CN104950176B - A kind of internal resistance measurement device of contactless electric automobile energy-storage system - Google Patents

Abstract

The invention discloses a non-contact internal resistance measuring device of an electric vehicle energy storage system, comprising: a controller, a drive circuit, a switch circuit, a primary side resonant circuit, a secondary side resonant circuit, a signal conditioning circuit, and an envelope detection circuit , Voltage follower and low-pass filter circuit. The present invention is based on the beat frequency phenomenon generated when two similar but different frequency sinusoidal attenuation oscillation signals are superimposed, by performing signal conditioning, envelope detection, low-pass filtering, and peak sampling on the beat frequency voltage waveform of the inductance of the primary side resonant circuit, and then The controller calculates the attenuation coefficient, and uses the mathematical relationship between the resistance to be measured and the attenuation coefficient to obtain the resistance to be measured. In addition, since the frequency of each beat is much smaller than the resonant frequency, the sampling frequency can be reduced, thereby reducing the requirement for a high sampling frequency of the controller.

Description

A non-contact internal resistance measuring device for an electric vehicle energy storage system

technical field

The invention belongs to the technical field of measurement, and in particular relates to a non-contact internal resistance measuring device of an electric vehicle energy storage system.

Background technique

The development of electric vehicles and the advancement of their industrialization have increasingly become the focus of governments and the focus of scientific research. The battery pack, the key equipment of the electric vehicle energy storage system and power system, has always been the focus of attention. Due to reasons such as power battery manufacturing, even the same batch of battery cells, there are differences in performance. When the battery cells are used in groups for a long time, the batteries with slightly poor performance will cause the battery group to fail as a whole, and the failure of the storage battery group will bring huge losses. Secondly, during the battery charging process, the battery is easily affected by temperature, humidity, charging current, charge amount, etc., and presents different nonlinear characteristics in each charging stage. A charging strategy that ignores the battery state will cause battery fires and shorten service life. Preventing failures through online monitoring of battery status is an important means to improve the safety of energy storage systems. Among them, the internal resistance of the battery is an important parameter index representing the performance of the battery; the convenient, fast and accurate extraction of the resistance of the battery pack and its monomers is the key technology for realizing a high-performance electric vehicle energy storage system.

With the development of science and technology, the charging methods of electric vehicles are also diversified, mainly divided into two types: contact charging and non-contact charging. Contact charging relies on a plug-in cable to charge the vehicle, while non-contact charging eliminates the cable and enables "space" charging between the charger and the electric vehicle. This will significantly increase the automation level of charging stations and simplify the charging process. When using non-contact power transmission, there is no conventional online status monitoring and communication between the charging station and the electric vehicle, and it is difficult for the charging station to obtain the status information of the on-board energy storage system to adjust the charging method and take protective measures. Most of the existing on-board status detection uses active detection, and its performance depends on the accuracy of the sampling system measurement. Since the non-contact power transmission will form a magnetic coupling channel for high-power power transmission at the bottom of the car, it will interfere with the sensitive components of the electronic sampling system and cause measurement errors. Improving the adaptability of the sampling system to strong magnetic fields will undoubtedly Increase overall system cost.

Therefore, it is necessary to study the detection method of the state parameters (such as temperature, internal resistance, etc.) of the electric vehicle energy storage system in the non-contact power transmission mode, analyze and diagnose the state of the energy storage system, and detect abnormal or faulty battery packs early when parking and charging. , which can not only ensure the high efficiency and reliability of non-contact power transmission, but also protect the vehicle energy storage system and the safe operation of electric vehicles.

The Chinese patent with the publication number CN102539005A proposes a non-contact temperature measurement method, whose essence is to measure the resistance of the thermistor; this measurement method has certain limitations: when measuring the voltage signal cycle, due to the high signal frequency , the controller is not easy to measure the accurate signal period, which affects the accuracy and resolution of resistance calculation. The Chinese patent with the publication number CN103207031A proposes another non-contact temperature measurement method, which is essentially resistance measurement, but it replaces the thermistor with the resistance of the resonant inductance itself, which reduces the volume of the measurement device; its measurement method There are also limitations: when the resonant frequency is high, the requirements for the sampling frequency of the controller are also increased, and direct sampling of the resonant voltage signal has an impact on the accuracy of resistance calculation.

Contents of the invention

Aiming at the above-mentioned technical problems existing in the prior art, the present invention provides a non-contact internal resistance measuring device for an electric vehicle energy storage system, which does not need to measure the voltage signal period, reduces the sampling frequency, increases the sampling accuracy, and can realize small Measurement of resistance.

A non-contact internal resistance measuring device for an electric vehicle energy storage system, including: a controller, a drive circuit, a switch circuit, a primary side resonant circuit, a secondary side resonant circuit, a signal conditioning circuit, an envelope detection circuit, and a voltage follower and low-pass filter circuit; where:

The drive circuit amplifies the power of a pair of complementary switch drive signals provided by the controller;

The switch circuit performs a switching action according to the amplified switch driving signal, and converts the power supply voltage into a square wave voltage signal;

The primary side resonant circuit is coupled with the secondary side resonant circuit, which is used to convert the square wave voltage signal into an AC voltage signal to excite the secondary side resonant circuit to work;

The secondary resonant circuit generates a resistance voltage signal corresponding to the resistance to be measured by inducing the resistance to be measured, and the resistance voltage signal is coupled to the primary side and superimposed with the sinusoidal voltage signal on the inductor in the primary side resonant circuit to generate a beat frequency voltage Signal;

The signal conditioning circuit collects the beat frequency voltage signal, and performs conditioning and shaping on the signal;

The envelope detection circuit performs envelope detection on the adjusted and shaped resistance voltage signal, and outputs an envelope signal;

After the low-pass filter circuit is isolated by a voltage follower, the envelope signal is low-pass filtered to filter out high-frequency components;

The controller samples the low-pass filtered envelope signal, and calculates the resistance value of the resistance to be measured according to the obtained envelope signal.

Further, the controller adopts DSP or MCU with an external A/D sampling chip.

Further, the switch circuit includes two switch tubes Q1-Q2 with anti-parallel diodes and two diodes D1-D2; wherein, one end of the switch tube Q1 is connected to the power supply voltage, and the other end of the switch tube Q1 is connected to the diode D1. The anodes are connected, the cathode of the diode D1 is connected to the anode of the diode D2, the cathode of the diode D2 is connected to one end of the switching tube Q2, the other end of the switching tube Q2 is grounded, and the control poles of the switching tubes Q1 and Q2 respectively receive a power amplified pair of complementary switch drive signals.

Further, the primary side resonant circuit includes a resistor R1, a capacitor C1 and an inductor L1; wherein, one end of the resistor R1 is connected to one end of the capacitor C1 and the cathode of the diode D1, and the other end of the capacitor C1 is connected to one end of the inductor L1, The other end of the inductor L1 is connected to the other end of the resistor R1 and grounded.

Further, the secondary resonant circuit includes a capacitor C2 and an inductor L2; wherein, the inductor L2 is coupled to the inductor L1, one end of the inductor L2 is connected to one end of the capacitor C2, and the other end of the capacitor C2 is connected to one end of the resistance to be measured, The other end of the resistor to be tested is connected to the other end of the inductor L2.

Further, the signal conditioning circuit includes a resistor R3, a resistor R4 and an operational amplifier U1; wherein, one end of the resistor R3 is connected to the other end of the capacitor C1, and the other end of the resistor R3 is connected to the inverting input terminal of the operational amplifier U1 and the resistor One terminal of R4 is connected, the non-inverting input terminal of the operational amplifier U1 is connected with the other terminal of the inductor L1, and the other terminal of the resistor R4 is connected with the output terminal of the operational amplifier U1.

Further, the envelope detection circuit includes a diode D3, a capacitor C4 and a resistor R5; wherein, the anode of the diode D3 is connected to the output terminal of the operational amplifier U1, and the cathode of the diode D3 is connected to one end of the capacitor C4 and one end of the resistor R5 , the other end of the capacitor C4 is connected to the other end of the resistor R5 and grounded.

Further, the voltage follower is composed of an operational amplifier U2, the non-inverting input terminal of the operational amplifier U2 is connected to the cathode of the diode D3, and the inverting input terminal and the output terminal of the operational amplifier U2 are connected in common.

Further, the low-pass filter circuit includes an inductor L3, a resistor R6 and a capacitor C3; wherein, one end of the inductor L3 is connected to the output terminal of the operational amplifier U2, the other end of the inductor L3 is connected to one end of the resistor R6, and the resistor R6 The other end is connected to one end of the capacitor C3 and the controller, and the other end of the capacitor C3 is grounded.

Further, the specific process of the controller calculating the resistance value of the resistance to be measured according to the envelope sampling signal is as follows:

First, extract the peak values Y ₁ ~Y _N of N beats before the envelope sampling signal and their corresponding time diagrams t ₁ ~t _N , where N is an even number greater than 1;

Then, calculate the peak attenuation coefficient α of the envelope sampling signal according to the following formula:

Where: i is a natural number and 1≤i≤N/2;

Then, calculate the resistance value R of the resistor to be tested according to the following formula:

4Lα＝R _b +RR _b ＝R _L1 +R _L2 +R ₁

Wherein: R ₁ is the resistance value of the resistor R1, R _L1 and R _L2 are the internal resistance values of the inductors L1 and L2 respectively, and L is the inductance value of the inductor L1 or L2.

The beneficial technical effect of the present invention is:

(1) The present invention utilizes the beat frequency phenomenon to measure the resistance as the first creation;

(2) In the beat frequency phenomenon of the present invention, the frequency of each beat is the difference between two sinusoidal signal frequencies, and its value is far smaller than the resonance frequency, so it is convenient for the controller to sample. It is more accurate to calculate the resistance to be measured by measuring the peak value of the envelope (that is, the peak value of each beat) at the same sampling frequency;

(3) secondary resonance resistance in the resistance measuring device of the present invention is the sum of the inductance resistance and the resistance to be measured, and its value is small; the voltage decay rate is low during resonance, and can produce more periodic decaying sinusoidal signals, thereby producing more The number of beats to facilitate sampling.

Description of drawings

Fig. 1 is a schematic structural diagram of the internal resistance measuring device of the present invention.

Fig. 2 is a circuit schematic diagram of the internal resistance measuring device of the present invention.

Fig. 3 is a schematic diagram of the driving circuit in the internal resistance measuring device of the present invention.

Fig. 4 is a schematic diagram of the waveform of the envelope sampling signal of the present invention.

detailed description

In order to describe the present invention more specifically, the measuring system and measuring method of the present invention will be described below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1 and Figure 2, the internal resistance measurement device of the non-contact electric vehicle energy storage system of the present invention includes: a controller, a drive circuit, a switch circuit, a resonant circuit (primary side, secondary side), and a signal conditioning circuit , Envelope detection circuit, voltage follower and low-pass filter circuit.

The driving circuit is connected to the controller, which amplifies the two driving signals provided by the controller and outputs them; in this embodiment, as shown in FIG. 3 , the driving circuit uses two optocouplers 3120 and a driving chip 4420 for independent isolation and driving.

The switch circuit is connected with the drive circuit, and outputs a corresponding square wave signal according to the amplified drive signal output by the drive circuit; in this embodiment, the switch circuit is composed of MOS transistors Q1, Q2, diodes D1, D2; MOS transistor Q1 drains The pole is connected to the +5V power supply, the gate is the first input terminal of the switch circuit, and receives the first drive signal of the drive circuit, and the source is connected to the anode of the diode D1; the source of the MOS transistor Q2 is grounded, and the gate is the second input terminal of the switch circuit, which receives the drive circuit The drain of the second drive signal is connected to the cathode of the diode D2; the cathode of the diode D1 is connected to the anode of D2 to form an output end of the switch circuit and output a square wave signal.

The primary resonant circuit is connected with the switch circuit, and converts the square wave generated by the switch circuit into a sinusoidal AC signal; in this embodiment, the components of the primary resonant circuit are inductor L1, capacitor C1, and resistor R1, and adopt series resonance. One end of the resistor R1 is connected with the capacitor C1 to form an input end of the resonant circuit to receive the square wave signal output by the switch circuit. The other end of the resistor R1 is grounded, the capacitor C1 is connected in series with the inductor L1, and the other end of the inductor L1 is grounded.

The secondary side resonant circuit is coupled with the primary side resonant circuit, which uses the AC voltage signal coupled from the primary side resonant circuit inductance L1 as its own operating voltage; in this embodiment, the measurement object is the resistance to be measured, and the voltage generated by the secondary side resonant circuit The signal is transmitted back to the primary side resonant circuit; the components of the secondary side resonant circuit are inductor L2, capacitor C2, and the resistance to be tested R2; The sum of R2, the resonant inductance L2 is coupled with the resonant inductance L1.

The signal conditioning circuit is connected to the primary side resonant circuit, collects the voltage signal received by the primary side resonant circuit, and outputs the conditioned voltage signal through conditioning and shaping; the reason for the signal conditioning is that the original signal voltage value is too high and cannot be directly introduced into the control Therefore, it is necessary to reduce the original signal to the range that the controller can collect; in this embodiment, the signal conditioning circuit is composed of resistors R3, R4 and operational amplifier U1; wherein, one end of resistor R3 is the signal conditioning circuit The input terminal of the circuit collects the voltage signal received by the resonant circuit on the primary side, the other end of the resistor R3 is connected to one end of the resistor R4 and the inverting input terminal of the operational amplifier U1, and the other end of the resistor R4 is connected to the output terminal of the operational amplifier U1 to form a signal The output terminal of the conditioning circuit; the non-inverting input terminal of the operational amplifier U1 is grounded; the positive power supply terminal of the operational amplifier U1 is connected to the +5V power supply, and the negative power supply terminal is connected to the -5V power supply.

The envelope detection circuit is connected with the signal conditioning circuit, receives the signal conditioned by the signal conditioning circuit, and outputs the envelope signal of the beat frequency waveform; in this embodiment, the envelope detection circuit is composed of a diode D3, a resistor R5 and a capacitor C4; The anode of the diode D3 is connected to the output end of the signal conditioning circuit, and the cathode is connected to one end of the capacitor C4 and the resistor R5 to form the output end of the envelope detection circuit; the other end of the capacitor C4 and the resistor R5 is connected to ground.

The voltage follower is connected to the envelope detection circuit, receives the output signal of the envelope detection circuit, outputs signals with the same amplitude and phase, and isolates the front-stage envelope detection circuit from the subsequent low-pass filter circuit to prevent the subsequent stage from affecting the previous stage circuit. In this embodiment, the voltage follower is composed of an operational amplifier U2; wherein the non-inverting input terminal of the operational amplifier U2 is connected to the output terminal of the envelope detection circuit, and the output terminal is connected to the inverting input terminal to form the output terminal of the voltage follower ; The positive power supply of the operational amplifier U2 is connected to the +5V power supply, and the negative power supply is connected to the -5V power supply.

The low-pass filter circuit is connected to the voltage follower, receives the output signal of the voltage follower, filters out the high-frequency components, and outputs a smooth envelope signal, which is convenient for the controller to perform peak sampling; in this embodiment, the low-pass filter circuit consists of an inductor Composed of L3, capacitor C3, and resistor R6, it is a second-order passive LC low-pass filter; one end of the inductor L3 is connected to the output end of the voltage follower, the other end is connected to one end of the resistor R6, and the other end of the resistor R6 is connected to the One end of the capacitor C3 is connected to form an output end of the low-pass filter circuit, and the other end of the capacitor C3 is grounded.

The controller is connected with the low-pass filter circuit, samples the output signal of the low-pass filter circuit, and calculates the resistance value of the resistance to be tested according to the signal; A/D conversion function.

The measuring method of the resistance measuring device of the present embodiment comprises the following steps:

(1) The controller outputs a duty cycle of 50% through the driving circuit, and the two complementary driving signals are respectively given to the MOS transistors Q1 and Q2 in the switching circuit, and the two MOS transistors Q1 and Q2 work in a complementary manner. The switch circuit outputs a high-frequency square wave signal, and the primary-side resonant circuit converts the high-frequency square-wave signal into a high-frequency sinusoidal AC signal, and couples the signal to the secondary _- side resonant circuit through the inductor L1. After it works stably, the controller Stop outputting the drive signal. In this embodiment, the driving signal frequency is L and C are the values of inductance L1, L2 and capacitance C1, C2 of the resonant circuit (primary side and secondary side), respectively, wherein L=465μH, C=2.2nF.

(2) After the output drive signal is stopped, the resonant circuit (primary side, secondary side) starts to enter the sinusoidal attenuation oscillation respectively. The secondary side resonant circuit induces a voltage signal corresponding to the resistance to be measured, and is coupled to the primary side through the inductor L2, and superimposed with the sinusoidal attenuation signal in the primary side resonant circuit, resulting in a beat frequency phenomenon. The beat frequency voltage is conditioned and shaped by the signal conditioning circuit and then transmitted to the input terminal of the envelope detection circuit. Among them, the model of the operational amplifier U in the signal conditioning circuit is LF353, the resistance value of R3 is 10k ohms, the resistance value of R4 is 4k ohms, and the amplification factor is -2/5.

(3) After signal conditioning, the signal passes through the envelope detection circuit to output the envelope signal. The envelope signal is transmitted to the input end of the low-pass filter circuit through the voltage follower. Among them, the type of diode D3 in the envelope detection circuit is 1N5819, and the type of U2 of the operational amplifier in the voltage follower is LF353.

(4) The output end of the low-pass filter circuit is connected to the controller, and the controller calculates the resistance value of the resistance to be tested according to the output signal of the low-pass filter circuit. The specific process is as follows:

a. Use the controller to sample the low-pass filtered signal (the signal waveform is shown in Figure 4), and measure the peak point X _i (t _i , Y _i ) of each beat, where i=1,2,3 ... N; in this embodiment, N is 6 or 4.

b. Perform algorithmic processing on N and N peak points according to the following formula to obtain the attenuation coefficient.

Let N be an even number and find the average.

Averaging the attenuation coefficients,

c. Calculate the resistance value to be tested according to the following formula:

4Lα＝R _b +R ₂

Among them, R _b =R _L1 +R _L2 +R ₁ , R _L1 and R _L2 are the resistance values of inductors L1 and L2, α is the envelope peak attenuation coefficient, L is the inductance value of inductors L1 and L2, and R ₂ is The resistance value of the resistance to be measured; in this embodiment, the inductance value L and the resistance value R _L1 and R _L2 of the inductors L1 and L2 are measured by a precision instrument (digital bridge) before measurement. Different winding methods, different materials, and the number of turns of the coil will affect the inductance and resistance (the existence of the skin effect makes the inductance resistance increase with the increase of frequency). In order to improve the accuracy of the experiment, the resistance value of the inductor should be made as small as possible (so that the attenuation coefficient becomes smaller and more cycles can be measured). In this embodiment, the inductor adopts a plastic hollow cylinder as a skeleton, and is wound with copper wire. Since the skin effect of ordinary copper wire is obvious, and the skin effect of Litz wire is small, it is recommended to use Litz wire.

In this example, the resonant frequency Set to 157kHz. Due to the skin effect, the resistance of the air-core inductor is easily affected by frequency, so the attenuation coefficient α is used to calculate the inductance resistance first (using the known resistance value R ₂ of the resistance to be measured and the measured attenuation coefficient to deduce the inductance resistance R _L , and Let R _L1 =R _L2 =R _L ). On this basis, the inductance resistance is corrected before measurement. Finally, the obtained inductor resistance value is 10.46 ohms.

The resistance measurement results and errors based on this algorithm are shown in Table 1 and Table 2:

Table 1

R _{2 RL} correction value 0.5 10.49 1 10.43

Table 2

R ₂ R ₂ (measured value) Relative error 0.5 0.55 10% 1 0.95 5%

It can be seen from Table 1 and Table 2 that the experimental test is carried out by signal conditioning, envelope detection, second-order low-pass filtering, peak sampling, and calculating the average value of the attenuation coefficient to calculate the resistance to be tested. The relative error value of the test result is in Within 10%. The calculated results are close to the actual values, which proves the effectiveness of the measurement method.

Claims (10)

1. A non-contact internal resistance measuring device for an electric vehicle energy storage system, comprising: a controller, a drive circuit, a switch circuit, a primary side resonant circuit, a secondary side resonant circuit, a signal conditioning circuit, an envelope Detection circuit, voltage follower and low-pass filter circuit; where: The drive circuit amplifies the power of a pair of complementary switch drive signals provided by the controller; The switch circuit performs a switching action according to the amplified switch driving signal, and converts the power supply voltage into a square wave voltage signal; The primary side resonant circuit is coupled with the secondary side resonant circuit, which is used to convert the square wave voltage signal into an AC voltage signal to excite the secondary side resonant circuit to work; The secondary resonant circuit generates a resistance voltage signal corresponding to the resistance to be measured by inducing the resistance to be measured, and the resistance voltage signal is coupled to the primary side and superimposed with the sinusoidal voltage signal on the inductor in the primary side resonant circuit to generate a beat frequency voltage Signal; The signal conditioning circuit collects the beat frequency voltage signal, and performs conditioning and shaping on the signal; The envelope detection circuit performs envelope detection on the adjusted and shaped resistance voltage signal, and outputs an envelope signal; After the low-pass filter circuit is isolated by a voltage follower, the envelope signal is low-pass filtered to filter out high-frequency components; The controller samples the low-pass filtered envelope signal, and calculates the resistance value of the resistance to be measured according to the obtained envelope signal. 2. The internal resistance measuring device according to claim 1, characterized in that: the controller adopts a DSP or an MCU with an external A/D sampling chip. 3. The internal resistance measuring device according to claim 1, characterized in that: the switch circuit includes two switch tubes Q1-Q2 with anti-parallel diodes and two diodes D1-D2; wherein, the switch tube Q1 One end is connected to the power supply voltage, the other end of the switching tube Q1 is connected to the anode of the diode D1, the cathode of the diode D1 is connected to the anode of the diode D2, the cathode of the diode D2 is connected to one end of the switching tube Q2, the other end of the switching tube Q2 is grounded, and the switch The control poles of the transistors Q1 and Q2 respectively receive a pair of complementary switch drive signals after power amplification. 4. The internal resistance measuring device according to claim 3, characterized in that: the primary side resonant circuit includes a resistor R1, a capacitor C1 and an inductor L1; wherein, one end of the resistor R1 is connected to one end of the capacitor C1 and the diode D1 The cathodes are connected, the other end of the capacitor C1 is connected to one end of the inductor L1, the other end of the inductor L1 is connected to the other end of the resistor R1 and grounded. 5. The internal resistance measuring device according to claim 4, characterized in that: the secondary resonant circuit comprises a capacitor C2 and an inductor L2; wherein the inductor L2 is coupled to the inductor L1, and one end of the inductor L2 is connected to one end of the capacitor C2 The other end of the capacitor C2 is connected to one end of the resistance to be measured, and the other end of the resistance to be measured is connected to the other end of the inductor L2. 6. The internal resistance measuring device according to claim 4, characterized in that: the signal conditioning circuit comprises a resistor R3, a resistor R4 and an operational amplifier U1; wherein, one end of the resistor R3 is connected to the other end of the capacitor C1, and the resistor R3 is connected to the other end of the capacitor C1. The other end of R3 is connected to the inverting input end of the operational amplifier U1 and one end of the resistor R4, the non-inverting input end of the operational amplifier U1 is connected to the other end of the inductor L1, and the other end of the resistor R4 is connected to the output end of the operational amplifier U1. 7. The internal resistance measuring device according to claim 6, characterized in that: the envelope detection circuit comprises a diode D3, a capacitor C4 and a resistor R5; wherein, the anode of the diode D3 is connected to the output terminal of the operational amplifier U1, The cathode of the diode D3 is connected to one end of the capacitor C4 and one end of the resistor R5, and the other end of the capacitor C4 is connected to the other end of the resistor R5 and grounded. 8. The internal resistance measuring device according to claim 7, characterized in that: the voltage follower is composed of an operational amplifier U2, the non-inverting input of the operational amplifier U2 is connected to the cathode of the diode D3, and the negative phase of the operational amplifier U2 is connected to the cathode of the diode D3. The phase input and output terminals are connected together. 9. internal resistance measuring device according to claim 8, is characterized in that: described low-pass filter circuit comprises inductance L3, resistance R6 and electric capacity C3; Wherein, one end of inductance L3 is connected with the output terminal of operational amplifier U2, The other end of the inductor L3 is connected to one end of the resistor R6, the other end of the resistor R6 is connected to one end of the capacitor C3 and the controller, and the other end of the capacitor C3 is grounded. 10. The internal resistance measuring device according to claim 5, characterized in that: the specific process of the controller calculating the resistance value of the resistance to be measured according to the envelope sampling signal is as follows: First, extract the peak values Y ₁ to Y _N of N beats before the envelope sampling signal and the corresponding time t ₁ to t _N , where N is an even number greater than 1; Then, calculate the peak attenuation coefficient α of the envelope sampling signal according to the following formula: $\begin{array}{cc}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\frac{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\frac{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\frac{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\end{array}$ Where: i is a natural number and 1≤i≤N/2; Then, calculate the resistance value R of the resistor to be tested according to the following formula: 4Lα＝R _b +RR _b ＝R _L1 +R _L2 +R ₁ Wherein: R ₁ is the resistance value of the resistor R1, R _L1 and R _L2 are the internal resistance values of the inductors L1 and L2 respectively, and L is the inductance value of the inductor L1 or L2.