Coreless transformer based on virtual relative permeability principle

Abstract

The present invention discloses a coreless transformer based on the principle of virtual relative magnetic permeability, comprising a primary circuit, a secondary circuit, and an intermediate multi-circuit; the primary circuit comprises a primary coil and a sinusoidal voltage source that provides energy to the transformer, and the sinusoidal voltage source and the primary coil are connected in series; the secondary circuit comprises a secondary coil and a load resistor, and the secondary coil and the load resistor are connected in series; there is no core connection between the primary coil and the secondary coil; the intermediate multi-circuit refers to no less than one intermediate circuit, each intermediate circuit comprises an intermediate coil and an intermediate capacitor, and the intermediate coil and the intermediate capacitor are connected in series. Without using an iron core, the primary coil, the secondary coil, and each intermediate coil are coupled to each other only through the magnetic field in the air. Based on the principle of virtual relative magnetic permeability, the present invention proposes for the first time the overall resonance condition of multiple intermediate coils, achieving the effect of increasing the excitation impedance and reducing the excitation current.

Description

Technical Field

[0001] The present invention relates to the technical field of transformers, and in particular to a coreless transformer based on the principle of virtual relative magnetic permeability. Background Art

[0002] Transformers are indispensable power devices in the field of electrical engineering, playing an irreplaceable role in voltage conversion, current conversion, impedance conversion, isolation, and voltage stabilization.

[0003] However, complaints about core components, such as "too large, too high a temperature rise, too much noise, and too heavy," have long plagued transformer designers and hindered the development of related electrical fields. Removing the core and achieving the same transformer effect would greatly optimize related electrical designs. Therefore, coreless transformers have long been a goal sought both domestically and internationally, and their advantages are obvious:

[0004] 1. Reduce transformer weight and volume;

[0005] 2. There is no eddy current and hysteresis loss;

[0006] 3. There is no problem of core saturation, which is more suitable for high-energy applications;

[0007] 4. Harmonics and surge currents caused by nonlinear characteristics of the ironless core;

[0008] 5. No noise caused by oscillation between core layers;

[0009] 6. No need to consider the insulation problem between the core and the winding;

[0010] 7. Easier to integrate and design.

[0011] Over the years, various coreless transformers have been proposed, including Tesla coreless transformers, superconducting coreless transformers, PCB high-frequency coreless transformers, and semiconductor planar coreless transformers. However, these coreless transformers all have significant shortcomings and fail to address the coreless transformer's inherent problems: low main magnetic flux, high excitation current, and high magnetic leakage. Tesla coreless transformers utilize a two-coil resonant principle to generate a high voltage output, primarily used in high-voltage testing and research, such as withstand voltage testing and lightning simulation. However, their low efficiency and lack of load capacity make them unsuitable for civilian and industrial applications. Superconducting coreless transformers require extremely low temperatures and have extremely high operating costs, hindering widespread application. PCB high-frequency coreless transformers offer the advantage of high integration, but suffer from extremely high operating frequencies, typically reaching several to tens of MHz. Transmission power is low, limited to a few to tens of watts, and maximum efficiency below 90%. Semiconductor coreless transformers also suffer from extremely high operating frequencies, low power output, and significant parasitic influence. Summary of the Invention

[0012] The present invention aims to overcome the shortcomings and deficiencies of existing technologies by proposing a coreless transformer based on the principle of virtual relative permeability. By applying this principle to the design of a coreless transformer, the transformer achieves the same voltage conversion function as a traditional iron-core transformer and enables high-efficiency transmission. Compared with existing coreless transformers, the coreless transformer achieves a substantially improved excitation impedance, resolving the problems of low main magnetic flux, high excitation current, and high magnetic leakage that coreless transformers often face. While achieving the same voltage conversion function as traditional transformers, the coreless transformer is expected to replace traditional iron-core transformers.

[0013] To achieve the above-mentioned purpose, the technical solution provided by the present invention is: a coreless transformer based on the principle of virtual relative magnetic permeability, the transformer including a primary circuit, a secondary circuit and an intermediate multi-circuit; the primary circuit includes a primary coil and a sinusoidal voltage source that provides energy to the transformer, and the sinusoidal voltage source and the primary coil are connected in series; the secondary circuit includes a secondary coil and a load resistor, and the secondary coil and the load resistor are connected in series; there is no iron core connection between the primary coil and the secondary coil; the intermediate multi-circuit refers to no less than one intermediate circuit, each intermediate circuit includes an intermediate coil and an intermediate capacitor, and the intermediate coil and the intermediate capacitor are connected in series; when no iron core is used, the primary coil, the secondary coil and each intermediate coil are coupled to each other only through the magnetic field in the air.

[0014] Furthermore, the intermediate coil and the intermediate capacitor must satisfy the following overall resonance condition with the determinant being zero:

[0015] det(Z xx )=0

[0016] in,

[0017]

[0018] Where Z xx is the impedance matrix between the middle coils, R (2+i) is the internal resistance of the ith intermediate circuit, C (2+i) is the capacitance value of the ith intermediate circuit, L (2+i) is the inductance of the i-th intermediate loop, assuming that the first coil represents the primary coil, the second coil represents the secondary coil, and the third, fourth, ..., (2+E) coils are all intermediate coils; M (2+i)3 、M 3(2+i) is the mutual inductance between the first intermediate circuit and the i-th intermediate circuit, M (2+E)3 、M 3(2+E)is the mutual inductance between the first intermediate loop and the Eth intermediate loop, where i, j = 1, 2, ..., E, E is the number of intermediate coils used; ω is the operating angular frequency; it can be seen that the above equation is an equation about ω, and the solution of the equation about ω is recorded as the resonant angular frequency α0. When there is only one intermediate loop, that is, E = 1, the resonant angular frequency

[0019] Furthermore, after adding the intermediate circuit, the following virtual relative permeability expression is equivalently obtained:

[0020]

[0021] in,

[0022] A=(X T X) -1 X T

[0023]

[0024] z x1 ={Z 31 , Z 41 ,…,Z (2+E)1}

[0025] z x2 ={Z 32 , Z 42 ,…,Z (2+E)2}

[0026] y = [1, 0, ..., 0] T

[0027] Where A, X, and z x1 、z x2 , y are both intermediate matrices for expression calculation; Z (2+E)1 represents the mutual impedance between the first coil and the (2+E)th coil, Z (2+E)2 represents the mutual impedance between the second coil and the (2+E)th coil; is the virtual relative permeability of the proposed transformer at the resonant frequency, which directly represents the multiple of the equivalent increase in the transformer mutual inductance / excitation impedance.

[0028] Furthermore, the equivalent turns ratio n of the transformer e Satisfies the relationship:

[0029]

[0030] The above equivalent turns ratio n e It represents the ratio of the primary voltage to the secondary voltage of the transformer under no-load conditions.

[0031] The operating principle of this invention is that by adding an intermediate coil, the virtual relative permeability of the space between the primary and secondary coils is altered, thereby changing the magnetic circuit properties, thereby increasing the excitation impedance and reducing the excitation current. When the excitation impedance is sufficiently large, reaching the level of a conventional iron-core transformer, efficient power transmission can be achieved while maintaining the voltage transformation ratio. Therefore, the coreless transformer of this invention can achieve nearly the same functions as a conventional iron-core transformer.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] 1. Compared with traditional iron core transformers, the transformer of the present invention does not require an iron core and has no saturation, harmonic, surge current, or noise problems.

[0034] 2. Compared with traditional iron core transformers, the weight and volume of the present invention are greatly reduced, and it is easy to integrate and design, and is suitable for lightweight design.

[0035] 3. Compared with the existing coreless transformer, the present invention has low operating frequency, extremely small excitation current and large output power.

[0036] 4. Compared with the existing coreless transformer, the present invention can work normally within the full load range, the voltage ratio is constant, and the voltage ratio is proportional to the square root of the ratio of the primary and secondary coil inductances, which is consistent with the law of traditional transformers.

[0037] In summary, this invention, based on the principle of virtual relative permeability, proposes for the first time the overall resonance condition of multiple intermediate coils, achieving the effect of increasing the excitation impedance and reducing the excitation current. When the excitation impedance is sufficiently large, reaching the level of a traditional iron-core transformer, efficient power transmission can be achieved while maintaining the voltage transformation ratio. This invention achieves a coreless design, reducing the weight, volume, and cost of the transformer, making it worthy of widespread adoption. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the circuit diagram of the coreless transformer structure based on the principle of virtual relative magnetic permeability.

[0039] Figure 2 Schematic diagram of the principle of virtual relative magnetic permeability.

[0040] Figure 3 This is the equivalent circuit diagram of the transformer leakage inductance.

[0041] Figure 4 The diagrams are the transformer T-type equivalent circuit and the cantilever equivalent circuit.

[0042] Figure 5 is a curve diagram of the relationship between the virtual relative permeability amplitude and frequency.

[0043] Figure 6It is the virtual relative permeability phase angle curve.

[0044] Figure 7 These are the transformer input voltage, input current, output current, and output voltage waveforms.

[0045] Figure 8 This is the transformer power factor curve.

[0046] Figure 9 This is the transformer load adjustment rate curve.

[0047] Figure 10 Transformer efficiency diagram. DETAILED DESCRIPTION

[0048] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0049] like Figure 1 As shown, this embodiment discloses a coreless transformer based on the virtual relative permeability principle, including a primary circuit, a secondary circuit and an intermediate multi-circuit; the primary circuit includes a primary coil L1 and a sinusoidal voltage source; the primary coil L1 and the sinusoidal voltage source are connected in series, the voltage across the sinusoidal voltage source is V1, and the angular frequency is ω; the secondary circuit includes a secondary coil L2 and a load resistor R L The secondary coil L2, load resistor R L Series connection; the intermediate multi-circuit refers to at least one intermediate circuit, each intermediate circuit includes an intermediate coil and an intermediate capacitor; the intermediate coil and the intermediate capacitor are connected in series; when no iron core is used, the primary coil, the secondary coil and each intermediate coil are coupled to each other only through the magnetic field in the air.

[0050] Now consider the simplest case, that is, adding only one intermediate resonant coil. The mutual inductance equivalent circuit obtains the voltage equation in the form of the following node impedance matrix:

[0051]

[0052] in,

[0053]

[0054] Where M 12 is the mutual inductance between the primary and secondary coils; M 23 is the mutual inductance between the secondary coil and the middle coil; M 13 is the mutual inductance between the primary coil and the intermediate coil; Z ii (i=1,2,3) is the self-impedance, Z ij(i≠j, i,j=1,2,3). L1, L2, L3 are the inductance values ​​of the primary, secondary, and middle coils respectively; are the currents of the primary, secondary and middle coils respectively; R1, R2 and R3 are the internal resistances of the primary, secondary and middle coils respectively; The primary input voltage and the secondary output voltage respectively.

[0055] eliminate Rearranging the equations yields the following equivalent two-port circuit:

[0056]

[0057] Since the coil inductance is proportional to the relative magnetic permeability, the coil impedance is also approximately proportional to the relative magnetic permeability, so the virtual relative magnetic permeability matrix μ is introduced r , the circuit equation is rewritten as follows:

[0058]

[0059] Among them, the virtual relative permeability matrix is:

[0060]

[0061] It can be seen that the intermediate resonant coil can change the relative magnetic permeability of the coreless transformer equivalently, which is equivalent to changing the inductance. Since mutual inductance reflects the power transmission capacity, compared with the virtual relative magnetic permeability of self-inductance We are more concerned about the relative permeability of mutual inductance. Virtual relative permeability of mutual inductance This is the virtual relative permeability defined as:

[0062]

[0063] Z′ 12 is the equivalent mutual inductance of the equivalent two-port matrix. The virtual relative permeability at the resonant frequency is recorded as Its expression is:

[0064]

[0065] When Z 33 When Z is approximately zero, 33 is very small, the virtual relative permeability becomes very large, which is approximately equivalent to the effect of the iron core. The mutual coupling flux of the original secondary coil is approximately at the permeability of In the equivalent medium, Figure 2 shown. Figure 2 In fact, from (4) we can see that when Z 33 When it is equal to 0, and It has nothing to do with it. It can be regarded as an excitation current of reactive nature. and It can be approximately regarded as the load current.

[0066] Extending to the case of multiple intermediate coils, assuming that E intermediate resonant coils are used and the positions of the resonant coils are not fixed, let indices 1 and 2 represent the original secondary coils, and the next E indices represent the intermediate resonant coils. At this time, the voltage equation in the form of the following impedance matrix is ​​obtained:

[0067] Z·i=v (8)

[0068] in,

[0069]

[0070] vector Similar to the case of a single middle coil, in order to ensure that the transformer characteristic of the excitation current is independent of the load current in the case of multiple coils, the current of the middle coil should be Regardless, the following generalized conditions for the overall resonance of the middle coil must be met:

[0071] det(Z xx )=0 (10)

[0072] in,

[0073]

[0074] Where Z xx is the impedance matrix between the middle coils, R (2+i) is the internal resistance of the ith intermediate circuit, C (2+i) is the capacitance value of the ith intermediate circuit, L (2+i) is the inductance of the i-th intermediate circuit, assuming that the first coil represents the primary coil, the second coil represents the secondary coil, and the third, fourth, ..., (2 + E) coils are all intermediate coils; M (2+i)3 、M 3(2+i) is the mutual inductance between the first intermediate circuit and the i-th intermediate circuit, M (2+E)3 、M 3(2+E) is the mutual inductance between 1 intermediate loop and the Eth intermediate loop, where i, j = 1, 2, ..., E, E is the number of intermediate coils used; ω is the operating angular frequency; it can be seen that the above equation is an equation about ω, and the solution of the equation about ω is recorded as the resonant angular frequency ω0. When there is only one intermediate loop, that is, E = 1, the resonant angular frequency To calculate The following simplifications are required:

[0075]

[0076] in, t=[t1,t2,…,t E ] T . The equivalent current introduced is used to convert all intermediate coils into a single equivalent intermediate coil. The E intermediate resonant coils have been replaced by an equivalent resonant coil, represented by the index x. When E = 1, the equivalent resonant coil is the single intermediate resonant coil itself. According to (14), (10) can be transformed into the following form:

[0077]

[0078] Equivalent impedance Z x1 , Z x2 、Z xx for:

[0079]

[0080] Where z x1 ={Z 31 ,Z 41 ,…,Z (2+E)1}, z x2 ={Z 32 ,Z 42 ,…,Z (2+E)2}. The inductance L of the equivalent resonant coil x , the equivalent mutual inductance coefficient M of the equivalent resonant coil and the original secondary coil x1 、M x2 It can be calculated as:

[0081] M x1 =Z x1 / (jω),M x2 =Z x2 / (jω),

[0082]

[0083] From (15) we can deduce:

[0084]

[0085] When condition (12) is satisfied, assuming and is zero, t can be calculated as:

[0086] t=Ay (17)

[0087] Where A=(X T X) -1 X T , y=[1,0,…,0] T , Therefore, (16) can be simplified into the following formula:

[0088]

[0089] The equivalent turns ratio of the proposed coreless transformer is:

[0090]

[0091] Among them, k x1 and Represents the coupling coefficient of the equivalent coil. Similar to the derivation of (20), n e The following approximate calculation expressions are available:

[0092]

[0093] In addition, the leakage inductance equivalent circuit parameters of the proposed coreless transformer can be calculated as:

[0094]

[0095] L lp 、L ls 、L lx 、L m They represent the primary leakage inductance, secondary leakage inductance, equivalent resonant coil leakage inductance and primary magnetizing inductance respectively. The leakage inductance equivalent circuit is as follows: Figure 3 By converting the parameters to the primary side and considering the internal resistance, we can get Figure 4 The T-type equivalent circuit in. Equivalent excitation impedance Z me It can be calculated by the following formula:

[0096]

[0097] where R m =Re(Z me ). Figure 4 It is also shown that the T-type equivalent circuit can be further simplified into a cantilever circuit, so the short-circuit impedance Z of the proposed transformer is k It can be calculated by the following formula:

[0098]

[0099] In addition, for the loss model, consistent with the iron core transformer, the loss of the proposed coreless transformer can also be divided into two parts, namely load loss and no-load loss. l12 is the ohmic loss of the original secondary coil, and the no-load loss P lx is the ohmic loss of the middle coil, which has nothing to do with the load current. The loss calculation formula is:

[0100]

[0101] Therefore, the proposed transformer efficiency is:

[0102]

[0103] Where θ2 represents the load power factor angle. In addition, the following efficiency calculation formula can be derived:

[0104]

[0105] where Z L Indicates the load impedance.

[0106] To illustrate the accuracy and feasibility of the present invention, a coreless transformer based on the virtual relative permeability principle is designed in this embodiment. The parameters of the designed coreless transformer are as follows: the effective value of the sinusoidal voltage source voltage V1 = 95V; the equivalent turns ratio n e =1.85; resonant frequency f0 is 101.9KHz; inductance matrix parameters are: [19.78, 8.20, 16.54, 15.92; 8.20, 4.32, 9.00, 8.54; 16.54, 9.00, 40.97, 11.81; 15.92, 8.54, 11.81, 39.26] (μH); the two resonant capacitors added to the two middle coils are C3 = C4 = 47nF. Considering that the internal resistance of the primary coil R1 is 120mΩ, the internal resistance of the secondary coil R2 is 15mΩ, and the internal resistance of the middle coil R3 and R4 are both 180mΩ. The analysis results are as follows Figures 5-10 shown.

[0107] Figure 5 is the curve of the relationship between the virtual relative permeability amplitude and frequency. It can be seen that the virtual relative permeability amplitude reaches its maximum value at f0 (f0=ω0 / (2π)), and the maximum value Reached 1144. Figure 6 The virtual permeability phase angle curve is shown in Figure 2. When the frequency is lower than f0, the equivalent excitation impedance is inductive, when it is equal to f0, it is almost purely resistive, and when it is greater than f0, it is capacitive. Figure 7 The waveforms of transformer input voltage v1, input current i1, output current i2, and output voltage v2 are shown. Figure 8 、 Figure 9 and Figure 10 The following are the power factor, load regulation and efficiency curves. It can be seen that the maximum efficiency is 98.1% when the load resistance is 4 ohms, and the efficiency can reach 97.7% when the full load is 500W.

[0108] According to the above analysis, the coreless transformer based on the flux maximization principle described in the present invention can completely replace the traditional iron-core transformer. The advantages of the present invention are obvious and worthy of promotion.

[0109] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A coreless transformer based on the principle of virtual relative permeability, characterized by: The transformer includes a primary circuit, a secondary circuit, and an intermediate multi-circuit; the primary circuit includes a primary coil and a sinusoidal voltage source that provides energy to the transformer, and the sinusoidal voltage source and the primary coil are connected in series; the secondary circuit includes a secondary coil and a load resistor, and the secondary coil and the load resistor are connected in series; there is no iron core connection between the primary coil and the secondary coil; the intermediate multi-circuit refers to at least one intermediate circuit, each intermediate circuit includes an intermediate coil and an intermediate capacitor, and the intermediate coil and the intermediate capacitor are connected in series; when no iron core is used, the primary coil, the secondary coil, and each intermediate coil are coupled to each other only through the magnetic field in the air; After adding the intermediate circuit, the following virtual relative permeability expression is equivalently obtained: ； in, ； ； ； ； ； Where, 、 、 、 、 They are all intermediate matrices for expression calculation; The impedance matrix between the middle coils is defined as , and the middle coils and the middle capacitors need to satisfy the following overall resonance condition with zero determinant: ; represents the mutual impedance between the first coil and the (2+E)th coil, represents the mutual impedance between the second coil and the (2+E)th coil; is the virtual relative permeability of the proposed transformer at the resonant frequency, which directly represents the multiple of the equivalent increase in the transformer mutual inductance / excitation impedance.

2. The coreless transformer based on the virtual relative permeability principle according to claim 1, characterized in that: ； Where, is the internal resistance of the ith intermediate circuit, is the capacitance value of the ith intermediate circuit, is the inductance of the i-th intermediate loop, let the first coil represent the primary coil, the second coil represent the secondary coil, and the third, fourth, …, (2 + E) coils are all intermediate coils; 、 is the mutual inductance between the first intermediate loop and the i-th intermediate loop, 、 is the mutual inductance between the 1st intermediate loop and the Eth intermediate loop, where i, j = 1, 2, ..., E, is the number of intermediate coils used; is the working angular frequency; it can be seen that the above equation is about The equation of The solution is recorded as the resonant angular frequency , when there is only one intermediate loop, that is When the resonant angular frequency .

3. The coreless transformer based on the virtual relative permeability principle according to claim 2, characterized in that: The equivalent turns ratio of the transformer Satisfies the relationship: ； The above equivalent turns ratio It represents the ratio of the primary voltage to the secondary voltage of the transformer under no-load conditions.

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