A method for determining electrical parameters of a differential current detector

Abstract

The present invention relates to a method for determining the electrical parameters of a differential current detector, which is applied to the design of pulse current detectors with leading-edge times in the order of ns to hundreds of ns and amplitudes in the order of hundreds of kA. The method solves the technical problems in existing B‑dot development work, such as incomplete circuit design, oversimplified B‑dot circuit models that cannot fully reflect the sensor's responsiveness, and the difficulty in giving B‑dot circuit parameters in most cases that rely on experimental verification. The method for determining the electrical parameters of the differential current detector comprises the following steps: 1) setting the B‑dot circuit model to define the output voltage of the B‑dot circuit model as u; 2) applying different excitation sources to the B‑dot circuit model obtained in step 1) to obtain different equivalent circuits; 3) using the circuit obtained in step 2) to determine the electrical parameters of the differential current detector; the electrical parameters include the B‑dot inductance L, the ground capacitance C, and the high-voltage capacitance C. H The value range of ; improves the physical design of B‑dot.

Description

Technical Field

[0001] The present invention relates to a method for determining electrical parameters of a differential current detector, which is applied to the design of a pulse current detector with a leading edge time in the order of ns to hundreds of ns and an amplitude in the order of hundreds of kA. Background Art

[0002] In pulse power devices, electromagnetic induction coil detectors are typically used to measure pulsed currents in the hundreds of kA range. When the detector circuit parameters are properly set, and its output signal is a differential waveform of the current pulse to be measured, it becomes a differential current detector (also known as a B-dot). The differential signal obtained by a differential current detector can be restored through numerical integration or an RC integration circuit. If numerical integration is used, the measurement system hardware is very simple, consisting only of the B-dot itself and the measurement cable; the measurement system's response characteristics are fundamentally determined by the B-dot's geometric structure. Therefore, the core of B-dot fabrication is to clarify the numerical relationship between the detector's structural parameters and its response characteristics.

[0003] B-dots are now widely used in pulsed power devices. Sandia Laboratories' PBFA-Z (ParticleBeam Fusion Accelerator) device uses this B-dot to measure the current in magnetically insulated transmission lines. Wei Bing and others at the China Academy of Engineering Physics also used B-dots to measure the current in vacuum magnetically insulated transmission lines at the Yang accelerator and the Julong-1 accelerator. Although these studies have successfully applied B-dots to pulsed power devices, the following issues remain:

[0004] (1) The B-dot circuit model is too simplified and cannot reflect the sensor’s responsiveness. The model usually only includes the measured current I o The mutual inductance M between the B-dot and the B-dot, the B-dot's own inductance L and the signal cable impedance Z are the main components. The influence of stray parameters is not considered. Only under the condition of L / Z<<1 / ω, the output voltage u1 and I o The approximate relationship:

[0005]

[0006] The formula only describes the ideal working state of B-dot and cannot describe the actual response capability of B-dot.

[0007] (2) The analysis of the excitation source is not thorough enough, and the influence of voltage waves is not considered. In special cases, the influence of voltage waves may cause significant interference to the B-dot output.

[0008] In summary, the physical design in the existing B-dot development work is incomplete. In most cases that rely on experimental verification, it is difficult for B-dot to provide more comprehensive circuit parameter requirements and thus achieve a more complete physical design. Summary of the Invention

[0009] The purpose of the present invention is to solve the technical problems in the existing B-dot development work, such as incomplete circuit design, over-simplified B-dot circuit models that cannot fully reflect the response capability of the sensor, and difficulty in giving circuit parameters of B-dot in most cases that rely on experimental verification. The present invention provides a method for determining the electrical parameters of a differential current detector to improve the physical design of the B-dot.

[0010] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0011] A method for determining electrical parameters of a differential current detector is characterized in that it includes the following steps:

[0012] 1) Set up the B-dot circuit model

[0013] Define the output voltage of the B-dot circuit model as u;

[0014] The B-dot circuit model includes a high-voltage capacitor C H , capacitance to ground C, and the B-dot inductor L and signal cable impedance Z connected in parallel at both ends of capacitance to ground C;

[0015] One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected and the other end is grounded;

[0016] The high voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0;

[0017] The B-dot inductor L and the measured current I o The mutual inductance between them is M;

[0018] 2) applying different excitation sources to the B-dot circuit model obtained in step 1) to obtain different equivalent circuits;

[0019] 3) Using the different equivalent circuits obtained in step 2), establish a set of equations, and solve the set of equations to determine the electrical parameters of the differential current detector; the electrical parameters include the B-dot inductance L, the ground capacitance C, and the high-voltage capacitance C. H The value range of .

[0020] Furthermore, in step 2), the excitation source is the current to be measured I o Or high voltage electrode voltage u0;

[0021] Step 2) is specifically as follows:

[0022] 2.1. Input the current to be measured I into the B-dot circuit model obtained in step 1) o , obtaining a first circuit;

[0023] 2.2. Input the high-voltage electrode voltage u0 into the B-dot circuit model obtained in step 1) to obtain the second circuit.

[0024] Furthermore, in step 2.1), the first circuit is specifically:

[0025] Define the output voltage of the first circuit as u1;

[0026] The first circuit includes a B-dot inductor L and a high-voltage capacitor C in parallel. H , capacitance to ground C and signal cable impedance Z; one end of capacitance to ground C outputs voltage u1 and the other end is grounded;

[0027] The B-dot inductor L and the measured current I o Mutual inductance M is formed between them.

[0028] Furthermore, in step 2.2), the second circuit is specifically:

[0029] Define the output voltage of the second circuit as u2;

[0030] The second circuit includes a high voltage capacitor C H , capacitance to ground C, B-dot inductance L connected in parallel at both ends of capacitance to ground C, and signal cable impedance Z;

[0031] One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected to output voltage u2, and the other end is grounded;

[0032] The high voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0.

[0033] Furthermore, step 3) is specifically as follows:

[0034] 3.1. Establish the first equation based on the first circuit in step 2.1 and solve it;

[0035] 3.1.1、Establish the first equation:

[0036]

[0037] Where: u j1 is the integral of the output voltage u1 of the first circuit, u j1 =∫u1dt, t is time;

[0038] 3.1.2. Solve the characteristic roots of the first equation obtained in step 3.1.1. The characteristic roots p1 and p2 of the first equation are

[0039]

[0040] And the characteristic root p1 and the characteristic root p2 satisfy the following formula:

[0041] L 2 -4(C+C H )LZ 2 ≥0

[0042] 3.1.3. Based on the characteristic roots p1 and p2 obtained in step 3.1.2, find the solution to the first equation:

[0043]

[0044] 3.1.4, according to the u obtained in step 3.1.3 j1 10% to 90% of the waveform amplitude, obtain the B-dot step response leading edge time t rD The value range of is:

[0045] 1.68L / Z≤t rD ≤2.2L / Z;

[0046] 3.2. Establish a second equation based on the second circuit in step 2.2 and solve it;

[0047] 3.2.1、Establish the second equation:

[0048]

[0049] Where: u j2 is the integral of the output voltage u2 of the second circuit, u j2 =∫u2dt;

[0050] 3.2.2. Solve the characteristic roots of the second equation obtained in step 3.2.1, and obtain the characteristic roots p3 and p4 of the second equation respectively.

[0051]

[0052] 3.2.3. From steps 3.1.2 and 3.2.2, we can get p3 = p1, p4 = p2. The solution to the second equation is:

[0053]

[0054] 3.3. Determine the values of the B-dot inductance L, the capacitance to ground C, and the high-voltage capacitance C of the differential current detector based on the first equation obtained in step 3.1 and the second equation obtained in step 3.2. H Range of values.

[0055] Furthermore, step 3.3 is specifically as follows:

[0056] 3.3.1. Define the leading edge of the current I to be measured o as t r . According to 1.68L / Z ≤ t rD ≤ 2.2L / Z in step 3.1.4, determine the B-dot inductance L through the following formula

[0057] t rD ≤ 2.2L / Z < t r / 3

[0058] We can obtain: L < t r ·Z / 6.6;

[0059] 3.3.2. According to C H << C and L in step 3.1.2 2 -4(C + C H )LZ 2 ≥ 0, we can obtain

[0060] C ≤ L / (4Z 2 );

[0061] 3.3.3. According to the solution of the first equation in step 3.1.3 and the solution of the second equation in step 3.2.3, determine the high-voltage capacitance C through the following formula H ;

[0062]

[0063] We can obtain:

[0064] In the formula: k u is a constant.

[0065] Furthermore, the value of Z is 50 Ω.

[0066] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0067] 1) The method for determining the electrical parameters of the differential current detector of the present invention uses an excitation source to determine the B-dot inductance L, the capacitance to ground C, and the high-voltage capacitance C in the B-dot circuit model H , which can more fully reflect the response ability of the differential current detector.

[0068] 2) The method for determining the electrical parameters of the differential current detector of the present invention is to determine the electrical parameters of the differential current detector by measuring the current I o Compared with the high-voltage electrode voltage u0, a more definite B-dot circuit model can be obtained, which can more fully carry out circuit design in B-dot development work.

[0069] 3) The method for determining the electrical parameters of the differential current detector of the present invention is to set a B-dot circuit model including a high-voltage capacitor C H , ground capacitance C, B-dot inductance L and signal cable impedance Z, taking into account more measurement requirements; not only including the B-dot amplitude and step response leading edge time, but also introducing the step response no overshoot oscillation restriction condition to avoid waveform oscillation.

[0070] 4) The electrical parameter determination method of the differential current detector of the present invention adds the ground capacitance C and the high voltage capacitance C H The influence analysis makes the estimation of B-dot response characteristics more complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The B-dot circuit model in the method for determining the electrical parameters of the differential current detector of the present invention, in which L is the B-dot inductance, C is the B-dot capacitance to ground, Z is the signal cable impedance, and I o is the current to be measured (i.e. the pulse current on the high voltage electrode), M is the current to be measured I o The mutual inductance between the C and B-dot, u0 is the high voltage electrode voltage, C H is the high-voltage capacitor (i.e., the structural capacitance between the high-voltage electrode and the B-dot), and u is the output voltage of the B-dot circuit model (i.e., the measurement loop output voltage).

[0072] Figure 2 Schematic diagram of the first circuit in an embodiment of the method for determining electrical parameters of a differential current detector of the present invention, where u1 is the output voltage of the measurement loop of the first circuit.

[0073] Figure 3 Schematic diagram of the second circuit in the embodiment of the method for determining electrical parameters of a differential current detector of the present invention, where u2 is the output voltage of the measurement loop of the second circuit. DETAILED DESCRIPTION

[0074] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the technical solution of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0075] The present invention provides a method for determining electrical parameters of a differential current detector, comprising the following steps:

[0076] 1) Set up the B-dot circuit model

[0077] like Figure 1 As shown, the output voltage of the B-dot circuit model is defined as u; the B-dot circuit model includes a high-voltage capacitor C H , capacitance to ground C, B-dot inductance L connected in parallel at both ends of capacitance to ground C, and signal cable impedance Z;

[0078] One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected and the other end is grounded;

[0079] High voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0;

[0080] B-dot inductor L and current to be measured I o Mutual inductance M is formed between them;

[0081] 2) Determine the circuit of the B-dot circuit model obtained in step 1) according to the excitation source; wherein the excitation source is the current to be measured I o and the high voltage electrode voltage u0;

[0082] 2.1、As Figure 2 As shown, the B-dot circuit model obtained in step 1) is input with the current to be measured I o , obtain the first circuit, the first circuit only focuses on the current to be measured I o the impact of;

[0083] Define the output voltage of the first circuit as u1;

[0084] The first circuit includes a B-dot inductor L and a high-voltage capacitor C in parallel. H , capacitance to ground C and signal cable impedance Z; one end of capacitance to ground C outputs voltage u1 and the other end is grounded;

[0085] B-dot inductor L and current to be measured I o Mutual inductance M is formed between them;

[0086] 2.2, such as Figure 3 As shown, the high-voltage electrode voltage u0 is input into the B-dot circuit model obtained in step 1) to obtain a second circuit, which only focuses on the influence of the high-voltage electrode voltage u0;

[0087] Define the output voltage of the second circuit as u2;

[0088] The second circuit includes a high voltage capacitor C H, capacitance to ground C, B-dot inductance L connected in parallel at both ends of capacitance to ground C, and signal cable impedance Z;

[0089] One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected to output voltage u2, and the other end is grounded;

[0090] High voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0.

[0091] 3) Using the circuit equation obtained in step 2), determine the electrical parameters of the differential current detector, where the electrical parameters include the B-dot inductor L, the ground capacitance C, and the high-voltage capacitance C. H The value range of .

[0092] 3.1. Establish the first equation based on the first circuit in step 2.1 and solve it;

[0093] 3.1.1、Establish the first equation:

[0094]

[0095] Where: u j1 is the integral of the output voltage u1 of the first circuit, u j1 =∫u1dt, t is time;

[0096] 3.1.2. Solve the characteristic roots of the first equation obtained in step 3.1.1. The characteristic roots p1 and p2 of the first equation are

[0097]

[0098] If L 2 -4(C+C H )LZ 2 <0, the characteristic roots p1 and p2 are imaginary numbers. This causes a high-frequency oscillation to be superimposed on the output waveform of the B-dot circuit model, known as waveform oscillation. To ensure reliable measurement results, waveform oscillation should be avoided during B-dot circuit model measurements.

[0099] To avoid waveform oscillation, it is necessary to ensure that the characteristic root p1 and the characteristic root p2 satisfy the following formula:

[0100] L 2 -4(C+C H )LZ 2 ≥0;

[0101] 3.1.3. Find the solution of the first equation based on the characteristic roots p1 and p2

[0102] Due to the ground capacitance C and high voltage capacitance CH It is related to the structure of the surrounding environment of B-dot, so it is difficult to control L 2 -4(C+C H )LZ 2 =0, p1≠p2, then the solution of equation (1) is

[0103]

[0104] 3.1.4. Define u obtained in step 3.1.3 j1 The rise time from 10% to 90% of the waveform amplitude is the leading edge time of the waveform. Through mathematical experiments, we know that L 2 -4(C+C H )LZ 2 =0, the shortest step response front time of B-dot is obtained; C+C H =0, the longest step response leading edge time of B-dot is obtained.

[0105] According to formula (3), when L 2 -4(C+C H )LZ 2 = 0, the solution of equation (1) is

[0106]

[0107] Now find the leading edge time of the step response:

[0108] (4) where MI o is a constant, and the term that changes with time is The peak value of this item is 1. Assume that the amplitude at time t1 is 0.1 and the amplitude at time t2 is 0.9, that is,

[0109]

[0110] Solved Then t2-t1=1.679L / Z≈1.68L / Z, so the shortest step response front time is 1.68L / Z.

[0111] According to formula (4), when C+C H = 0, the solution of equation (1) is

[0112] u jb =MI o (1-e -tZ / L ) (5)

[0113] (5) The term that changes with time is 1-e -tZ / L , the peak value of this item is 1, then the amplitude at time t1 is 0.1, and the amplitude at time t2 is 0.9, that is,

[0114]

[0115] The solution is t2-t1=-(ln0.1-ln0.9)L / Z≈2.2L / Z, so the longest step response front time is 2.2L / Z.

[0116] In summary, the B-dot step response leading edge time t rD The value range of is:

[0117] 1.68L / Z≤t rD ≤2.2L / Z (6) where L 2 -4CLZ 2 The closer to 0, the rD The smaller it is, the faster the B-dot leading edge response.

[0118] 3.2. Establish a second equation based on the second circuit in step 2.2 and solve it;

[0119] 3.2.1、Establish the second equation:

[0120]

[0121] Where: u j2 is the integral of the output voltage u2 of the second circuit, that is, u j2 =∫u2dt;

[0122] 3.2.2. Solve the characteristic roots of the second equation obtained in step 3.2.1, and obtain the characteristic roots p3 and p4 of the second equation respectively.

[0123]

[0124] Under non-oscillation conditions, the three characteristic roots p3 and p4 should satisfy the following formula:

[0125] L 2 -4(C+C H )LZ 2 ≥0

[0126] 3.2.3. From steps 3.1.2 and 3.2.2, we can get p3 = p1, p4 = p2. The solution to the second equation is:

[0127]

[0128] 3.3. Based on the first equation obtained in step 3.1 and the second equation obtained in step 3.2, determine the B-dot inductance L, ground capacitance C, and high-voltage capacitance C of the differential current detector. H The value range of .

[0129] 3.3.1. Define the current I to be measured o The leading edge of r is t. To accurately measure, the B-dot response time is required to be less than t r / 3. Then, according to 1.68L / Z ≤ t rD ≤ 2.2L / Z in step 3.1.4, determine the B-dot inductance L through the following formula

[0130] t rD ≤ 2.2L / Z < t r / 3

[0131] It can be obtained that: L < t r ·Z / 6.6;

[0132] In this embodiment, the value of Z is 50Ω, then there is

[0133]

[0134] 3.3.2. In engineering applications, there is often a high-voltage capacitor C H << C, so the non-oscillation condition can be changed to L 2 -4CLZ 2 ≥ 0, and it can be obtained that C ≤ L / (4Z 2 ), then there is

[0135] C ≤ L / 10000

[0136] The ground capacitance C can be obtained through methods such as theoretical analysis or finite element analysis.

[0137] 3.3.3. According to the solution of the first equation in step 3.1.3 and the solution of the second equation in step 3.2.3, it can be known that u j1 is the response of the current I to be measured, which is the required signal, while u o is the response of the high-voltage electrode voltage u0, which is the interference signal brought by the high-voltage capacitor C j2 , and its interference ratio is H Set the interference ratio not to exceed the constant k

[0138]

[0139] , then the value limit of the high-voltage capacitor C u is H In the formula: k

[0140] <�

[0141] is a constant. u is a constant.

Claims

1. A method for determining electrical parameters of a differential current detector, characterized in that: The following steps are involved: 1) Set up the B-dot circuit model Define the output voltage of the B-dot circuit model as u; The B-dot circuit model includes a high-voltage capacitor C H , capacitance to ground C, and the B-dot inductor L and signal cable impedance Z connected in parallel at both ends of capacitance to ground C; One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected and the other end is grounded; The high voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0; The B-dot inductor L and the measured current I o The mutual inductance between them is M; 2) Apply different excitation sources to the B-dot circuit model obtained in step 1) to obtain different equivalent circuits; the excitation source is the current to be measured I o Or high voltage electrode voltage u0; 2.

1. Input the current to be measured I into the B-dot circuit model obtained in step 1) o , obtaining a first circuit; 2.

2. Input the high-voltage electrode voltage u0 to the B-dot circuit model obtained in step 1) to obtain a second circuit; 3) Using the different equivalent circuits obtained in step 2), establish a set of equations, and solve the set of equations to determine the electrical parameters of the differential current detector; the electrical parameters include the B-dot inductance L, the ground capacitance C, and the high-voltage capacitance C. H The value range of is as follows: 3.

1. Establish the first equation based on the first circuit in step 2.1 and solve it; 3.1.1、Establish the first equation: Where: u j1 is the integral of the output voltage u1 of the first circuit, u j1 =∫u1dt, t is time; 3.1.

2. Solve the characteristic roots of the first equation obtained in step 3.1.

1. The characteristic roots p1 and p2 of the first equation are And the characteristic root p1 and the characteristic root p2 satisfy the following formula: L 2 -4(C+C H )LZ 2 ≥0 3.1.

3. Based on the characteristic roots p1 and p2 obtained in step 3.1.2, find the solution to the first equation: 3.1.4, according to the u obtained in step 3.1.3 j1 10% to 90% of the waveform amplitude, obtain the B-dot step response leading edge time t rD The value range of is: <h2 style=";text-align:left;direction:ltr">1.68L / Z≤t<h2 style=";text-align:left;direction:ltr"> rD <h2 style=";text-align:left;direction:ltr"> ≤2.2L / Z; 3.

2. Establish a second equation based on the second circuit in step 2.2 and solve it; 3.2.1、Establish the second equation: Where: u j2 is the integral of the output voltage u2 of the second circuit, u j2 =∫u2dt; 3.2.

2. Solve the characteristic roots of the second equation obtained in step 3.2.1, and obtain the characteristic roots p3 and p4 of the second equation respectively. 3.2.

3. From steps 3.1.2 and 3.2.2, we can get p3 = p1, p4 = p2. The solution to the second equation is: 3.

3. Based on the first equation obtained in step 3.1 and the second equation obtained in step 3.2, determine the B-dot inductance L, ground capacitance C, and high-voltage capacitance C of the differential current detector. H The value range of .

2. The method for determining electrical parameters of a differential current detector according to claim 1, wherein: In step 2.1), the first circuit is specifically: Define the output voltage of the first circuit as u1; The first circuit includes a B-dot inductor L and a high-voltage capacitor C in parallel. H , capacitance to ground C and signal cable impedance Z; one end of capacitance to ground C outputs voltage u1 and the other end is grounded; The B-dot inductor L and the measured current I o Mutual inductance M is formed between them.

3. The method for determining electrical parameters of a differential current detector according to claim 2, wherein: In step 2.2), the second circuit is specifically: Define the output voltage of the second circuit as u2; The second circuit includes a high voltage capacitor C H , capacitance to ground C, B-dot inductance L connected in parallel at both ends of capacitance to ground C, and signal cable impedance Z; One end of the ground capacitor C is connected to the high voltage capacitor C H One end is connected to output voltage u2, and the other end is grounded; The high voltage capacitor C H The other end is used to connect the high voltage electrode voltage u0.

4. The method for determining electrical parameters of a differential current detector according to claim 3, wherein: Step 3.3 is as follows: 3.3.1、Define the current to be measured I o The frontier is t r , according to step 3.1.4, 1.68L / Z≤t rD ≤2.2L / Z, determine the B-dot inductance L using the following formula t rD ≤2.2L / Z<t r / 3 We can get: L <t r Z / 6.6; 3.3.

2. According to C H <<C and L in step 3.1.2 2 -4(C + C H )LZ 2 ≥0 can be obtained C≤L / (4Z 2 ); 3.3.

3. Based on the solution of the first equation in step 3.1.3 and the solution of the second equation in step 3.2.3, determine the high-voltage capacitor C using the following formula: H ; We can get: Where: k u is a constant.

5. A method for determining electrical parameters of a differential current detector according to any one of claims 1 to 4, characterized in that: The value of Z is 50Ω.

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