Bandwidth broadening design method for passive PCB Rogowski coil

Abstract

The invention discloses a bandwidth broadening design method for a passive PCB Rogowski coil, and belongs to the technical field of coil design, and the method comprises the steps: building a circuit model; structure parameters of the coil are calculated according to the Faraday electron induction law; establishing a transfer function of the circuit model, and determining to-be-designed electrical parameters; performing calculation simulation on the to-be-designed electrical parameters, and determining the influence degree of the to-be-designed electrical parameters on the coil bandwidth; setting value ranges or combinations of different to-be-designed electrical parameters, and simulating and analyzing amplitude-frequency characteristics and phase-frequency characteristics of the transfer function; determining an influence trend of each to-be-designed electrical parameter on the coil bandwidth by measuring a change rule of a Baud diagram of the circuit model; and determining an adjustable electrical parameter, determining a value of the adjustable electrical parameter, and adjusting the circuit model. According to the PCB Rogowski coil, the bandwidth of the PCB Rogowski coil is widened on the basis that the use advantage that a power source is not needed for power supply is reserved, and the PCB Rogowski coil capable of measuring rapidly-changing current signals is designed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of coil design, and particularly relates to a bandwidth widening design method for a passive PCB Rogowski coil. BACKGROUND

[0002] Measurement of large current pulses is essential for many applications, including power system fault analysis, protection testing, power electronics evaluation, lightning pulse testing, inverter verification, and field lightning monitoring, which require accurate capture of high-frequency large-amplitude alternating current. At present, current sensors for large current pulse measurement mainly include shunts, current transformers, Hall sensors, and Rogowski coils. Shunts provide high precision and fast response speed, current transformers measure large currents in an isolated mode, closed-loop Hall sensors exhibit low temperature drift and strong anti-interference ability, and Rogowski coils are commonly used to measure high-frequency transient signals such as pulse current and capacitor discharge current (peak current usually reaches hundreds of amperes or even thousands of amperes).

[0003] A Rogowski coil is a hollow coil wound on a non-ferromagnetic material skeleton. Due to its small size and low magnetic permeability, it will not be magnetically saturated when measuring high-frequency transient large currents. Its basic principle is based on Faraday's law of electromagnetic induction and Ampere's law, and it has the characteristics of fast response speed, high sensitivity, and high measurement accuracy. Among them, the PCB Rogowski coil is completely produced automatically by advanced manufacturing processes, eliminating the non-uniformity effects caused by manual winding, so its measurement accuracy is much higher than that of ordinary Rogowski coils. In particular, the measurement accuracy of an ordinary Rogowski coil is 1% to 3%, while the measurement accuracy of a PCB Rogowski coil can be better than 1%.

[0004] According to the principle of electromagnetic induction, the voltage signal measured by the PCB Rogowski coil is the derivative of the current signal. To restore the original current signal, an integrator must be used. The prior art has studied the self-integration and differentiation of the PCB Rogowski coil, and has calculated and analyzed the optimization of the PCB design parameters. The PCB Rogowski coil can be divided into active and passive types, the former of which requires a power supply and often uses an operational amplifier to build an integration circuit, and the latter can work in a self-integration state without a power supply through certain coil parameter design.

[0005] Among the key performance indicators of current sensors, bandwidth is crucial, as it fundamentally determines the sensor's ability to accurately measure rapidly changing current signals without distortion. Active PCB Rogowski coils, leveraging the characteristics of operational amplifiers, sacrifice ease of use for high bandwidth, enabling the measurement of both low-frequency and high-frequency signals. In contrast, passive PCB Rogowski coils are easier to use but have narrower bandwidth, making low-frequency signal measurement particularly challenging. Therefore, expanding the bandwidth of passive PCB Rogowski coils is highly significant. Summary of the Invention

[0006] This application aims to solve the technical problem of how to broaden the bandwidth of passive PCB Rogowski coils. To this end, this application provides a design method for broadening the bandwidth of passive PCB Rogowski coils. While retaining the advantage of not requiring power supply, the bandwidth of the PCB Rogowski coil is broadened, and a PCB Rogowski coil capable of measuring rapidly changing current signals is designed.

[0007] This application provides a method for widening the bandwidth of passive PCB Rogowski coils, comprising:

[0008] S1. Establish a circuit model, including a conductor and a coil for electromagnetic induction with the conductor, wherein the coil is connected in parallel with a damping resistor R to eliminate resonance spikes. D The coil circuit is equivalent to having a stray resistance R connected in series. s Stray inductance L s and the parallel stray capacitance C s ;

[0009] S2. Calculate the structural parameters of the coil according to Faraday's law of electron induction;

[0010] S3. Based on the structural parameters, establish the transfer function of the circuit model, determine the electrical parameters to be designed that affect the transfer function, and exclude the fixed electrical parameters.

[0011] S4. Perform calculations and simulations on the electrical parameters to be designed to determine the degree of influence of the electrical parameters to be designed on the coil bandwidth.

[0012] S5. Based on the degree of influence, set different ranges or combinations of values ​​for the electrical parameters to be designed, and simulate and analyze the amplitude-frequency and phase-frequency characteristics of the transfer function.

[0013] S6. Based on the fact that the amplitude attenuation is the smallest and the phase change is the lowest among the amplitude-frequency and phase-frequency characteristics, the influence trend of each electrical parameter to be designed on the coil bandwidth is determined by measuring the change law of the Bode plot of the circuit model.

[0014] S7. Based on the influence trend and the fixed electrical parameters, determine the adjustable electrical parameters, and determine the values ​​of the adjustable electrical parameters based on widening the coil bandwidth, and adjust the circuit model accordingly.

[0015] In some implementations, the transfer function is:

[0016]

[0017] Where s is a complex frequency variable; V coil I(s) is the Laplace transform of the coil output voltage; I(s) is the Laplace transform of the measured current; M is the mutual inductance coefficient of the coil; L s The stray inductance is inherent to the coil; C s The stray capacitance is inherent to the coil; R s R is the stray resistance inherent in the coil. D This is a damping resistor used to eliminate resonant spikes.

[0018] In some implementations, before determining the electrical parameters to be designed that affect the transfer function, the relationship between the transfer function and the structural parameters is first established:

[0019]

[0020] Where j is the complex unit; ω is the angular frequency; N is the number of turns of the coil; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

[0021] In some implementations, when determining the influence trend of each electrical parameter to be designed on the coil bandwidth, the influence of the electrical parameter to be designed on the coil bandwidth is determined based on the relationship between the electrical parameter to be designed and the coil bandwidth in the Bode plot.

[0022] In some implementations, structural parameters include induced electromotive force, coil mutual inductance, and stray inductance.

[0023] In some implementations, the electrical parameters to be designed include resistance, capacitance, and inductance.

[0024] In some implementations, the adjustable electrical parameters are resistance and capacitance.

[0025] In some implementations, the induced electromotive force is:

[0026]

[0027] Where M is the mutual inductance of the coils; i1(t) is the alternating current flowing through the conductor; and t is time.

[0028] In some implementations, the mutual inductance of the coils is:

[0029]

[0030] Where N is the number of coil turns; μ0 is the vacuum permeability; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

[0031] In some implementations, the stray inductance is:

[0032]

[0033] Where N is the number of coil turns; M is the mutual inductance of the coils; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

[0034] As can be seen from the above technical solution, the beneficial effects of this application are as follows:

[0035] In existing technologies, while passive PCB Rogowski coils have a large number of parameters, many of these parameters cannot be changed once the physical structure design is finalized, such as series resistance, series inductance, and parallel capacitance. Once these parameters are determined, the adjustable bandwidth range is very limited. Therefore, existing PCB Rogowski coils have narrow bandwidths and significant limitations. This application establishes a circuit model that includes damping resistance and the equivalent self-contained electrical parameters of the coil. Based on Faraday's law of electromagnetic induction, the structural parameters of the coil are calculated, and a transfer function is constructed to convert the structural parameters into a mathematical model for solution. Then, simulation analysis is used to analyze the influence of these structural parameters on the bandwidth, facilitating the identification of the electrical parameters to be adjusted and optimized. Finally, the combination of the electrical parameters to be designed is optimized to minimize amplitude attenuation and phase change, clarifying the final influence trend of the electrical parameters on the bandwidth. This clarifies the electrical parameters to be designed and serves as a basis for adjusting the circuit model. Thus, while retaining the advantage of not requiring a power supply, the bandwidth of the PCB Rogowski coil is broadened, and a PCB Rogowski coil capable of measuring rapidly changing current signals is designed. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced one by one below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other embodiments and drawings can be obtained based on these drawings without creative effort. Various schematic diagrams according to the embodiments of this application are shown in the accompanying drawings. These drawings are not necessarily drawn to scale. For the purpose of clarity, some details have been enlarged and some details may have been omitted.

[0037] Figure 1A schematic diagram of an embodiment of the preliminary design structure of the present invention for a passive PCB Rogowski coil is shown;

[0038] Figure 2 A schematic diagram of an embodiment of the present invention for widening the bandwidth design circuit model of a passive PCB Rogowski coil is shown;

[0039] Figure 3 The Bode plot of the circuit model is shown for different combinations of resistor values ​​according to the present invention;

[0040] Figure 4 The Bode plot of the circuit model is shown for different combinations of capacitor values ​​according to the present invention;

[0041] Figure 5 The Bode plots of the circuit model are shown for different combinations of inductor values ​​according to the present invention.

[0042] Figure 6 A schematic diagram of an embodiment of the present invention for a bandwidth-enhancing design structure of a passive PCB Rogowski coil is shown.

[0043] Figure label: Detailed Implementation

[0044] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. The detailed description of the embodiments of this application provided in the drawings is not intended to limit the scope of the claimed application. The described embodiments are only a part of the embodiments of this application, not all of them. Based on the embodiments in this application, they can be arranged and designed in various different configurations. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0045] This application is described below with reference to the accompanying drawings and specific embodiments:

[0046] Please refer to Figure 1 and Figure 2 This application provides a method for widening the bandwidth of passive PCB Rogowski coils, comprising:

[0047] S1. Based on the structural diagram of a passive PCB Rogowski coil, establish a lumped-parameter circuit model. The circuit model includes a conductor and a coil for electromagnetic induction with the conductor. The coil is connected in parallel with a damping resistor R to eliminate resonance spikes. D The coil circuit is equivalent to having a stray resistance R connected in series. s (i.e., coil parasitic resistance), stray inductance L s (i.e., coil self-inductance), and the parallel stray capacitance C s(i.e., the parasitic capacitance of the coil), the two ends of the circuit are connected to the positive and negative terminals.

[0048] S2. Based on the circuit model with lumped parameters established above, calculate the structural parameters of the coil according to Faraday's law of electron induction; such as the induced electromotive force e, the mutual inductance M of the coil, and the stray inductance L. s .

[0049] S3. Based on the structural parameters, establish the transfer function of the circuit model, determine the electrical parameters to be designed that affect the transfer function, and exclude fixed electrical parameters; such as electrical parameters to be designed including resistance, capacitance and inductance.

[0050] S4. Based on the adjustable resistance, capacitance, and inductance, calculate and simulate the electrical parameters to be designed to determine the degree of influence of the electrical parameters to be designed on the coil bandwidth.

[0051] S5. Based on the degree of influence, set different ranges or combinations of values ​​for the electrical parameters to be designed, and simulate and analyze the amplitude-frequency and phase-frequency characteristics of the transfer function.

[0052] S6. Based on the minimum amplitude attenuation and the lowest phase change in the amplitude-frequency and phase-frequency characteristics, the influence of each parameter on the bandwidth is refined. By measuring the change of the Bode plot of the circuit model, the influence trend of each electrical parameter to be designed on the coil bandwidth is determined.

[0053] S7. Based on the influence trend and the fixed electrical parameters, determine the adjustable electrical parameters, and determine the values ​​of the adjustable electrical parameters based on widening the coil bandwidth, and adjust the circuit model accordingly; the adjustable electrical parameters here include: resistance and capacitance.

[0054] In some implementations, the transfer function is:

[0055]

[0056] Where s is a complex frequency variable; V coil I(s) is the Laplace transform of the coil output voltage; I(s) is the Laplace transform of the measured current; M is the mutual inductance coefficient of the coil; L s The stray inductance is inherent to the coil; C s The stray capacitance is inherent to the coil; R s R is the stray resistance inherent in the coil. D This is a damping resistor used to eliminate resonant spikes.

[0057] In some implementations, before determining the electrical parameters to be designed that affect the transfer function, the relationship between the transfer function and the structural parameters is first established. According to formula (1), let s = jω:

[0058]

[0059] Where j is the complex unit; ω is the angular frequency; N is the number of turns of the coil; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

[0060] In some implementations, when determining the influence trend of each electrical parameter to be designed on the coil bandwidth, the influence of the electrical parameter to be designed on the coil bandwidth is determined based on the relationship between the electrical parameter to be designed and the coil bandwidth in the Bode plot.

[0061] In some implementations, when an alternating current i1(t) flows through the conductor, an induced electromotive force is generated in the coil as follows:

[0062]

[0063] Where M is the mutual inductance of the coils; i1(t) is the alternating current flowing through the conductor; and t is time. It can be seen that the magnitude of the induced electromotive force is directly determined by the mutual inductance M of the coils; the larger the mutual inductance, the higher the sensitivity.

[0064] In some implementations, the mutual inductance M of the PCB Rogowski coil is:

[0065]

[0066] Where N is the number of turns in the coil; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil. From the above formula, it can be seen that the geometric parameters of the coil (a, b, h, N) directly determine the mutual inductance M and self-inductance L of the coil. s The magnitude of the induced electromotive force is influenced by the magnitude of the induced electromotive force.

[0067] In some implementations, the stray inductance L s for:

[0068]

[0069] Where N is the number of turns in the coil; M is the mutual inductance of the coils; μ0 is the permeability of free space; h is the thickness of the PCB; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil. It is evident that the structural parameters of the coil determine the magnitude of the mutual inductance and self-inductance, thus directly affecting the magnitude of the induced electromotive force.

[0070] In the embodiments of this application, the PCB Rogowski coil is designed according to steps S1-S7. It is calculated by formulas (1) to (5). From formula (2), it can be seen that there are 7 coil parameters that affect the transfer function of the measurement system. After the physical structure design of the coil is determined, the influence of each parameter on the coil bandwidth is determined by the change law of the Bode plot of the measurement circuit model. Then, different electrical parameters are set with different combinations of values, and the amplitude-frequency characteristics and phase-frequency characteristics of the transfer function are simulated and analyzed. The simulation target is to minimize the amplitude attenuation and minimize the phase change. Since the inner diameter a, outer diameter b, board thickness h and number of turns N are fixed, only the electrical parameters resistance, damping resistance, capacitance and inductance are simulated and analyzed to finally determine the influence trend of the electrical parameters on the coil bandwidth.

[0071] To ensure Figure 2 The output impedance is 50Ω, and the stray resistance R S and damping resistor R D The calculation formula is as follows.

[0072]

[0073] Five sets of stray resistors and damping resistors that satisfy formula (6) are selected. The stray resistors are used as resistors to be connected in series, and the damping resistors are used as sampling resistors to be connected in parallel, as shown in Table 1 below.

[0074] Table 1. Values ​​of series resistance and sampling resistance for different curves.

[0075]

[0076] The influence trend of circuit resistance parameters on the Bode plot of the measurement system is obtained as follows: Figure 3 As shown, since bandwidth is the frequency band where the phase difference between the output and input is near 0°, it can be seen from curve H1(R) s =2550Ω, R D =51Ω) has the largest bandwidth and amplitude attenuation, H5(R s =52.6Ω, R D =1000Ω) has the smallest bandwidth and amplitude attenuation. However, there is a contradiction between amplitude attenuation and bandwidth. In order to ensure that the signal can be detected, the amplitude attenuation cannot be too large. Therefore, amplitude attenuation is a contradictory factor that needs to be considered in conjunction with bandwidth during the design.

[0077] Similarly, the parallel capacitor C is obtained. S and series inductor L S The trend of the impact on the system's Bode plot is as follows Figure 4 and Figure 5 As shown, the series resistor R in the circuit model is visible. S Parallel damping resistor R D Series inductor LS and parallel capacitor C S All of these are important factors affecting coil bandwidth, and C S A larger value results in a wider phase frequency response of the circuit model, meaning a wider coil bandwidth. However, the coil's own parasitic capacitance is only in the pF to nF range, which cannot meet the bandwidth requirements. Simulation results show that L... s This only affects bandwidth and not amplitude attenuation, L s The smaller the value, the wider the coil bandwidth, and L s It only affects bandwidth and not amplitude attenuation.

[0078] Damping resistor R D These are parameters that can be actively adjusted, except for R. D All parameters other than L are parasitic parameters resulting from the coil structure design and cannot be changed independently. s The larger the inductance, the narrower the bandwidth. Therefore, it's not advisable to further increase the total inductance by connecting series inductors. This application proposes a method that directly adds resistors and capacitors during PCB design, changing the electrical parameters without affecting the physical parameters, thereby widening the bandwidth of the passive PCB Rogowski coil. Figure 6 As shown, the series resistor R S (Value range 50Ω~100Ω), parallel damping resistor R D (Value range 100Ω~2kΩ), parallel inductor C S (Value range: 1μF~100μF).

[0079] Therefore, in the PCB design stage, this application directly adds a series resistor to increase the stray resistance of the coil. Simultaneously, the value of the sampling resistor is determined based on the requirements of stray resistance and damping resistance, ensuring that the coil output impedance meets design requirements after the two are combined. Furthermore, a parallel capacitor is added in the PCB design stage to compensate for the narrow bandwidth, inability to achieve integrator effect, and difficulty in reproducing the detected current signal caused by the coil's own parasitic capacitance (pF to nF level). Through these adjustments, this application effectively broadens the bandwidth of the passive PCB Rogowski coil while retaining its advantage of not requiring a power supply, enabling accurate measurement of rapidly changing current signals.

[0080] Regarding the specific implementation methods of this application, it should be noted that:

[0081] In the description of this application, unless otherwise expressly specified and limited, the terms "connection," "fixed," "connected," etc., should be interpreted broadly. For example, "fixed" can refer to a fixed connection, a detachable connection, or an integral molding; "connection" can refer to a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can refer to the internal connection of two components or the interaction between two components, unless otherwise expressly limited; "connected" can refer to the internal connection of two parts and the connection between two parts, or the spatial connection between them, whereby the two parts are directly or indirectly connected through the part forming the space. The terms "set," "installed," "equipped with," "configured," etc., should also be interpreted broadly. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0082] In the description of this application, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the system or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. All directional indications are only used to explain the relative positional relationship and movement between components in a specific orientation. If the specific orientation changes, the directional indication will also change accordingly.

[0083] In the description of this application, the use of terms such as "some embodiments," "optional embodiments," "example," "specific example," "optional example," or "optional embodiment," etc., indicates that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application, but does not imply that these embodiments illustrate and describe all possible forms of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0084] The present invention has been described in detail above with reference to specific embodiments and exemplary examples. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments; the above description should not be construed as a limitation of the present invention. Technical solutions between various embodiments can be combined with each other, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed in this application. Although embodiments of the present application have been shown and described, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present application. Those skilled in the art will understand that various other specific changes and combinations of embodiments based on the technical teachings disclosed in this application, without departing from the essence of the present application, are still within the scope of protection defined by the claims of the present invention and their equivalent technical solutions.

Claims

1. A method for widening the bandwidth of passive PCB Rogowski coils, characterized in that, include: Establish a circuit model, including a conductor and a coil for electromagnetic induction with the conductor, wherein the coil is connected in parallel with a damping resistor R that terminates to eliminate resonance spikes. D The coil circuit is equivalent to having a stray resistance R connected in series. s Stray inductance L s and the parallel stray capacitance C s ; The structural parameters of the coil were calculated based on Faraday's law of electron induction. Based on the structural parameters, the transfer function of the circuit model is established, the electrical parameters to be designed that affect the transfer function are determined, and the fixed electrical parameters are excluded. The electrical parameters to be designed are calculated and simulated to determine the degree of influence of the electrical parameters to be designed on the coil bandwidth. Based on the degree of influence, different ranges or combinations of values ​​for the electrical parameters to be designed are set, and the amplitude-frequency and phase-frequency characteristics of the transfer function are simulated and analyzed. Based on the fact that the amplitude attenuation is the smallest and the phase change is the lowest among the amplitude-frequency and phase-frequency characteristics, the influence trend of each electrical parameter to be designed on the coil bandwidth is determined by measuring the change law of the Bode plot of the circuit model. Based on the aforementioned influence trend and the fixed electrical parameters, the adjustable electrical parameters are determined, and the values ​​of the adjustable electrical parameters are determined based on the widened coil bandwidth, thereby adjusting the circuit model.

2. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 1, characterized in that, The transfer function is: Where s is a complex frequency variable; V coil I(s) is the Laplace transform of the coil output voltage; I(s) is the Laplace transform of the measured current; M is the mutual inductance coefficient of the coil; L s The stray inductance is inherent to the coil; C s The stray capacitance is inherent to the coil; R s R is the stray resistance inherent in the coil. D This is a damping resistor used to eliminate resonant spikes.

3. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 2, characterized in that, Before determining the electrical parameters to be designed that affect the transfer function, the relationship between the transfer function and the structural parameters is first established: Where j is the complex unit; ω is the angular frequency; N is the number of turns of the coil; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

4. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 1, characterized in that, When determining the influence trend of each of the electrical parameters to be designed on the coil bandwidth, the influence of the electrical parameters to be designed on the coil bandwidth is determined according to the relationship between the electrical parameters to be designed and the coil bandwidth in the Bode plot.

5. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 1, characterized in that, The structural parameters include induced electromotive force, coil mutual inductance, and stray inductance.

6. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 5, characterized in that, The electrical parameters to be designed include resistance, capacitance, and inductance.

7. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 6, characterized in that, The adjustable electrical parameters are resistance and capacitance.

8. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 5, characterized in that, The induced electromotive force is: Where M is the mutual inductance of the coils; i1(t) is the alternating current flowing through the conductor; and t is time.

9. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 5, characterized in that, The mutual inductance of the coils is: Where N is the number of coil turns; μ0 is the vacuum permeability; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

10. The method for widening the bandwidth of a passive PCB Rogowski coil according to claim 5, characterized in that, The stray inductance is: Where N is the number of coil turns; M is the mutual inductance of the coils; μ0 is the permeability of free space; h is the PCB thickness; b is the outer diameter of the PCB Rogowski coil; and a is the inner diameter of the PCB Rogowski coil.

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