Method for calculating leakage inductance of high-frequency transformer under non-sine excitation

Abstract

The invention discloses a method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation, and the method comprises the following steps: decomposing a non-sinusoidal high-frequency excitation source introduced into the high-frequency transformer into a plurality of sinusoidal high-frequency excitation sources through Fourier decomposition; according to the winding insulation gap of the high-frequency transformer needing to be calculated, a proper basic algorithm is selected, and the leakage inductance of the small-capacity high-frequency transformer is calculated through two Dowell correction algorithms; the sum of the leakage inductance energy generated by each sine excitation source is equal to the leakage inductance energy generated by the non-sine excitation source; respectively calculating leakage inductance energy of the high-frequency transformer under each high-frequency sine excitation source by using a basic algorithm so as to obtain leakage inductance under each harmonic wave; according to the proportion of the effective value of the harmonic component in the total effective value of the non-sine excitation, performing weighted correction calculation on the basic leakage inductance algorithm to obtain the leakage inductance of the high-frequency transformer under the non-sine excitation; according to the method, the leakage inductance of the high-frequency transformer under non-sine excitation is corrected and calculated, and the precision is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer technology, and in particular to a method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation. Background Technology

[0002] The leakage inductance of a high-frequency transformer is a crucial technical indicator, affecting its efficiency, stability, and temperature rise. Excessive leakage inductance leads to significant voltage spikes and reduces transformer efficiency, while insufficient leakage inductance typically increases parasitic capacitance. Furthermore, the leakage inductance of high-frequency transformers is frequently utilized in the circuit design of power transformers, making its analysis and calculation necessary.

[0003] Because the permeability of transformer core materials cannot reach infinity, and because the windings cannot be completely flush with the outer surface of the core during actual transformer manufacturing, gaps exist between the windings and the core. Similarly, gaps also exist between windings in the same layer. Furthermore, a certain insulation distance must be maintained between each layer of windings. These factors cause some magnetic flux to leak during the coupling process of the primary and secondary windings of the transformer. This leakage flux can be represented as an inductance, hence the term leakage inductance. Unlike traditional power frequency transformers, the leakage inductance of high-frequency transformers exhibits a frequency-dependent effect; that is, the leakage inductance of high-frequency transformers changes with frequency. The calculation formulas for the leakage inductance of high-frequency transformers should fully consider this. Since leakage energy is mainly located within and between windings, the winding method and wire diameter will affect the magnitude of the leakage inductance. Many existing formulas for analytically calculating leakage inductance are based on Dowell's assumption of a one-dimensional electromagnetic field. However, in reality, accurately calculating the energy of the leakage magnetic field using formulas is very difficult because the electromagnetic field distribution of high-frequency transformers is quite complex. The finite element method (FEM) model inherently considers conductor edge effects, resulting in high calculation accuracy. It is also applicable to conductors and winding structures of arbitrary shapes, making it commonly used to calculate the leakage inductance of high-frequency transformers. All the research on high-frequency transformer leakage inductance mentioned above has been conducted under sinusoidal excitation conditions. Further research is needed on leakage inductance of high-frequency transformers under non-sinusoidal excitation conditions. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation, so as to solve the problems mentioned in the background art.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation, comprising the following steps: Step 1: Using Fourier decomposition, the non-sinusoidal high-frequency excitation source fed into the high-frequency transformer is decomposed into multiple sinusoidal high-frequency excitation sources; Step 2: Select the appropriate basic algorithm based on the insulation gap between the primary and secondary windings of the high-frequency transformer that needs to be calculated. For small-capacity high-frequency transformers, leakage inductance is calculated using two Dowell correction algorithms. Algorithm 1 is suitable for smaller insulation gaps, while Algorithm 2 is suitable for larger insulation gaps. Step 3: Assume that the leakage magnetic energy generated by each of the decomposed high-frequency sinusoidal excitation sources in the high-frequency transformer is independent of each other and does not affect each other, that is, the sum of the leakage inductance energy generated by each sinusoidal excitation source is equal to the leakage inductance energy generated by the non-sinusoidal excitation source. Step 4: Use the basic algorithm to calculate the leakage inductance energy of the high-frequency transformer under each high-frequency sinusoidal excitation source, and then obtain the leakage inductance under each harmonic. Step 5: Based on the proportion of the effective value of the harmonic components in the total effective value of the non-sinusoidal excitation, perform weighted correction calculation on the basic leakage inductance algorithm to finally obtain the leakage inductance of the high-frequency transformer under non-sinusoidal excitation.

[0006] Preferably, step 1 specifically includes: (1); in For non-sinusoidal excitation sources, The even harmonics after Fourier decomposition These are the odd harmonics after Fourier decomposition. For harmonic order, For the period of this non-sinusoidal excitation, Let ω be the angular velocity of the excitation. For time.

[0007] Preferably, in step 2, Algorithm 1 is applicable to areas with smaller insulation gaps, where the insulation gap between the primary and secondary windings is less than 6 times the winding thickness.

[0008] Preferably, in step 2, algorithm 2 is applicable to a larger insulation gap, that is, the insulation gap between the primary and secondary windings is greater than 6 times the winding thickness.

[0009] Preferably, in step 2, the calculation of leakage inductance of the small-capacity high-frequency transformer using two Dowell correction algorithms includes the following process: The total leakage flux energy is divided into five parts: leakage flux energy in the primary winding, leakage flux energy in the secondary winding, leakage flux energy in the primary winding gap, leakage flux energy in the secondary winding gap, and leakage flux energy in the insulation gap between the primary and secondary windings. In actual leakage inductance calculation, the total leakage inductance energy is calculated first, and then the transformer leakage inductance is calculated. There are two Dowell correction leakage inductance algorithms, namely Dowell correction algorithm 1 and Dowell correction algorithm 2.

[0010] Preferably, the Dowell correction algorithm 1 is as follows: The leakage flux energy between the primary and secondary winding insulation gaps is: (2); The leakage flux energy in the primary winding gap is: (3); The leakage flux energy in the secondary winding gap is: (4); Leakage magnetic energy in primary winding: (5); Leakage magnetic energy in the secondary winding: (6); In the formula and These are the effective values ​​of the primary and secondary winding currents, respectively. and These represent the number of turns in each layer of the primary and secondary windings, respectively. , and These are the average lengths of the insulation gap between the primary winding, the secondary winding, and the primary-secondary winding, respectively. and These refer to the number of layers in the primary winding and the secondary winding, respectively. The conductivity of a conductor. For winding height, , and This refers to the thickness of the primary winding, the thickness of the secondary winding, and the thickness of the insulation gap between the primary and secondary windings. and These represent the thickness of the i-th interlayer gap between the primary and secondary windings, respectively. The skin depth of the winding conductor. For conductor transmittance; Skin depth of winding conductors: (7); In the formula The frequency of the current in the winding conductor; The total leakage magnetic energy of the high-frequency transformer can be calculated from the above formula. The leakage inductance of the transformer referred to the primary side is shown in equation (8): (8); In practical high-frequency transformer design cases, high-frequency transformers cannot perfectly conform to Dowell's ideal transformer magnetic field model. The permeability of the transformer core is not infinite, and the height of the winding layers and the core window are inconsistent. Therefore, reasonable corrections are needed to reduce calculation errors. In actual calculations, the Rockwell coefficient is used. The calculated height of the winding is corrected, and its expression is shown in (9): (9); in The width of the leakage magnetic field inside the core window can be calculated using equation (10): (10).

[0011] Preferably, the Dowell correction algorithm 2 is as follows: Dowell correction algorithm 2, like Dowell correction algorithm 1, is based on the Dowell one-dimensional magnetic field model. It divides the leakage magnetic energy into five parts for calculation and then uses the total leakage magnetic energy to obtain the leakage inductance of the high-frequency transformer. The difference between the two methods lies in the different ways of handling the leakage magnetic energy inside the winding, resulting in different calculation formulas. Dowell correction algorithm 1 uses formula (11) to calculate the leakage magnetic energy inside the winding, while Dowell correction algorithm 2 uses formula (12) to calculate the leakage magnetic energy inside the winding. The formula obtained by Dowell correction algorithm 2 is shown in (13). (11); (12); (13); In the formula This represents the actual magnetic field strength. To calculate the magnetic field strength, It is an imaginary number. The number of turns in the winding. The magnitude of the current in the winding. This refers to the number of winding layers. For winding thickness, The conductivity of a conductor. This represents the average length of the winding. The real part of the result of equation (11) is the leakage inductance energy; If the windings of a high-frequency transformer are transposed during the winding process, the windings can be divided into several similar parts consisting of primary and secondary windings. The leakage magnetic energy of all similar parts can be calculated separately and then superimposed to obtain the total leakage magnetic energy. Finally, the total leakage inductance can be calculated.

[0012] Preferably, in step 3, it is assumed that the energy generated by each of the decomposed high-frequency sinusoidal excitation sources in the high-frequency transformer is independent and does not affect each other, that is, the sum of the leakage inductance energy generated by each sinusoidal excitation source is equal to the leakage inductance energy generated by the non-sinusoidal excitation source, including: (14); In the formula It is the leakage inductance energy generated by the i-th harmonic.

[0013] Preferably, in step 4, the leakage inductance energy of the high-frequency transformer under each high-frequency sinusoidal excitation source is calculated using the basic algorithm, thereby obtaining the leakage inductance under each harmonic order, including: (15); In the formula, The leakage inductance is the calculated value at the i-th harmonic frequency. Let be the effective value of the current for the i-th harmonic.

[0014] Preferably, in step 5, the basic leakage inductance algorithm is weighted and corrected based on the proportion of the effective value of the harmonic components in the total effective value of the non-sinusoidal excitation, and the leakage inductance of the high-frequency transformer under non-sinusoidal excitation is finally obtained as follows: (16); In the formula Let be the leakage inductance correction coefficient under the i-th harmonic. This represents the total effective value of the non-sinusoidal excitation current.

[0015] Beneficial effects of this invention: 1) This invention proposes an effective method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation. By assuming that the sum of leakage magnetic energy generated by each harmonic after Fourier decomposition is equivalent to the leakage magnetic energy generated by the original non-sinusoidal excitation, the leakage inductance of the high-frequency transformer under non-sinusoidal excitation is corrected and calculated. The accuracy of the corrected calculation results is greatly improved compared with the traditional calculation method.

[0016] 2) This invention obtains the leakage inductance of a high-frequency transformer under non-sinusoidal excitation by modifying the results of the basic sinusoidal excitation calculation method. Therefore, it is not limited by the basic algorithm and can be replaced with a more accurate sinusoidal excitation calculation method at any time to further improve the calculation accuracy. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process of the present invention.

[0018] Figure 2 This is a schematic diagram of the finite element model of a high-frequency transformer as an example.

[0019] Figure 3 The diagram shows the structural parameters of the high-frequency transformer in this embodiment.

[0020] Figure 4 The calculation results are shown in the figure for the example. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0022] Example 1: Combined with Appendix Figure 1 A method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation includes the following steps.

[0023] Step 1: Using Fourier decomposition, the non-sinusoidal high-frequency excitation source fed into the high-frequency transformer is decomposed into multiple sinusoidal high-frequency excitation sources. With the effective value of the current Taking a square wave as an example, using the effective value of the current... The square wave, used as a non-sinusoidal high-frequency excitation source, is decomposed into multiple sinusoidal excitation sources using Fourier decomposition, as shown in the following formula: (1); in For non-sinusoidal excitation sources, The even harmonics after Fourier decomposition These are the odd harmonics after Fourier decomposition. For general non-sinusoidal excitation, the number of harmonics after Fourier decomposition is very large. To simplify the calculation, only the first few harmonics with a relatively high proportion can be taken, while the higher harmonics with a lower proportion in the total waveform are ignored. For square waves, the first 15 harmonics account for more than 95% of the total waveform, so only the first 15 harmonics are taken for calculation here.

[0024] Step 2: Select the appropriate basic algorithm based on the winding insulation gap of the high-frequency transformer that needs to be calculated. Two Dowell correction algorithms are commonly used to calculate leakage inductance for small-capacity high-frequency transformers. Algorithm 1 is suitable for smaller insulation gaps, while Algorithm 2 is suitable for larger insulation gaps. according to Figure 2 Schematic winding structure and Figure 3 In this case, the insulation gap between the primary and secondary windings of the high-frequency transformer is relatively small. Therefore, Dowell's modified algorithm 1 should be used as the basic algorithm, and then this modified method should be used to correct the leakage inductance calculation results of the basic algorithm. Thus, Dowell's modified algorithm 1 should be used to calculate the leakage inductance under each harmonic after Fourier decomposition separately. The calculation formulas for the leakage inductance under each harmonic are as follows: 1) Dowell's Correction Algorithm 1: The leakage flux energy between the primary and secondary winding insulation gaps is: (2); The leakage flux energy in the primary winding gap is: (3); The leakage flux energy in the secondary winding gap is: (4); Leakage magnetic energy in primary winding: (5); Leakage magnetic energy in the secondary winding: (6); In the formula and These are the effective values ​​of the primary and secondary winding currents, respectively. and These represent the number of turns in each layer of the primary and secondary windings, respectively. , and These are the average lengths of the insulation gap between the primary winding, the secondary winding, and the primary-secondary winding, respectively. and These refer to the number of layers in the primary winding and the secondary winding, respectively. The conductivity of a conductor. For winding height, , and This refers to the thickness of the primary winding, the thickness of the secondary winding, and the thickness of the insulation gap between the primary and secondary windings. and These represent the thickness of the i-th interlayer gap between the primary and secondary windings, respectively. The skin depth of the winding conductor. For conductor transmittance; Skin depth of winding conductors: (7); In the formula The frequency of the current in the winding conductor; The total leakage magnetic energy of the high-frequency transformer can be calculated from the above formula. The leakage inductance of the transformer referred to the primary side is shown in equation (8): (8); In practical high-frequency transformer design cases, high-frequency transformers cannot perfectly conform to Dowell's ideal transformer magnetic field model. The permeability of the transformer core is not infinite, and the height of the winding layers and the core window are inconsistent. Therefore, reasonable corrections are needed to reduce calculation errors. In actual calculations, the Rockwell coefficient is used. The calculated height of the winding is corrected, and its expression is shown in (9): (9); in The width of the leakage magnetic field inside the core window can be calculated using equation (10): (10); Step 3: Assume that the leakage magnetic energy generated by each harmonic in the high-frequency transformer is independent and does not affect each other, that is, the sum of the leakage inductance energy generated by each sinusoidal excitation source is equal to the leakage inductance energy generated by the non-sinusoidal excitation source. The leakage flux energy generated by each harmonic decomposed on the high-frequency transformer is as follows: (11); In the formula It is the leakage inductance energy generated by the i-th harmonic.

[0025] Step 4: Use the basic algorithm to calculate the leakage inductance energy of the high-frequency transformer under each high-frequency sinusoidal excitation source, and then obtain the leakage inductance under each harmonic. For square waves, the effective values ​​of the first 15 harmonic currents account for the vast majority of the total effective current value. Therefore, to reduce the computational load, only the leakage inductance energy of the first 15 harmonics can be used for leakage inductance calculation. The specific calculation formula is as follows: (12) The leakage inductance is the calculated value at the i-th harmonic frequency. Let be the effective value of the current for the i-th harmonic.

[0026] Step 5: Based on the proportion of the effective value of the harmonic components in the total effective value of the non-sinusoidal excitation, the basic leakage inductance algorithm is weighted and corrected to obtain the leakage inductance of the high-frequency transformer under non-sinusoidal excitation. Based on the harmonic leakage inductance obtained above, a weighted calculation is performed to obtain the total leakage inductance under square wave excitation. The specific process is as follows: (13) In the formula Let be the leakage inductance correction coefficient under the i-th harmonic. This represents the total effective value of the non-sinusoidal excitation current.

[0027] The results calculated using the above steps at different frequencies are plotted as line graphs, such as... Figure 4 As shown. According to Figure 4 It can be concluded that after the correction by formula (12), the calculation accuracy of algorithm 1 is effectively improved and the average error can be controlled at around 15%.

[0028] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation, characterized in that, Includes the following steps: Step 1: Using Fourier decomposition, the non-sinusoidal high-frequency excitation source fed into the high-frequency transformer is decomposed into multiple sinusoidal high-frequency excitation sources; Step 2: Select the appropriate basic algorithm based on the insulation gap between the primary and secondary windings of the high-frequency transformer that needs to be calculated. For small-capacity high-frequency transformers, leakage inductance is calculated using two Dowell correction algorithms. Algorithm 1 is suitable for smaller insulation gaps, while Algorithm 2 is suitable for larger insulation gaps. Step 3: Assume that the leakage magnetic energy generated by each of the decomposed high-frequency sinusoidal excitation sources in the high-frequency transformer is independent of each other and does not affect each other, that is, the sum of the leakage inductance energy generated by each sinusoidal excitation source is equal to the leakage inductance energy generated by the non-sinusoidal excitation source. Step 4: Use the basic algorithm to calculate the leakage inductance energy of the high-frequency transformer under each high-frequency sinusoidal excitation source, and then obtain the leakage inductance under each harmonic. Step 5: Based on the proportion of the effective value of the harmonic components in the total effective value of the non-sinusoidal excitation, perform weighted correction calculation on the basic leakage inductance algorithm to finally obtain the leakage inductance of the high-frequency transformer under non-sinusoidal excitation.

2. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation as described in claim 1, characterized in that, Step 1 specifically includes: （1）； in For non-sinusoidal excitation sources, The even harmonics after Fourier decomposition These are the odd harmonics after Fourier decomposition. For harmonic order, For the period of this non-sinusoidal excitation, Let ω be the angular velocity of the excitation. For time.

3. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation as described in claim 1, characterized in that, In step 2, Algorithm 1 is applicable to smaller insulation gaps, where the insulation gap between the primary and secondary windings is less than 6 times the winding thickness.

4. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation as described in claim 1, characterized in that, In step 2, Algorithm 2 is applicable to a larger insulation gap, that is, the insulation gap between the primary and secondary windings is greater than 6 times the winding thickness.

5. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation according to claim 1, characterized in that, In step 2, the leakage inductance of the small-capacity high-frequency transformer is calculated using two Dowell correction algorithms, including the following process: The total leakage flux energy is divided into five parts: leakage flux energy in the primary winding, leakage flux energy in the secondary winding, leakage flux energy in the primary winding gap, leakage flux energy in the secondary winding gap, and leakage flux energy in the insulation gap between the primary and secondary windings. In actual leakage inductance calculation, the total leakage inductance energy is calculated first, and then the transformer leakage inductance is calculated. There are two Dowell correction leakage inductance algorithms, namely Dowell correction algorithm 1 and Dowell correction algorithm 2.

6. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation according to claim 5, characterized in that, The Dowell correction algorithm 1 is specifically as follows: The leakage flux energy between the primary and secondary winding insulation gaps is: （2）； The leakage flux energy in the primary winding gap is: （3）； The leakage flux energy in the secondary winding gap is: （4）； Leakage magnetic energy in primary winding: （5）； Leakage magnetic energy in the secondary winding: （6）； In the formula and These are the effective values ​​of the primary and secondary winding currents, respectively. and These represent the number of turns in each layer of the primary and secondary windings, respectively. , and These are the average lengths of the insulation gap between the primary winding, the secondary winding, and the primary-secondary winding, respectively. and These refer to the number of layers in the primary winding and the secondary winding, respectively. The conductivity of a conductor. For winding height, , and This refers to the thickness of the primary winding, the thickness of the secondary winding, and the thickness of the insulation gap between the primary and secondary windings. and These represent the thickness of the i-th interlayer gap between the primary and secondary windings, respectively. The skin depth of the winding conductor. For conductor transmittance; Skin depth of winding conductors: （7）； In the formula The frequency of the current in the winding conductor; The total leakage magnetic energy of the high-frequency transformer can be calculated from the above formula. The leakage inductance of the transformer referred to the primary side is shown in equation (8): （8）； In practical high-frequency transformer design cases, high-frequency transformers cannot perfectly conform to Dowell's ideal transformer magnetic field model. The permeability of the transformer core is not infinite, and the height of the winding layers and the core window are inconsistent. Therefore, reasonable corrections are needed to reduce calculation errors. In actual calculations, the Rockwell coefficient is used. The calculated height of the winding is corrected, and its expression is shown in (9): （9）； in The width of the leakage magnetic field inside the core window can be calculated using equation (10): （10）。 7. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation as described in claim 6, characterized in that, The Dowell correction algorithm 2 is specifically as follows: Dowell correction algorithm 2, like Dowell correction algorithm 1, is based on the Dowell one-dimensional magnetic field model. It divides the leakage magnetic energy into five parts for calculation and then uses the total leakage magnetic energy to obtain the leakage inductance of the high-frequency transformer. The difference between the two methods lies in the different ways of handling the leakage magnetic energy inside the winding, resulting in different calculation formulas. Dowell correction algorithm 1 uses formula (11) to calculate the leakage magnetic energy inside the winding, while Dowell correction algorithm 2 uses formula (12) to calculate the leakage magnetic energy inside the winding. The formula obtained by Dowell correction algorithm 2 is shown in (13). （11）； （12）； （13）； In the formula This represents the actual magnetic field strength. To calculate the magnetic field strength, It is an imaginary number. The number of turns in the winding. The magnitude of the current in the winding. This refers to the number of winding layers. For winding thickness, The conductivity of a conductor. This represents the average length of the winding. The real part of the result of equation (11) is the leakage inductance energy; If the windings of a high-frequency transformer are transposed during the winding process, the windings can be divided into several similar parts consisting of primary and secondary windings. The leakage magnetic energy of all similar parts can be calculated separately and then superimposed to obtain the total leakage magnetic energy. Finally, the total leakage inductance can be calculated.

8. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation according to claim 1, characterized in that, In step 3, it is assumed that the energy generated by each decomposed high-frequency sinusoidal excitation source in the high-frequency transformer is independent and does not affect each other. That is, the sum of the leakage inductance energy generated by each sinusoidal excitation source is equal to the leakage inductance energy generated by the non-sinusoidal excitation source, including: （14）； In the formula It is the leakage inductance energy generated by the i-th harmonic.

9. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation according to claim 1, characterized in that, In step 4, the leakage inductance energy of the high-frequency transformer under each high-frequency sinusoidal excitation source is calculated using the basic algorithm, thereby obtaining the leakage inductance under each harmonic order, including: （15）； In the formula, The leakage inductance is the calculated value at the i-th harmonic frequency. Let be the effective value of the current for the i-th harmonic.

10. The method for calculating the leakage inductance of a high-frequency transformer under non-sinusoidal excitation according to claim 1, characterized in that, In step 5, based on the proportion of the effective value of harmonic components in the total effective value of non-sinusoidal excitation, a weighted correction calculation is performed on the basic leakage inductance algorithm to finally obtain the leakage inductance of the high-frequency transformer under non-sinusoidal excitation, including: （16）； In the formula Let be the leakage inductance correction coefficient under the i-th harmonic. This represents the total effective value of the non-sinusoidal excitation current.

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