A multi-frequency transmitting band extension method based on SHEPWM

Abstract

The present application belongs to the technical field of geophysical exploration in frequency domain electromagnetic method, and particularly relates to a multi-frequency transmitting band extension method based on SHEPWM. The present application utilizes the advantage of SHEPWM that can flexibly control the amplitude of each harmonic, generates a transmitting waveform with a main frequency close to each other, and combines the general parameters in engineering practice, widens the passband by reducing the quality factor of resonance, comprehensively improves the amplitude of the main transmitting frequency, and is simulated, verified and adjusted. The problems of low efficiency of traditional single-frequency resonance exploration and inability to realize large-current transmission when multi-frequency pseudo-random transmission is used in high-frequency transmission are solved.

Description

Technical Field

[0001] This invention belongs to the frequency domain electromagnetic method in the field of geophysical exploration technology, specifically involving a multi-frequency radio frequency band extension method based on SHEPWM for ground-to-space frequency domain electromagnetic method. Background Technology

[0002] In frequency-domain electromagnetic exploration, the transmitting circuit can be equivalent to a series circuit of an inductor and a resistor. The total impedance of the circuit can be expressed as Z = R + jωL (where ω = 2πf, f is the frequency in Hz, R is the resistance in Ω, L is the inductance in H, and j is the imaginary unit). As the frequency of the transmitting current increases, jωL increases, meaning the total impedance of the circuit increases. However, the power supply voltage is constant. Therefore, at high frequencies, the transmitting current drops sharply, especially above 8000Hz.

[0003] To address the aforementioned issues, some scholars have proposed using RLC series resonance to enhance the amplitude of the transmit current. However, this method is only applicable to single-frequency transmission, significantly reducing detection efficiency. Furthermore, the amplitude of the transmit current is affected by the quality factor Q of the resonance (wherein...). The larger the Q value, the better the resonance effect and the larger the current amplitude. However, in actual electromagnetic exploration, the resistance of the transmitting circuit is relatively large, generally above 20Ω. Therefore, the method of increasing the amplitude of a single frequency using RLC series resonance remains only at the laboratory stage.

[0004] In addition, to improve transmission efficiency, some scholars have proposed using m-sequences, Golay complementary codes, and 2... n Pseudo-random encoding methods, such as gold codes, are used to generate pseudo-random transmission waveforms, aiming to transmit multiple frequencies simultaneously and improve transmission efficiency. However, while this method improves transmission efficiency, it can only transmit current at a fixed frequency ratio, and at high frequencies, the problem of reduced transmission current cannot be avoided. For example, using 2... n Taking pseudo-random five-frequency transmission as an example, when the fundamental frequency is 500Hz, the main transmission frequencies are the 1st (500Hz), 2nd (1000Hz), 4th (2000Hz), 8th (4000Hz), and 16th (8000Hz) harmonics. When the current amplitude of the 16th (8000Hz) harmonic is increased by resonance, the amplitudes of the 1st (500Hz), 2nd (1000Hz), 4th (2000Hz), and 8th (4000Hz) harmonics will decrease sharply due to the series connection of the capacitor. Summary of the Invention

[0005] To overcome the above problems, this invention provides a method based on SHEPWM and series resonance, which is applicable to the problem of multi-frequency high-frequency current emission in the ground-space frequency domain electromagnetic method for exploration of specific targets on shallow surfaces.

[0006] This invention is implemented as follows:

[0007] A multi-frequency transmission band extension method based on SHEPWM, the method includes: generating a transmission waveform with a main frequency close to the main frequency using SHEPWM;

[0008] A matching capacitor is connected in series with the transmitting coil, and the resistance R and inductance L of the transmitting coil are estimated empirically.

[0009] The fundamental frequency is selected based on the depth of the target being detected, thus obtaining the main frequency of the transmission current;

[0010] The resonant frequency is the frequency of the midpoint symmetrical point in the main frequency of the transmitting current.

[0011] Calculate the required capacitance for resonance based on the resonant frequency and the inductance L of the transmitting coil;

[0012] The passband width is calculated based on the resonant frequency and the estimated resistance and inductance of the transmitting coil.

[0013] Furthermore, generating a transmit waveform with a frequency close to the main frequency using SHEPWM includes:

[0014] Perform Fourier decomposition on the desired output voltage of the inverter to obtain the frequency domain information of the desired output voltage;

[0015] Based on the frequency domain information of the desired output voltage, a set of SHEPWM nonlinear transcendental equations consisting of a sequence of switching times is established.

[0016] An iterative algorithm is used to solve the SHEPWM nonlinear transcendental equations and obtain an accurate sequence of switching times.

[0017] By using the obtained switching timing sequence to control the on and off of the switching devices in the inverter, the desired output voltage can be obtained on the AC side of the inverter.

[0018] Furthermore, when the number of switching operations is even, the SHEPWM nonlinear transcendental equations are:

[0019] The general formula of the full-cycle asymmetric SHEPWM nonlinear equations is shown in Equation 1:

[0020]

[0021] Where α1~α N The switching angle of the circuit, in radians; a0, a i b i U represents the Fourier coefficients; d A represents the output voltage amplitude of the inverter. i Let θ be the amplitude of the i-th harmonic; i Let be the phase of the i-th harmonic, and have

[0022] Let the number of switching N = 20, the amplitude of the 7th, 8th, and 9th harmonics be 0.5, the phase be 0, the amplitude of all other harmonics be 0, and the DC component be 0. Substituting these values ​​into Equation 1, we obtain Equation 2, the set of nonlinear equations for generating the waveform.

[0023] By solving Equation 2, we obtain the switching angles α1~α 20 .

[0024] Furthermore, adopt Calculate the passband width, where f is the resonant frequency. R is the resonant quality factor, L is the resistance of the transmitting coil, L is the inductance of the transmitting coil, and C is the matching capacitor.

[0025] Furthermore, the matching capacitor is Where ω = 2πf, f is the frequency in Hz.

[0026] This invention utilizes the advantage of SHEPWM in flexibly controlling the amplitude of each harmonic to generate a transmission waveform with a relatively close main frequency. Secondly, it determines the resonant frequency based on the main frequency distribution of the transmission waveform and calculates the capacitance and bandwidth required for resonance based on the general parameters of the transmission coil. By determining whether the bandwidth can cover the entire main frequency, if so, the goal of increasing the amplitude of the entire main frequency can be achieved.

[0027] Compared with the prior art, the beneficial effects of this invention are as follows:

[0028] This invention enhances the high-frequency current amplitude during multi-frequency transmission using the SHEPWM method to generate specific multi-frequency transmission waveforms and employs series capacitors. Compared to traditional single-frequency resonant methods, it offers better feasibility and efficiency. It also provides greater flexibility, interference resistance, and feasibility compared to traditional multi-frequency transmission methods. For the first time, this invention applies the method of reducing the resonant quality factor Q to extend the bandwidth to the problem of multi-frequency high-frequency transmission using the frequency domain electromagnetic method. This is beneficial for enhancing the exploration effect of the frequency domain electromagnetic method on shallow, specific targets, and also improves the exploration efficiency and interference resistance of the frequency domain electromagnetic method. Attached Figure Description

[0029] Figure 1 The transmission waveform simulation circuit diagram provided for the embodiments of the present invention;

[0030] Figure 2 The time-domain information of the transmitted waveform provided in the embodiments of the present invention;

[0031] Figure 3 Frequency domain information of the transmitted waveform provided in the embodiments of the present invention;

[0032] Figure 4 Frequency domain information of the transmitting current waveform when the power supply voltage is 1000V, R=50Ω, and L=2mH is provided for embodiments of the present invention.

[0033] Figure 5 The resonant current-frequency curve provided for the theoretical explanation of this invention;

[0034] Figure 6 Frequency domain information of the transmitting current waveform provided in this embodiment of the invention when the power supply voltage is 1000V, R=50Ω, L=2mH, and C=0.156μF;

[0035] Figure 7 Frequency domain information of the emission current waveform provided for embodiments of the present invention when the power supply voltage is 1000V, R=50Ω, L=2mH, and C=0.2μF. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] A multi-frequency radio frequency band extension method based on SHEPWM, the method includes the following steps:

[0038] SHEPWM is used to generate a transmit waveform with a frequency close to the main frequency;

[0039] A matching capacitor is connected in series with the transmitting coil, and the resistance R and inductance L of the transmitting coil are estimated empirically.

[0040] The fundamental frequency is selected based on the depth of the target being detected, thus obtaining the main frequency of the transmission current;

[0041] The resonant frequency is the frequency of the midpoint symmetrical point in the main frequency of the transmitting current.

[0042] Calculate the required matching capacitor size for resonance based on the resonant frequency and the inductance L of the transmitting coil;

[0043] The passband width is calculated based on the resonant frequency and the estimated resistance and inductance of the transmitting coil.

[0044] The passband width is calculated based on the resonant frequency and the estimated resistance and inductance values ​​of the transmitting coil. (where f is the resonant frequency) (Resonance quality factor) Cutoff frequency of the passband (where f is the resonant frequency). If the main transmission frequency is between f1 and f2, the amplitude of the high-frequency transmission current can be increased.

[0045] Specifically,

[0046] Taking advantage of SHEPWM's ability to flexibly control the amplitude of each harmonic, generating a transmit waveform with a relatively close main frequency involves the following steps: First, Fourier decomposition is performed on the desired output voltage of the inverter to obtain its frequency domain information. Second, based on the frequency domain information of the desired output voltage, a set of SHEPWM nonlinear transcendental equations consisting of a sequence of switching times is established. Then, an iterative algorithm is used to solve the SHEPWM nonlinear transcendental equations and obtain an accurate sequence of switching times. Finally, the obtained sequence of switching times is used to control the on and off states of the switching devices in the inverter, thus obtaining the desired output voltage on the AC side of the inverter.

[0047] The general formula of the full-cycle asymmetric SHEPWM nonlinear equation set with an even number of switching cycles is shown in Equation 1.

[0048]

[0049] Where α1~α N The switching angle of the circuit, in radians; a0, a i b i U represents the Fourier coefficients; d A represents the output voltage amplitude of the inverter. i Let θ be the amplitude of the i-th harmonic; i Let be the phase of the i-th harmonic, and have

[0050] Since the target is at a specific depth, the frequencies of the transmitting current should be close. Therefore, the number of switching cycles N = 20, the amplitudes of the 7th, 8th, and 9th harmonics are 0.5A (per unit, meaning that when the power supply voltage is 1V and the resistance is 1Ω, the amplitudes of the 7th, 8th, and 9th harmonics are 0.5A), and the phase is 0. The amplitudes of all other harmonics are 0, and the DC component is 0. Substituting the above information into Equation 1, we can obtain the nonlinear equations for generating the waveform as Equation 2:

[0051]

[0052] By solving Equation 2, we obtain the switching angles α1~α 20 Then it can be done through Figure 1 The simulated transmitter circuit shown controls the IGBT modules S1-S4 to conduct at specific times within each cycle based on the switching angles obtained above, outputting a transmitter current waveform (the principle of transmitter current generation is the same as that of the inverter circuit). Taking a power supply voltage of 1V, a resistance of 1Ω, and a base frequency of 1Hz as an example, using... Figure 1 The simulation circuit shown generates the following emission current waveform: Figure 2 As shown, for Figure 2The frequency domain information of the emitted current waveform is obtained by performing an FFT (Fast Fourier Transform). Figure 3 .Depend on Figure 3 It can be seen that the 7th, 8th, 9th, 10th and 11th harmonics of the transmitted waveform have larger amplitudes, while the amplitudes of other harmonics are smaller. It is worth noting that the 10th and 11th harmonics are uncontrollable harmonics, and because of their larger amplitudes, they can be included in the main frequency range.

[0053] The resistance R and inductance L of the transmitting coil are estimated based on experience. Generally, the transmitting coil used in the frequency domain ground-to-air electromagnetic method is a long wire of about 1 to 3 km, with a resistance generally above 20 Ω and an inductance generally above 1.8 mH. Considering that the loop resistance will be even greater when using an electrical source, an example of R = 50 Ω and L = 2 mH is used.

[0054] The fundamental frequency is selected based on the target depth to obtain the dominant frequency of the transmission current. In frequency domain electromagnetic detection, targets at low and medium frequencies (below 2000Hz) are deep, while targets at high frequencies are shallow, and the higher the frequency, the better the detection effect on shallow areas. Therefore, when exploring shallow surface targets, a high-frequency transmission current should be selected. From step one, we know that the harmonics of the transmission current are the 7th, 8th, 9th, 10th, and 11th harmonics (i.e., the dominant frequency of the transmission current). To ensure that each dominant frequency covers the high-frequency portion, taking a 1000Hz dominant frequency as an example, the dominant frequencies of the transmission current are 7000Hz, 8000Hz, 9000Hz, 10000Hz, and 11000Hz. The frequency domain information of the simulated transmission waveform is as follows: Figure 4 As shown.

[0055] The midpoint symmetrical point frequency in the dominant frequency of the transmitting current is taken as the resonant frequency. At resonance, the relationship between current and frequency is as follows: Figure 5 As shown. By Figure 5 It can be seen that the current waveform is a curve symmetrical about the resonant frequency, with the maximum current amplitude at the resonant frequency. The current amplitude at the passband cutoff frequencies (f1, f2) is 0.707 times the current amplitude at the resonant frequency. To significantly improve the current amplitude at each major frequency, each major frequency should be within the passband (i.e., f1 to f2). The major frequencies are 7000Hz, 8000Hz, 9000Hz, 10000Hz, and 11000Hz. These five major frequencies are symmetrical about 9000Hz; therefore, 9000Hz should be the resonant frequency. The matching capacitor is then... (Where ω = 2πf, f is the frequency in Hz). C = 1.5635985129990396827759176421254 * 10 -7 F, take C = 1.56 * 10 -7 F is equivalent to C = 0.156 μF.

[0056] Calculate the passband width (where f is the resonant frequency) (Resonance quality factor) Cutoff frequency of the passband (Where f is the resonant frequency). Assuming the harmonic current amplitude is I at the resonant frequency f = 9000Hz, then the harmonic current amplitudes at f2 = 11000Hz and f1 = 7000Hz are approximately 0.707I. Within the passband, the harmonic current amplitudes at 8000Hz and 10000Hz are between 0.707I and I. All harmonic current amplitudes within the passband are increased. This achieves the goal of increasing the transmit current amplitude. The frequency domain information of the simulated transmit waveform after adding the capacitor is as follows: Figure 5 ,and Figure 4 Compared to previous models, the amplitudes of all harmonic currents have increased. Since the amplitudes of the 10th and 11th uncontrollable harmonics in the generated transmitted waveform are relatively large, the resonant frequency can be adjusted downwards, i.e., the passband can be shifted left to 6000Hz to 10000Hz. This achieves the goal of making the amplitudes of the main frequencies of the transmitted current closer together and simultaneously increasing their amplitudes. In this case, C = 0.2μF is chosen. The frequency domain information of the simulated transmitted waveform is as follows: Figure 6 ,and Figure 4 Compared to other clock frequencies, the amplitudes of each clock frequency are similar and all of them have increased.

[0057] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-frequency radio frequency band extension method based on SHEPWM, characterized in that, The method includes: using SHEPWM to generate a transmit waveform with a frequency close to the main frequency; A matching capacitor is connected in series with the transmitting coil, and the resistance R and inductance L of the transmitting coil are estimated empirically. The fundamental frequency is selected based on the depth of the target being detected, thus obtaining the main frequency of the transmission current; The resonant frequency is the frequency of the midpoint symmetrical point in the main frequency of the transmitting current. Calculate the required matching capacitor size for resonance based on the resonant frequency and the inductance L of the transmitting coil; The passband width is calculated based on the resonant frequency and the estimated resistance and inductance of the transmitting coil.

2. The multi-frequency radio band extension method based on SHEPWM according to claim 1, characterized in that, The SHEPWM method is used to generate transmit waveforms with frequencies close to the main frequency, including: Perform Fourier decomposition on the desired output voltage of the inverter to obtain the frequency domain information of the desired output voltage; Based on the frequency domain information of the desired output voltage, a set of SHEPWM nonlinear transcendental equations consisting of a sequence of switching times is established. An iterative algorithm is used to solve the SHEPWM nonlinear transcendental equations and obtain an accurate sequence of switching times. By using the obtained switching timing sequence to control the on and off of the switching devices in the inverter, the desired output voltage can be obtained on the AC side of the inverter.

3. The multi-frequency radio band extension method based on SHEPWM according to claim 2, characterized in that, When the number of switching operations is even, the SHEPWM nonlinear transcendental equations are: The general formula of the full-cycle asymmetric SHEPWM nonlinear equations is shown in Equation 1: Where α1~α N The switching angle of the circuit, in radians; a0, a i b i U represents the Fourier coefficients; d A represents the output voltage amplitude of the inverter. i Let θ be the amplitude of the i-th harmonic; i Let be the phase of the i-th harmonic, and have Let the number of switching N = 20, the amplitude of the 7th, 8th, and 9th harmonics be 0.5, the phase be 0, the amplitude of all other harmonics be 0, and the DC component be 0. Substituting these values ​​into Equation 1, we obtain Equation 2, the set of nonlinear equations for generating the waveform. By solving Equation 2, we obtain the switching angles α1~α 20 .

4. The multi-frequency radio band extension method based on SHEPWM according to claim 1, characterized in that, use Calculate the passband width, where f is the resonant frequency. R is the resonant quality factor, L is the resistance of the transmitting coil, L is the inductance of the transmitting coil, and C is the matching capacitor.

5. The multi-frequency radio band extension method based on SHEPWM according to claim 1, characterized in that, Matching capacitor is Where ω = 2πf, f is the frequency in Hz.

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