Design of a novel high-frequency link broadband inverter based on beat frequency principle

As a kind of special power supply for testing, the broadband inverter has relatively high research value for technological innovation. With the goal of broadband output, this paper proposes a novel high-frequency link inverter topology based on the beat frequency and LCC resonance. Firstly, the working principle is studied. Then, aiming at large circulation problems in the beat frequency modulation process, the method of the series-connected four-coupling reactor is adopted. Finally, experimental results show that this novel inverter can realize broadband output from 20Hz to 1010Hz with voltage THD not exceeding 3% and the relative frequency error between setting and actual is within 0.2%. The whole work proves that this novel inverter has characteristics of broadband output, high-frequency link, current mode, and soft switching.


Introduction
A broadband inverter power supply is a special test power supply used to detect the operation status of electrical equipment and measure electrical parameters [1] .Under certain power conditions, the broadband power supply should be generated by switching mode.However, when the output frequency is too wide or too low, the following technical difficulties exist.One is that the design of the output transformer is difficult.Due to the high output voltage of the power supply, in order to ensure the safety of the circuit, it is necessary to have a transformer to realize electrical isolation.Too wide or too low operating frequency will cause the transformer to be unable to design.The other is that the design of the output filter is very difficult.The cut-off frequency of the output filter is related to the lowest harmonic frequency.Due to the "dead zone" and nonlinear effects of the switching process, the cut-off frequency is far less than the operating frequency of the circuit [2] .In the wide frequency range, it is difficult to meet the above requirements.
For the first technical difficulty, we can learn from the isolation technology with high-frequency links, namely high-frequency link technology [3] .Chu et al. [4] proposed the bidirectional forward and flyback combined DC converter type high-frequency link inverter technology.Although the bidirectional power flow problem was solved, the forced cut-off of the inductance current path in the process of commutation would cause high pulse voltage and disruptive damage to the converter.Additional "active voltage clamping" circuits were added to eliminate the voltage overshoot during cycle converter commutation [5~6] .However, the circuit became very complex and the effect is not ideal.
For the second technical difficulty, there are "segmented modulation" technology [7] and current-mode series resonance high-frequency chain inverter technology [8~9] in the control strategy.The segmented modulation technology is conducive to the parameter design of the output filter in a wide frequency range, and the purpose is to ensure that the carrier frequency is roughly unchanged when the modulation wave frequency changes.However, the number of segments of this technology is limited and the frequency conversion range is not wide.Meanwhile, because the LC filter is serially connected with inductors, there are hidden dangers in the demodulation process.To solve these problems, the resonant converter has become a research hotspot in recent years.Zeng et al. [10] proposed a new topology of the series resonant current source high-frequency chain sine wave inverter.The output filter is implemented by capacitance only, which has two-stage energy transformation, zero current switches for all switches and lightweight transformers, etc.However, based on the above mainstream high-frequency chain inversion technologies, the broadband output of isolated power supply cannot be realized.
In this paper, a novel broadband inverter based on beat frequency high-frequency chain technology is presented, including a novel inverter topology and novel loop suppression method.

Basic principle
The principle of beat frequency high-frequency chain inverter is shown in Figure 1.

Figure 1. Schematic diagram of beat frequency high-frequency chain inverter
The outputs of high-frequency inverters Ⅰ and Ⅱ are: The secondary output voltage obtained by the reverse series connection of the transformer is: Formula ( 2) contains low-frequency modulation frequency and carrier frequency.The desired output of the inverter can be obtained by demodulating the low-frequency modulated signal.As a kind of highfrequency chain inverter technology, this technology has no absolute advantages and can not regulate voltage itself, so it has not attracted enough attention and in-depth exploration.However, the unique advantage of this technology is that when modulation frequency changes in a large range, the carrier frequency changes relatively little, which greatly facilitates the design of the filter.Therefore, this inverter technology can theoretically realize wide output frequency range adjustment of power supply.

Inverter topology
Figure 2 is the schematic diagram of the novel beat frequency LCC resonant high-frequency chain inverter circuit.High-frequency inverters I and II realize pre-stage beat frequency modulation, which has the same structure.A double-winding complementary circumferential wave converter completes the demodulation of the modulated wave.i 1 , i 2 , i f1 , and i f2 stand for the positive direction of the primary current and the secondary current respectively.U d is a DC power supply.K1~K4 are four switches.Lr1~Lr2 are resonance inductors.Cr1~Cr2 are series resonant capacitors.Cp1~Cp2 are parallel resonant capacitors.T1 and T2 are high-frequency transformers, having a single primary side and double secondary side, which are respectively in reverse parallel.SA~SD are four switches of the cycle converter.Cf is the output filter capacitor.Rf is load, and U 0 is output load voltage.

Working principle analysis
The switching frequency of high-frequency inverter I is higher than that of inverter II, and takes the ratio of two 3:2 as an example to analyze.When the inverter works in the first or third quadrants, the output current and voltage are in phase, and overall energy is transferred from the DC power source to the load.Figure 3 shows the main waveform when the inverter works in the first quadrant.The main resonance states are analyzed below.[t1, t2]: High-frequency inverter I is in a forward excitation resonance state.Before the t1 moment, i 1 flows through the D1 to the DC power supply.At t1 time, i 1 reverses, and K1 realizes zero voltage and zero current turning on.Cyclic converter switches SA and SB are normally on, while SC and SD are normally off.High-frequency inverter II is in forward double-excited resonance, which means both the DC power supply and load provide energy to the resonant slot.

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[t2, t3]: High-frequency inverter I is in a forward double-excitation resonance state.High-frequency inverter II is in forward excitation resonance.
[t4, t5]: High-frequency inverter I works in a feedback resonance state, and the resonant slot feeds back energy to the DC power supply.In this stage, Lr1, Cr1, and Cp1 form series resonance.The characteristic impedance of the resonant channel and the frequency of the resonance angle substantially increase compared with [t2, t3].Therefore, primary resonant current i 1 decreases rapidly, which creates the condition for K1 to approximate turn off with zero current.
[t5, t6]: High-frequency inverter I is in a reverse excitation resonance state.High-frequency inverter II is in a forward excitation resonance state.
[t7, t8]: High-frequency inverter II works in a feedback resonance state.The resonant slot feeds back energy to the DC power supply.Parallel resonant capacitance Cp2 participates in resonance, forming Lr2, Cr2, and Cp2 three-element series resonance.In this stage, the characteristic impedance and resonance angle frequency of high-frequency inverter II greatly increases.Therefore, i 2 decreases rapidly, which creates the condition for K3 to approximate turn off with zero current.

Loop suppression method based on coupling inductance
The steady-state equivalent circuit of the secondary side of the transformer with coupling inductance is shown in Figure 4.

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In this formula, R eq is load equivalent resistance.SA, SB or SC, and SD are only conducted on one side at any time.The current of one side of switches without conducting can only circulate within the secondary sides, so 12 , and output load current i f is: According to Formula (4), the existence of mutual inductance does not consume energy, and the output load current still satisfies the subtraction (or addition) of the original current, which achieves a desired output of beat frequency inversion.

Experimental prototype
The experimental prototype is shown in Figure 5.The main parameters of the power circuit are shown in Table 1.Voltage harmonic analysis with a power quality analyzer gives the curve between output voltage THD and output frequency as shown in Figure 8. Figure 9 shows the relative error curve between the setting frequency and the actual output frequency.It can be seen that the output frequency varies from 25 Hz to 1010 Hz, and the measured output voltage THD does not exceed 3%.Even at a lower frequency like 15 Hz, no obvious distortion of voltage waveform is observed.Meanwhile, the relative frequency error between the setting and the actual is within 0.2%.

Conclusion
In this paper, aiming at the broadband output of inverter power supply, a novel beat frequency LCC resonant high-frequency link inverter is proposed.To solve the large circulation problem in the process of beat frequency modulation, the method of a series-connected four-coupling reactor is adopted for loop suppression.Experimental results show that this novel inverter can realize wide frequency output from 20Hz to 1010Hz with voltage THD not exceeding 3%, and the relative frequency error between setting and actual is within 0.2%.At the same time, the full-range soft switch of the power device is implemented, and the soft switch property does not change along with frequency, which greatly reduces switch loss and electromagnetic interference.Therefore, the whole work proves this novel inverter has characteristics of broadband output, high-frequency link, current mode, and soft switching.

Figure 2 .
Figure 2. Schematic diagram of the novel beat frequency LCC resonant high-frequency chain inverter

Figure 3 .
Figure 3.The main waveform when the inverter works in the first quadrant

Figure 8 .Figure 9 .
Figure 8.The curve between output voltage THD and output frequency Figure 4.The steady-state equivalent circuit of the secondary side of the transformer U 1 and U 3 are two sets of secondary voltage for high-frequency inverter I transformer respectively, and U 3 = -U 1 .U 2 and U 4 are two sets of secondary voltage for high-frequency inverter II transformer respectively, and U 4 = -U 2 .i 11 , i 21 , i 12 , and i 22 are branch currents corresponding to four sets of side voltage.Assuming self-inductance L 1 =L 2 =L 3 =L 4 =L and mutual-inductance M 12 =M 34 =M.Write loop formula when SA, SB, SC, and SD are all on: