Harmonic analysis and filter design based on high power electromagnetic transmitter

In order to effectively suppress the higher harmonics contained in the output voltage of high-power electromagnetic transmitter, the waveform expression of the output voltage of bipolar pulse width modulation (SPWM) circuit is derived, which can accurately obtain the fundamental wave and each harmonic content in the inverter bridge transmission voltage, and provide a theoretical basis for the design of output filter. At the same time, a design method of output LC filter based on high power electromagnetic transmitter is proposed based on MATLAB simulation calculation and considering the fundamental voltage drop, inductor current ripple and reactive power capacity on the filter inductor. Finally, the feasibility of this design method is verified by the field experiment of transmitter, and the output filtering effect is good.


Introduction Electromagnetic detection technology
is commonly used in geophysical exploration technology, in which electromagnetic transmitter as electromagnetic signal transmission equipment, the main function is to convert electric energy, the input power frequency sine alternating current AC-DC-AC-DC-AC conversion, so as to obtain the output frequency controllable AC signal, and input to the earth.The receiver receives and interprets the signal transmitted by the transmitter through the mine to derive the underground mine information.When the sinusoidal AC signal is transmitted to the earth, the power device IGBT on the inverter side is frequently turned on and off, which makes the output voltage contain high-frequency high-order harmonics, thus reducing the accuracy of the signal collected by the receiver and affecting the inversion result of the final data.Aiming at this problem, this paper firstly analyzes the modulation principle of inverter circuit of transmitter, theoretically deduces the fundamental wave of transmitting voltage and each harmonic content, and verifies the correctness of theoretical derivation through MATLAB software simulation.On this basis, a low-pass LC filter for high-power electromagnetic transmitter is designed by selecting a suitable cut-off frequency and combining with the earth load equivalent model.

Harmonic analysis of transmitter output
In order to design a suitable filter, the harmonic analysis of the topology and output waveform of the high-power transmitter is very important, which determines which design method should be adopted for the filter, and what appropriate inductance and capacitance parameters should be selected.

Transmitter topology and SPWM harmonic analysis
The overall circuit topology of the high-power electromagnetic transmitter is shown in Figure 1, which is mainly composed of four parts, corresponding to H1, H2, H3 and H4 in the topology diagram, respectively realizing the three-phase rectification, first-level inverter, high-frequency rectification and inverter output functions of electric energy.It can realize the emission of square wave, pseudo-random wave and sine wave to meet various exploration needs, with the highest emission voltage of 1kV, the maximum emission current of 50A, and the transmission power of 50kW.
Overall topology of high power electromagnetic transmitter.
The H4 output part can be equivalent to a voltage inverter, and the high-frequency rectifier provides a stable DC voltage input, and the four high-frequency switching tubes Q1, Q2, Q3 and Q4 are inverted into square waves of different frequencies, thus generating magnetic field signals of different frequencies on the transmitting electrode.When the sinusoidal wave is output, the bipolar SPWM modulation principle is adopted (in Figure 2), SPWM wave is generated on the transmitting electrode, and after inductive filtering on the transmitting line, the sinusoidal voltage signal is transmitted to the earth load, but this filtering is only a first-order L-type filter, and the voltage after filtering still contains extremely rich high-order harmonics.Therefore, harmonic analysis of the output voltage is required.In order to design a suitable filter to ensure the sinusoidal degree of the transmitted signal.
U o (a) The whole sine wave period (b) Single carrier cycle Figure 2. Principle of bipolar SPWM modulation.FIG. 2 (a) shows the waveform of carrier, modulation and output voltage in single-phase full-bridge bipolar SPWM mode [2].The modulated wave function is assumed to be: Carrier function: Carrier ratio: , Modulation ratio: This paper adopts the Fourier analysis method based on carrier angular frequency [3], and takes a carrier period as shown in Figure 2 (b), the output voltage of single-phase full-bridge operation in one carrier cycle is: Fourier expansion of this expression is: According to Bessel's formula, the harmonic component H is: By discussing n-division parity, the harmonic distribution of the output voltage of single-phase fullbridge bipolar SPWM [4] is obtained: x The fundamental component of the output voltage is: Harmonic component of output voltage: harmonic amplitude of angular frequency ݊߱ ± ݇߱ 1,3,5 ; 0, 2, 4 42, 4, 6 ; 1,3,5 2 x It can be seen that each harmonic mainly appears in the vicinity of the n times carrier frequency and its side band (n=1, 2, 3...).It only occurs at frequencies where n k r is odd, and the angular frequency of the harmonic component with the largest amplitude is ߱ .
Here: l n k r , the magnitude of THD is not dependent on ܷ ௗ , only on ݉.
Based on MATLAB/Simulink, the above voltage-type inverter circuit and its output voltage harmonics under bipolar carrier mode are simulated and analyzed [5].The inverter circuit is single-phase fullbridge type, adopts IGBT switching device, and the load is consistent with the load of the earth model, which is inductive load.MATLAB/Simulink was used to build the inverter circuit of transmitter H4 bridge, and the simulation circuit diagram was shown in Figure 3.

EPATS-2023 Journal of Physics: Conference Series 2636 (2023) 012038
Fourier analysis tool in Powergui was used for harmonic analysis of SPWM output current (FIG.5  (b)).It can be seen that the current base amplitude is 10.77A, the total harmonic distortion degree is 12.45%, the harmonics are mainly distributed in the carrier frequency and its frequency doubling, and there are only even harmonics, but no odd harmonics.The lowest harmonic frequency is 1.96kHz, and the harmonic component is highest at the carrier frequency of 20kHz, which is consistent with the previous theoretical analysis results, and verifies the correctness of the theoretical analysis.The carrier wave has the greatest influence on the total harmonic distortion degree, and the 20kHz carrier wave and its frequency doubling need to be filtered to make the output waveform closer to the expected sine wave.

Output LC filter design
Through the above theoretical and simulation analysis, it can be seen that the output voltage waveform [6] of the inverter circuit contains a large number of high-order switching harmonics, which must be filtered before being put into the field experiment.The main function of the filter is to ensure that the output of the system contains a very small number of low-order harmonics, so that the system output is stable.The actual output sine wave frequency of the transmitter in the field ranges from 0.1Hz to 1kHz, the fundamental frequency range is wide, and the comparison between the switching frequency and the fundamental frequency is small.The existing LC filter design method [7] is no longer applicable, and it is necessary to consider the fundamental voltage drop on the filter inductor, the current ripple of the filter inductor, and other factors on the filter inductor according to the characteristics of the output voltage spectrum distribution [8].The appropriate output filter parameters are designed.

Inductance constraint on inverter side
Figure 5 shows the main waveform of the bipolar SPWM single-phase full-bridge inverter, where ݅ ଵ_ is the fundamental wave component of the current ݅ ଵ of the inverter measuring inductance ‫ܮ‬ ଵ , and ܶ ௦௪ is the carrier period.When ܷ > ܷ , the switch tube IGBT1 and IGBT4 are on at the same time, In a carrier cycle, ܸ changes very little, the inductance current ݅ ଵ increases linearly, It's increase is Similarly, when IGBT2 and IGBT3 are simultaneously on, ݅ ଵ decreases linearly, and it's decrease is Formula,ܶ ା = ‫ݐ‬ ଵଶ , ܶ ି = ‫ݐ‬ ଶଷ , the regular sampling method is used to approximate solve ܶ ା , that is, a straight line parallel to the time axis is made at ܷ corresponding to the carrier trough, and two time points ‫ݐ‬ ଵ ᇱ and ‫ݐ‬ ଶ ᇱ are obtained after cross-cutting with the triangular carrier, because the fundamental wave frequency is much lower than the carrier frequency, it can be approximated that ܶ ା = ‫ݐ‬ ଵଶ = ‫ݐ‬ ଵଶ ᇱ .According to Figure 5: Since the voltage drop on the inductor is very small, the filter capacitance voltage ܷ is approximately equal to the fundamental wave component of the output voltage between the bridge arms, combine the above formula to obtain: As can be seen from the above formula, in a carrier cycle, The circuit maximum ݅ ଵ_௫ is present when ‫߱݊݅ݏ‬ ‫ݐ‬ = 0, Define the ripple coefficient : Where ‫ܫ‬ ଵ is the fundamental RMS value of the inductance current measured by the inverter when the rated output current is specified.The minimum value of inductance ‫ܮ‬ ଵ is thus: The maximum value of ‫ܮ‬ ଵ can be selected according to the fundamental voltage drop ܷ ଵ at both ends; the smaller the ܷ ଵ , the smaller the DC bus voltage required for the transmitting bridge.The ratio of the effective value of ܷ ଵ to the effective value of the capacitance voltage ܷ is ߣ ௩_ଵ ,the maximum value of ‫ܮ‬ ଵ is:

Filter capacitance constraint
When selecting the filter capacitor, it is necessary to consider the reactive power introduced by the filter capacitor C. The larger the capacity of the filter capacitor, the larger the reactive power introduced by the capacitor, the larger the current flowing through the inductor 1 and the switching tube, and the switching tube conduction loss also increases.The ratio between the reactive power introduced by the filter capacitor C and the rated active power output of the transmitting bridge is defined as, then the maximum value of the filter capacitor C is: In the formula, ܲ is the rated active power of the output of the transmitting bridge.In practical applications, λ c =5% is generally selected.

Selection of filter parameters
The output voltage of the transmitter is 0~1000V, the output current is 0~20A, the rated power is 20KW, and the transmission frequency is 0.1~1kHz.By bringing the above parameters into the above equation, the value range of the inverter inductance and filter capacitance can be obtained: the inverter inductance L1: 0.4mH~3.583H;Filter capacitance: 0.318μF~1.59mF.
In order to make the output voltage of the filter close to the sine wave, while not causing resonance, the cut-off frequency of the LC filter must be far less than the lowest harmonic frequency contained in the SPWM voltage, and the resonant frequency must be greater than the modulation frequency.For the filters required for high-power electromagnetic transmitters, a wide band range is required, and for this, the Butterworth [9] filter with the largest flat amplitude response is chosen as the preferred filter.
Select the filter cut-off frequency f 0 =0.1f c =2kHz , Transmitter ground impedance Z=50Ω , The parameters are calculated by introducing the normalized Butterworth type second-order filter: Inverter inductance L 1 =4.5mH , Filter capacitance C=2μF ,Under the inductance capacitance constraint condition.The inductance on the transmitting line L 2 =2mH is brought into the third-order LCL filter transfer function, and the cut-off frequency of the transfer function can be calculated.
It is calculated that the fundamental wave with an angular frequency within 12400rad/s can pass without attenuation, that is, the signal with a frequency within 1kHz can pass without attenuation.For the transmitting circuit with a switching frequency of 20kHz, the generated high frequency component harmonics can be well suppressed, and the filter meets our design requirements.

Simulation and experimental verification
In order to verify the effectiveness of the designed LC filter [10], based on the simulation model of the inverter circuit built above, the LC filter model is added.The inductance and capacitance parameters are calculated and set according to the above theoretical calculation, and other simulation parameters are the same as before.The load voltage and current after filtering are shown in Figure 6   In order to better verify the practicability of the designed LC filter, appropriate inductors and capacitors are customized according to the output voltage, current and power level of the transmitter.The capacitors choose 1200VAC voltage resistant film capacitors, and the inductors choose current resistant 30A ferrosilicon magnetic powder core inductors, and then connect the filter to the output end of the transmitter to do field actual emission tests.First, only 2mH inductors are inserted in series.When transmitting voltage is 600V and frequency is 300Hz, the measured voltage and current after inductance filtering are shown in Figure 7(a).Channel 2 is the output SPWM voltage waveform, channel 1 is the filtered voltage waveform, and channel 3 is the filtered current waveform.It can be seen that the voltage and current waveform is more burr, because it still contains high-order harmonic components caused by the 20kHz switching frequency, which cannot be completely filtered out.After adding the designed LC filter, the transmitting voltage is 600V, the frequency is 300Hz, and the voltage and load current waveforms at both ends of the filter capacitor are obtained by Tek oscilloscope, as shown in Figure 7(b) .It can be seen from the graph of the oscilloscope that the voltage and current waveform is relatively smooth and the sinusoidal degree is high.The oscilloscope is used to save the data in CSV format and Fourier analysis is carried out on the acquired data with MATLAB software to obtain the load voltage distortion rate, which can meet the needs of the actual project.

Conclusion
In this paper, the expression of harmonic distribution is derived by analyzing the harmonic of SPWM waveform of inverter circuit of transmitter.The switching frequency and its frequency doubling harmonic are the harmonics that should be considered, and the design requirements of filter are obtained.Considering the properties of the earth load, the fundamental voltage drop on the filter inductor, the inductor current ripple, the reactive power capacity and the output voltage THD and other factors, combined with the general design process of Butterworth low-pass filter, the filter parameters are selected by MATLAB simulation software.Finally, the effectiveness of the designed low-pass filter is verified by the field experiment of the transmitter, which has high engineering application value.
setting relevant simulation parameters and selecting appropriate simulation step size and simulation time, different simulation algorithms have different convergence.This model adopts ode23 solver with simulation step size 1e-6s, and the simulation results are shown in Figure 4: (a) Bipolar SPWM output voltage and current (b) Bipolar SPWM spectrogram Figure 4. Simulation results.
(a), and both voltage and current are sinusoidal waveforms.The spectrum diagram obtained by FFT analysis of the output voltage is shown in Figure 6(b).
(a) Voltage and current waveform after filtering (b) Filtered load voltage spectrum diagram