output of secondary coil, and the peak power output of secondary coil is greater than bearing power.If: the power that main coil and iron core carry out energy exchange is P1, and the peak power output of secondary coil is P2, and bearing power is P3, has:
P1＞P2＞P3
..............(20)
(4) equivalent resistance of the pull-up resistor of secondary coil on main coil.
If the total number of turns of main coil is Na, the total number of turns of secondary coil is Nb, and the voltage of main coil is Ua, and the output voltage of secondary coil is Ub, and the equivalent resistance of pull-up resistor R3 on main coil is R13, has:
P3＝Ub
2/R3＝Ua
2/R13
R13＝Ua
2/Ub
2×R3
∵：Ua/Ub＝Na/Nb
∴：R13＝Na
2/Nb
2×R3
..............(21)
(6) equivalent current of the pull-up resistor of secondary coil on main coil.
If the electric current of pull-up resistor is I3, the equivalent current on main coil is I13, has:
I13＝Ua/R13
＝Nb
2/Na
2×Ua/R3
..............(22)
The frequency impedance of main coil energy conversion when in the nine LC relation in parallel load being arranged
In the experimental data of table one, table two, table three, secondary coil does not have bringing onto load, so secondary coil is to not influence of the frequency impedance in the main coil conversion process of energy.When secondary coil has load, the load of secondary coil exerts an influence to the frequency impedance in the main coil conversion process of energy, the Frequency point of main coil had taken place to move the variation of frequency impedance when the variation of main coil Frequency point has also brought the main coil energy conversion when Frequency point of main coil was with zero load when load was arranged.The frequency impedance of main coil was exactly the frequency relation of main coil when unloaded and load when therefore, secondary coil had load.
The relation of main coil energy conversion was relevant with the pull-up resistor of secondary coil when secondary coil had load, and the pull-up resistor of secondary coil can be converted into the equivalent resistance on main coil.
The load of secondary coil can be the complete period load, also can be the semiperiod load.The voltage that applies at the main coil port can be unidirectional accelerating potential, also can be two-way accelerating potential.Therefore, the frequency impedance during load is divided into the frequency impedance of the unidirectional accelerating potential of complete period load, the frequency impedance of the two-way accelerating potential of complete period load, the frequency impedance of the unidirectional accelerating potential of semiperiod load, the frequency impedance of the two-way accelerating potential of semiperiod load.Frequency impedance when load is arranged is the mean value of the frequency impedance of the frequency impedance of positive half cycle in the one-period and negative half period.
(1) frequency impedance of the unidirectional accelerating potential of complete period load
If idling frequency is f, no-load current is I; When pull-up resistor was R3, the semiperiod frequency that applies unidirectional accelerating potential at the main coil port was f10, and the semiperiod frequency that does not have accelerating potential is f01, and the complete period frequency of the unidirectional accelerating potential of complete period load is f21
(1) secondary coil has load, the semiperiod frequency impedance when main coil has accelerating potential
If: the electric current when main coil quickens the moving charge in the iron core is I1, and the equivalent current that secondary coil loads on the main coil is I13,
I1＝I+I13
∵：I＝4×C×U×f
I1＝4×C×U×f10
∴：f10＝I1/I×f
＝(1+I13/I)×f
(22) formula substitution following formula, have:
f10＝(1+Nb
2/Na
2×R0/R3)×f
..............(23)
Semiperiod frequency impedance when (2) secondary coil has load, when main coil does not have accelerating potential
If: the electric current when iron core quickens the moving charge in the main coil is I12, has:
I12＝I1-I13-I13
＝I-I13
f01＝(1-Nb
2/Na
2×R0/R3)×f
..............(24)
(3) frequency impedance of the unidirectional accelerating potential of complete period load
f21＝(f10+f01)÷2
＝f
..............(25)
(4) dutycycle during the unidirectional accelerating potential of complete period load
If: dutycycle is K1, has:
K1＝f10/f01
＝(1+Nb
2/Na
2×R0/R3)/(1-Nb
2/Na
2×R0/R3)
..............(26)
(2) frequency impedance of the two-way accelerating potential of complete period load
If: the complete period frequency of the two-way accelerating potential of complete period load is f22
With reference to (23) formula, frequency impedance is:
f22＝(1+Nb
2/Na
2×R0/R3)×f
..............(27)
Dutycycle during the two-way accelerating potential of complete period load
K1＝1
..............(28)
(3) frequency impedance of the unidirectional accelerating potential of semiperiod load
Two kinds of situations are arranged in the unidirectional accelerating potential of semiperiod load, and characteristic is inequality frequently for the resistance under two kinds of situations.First kind of situation has load when unidirectional voltage is applied on the main coil port.Second kind of situation do not have load when unidirectional voltage is applied on the main coil port.
(A) unidirectional voltage is applied to the frequency impedance when on the main coil port load being arranged
If the frequency when unloaded is f, the electric current when unloaded is I; It is f10 that secondary coil has load, the semiperiod frequency when main coil has accelerating potential, and the semiperiod frequency when main coil does not have accelerating potential is f01, and the complete period frequency of the unidirectional accelerating potential of semiperiod load is f11
(1) secondary coil has load, the semiperiod frequency impedance when main coil has accelerating potential
With reference to (23) formula, have:
f10＝(1+Nb
2/Na
2×R0/R3)×f
..............(29)
When (2) secondary coil does not have load, the semiperiod frequency impedance when main coil does not have accelerating potential to the moving charge in the iron core
If: the electric current when iron core quickens the moving charge in the main coil is I12, has:
I12＝I1-I13
＝I
f01＝f
..............(30)
(3) frequency impedance of the unidirectional accelerating potential of semiperiod load
f21＝(f10+f01)÷2
＝(1+0.5×Nb
2/Na
2×R0/R3)×f
..............(31)
(4) dutycycle during the unidirectional accelerating potential of semiperiod load
If: dutycycle is K1, has:
K1＝f10/f01
＝1+Nb
2/Na
2×R0/R3
..............(32)
(B) unidirectional voltage is applied to the frequency impedance when not having load on the main coil port.
In such cases, the semiperiod when unidirectional voltage is applied on the main coil port does not have load.
If the frequency when unloaded is f, the electric current when unloaded is I; It is f10 that secondary coil does not have load, the semiperiod frequency when main coil has accelerating potential, and it is f01 that main coil does not have accelerating potential, the semiperiod frequency when secondary coil has load, and the complete period frequency of the unidirectional accelerating potential of semiperiod load is f11
(1) secondary coil has load, the semiperiod frequency impedance when main coil does not have accelerating potential
With reference to (24) formula, have:
f10＝(1-Nb
2/Na
2×R0/R3)×f
..............(33)
Semiperiod frequency impedance when (2) secondary coil has load, main coil that the moving charge in the iron core is not had accelerating potential
If: the electric current when iron core quickens the moving charge in the main coil is I12, has:
I12＝I1-I13
＝I
f01＝f
..............(34)
(3) frequency impedance of the unidirectional accelerating potential of semiperiod load
f21＝(f10+f01)÷2
＝(1-0.5×Nb
2/Na
2×R0/R3)×f
..............(35)
(4) dutycycle during the unidirectional accelerating potential of semiperiod load
If: dutycycle is K1, has:
K1＝f10/f01
＝1-Nb
2/Na
2×R0/R3
..............(36)
(4) frequency impedance of the two-way accelerating potential of semiperiod load
The frequency impedance of (A) kind situation of the frequency impedance of the two-way accelerating potential of semiperiod load and the unidirectional accelerating potential of semiperiod load is identical.Have:
(1) frequency impedance of the two-way accelerating potential of semiperiod load
f21＝(f10+f01)÷2
＝(1+0.5×Nb
2/Na
2×R0/R3)×f
..............(35)
(4) dutycycle during the two-way accelerating potential of semiperiod load
If: dutycycle is K1, has:
K1＝f10/f01
＝1+Nb
2/Na
2×R0/R3
..............(36)
The frequency impedance of nine AC transformer energy conversion
The frequency impedance of energy conversion when (one) AC transformer is unloaded
AC transformer is that the port at main coil applies alternating voltage, alternating voltage be a voltage source be again an infinite jumbo capacitor, therefore, the conversion process of energy of AC transformer one-period still will be through concerning four identical processes with the LC parallel connection.Same transformer, the electric current by main coil during with the two-way accelerating circuit of LC (be push pull mode quicken) equate with the electric current of AC transformer by main coil, so, in AC transformer, can express electric current by coil with the capability value of capacitor.Can express capacitance with the R0 value according to (1) formula.Have:
C＝I/(4×U×f)
＝1/(4×R0×f)
..............(37)
In (37) formula substitution (16) formula, the resistance frequency general formula of main coil when getting the alternating circuit zero load:
Rk/R0×{K+A×Cos[B/(4×R0×f)]}×[N±M
1/M×(Ns/N0)
1.5×M]×S×F(α)＝1
..............(38)
(2) computing formula of secondary coil minimum resistance
If: the minimum output resistance of secondary coil is R2, has:
Rk/R2×{K+A×Cos[B/(4×R2×f)]}×[N±M
1/M×(Ns/N0)
1.5×M]×S×F(α)＝1
..............(39)
Frequency impedance when (three) secondary coil has pull-up resistor in the alternating circuit
If: the pull-up resistor of secondary coil is R3, and frequency is f3, has:
f3＝(1+Nb
2/Na
2×R0/R3)×f
..............(40)
The frequency impedance of ten electronic transformer energy conversion
Electronic transformer comprises specific type transformers such as power transformer, audio-frequency transformer (AFT), pulse transformer, switching mode power supply transformer, isolating transformer, line transformer, iron core inductor.Electronic transformer can use the main coil LC in parallel with capacitor relation, also can be at main coil port shnt capacitor not.Electronic transformer can be with the mode of alternating voltage, also can be with the mode of unidirectional back-lash voltage, and can also be with the push pull mode of two-way back-lash voltage.
In electronic transformer, if the transformer main coil does not adopt the mode of shnt capacitor, all can use the frequency impedance of the LC relation in parallel of main coil port shnt capacitor, need carry out mathematic(al) manipulation to the unloaded frequency impedance and the load frequency impedance of LC relation during use, the mode of mathematic(al) manipulation and (38), (39) formula are identical.For example: when the port of transformer does not have shnt capacitor and adopts complete period load unidirectional voltage, frequency impedance when unloaded frequency impedance is the zero load of LC relation, the load frequency impedance is the load frequency impedance of (23), (24) formula, and the frequency impedance when frequency impedance during to zero load and load carries out mathematic(al) manipulation.
Method for designing
Inventive principle has defined the transformer core parameter, clear and definite iron core and the coil frequency impedance under unloaded and two kinds of situations of load.According to inventive principle, method of the present invention has related to the measuring method of iron core parameter and the method for designing of coil parameter.
Among the present invention, the measurement of iron core parameter, the design of transformer core parameter and coil parameter, the frequency impedance when all being frequency impedance during with zero load and load is a foundation.
According to inventive principle, the measurement of iron core parameter is to carry out when zero load.
According to inventive principle, the parameter designing of transformer is exactly the iron core parameter and the coil parameter of design transformer, and design process has related to the iron core parameter, has also related to coil parameter, be at first to determine the iron core parameter generally speaking, determine coil parameter afterwards according to designing requirement and purpose.Coil parameter is not inequality yet simultaneously owing to the iron core parameter, and the iron core parameter is not inequality yet simultaneously for coil parameter, and a transformer has the design proposal of countless versions, optimizes optimal scheme.
The measuring method of one iron core parameter
The iron core parameter has Rk, N0, K, A, five parameters of B.The material of iron core, physical form, when physical size is identical, five parameters of iron core are identical.The iron core parameter will method by experiment be measured, and solves the iron core parameter according to experimental data.
Measuring method:
(1) coiling.
The multiple multi-form coil of coiling is also measured respectively respectively.To same iron core, the coil of the different numbers of plies of coiling and measurement respectively, also measure by the coil of different every layer of different numbers of turn of line footpath coiling respectively, adopt coil different of coiling in the same way and measurement respectively, respectively according to S.C. coil and the measurement different with the mode coiling of many leads parallel connection with the mode coiling of oppositely coiling.Improve the measurement and the computational accuracy of iron core parameter by the measurement of many groups coil.
(2) select capacitor.
Every kind of coil will three different capabilities values in parallel at least capacitor measure three groups of data, and the expressed angle value of the product that ensures the condenser capacity value of three measurement points and B value is between π/4 and π, if the capacitor volume value has exceeded above-mentioned scope, remeasure.
(3) measure.
Shnt capacitor on main coil, apply the interruption square-wave voltage in coil port by the power amplification circuit that signal source or signal source drive, constantly change the frequency of back-lash voltage, with oscillograph or other means floating voltage wave form varies, find out the voltage magnitude maximum point, gather the frequency values and the condenser capacity value of voltage magnitude maximum point.
(4) calculate.
Carry out mathematics manipulation according to the frequency impedance in the inventive principle, calculate five parameters of iron core.In resolving, preferably adopt mathematics error compensation method to resolve, to improve the data solver precision.
For the iron core of producing in batches, measure getting a plurality of iron cores, to estimate the parameter error of iron core product with a kind of iron core of model.
The two LC method for designing that concerns transformer core parameter and coil parameter in parallel
The design of iron core parameter and coil parameter is divided into fixed frequency design and servo-actuated Frequency Design in the LC relation in parallel.The fixed frequency design refers to that transformer is with a changeless frequency job, Frequency point when the fixed frequency point during transformer work is worked for rated power, idling frequency point all departs from the fixed rate Frequency point with the maximum load Frequency point, equivalent resistance according to energy conversion resistance and pull-up resistor is selected Frequency point, or select the equivalent resistance of energy conversion resistance and pull-up resistor according to Frequency point, by energy conversion resistance and equivalent resistance selection iron core parameter and coil parameter.The servo-actuated Frequency Design refers to the real-time sensing lead power of transformer energy when working and adjusts the Frequency point of transformer work according to bearing power in real time.
(1) fixed frequency design method of points
The fixed frequency design will be determined three Frequency points according to bearing power, three Frequency points are respectively unloaded operation Frequency point fa, rated power frequency of operation point fb and peak power output frequency of operation point fc, with the nominal operation Frequency point is the fixed frequency point of iron core and coil working, determine the frequency ratio ka of output rating and unloaded operation, the frequency of operation ratio k b of peak power output and output rating carries out the design of iron core parameter and coil parameter afterwards.
(1) clear and definite designing requirement: go into terminal voltage Ua, go out terminal voltage Ub, output rating P3, peak power output P4.
(2) calculate minimum output resistance: the R2=Rk of secondary coil * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)
Calculate nominal load resistance: R3=Ub
2/ P3
Calculate minimum load output resistance: R4=Ub
2/ P4
The condition that must satisfy: R2＜R3＜R4
(3) determine idling frequency fa, determine the frequency ratio Ka of output rating and unloaded operation, determine the frequency ratio Kb of peak power output and output rating
(4) determine the LC working method that concerns transformer in parallel.Different working methods has different load frequency impedances.For example: the load frequency impedance when two-way acceleration of main coil and complete period load is formula (27), fb=(1+Nb
2/ Na
2* R0/R3) * and fa, fc=(1+Nb
2/ Na
2* R0/R4) * fa
(5) five parameters of selection and definite iron core.And, make the value of B * C approximate π according to the definite capacitor volume value in parallel of iron core parameter.
Frequency impedance during (6) according to load, the energy exchange resistance of main coil when calculating zero load.Different working methods has different load frequency impedances.For example: the load frequency impedance when two-way acceleration of main coil and complete period load is formula (27), and the energy exchange resistance when unloaded is: R0=(fb/fa-1) * Na
2/ Nb
2* R3
Perhaps provide approximate value of Na/Nb, find the solution the approximate value of R0.
(7) according to the no-load current of the approximation calculation main coil of R0, according to the equivalent current of peak power output computational load on main coil, by the no-load current of main coil with load on equivalent current on the main coil and, the line footpath of calculating lead.
(8) determine the coiling mode of coil, the frequency impedance during according to zero load, design, the number of turn of calculating every layer line circle and the number of plies of coil.
(9) design content that repeats (6), (7), (8) item approaches, till the frequency impedance when frequency impedance when zero load and load all meets the demands.
(10) the general assembly (TW) of lead is not inequality simultaneously for the parameter of iron core, reselect the iron core parameter according to the result of calculation of (6), (7), (8), (9) item, carries out the calculating of (6), (7), (8), (9) item again.Multiple result of calculation is preferentially gone out optimal design scheme.
Frequency impedance during (11) according to zero load calculates the energy conversion resistance R 2 of secondary coil, because the number of turn Nb of secondary coil has become definite value after finishing design, if the energy conversion resistance R 2 of secondary coil is greater than R4, carry out bridging coil and calculate to determine the quantity of bridging coil and the line footpath of winding wire, make R2 less than R4.
(12) finish above-mentioned design after, according to the working method of fixed LC relation in parallel, the frequency impedance during according to load calculates fb, and calculates a complete work period upper half and the ratio of lower half.
(13) in circuit was implemented, the frequency of circuit voltage was fb, and dutycycle is the ratio of a complete cycle upper half and lower half.
(2) design of servo-actuated Frequency point
Its iron core parameter of transformer and coil parameter according to the design of the method for designs fix Frequency point are changeless parameters, when working with fixed frequency, as long as pull-up resistor is not its duty of nominal load resistance just not is best duty, the frequency impedance when having only frequency of operation and pull-up resistor to meet load in real time is only optimum Working.
The servo-actuated Frequency Design is exactly in the transformer circuit load to be monitored in real time, monitor its electric current, utilize the electric current of known voltage and monitoring to calculate pull-up resistor, or monitoring current, voltage calculate pull-up resistor, or direct sensing lead resistance, or set the pull-up resistor curve, when known load resistance by circuit frequency impedance evaluation work frequency and the dutycycle during according to load, frequency of operation and the dutycycle calculated by circuit apply back-lash voltage to the main coil port.
The method for designing of three AC transformer iron core parameters and coil parameter
In the transformer core parameter and coil parameter design of above-mentioned LC relation, the frequency of operation of transformer is to design in a scope generally speaking, frequency of operation is the back-lash voltage frequency of circuit, the frequency of back-lash voltage determines by circuit, so the frequency working point during rated power is not proper fixed frequency point.
And the characteristics of AC transformer are fixed frequency and alternating voltage, and the terminal voltage frequency of going into of AC transformer is generally determined by the outside, thereby it is strict fixed frequency design.
(1) clear and definite designing requirement: go into terminal voltage Ua, go out terminal voltage Ub, ac frequency fb, output rating P3, peak power output P4.
(2) calculate the minimum output resistance R2:Rk/R2 of secondary coil * { K+A * Cos[B/ (4 * R2 * fa)] } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1
Calculate nominal load resistance: R3=Ub
2/ P3
Calculate minimum load output resistance: R4=Ub
2/ P4
The condition that must satisfy; R2＜R4＜R3
Frequency impedance during (3) by load calculates idling frequency fa, the fc when calculating peak power output
(4) five parameters of selection and definite iron core.
Frequency impedance during (5) according to load, the energy exchange resistance R 0 of main coil when calculating zero load, R0=(f3/fa-1) * R3 * Na
2/ Nb
2Perhaps provide approximate value of Na/Nb, find the solution the approximate value of R0.
(6) according to the no-load current of the approximation calculation main coil of R0, according to the equivalent current of peak power output computational load on main coil, by the no-load current of main coil with load on equivalent current on the main coil and, the line footpath of calculating lead.
(7) determine the coiling mode of coil, the frequency impedance during according to zero load, design, the number of turn of calculating every layer line circle and the number of plies of coil.
(8) design content that repeats (5), (6), (7) item approaches, till the frequency impedance when frequency impedance when zero load and load all meets the demands.
(9) check Cos[B/ (4 * R0 * f)] in B/ (4 * R0 * f) whether greater than π, if B/ is (during 4 * R0 * f) greater than π, determine that (higher limit of 4 * R0 * f) redefines the iron core parameter to B/, according to the order redesign of (5), (6), (7), (8).If B/ (during 4 * R0 * f) less than π, also will heighten B/ (value and the redesign of 4 * R0 * f).
General frequency impedance during (10) according to zero load calculates the energy conversion resistance R 2 of secondary coil, because the number of turn Nb of secondary coil has become definite value after finishing design, if the energy conversion resistance R 2 of secondary coil is greater than R4, carry out bridging coil and calculate to determine the quantity of bridging coil and the line footpath of winding wire, make R2 less than R4.
The method for designing of three electronic transformer iron core parameters and coil parameter
(1), undertaken by the LC method for designing of transformer core parameter and coil parameter that concerns in parallel if electronic transformer has adopted the LC of main coil port shnt capacitor relation in parallel.If the main coil port does not have shnt capacitor, the line number conversion of going forward side by side of the frequency impedance in the time of determining frequency impedance when unloaded and load according to its handling characteristics.Whether whether what handling characteristics comprised that the main coil port applies is alternating voltage, be back-lash voltage, and back-lash voltage is unidirectional or two-way, and load is semiperiod load or complete period load.
(2) determine unloaded operation frequency and loaded work piece frequency according to request for utilization, determine that (usable range of 4 * R0 * f), for example voltage stabilized transformer will make angle value greater than π for angle value B * C or B/.
(3) method for designing of method for designing and LC method for designing that concerns transformer core parameter and coil parameter in parallel and AC transformer is identical.
(4) method for designing of iron inductance is by the unloaded design of transformer of unidirectional back-lash voltage.The iron inductance of using as current limliting will calculate it carries out energy exchange when rated frequency electric current.The iron inductance that filtering is used as smooth waveform, much lower the back-lash voltage frequency of the ratio front end of the frequency of operation of iron inductance design input, the electric current during the calculating energy exchange, and come the smoothness of calculation of filtered by two different frequencies.
Embodiment
The present invention generally should implement according to the following steps:
(1) from multiple core materials such as silicon steel, ferrite, amorphous, selects the core material that will use, select the shape type of iron core, determine the coiling mode of coil.
(2) after core material, shape are determined, prepare multiple different size, the iron core of Different Weight carries out parameter measurement respectively and calculates the iron core parameter, and the K value will be arranged to same value in five iron core parameters of commaterial when calculating the iron core parameter.When if the parameter of iron core is known, need not measures the iron core parameter again, but still will prepare multiple different size, the iron core of Different Weight.
When measuring an iron core parameter, coil on the iron core will adopt different coiling modes, different line footpaths, the different number of plies numbers of turn different with every layer to carry out coiling of many groups and measurement respectively, carry out mathematics manipulation with error compensation method, calculate with error compensation method and can improve measuring accuracy, can the statistical measurement precision.Want standard during coiling, the tight ness rating of coiling is identical with the tight ness rating of producing last coiling in the time of guaranteeing to measure iron core, can produce error effect to measuring accuracy when the coil winding tight ness rating is inequality.
(3) clear and definite designing requirement.For industrial frequency AC transformer, direct supply transformer type to clearly go into terminal voltage, go out terminal voltage, rated power, peak power, frequency of operation.Also want clear and definite its specific (special) requirements for special transformers such as audio-frequency transformer (AFT), pulse transformer, high-frequency transformer, voltage stabilized transformer, isolating transformer, iron core inductors, for example the specific (special) requirements of voltage stabilized transformer is a burning voltage, frequency angle B/ during design (4 * R0 * f) must be greater than π, for example the frequency range of audio-frequency transformer (AFT) requirement is big and highly sensitive, and frequency angle B * C or B/ (4 * R0 * f) must be less than π.
(4) design according to step listed in the method for designing.
Claims (18)
1 utilizes frequency impedance to measure the method for iron core parameter and design transformer core parameter and coil parameter
The method for designing of existing transformer is based on Theory of Electromagnetic Field, with magnetic field intensity as the iron core parameter,, form mathematical formulae with magnetic field intensity, coil total number of turns and voltage and calculate as coil parameter with the coil total number of turns, design of transformer mainly relies on experiment to carry out.The inventive method no longer designs transformer with magnetic field theory, it is characterized in that: the energy conversion that transformer carried out is defined as the conversion of energy of a charge between coil and the iron core, express the energy conversion of carrying out mutually between coil and the iron core with energy conversion resistance, use Rk, A, B, K, five parameters of N0 are as the iron core parameter, wherein, Rk is the resistance coefficient of single-turn circular coil energy conversion, intensity when A expresses energy conversion, B expresses the ratio of electric capacity (or electric current) in mathematical relation, K expresses A, the curve location that the B parameter forms, N0 expresses the number of turn coefficient of every layer line circle; As coil parameter, wherein, N is the equivalent number of turn of every layer line circle with N, S, three parameters of M, and S is the coil number of plies, and M is the quantity of bridging coil; The coil of coiling in the same way is distinguished into two different coefficients with the coil of oppositely coiling with function F (α), wherein, as coil F (α)=1 during, F when coil is reverse coiling (α)=1/[1-L1 ÷ (M * N for coiling in the same way
1/2* L2)]; The LC that the main coil shnt capacitor forms during with zero load relation in parallel is as basic model, iron core parameter and coil parameter are connected by mathematical relation, form the energy conversion resistance and the frequency impedance of frequency of operation when unloaded, the frequency impedance during zero load is 4 * C * f * Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1, the energy exchange resistance when frequency is f during no-load transformer are R0=Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α); Can not form the AC transformer of LC relation in parallel or the various types of electronic transformer frequency impedance when unloaded and be Rk/R0 * { K+A * Cos[B/ (4 * R0 * f)] } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1, the energy exchange resistance when AC transformer or various types of electronic transformer were unloaded when frequency was f are R0=Rk * { K+A * Cos[B/ (4 * R0 * f) } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α); Frequency impedance during according to zero load can calculate the minimum output resistance of secondary coil; The iron core parameter can be measured and calculate to unloaded frequency impedance according to LC relation in parallel; Energy conversion resistance when the frequency impedance during according to zero load can calculate idling frequency; When transformer has load, can be transformed into equivalent resistance on the main coil to pull-up resistor; Frequency impedance during with load is set up frequency impedance the getting in touch between the two when unloaded, and the load frequency impedance of LC relation in parallel has the frequency impedance of the unidirectional accelerating potential of complete period load, the frequency impedance of the two-way accelerating potential of complete period load, the frequency impedance of the unidirectional accelerating potential of semiperiod load, the frequency impedance of the two-way accelerating potential of semiperiod load; According to the unloaded frequency impedance and the load frequency impedance of LC relation in parallel, can obtain the unloaded frequency impedance and the load frequency impedance of AC transformer through mathematic(al) manipulation; According to the unloaded frequency impedance and the load frequency impedance of LC relation in parallel, can obtain the unloaded frequency impedance and the load frequency impedance of various types of electronic transformers through mathematic(al) manipulation; Design according to the unloaded frequency impedance of LC relation in parallel and load frequency impedance iron core parameter and the coil parameter can be to the transformer fixed frequency of main coil shnt capacitor the time, design process is that the Frequency point of transformer rated power is decided to be changeless Frequency point, idling frequency point all departs from the fixed frequency point with the maximum load Frequency point, equivalent resistance by energy conversion resistance and pull-up resistor is selected Frequency point, or select the equivalent resistance of energy conversion resistance and pull-up resistor by Frequency point, by energy conversion resistance and load equivalent resistance iron core parameter and coil parameter are designed; Transformer according to the main coil shnt capacitor of fixed frequency point design can be realized with dynamic frequency work by circuit; Iron core parameter and coil parameter when the frequency impedance when frequency impedance according to AC transformer when unloaded and load can be to the AC transformer fixed frequency design; Frequency impedance when frequency impedance when the various types of electronic transformers of foundation are unloaded and load can design the iron core parameter and the coil parameter of various types of electronic transformers.
The feature of 2 energy conversion resistance
" energy conversion that transformer carried out being defined as the conversion of energy of a charge between coil and the iron core; express the energy conversion of carrying out mutually between coil and the iron core with energy conversion resistance " described in the claim 1, finger is when the no-load transformer work of LC relation in parallel, per half work period inner capacitor and iron core carry out the primary energy conversion mutually by main coil, capacitor energy converts iron core energy and iron core energy to by main coil, and to convert capacitor energy to by main coil be two conversion process of energy, two conversion process of energy have two energy conversion resistance, two energy conversion resistance all is minimum value and is the resistance that iron core and coil carry out energy conversion when equal, energy conversion resistance is that the condition of definite value is and frequency dependence, for the energy conversion resistance of definite value meets Ohm law.
The feature of 3F (α)
Described in the claim 1 " as coil F (α)=1 during, F when coil is reverse coiling (α)=1/[1-L1 ÷ (M * N for coiling in the same way
1/2* L2)] ", its " coil is reverse coiling " refers to the starting point of the terminal point of two adjacent layer coil last layer coils for next layer line circle; Its " coil is coiling in the same way " refers to that the Origin And Destination of each layer line circle is all identical; Its when coiling " F (α)=1 " in the same way refers to that the coil in the different coil layer is identical at the lip-deep projecting direction of iron core, and the acceleration direction of all coils is identical; Its " reverse F (α)=1/[1-L1 ÷ (M * N during coiling
1/2* L2)] " referring to that the adjacent layer coil has angle in the lip-deep projected angle trend of iron core; the adjacent layer coil is inequality to the acceleration direction of moving charge in the iron core; the direction of motion that is accelerated electric charge in the iron core is the direction of closing of all coils layer acceleration direction, and F (α) is the coefficient that acceleration direction is closed direction; And projected angle is used the width L1 of coil layer by coil diameter and the decision of coil quantity, and every circle coil projects to the influence coefficient that the lip-deep length L 2 of iron core is expressed projected angle.
The feature of frequency impedance during the no-load transformer of 4 shnt capacitors
Described in the claim 1 " the LC relation in parallel that the main coil shnt capacitor forms when unloaded is as basic model; iron core parameter and coil parameter are connected by mathematical relation; form energy conversion resistance when unloaded and the frequency impedance of frequency of operation, and the frequency impedance during zero load is 4 * C * f * Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1, the energy exchange resistance when frequency is f during no-load transformer are R0=Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α) ", it is characterized in that: equivalent coil N refers to the 1/s power of the product of ground floor turn number N 1, second layer turn number N 2, S layer line circle number of turn Ns, that is: N=(N1 * N2 * ... * Ns)
1/sM refers to the quantity in parallel of lead in same layer line circle, that is: when coil is individual layer, the coiling in parallel of M root lead is arranged, when coil has the S layer, the coiling in parallel of M root lead is all arranged in each layer, have only lead situation in parallel that just is suitable in the above-mentioned formula in parallel in layer, will not produce effect in parallel if carry out layer with layer is in parallel, thereby also just can not calculate by parallel connection; Ns refers to the number of turn of S layer line circle; ± symbol refers to get positive sign when N＞N0 time ± symbol, when N≤N0 time ± symbol is got negative sign.
The scope of B * C in the frequency impedance during no-load transformer of 5 shnt capacitors
Described in the claim 1 " frequency impedance when unloaded is 4 * C * f * Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1 ", B * C wherein is an angle value, the scope of B * C is: π/4＜B * C＜π, the duty of B * C will approach π; As B * C during greater than π, duty is a state of saturation; As B * C during less than π/4, the utilization ratio of iron core and coil is low; (value and the actual value of B * C) are unequal, calculate revisal, carry out on the method for revisal that (B * C) replaces K+A * Cos (B * C) with K+y (x)+A * Ctg for K+A * Cos when B * C＜π/4; (value and the actual value of B * C) are unequal, and actual value is an asymptotic line, and the physical form of every kind of core material determines that its asymptotic line of back is unique, can method by experiment determine the approximate asymptotic line that replaces of straight line for K+A * Cos when B * C＞π.
The feature of frequency impedance when 6 AC transformer or various types of electronic transformer are unloaded
" can not form the AC transformer of LC relation in parallel or the various types of electronic transformer frequency impedance when unloaded and be Rk/R0 * { K+A * Cos[B/ (4 * R0 * f)] } * [N ± M described in the claim 1
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1, the energy exchange resistance when AC transformer or various types of electronic transformer were unloaded when frequency was f are R0=Rk * { K+A * Cos[B/ (4 * R0 * f) } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α) ", it is characterized in that: when AC transformer or various types of electronic transformer main coil port did not have shnt capacitor, (4 * R0 * f) carried out mathematics conversion to the frequency impedance when concern LC is in parallel with C=1/.
The feature of the minimum output resistance of 7 secondary coils
" frequency impedance during according to zero load can calculate the minimum output resistance of secondary coil " described in the claim 1, the computing method that refer to the minimum output resistance of secondary coil are identical with the computing method of main coil energy conversion resistance, and the computing formula of the minimum output resistance R2 of the transformer secondary coil of shnt capacitor is: R2=Rk * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α); (4 * R2 * f) carry out mathematic(al) manipulation, the computing formula of minimum output resistance R2 is the minimum output resistance of the secondary coil of AC transformer or various types of electronic transformers: Rk/R2 * { K+A * Cos[B/ (4 * R2 * f)] } * [N ± M with C=1/
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1.
The measuring method of 8 iron core parameters
" the iron core parameter can be measured and calculate to the unloaded frequency impedance according to LC relation in parallel " described in the claim 1, it is characterized in that: respectively according to coiling in the same way, the reverse mode of coiling, the coil of the different numbers of plies of coiling, not collinear footpath, every layer of different number of turn is measured respectively.The capacitor that every kind of coil will three different capabilities values in parallel at least when measuring is measured three groups of data, and will ensure that the expressed angle value of the product of the condenser capacity value of three measurement points and B value is between π/4 and π.Measuring method is to apply the interruption square-wave voltage at the main coil port of shnt capacitor by the power amplification circuit that signal source or signal source drive, constantly change the frequency of back-lash voltage, with oscillograph or other means floating voltage wave form varies, find out the voltage magnitude maximum point, gather the frequency values and the condenser capacity value of voltage magnitude maximum point.Calculate five parameters of iron core then with the unloaded frequency impedance of LC relation in parallel.In LC relation in parallel, square wave is the reference waveform that forms frequency impedance when LC is in parallel to be concerned.
The feature of 9 equivalent resistances
" when transformer has load; can be transformed into equivalent resistance on the main coil to pull-up resistor " described in the claim 1 refers to pull-up resistor R3 is converted into equivalent resistance R13 on the main coil, with the total number of turns of Na statement main coil, with the Nb statement secondary coil number of turn, equivalent resistance is R13=Na
2/ Nb
2* R3.
The feature of the frequency impedance of the unidirectional accelerating potential of transformer complete period load of 10 shnt capacitors
" the load frequency impedance of LC relation in parallel has the frequency impedance of the unidirectional accelerating potential of complete period load " described in the claim 1, feature is: during the complete period load, the semiperiod frequency that unidirectional accelerating potential is arranged is f10=(1+Nb
2/ Na
2* R0/R3) * and f, the semiperiod frequency that does not have unidirectional accelerating potential is f01=(1-Nb
2/ Na
2* R0/R3) * and f, the frequency of a complete cycle is f21, and frequency impedance is f21=f, and dutycycle is K1=(1+Nb
2/ Na
2* R0/R3)/(1-Nb
2/ Na
2* R0/R3).
The feature of the frequency impedance of the two-way accelerating potential of transformer complete period load of 11 shnt capacitors
" the load frequency impedance of LC relation in parallel has ... the frequency impedance of the two-way accelerating potential of complete period load " described in the claim 1, feature is: during the complete period load, the frequency of a complete cycle is f22, and frequency impedance is f22=(1+Nb
2/ Na
2* R0/R3) * and f, positive half cycle and negative half period symmetry, dutycycle is k1=1.
The feature of the frequency impedance of the unidirectional accelerating potential of transformer semiperiod load of 12 shnt capacitors
" the load frequency impedance of LC relation in parallel has ... the frequency impedance of the unidirectional accelerating potential of semiperiod load " described in the claim 1, feature is: when unidirectional voltage is applied to when on the main coil port load being arranged, it is f10=(1+Nb that the loaded semiperiod frequency of unidirectional accelerating potential is arranged
2/ Na
2* R0/R3) * and f, not having unidirectional accelerating potential not have the semiperiod frequency of load is f01=f, and the frequency of a complete cycle is f21, and frequency impedance is f21=(1+0.5 * Nb
2/ Na
2* R0/R3) * and f, dutycycle is K1=1+Nb
2/ Na
2* R0/R3; When unidirectional voltage was applied to the main coil port and does not have load, having unidirectional accelerating potential not have the semiperiod frequency of load was f10=f, and not having the loaded semiperiod frequency of unidirectional accelerating potential is f01=(1-Nb
2/ Na
2* R0/R3) * and f, the frequency of a complete cycle is f21, frequency impedance is f21=(1-0.5 * Nb
2/ Na
2* R0/R3) * and f, dutycycle is K1-1+Nb
2/ Na
2* R0/R3.
The feature of the frequency impedance of the two-way accelerating potential of transformer semiperiod load of 13 shnt capacitors
" the load frequency impedance of LC relation in parallel has ... the frequency impedance of the two-way accelerating potential of semiperiod load " described in the claim 1, feature is: during the two-way accelerating potential of semiperiod load, the frequency of a complete cycle is f21, and frequency impedance is f21=(1+0.5 * Nb
2/ Na
2* R0/R3) * and f, dutycycle is k1=1+Nb
2/ Na
2* R0/R3.
The feature of frequency impedance during 14 AC transformer loads
" frequency impedance is arranged during the AC transformer load " described in the claim 1, frequency of operation was f3 when the pull-up resistor that refers to AC transformer was R3, the frequency impedance when pull-up resistor is R3 is f3=(1+Nb
2/ Na
2* R0/R3) * f.
The method for designing of the transformer fixed frequency of 15 shnt capacitors
Described in the claim 1 " the frequency impedance design of the frequency impedance during according to load when unloaded LC is in parallel when concern the transformer fixed frequency iron core parameter and coil parameter; design process is that the Frequency point of transformer rated power is decided to be changeless Frequency point; idling frequency point and maximum load Frequency point all depart from the fixed rate Frequency point; according to the equivalent resistance selection Frequency point of energy conversion resistance and pull-up resistor; or according to the equivalent resistance of Frequency point selection energy conversion resistance and pull-up resistor; by energy conversion resistance and equivalent resistance iron core parameter and coil parameter are designed ", its method for designing refers to: set some call parameters earlier, carrying out repeated calculation also approaches one by one, select a kind of scheme from the multiple scheme kind that produces, step is, (1) clearly goes into terminal voltage Ua, go out terminal voltage Ub, output rating P3, peak power output P4; (2) calculate minimum output resistance: the R2=Rk of secondary coil * [K+A * Cos (B * C)] * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α) calculates nominal load resistance: R3=Ub
2/ P3 calculates minimum load output resistance: R4=Ub
2/ P4, the condition that must satisfy: R2＜R3＜R4; (3) set idling frequency point fa, the ratio K a of the frequency when frequency when determining output rating and unloaded operation determines the ratio K b of the frequency of the frequency of peak power output and output rating; (4) according to the selected LC clear and definite load frequency impedance of working method that concerns transformer in parallel; (5) select and five parameters of definite iron core, and determine the capability value of shnt capacitor to make the value of B * C approximate π according to the iron core parameter; Frequency impedance during (6) according to load calculates the energy exchange resistance of main coil when unloaded, or provides the ratio value of the main coil and the secondary coil number of turn, and the frequency impedance during according to load is found the solution R0; (7) calculate the no-load current of main coil according to the value of R0, according to the equivalent current of peak power output computational load on main coil, by the no-load current of main coil with load on maximum equivalent electric current on the main coil and, the line footpath of calculating lead; (8) determine the coiling mode of coil, the frequency impedance during according to zero load, design, the number of turn of calculating every layer line circle and the number of plies of coil; (9) design content that repeats 6,7,8 approaches, till the frequency impedance when frequency impedance when zero load and load all meets the demands; (10) the general assembly (TW) of lead is not inequality simultaneously for the parameter of iron core, carry out 6,7,8,9 calculating again according to 6,7,8,9 result of calculation optimized choice iron core parameter again; Frequency impedance during (11) according to zero load calculates the energy conversion resistance R 2 of secondary coil, because the total number of turns Nb of secondary coil has become definite value after finishing design, if the energy conversion resistance R 2 of secondary coil is greater than R4, carry out bridging coil and calculate to determine the quantity of bridging coil and the line footpath of winding wire, make R2 less than R4; (12) finish above-mentioned design after, according to the working method of fixed LC relation in parallel, the frequency impedance during according to load calculates fb, and calculates a complete work period upper half and the ratio of lower half; (13) in engineering construction, the frequency of operation of transformer is fb, and dutycycle is the ratio of a complete cycle upper half and lower half.
The transformer of 16 shnt capacitors is with the method for designing of dynamic frequency
" transformer according to the main coil shnt capacitor of fixed frequency point design can be realized with dynamic frequency work by circuit " described in the claim 1, it is characterized in that: real-time monitoring load electric current in transformer circuit, utilize the electric current of known voltage and monitoring to calculate pull-up resistor, or monitoring current, voltage calculate pull-up resistor, or direct sensing lead resistance, or setting pull-up resistor curve, frequency impedance evaluation work frequency and dutycycle during according to the pull-up resistor load, frequency of operation and the dutycycle calculated by circuit apply back-lash voltage to the main coil port.
The method for designing of 17 AC transformer fixed frequencies
" iron core parameter and coil parameter when the frequency impedance of the frequency impedance during according to load when unloaded can be to the AC transformer fixed frequency design " described in the claim 1, it is characterized in that: by the fixed frequency point of outside when transformer goes into to hold the ac frequency that provides to be exactly transformer work, its design process is, (1) clear and definite designing requirement: go into terminal voltage Ua, go out terminal voltage Ub, ac frequency fb, output rating P3, peak power output P4; (2) calculate the minimum output resistance Rk/R2 of secondary coil * { K+A * Cos[B/ (4 * R2 * fa] } * [N ± M
1/M* (Ns/N0)
1.5 * M] * S * F (α)=1 calculates nominal load resistance R 3=Ub
2/ P3 calculates minimum load output resistance R4=Ub
2/ P4; Frequency impedance during (3) by load calculates idling frequency fa, the fc when calculating peak power output; (4) five parameters of selection and definite iron core; Frequency impedance during (5) according to load, energy exchange resistance R 0=(f3/fa-1) * R3 * Na of main coil when calculating zero load
2/ Nb
2Perhaps provide approximate value of Na/Nb, find the solution the approximate value of R0; (6) according to the no-load current of the approximation calculation main coil of R0, according to the equivalent current of peak power output computational load on main coil, by the no-load current of main coil with load on equivalent current on the main coil and, the line footpath of calculating lead; (7) determine the coiling mode of coil, the frequency impedance during according to zero load, design, the number of turn of calculating every layer line circle and the number of plies of coil; (8) design content that repeats 5,6,7 approaches, till the frequency impedance when frequency impedance when zero load and load all meets the demands; (9) check Cos[B/ (4 * R0 * f)] in B/ (4 * R0 * f) whether greater than π, if B/ is (during 4 * R0 * f) greater than π, determine that (higher limit of 4 * R0 * f) redefines the iron core parameter to B/, according to the order redesign of (5), (6), (7), (8); General frequency impedance during (10) according to zero load calculates the energy conversion resistance R 2 of secondary coil, calculates to determine the quantity of bridging coil and the line footpath of winding wire if the energy conversion resistance R 2 of secondary coil, be carried out bridging coil greater than R4, makes R2 less than R4.
The method for designing of 18 electronic transformers
" frequency impedance of the frequency impedance during according to various types of electronic transformer load when unloaded can design the iron core parameter and the coil parameter of various types of electronic transformers " described in the claim 1, it is characterized in that: range transformer or the inductor formed by coil and iron core, can according to the main coil port whether shnt capacitor be divided into that LC relation in parallel is in parallel with non-LC to concern two types, by the unloaded frequency impedance and the mathematic(al) manipulation of load frequency impedance process of LC relation in parallel, can be transformed into the unloaded frequency impedance and the load frequency impedance of non-LC relation in parallel; The main coil port applies when being alternating voltage, and the method for designing by AC transformer designs; When the main coil port is unidirectional back-lash voltage or two-way back-lash voltage, also can concern that the method for designing of transformer designs by LC is in parallel even without shnt capacitor; Iron inductance designs by the method for designing of the unloaded transformer of the unidirectional back-lash voltage of design; Dissimilar transformers all has specific function request for utilization, when design ratio by determining unloaded operation frequency and loaded work piece frequency, (usable range of 4 * R0 * f) is with the realization designing requirement by determining angle value B * C or B/.
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| CN103364451A (en) * | 2013-06-03 | 2013-10-23 | 华中科技大学 | Frequency-characteristics-based method for identifying inner conductor materials of equipment based on |
| CN104198843A (en) * | 2014-08-14 | 2014-12-10 | 西南交通大学 | Power grid impedance frequency property testing method and device |
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| CN109655662A (en) * | 2018-08-23 | 2019-04-19 | 刘飞翠 | A kind of k-factor calculation method calculating power by transformer core sectional area |
| CN112259360A (en) * | 2020-12-22 | 2021-01-22 | 三变科技股份有限公司 | Production method and turn number verification method of epoxy resin cast coil of dry-type transformer |
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| CN103364451A (en) * | 2013-06-03 | 2013-10-23 | 华中科技大学 | Frequency-characteristics-based method for identifying inner conductor materials of equipment based on |
| CN103364451B (en) * | 2013-06-03 | 2016-01-20 | 华中科技大学 | A kind of equipment internal conductor material recognition methods based on frequency characteristic |
| CN104198843A (en) * | 2014-08-14 | 2014-12-10 | 西南交通大学 | Power grid impedance frequency property testing method and device |
| CN104198843B (en) * | 2014-08-14 | 2017-01-11 | 西南交通大学 | Power grid impedance frequency property testing method and device |
| CN107576847A (en) * | 2017-09-07 | 2018-01-12 | 西南交通大学 | A kind of vehicular tractive power supply system impedance frequency characteristic measurement apparatus and its measuring method |
| CN107576847B (en) * | 2017-09-07 | 2024-04-26 | 西南交通大学 | Impedance frequency characteristic measuring device and measuring method for vehicle-mounted traction power supply system |
| CN109655662A (en) * | 2018-08-23 | 2019-04-19 | 刘飞翠 | A kind of k-factor calculation method calculating power by transformer core sectional area |
| CN112259360A (en) * | 2020-12-22 | 2021-01-22 | 三变科技股份有限公司 | Production method and turn number verification method of epoxy resin cast coil of dry-type transformer |
| CN112259360B (en) * | 2020-12-22 | 2021-03-02 | 三变科技股份有限公司 | Production method and turn number verification method of epoxy resin cast coil of dry-type transformer |
| CN116380163A (en) * | 2023-03-29 | 2023-07-04 | 青岛峻海物联科技有限公司 | Sensing device for intelligent environment data acquisition of Internet of things |
| CN116380163B (en) * | 2023-03-29 | 2024-01-19 | 青岛峻海物联科技有限公司 | Sensing device for intelligent environment data acquisition of Internet of things |
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