Bilateral LCC compensation topology control system suitable for wireless charging of unmanned aerial vehicle and parameter design method

Abstract

The invention discloses a bilateral LCC compensation topology control system suitable for wireless charging of an unmanned aerial vehicle, and the system comprises an FPGA controller, the FPGA controller is connected with an AC current and voltage signal conditioning circuit, a full-bridge inverter drive circuit, and a transmitting side LCC compensation topology structure, the transmitting side LCC compensation topology structure is connected with a receiving side LCC compensation topology structure through a wireless signal, and the receiving side LCC compensation topology structure is connected with the receiving side LCC compensation topology structure through a wireless signal. And the receiving side LCC compensation topological structure is connected with the signal verification circuit. The invention further discloses a parameter design method of the bilateral LCC compensation topology control system suitable for wireless charging of the unmanned aerial vehicle. The problems of system detuning and transmission efficiency reduction caused by coupling coefficient and load fluctuation during wireless charging of the unmanned aerial vehicle are solved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless power transfer (WPT) and relates to a double-sided LCC compensation topology control system suitable for wireless charging of unmanned aerial vehicles. BACKGROUND

[0002] As a flexible and efficient aerial operation platform, unmanned aerial vehicles have been widely used in aerial photography, power inspection and logistics distribution. However, the endurance of unmanned aerial vehicles is limited by the battery capacity, and the traditional wired charging method needs manual intervention for docking, which is complicated and inefficient, and cannot meet the charging needs of large-scale and automated operation of unmanned aerial vehicles. Wireless power transfer technology has become one of the core technologies for solving the automatic charging of unmanned aerial vehicles due to its non-contact energy transmission advantage. At present, the double-sided inductance-capacitance-capacitance (LCC) compensation topology is widely used in WPT systems due to its good resonance characteristics. In the wireless charging scenario of unmanned aerial vehicles, the transmitting coil (fixed on the charging platform) and the receiving coil (carried on the unmanned aerial vehicle) are prone to offset due to the landing accuracy of the unmanned aerial vehicle and the wind field interference factors, resulting in a large fluctuation of the coupling coefficient. At the same time, the battery charging process of the unmanned aerial vehicle needs to go through two stages of "constant current pre-charging and constant voltage floating charging", and the equivalent resistance of the load increases with the increase of the battery capacity during the whole charging process. The large fluctuation of the coupling coefficient and the equivalent resistance will lead to: (1) the resonance frequency of the system deviates, and then the output current / voltage fluctuates, which cannot meet the strict requirements of constant current and constant voltage for battery charging, affecting the battery life and charging safety; (2) the system reactive power loss and switching loss increase, and the transmission efficiency decreases.

[0003] However, the current solutions have defects to varying degrees: (1) the resonance frequency tracking control needs the cooperation of the transmitting end and the receiving end, which increases the complexity of the system; (2) the increase of the DC-DC converter will lead to an additional energy transmission link, causing a decrease in transmission efficiency; (3) the traditional phase-shifted control strategy cannot balance the constant current / constant voltage output characteristics and the best efficiency point tracking. Therefore, there is an urgent need for a wireless charging system and design method suitable for unmanned aerial vehicles, which does not need a DC-DC converter, on the one hand, can realize the constant of the resonance frequency of the two output modes of constant current and constant voltage under the coil offset and load fluctuation, and saves the tracking control of the resonance frequency, and on the other hand, can balance the tracking of the best impedance point, thereby improving the transmission efficiency in the whole charging process. SUMMARY

[0004] The application aims to provide a double-sided LCC compensation topology control system suitable for wireless charging of unmanned aerial vehicles, which solves the problem of system detuning and transmission efficiency reduction caused by the fluctuation of the coupling coefficient and the load during the wireless charging of unmanned aerial vehicles.

[0005] Another object of the present application is to provide a parameter design method of a double-sided LCC compensation topology control system suitable for unmanned aerial vehicle wireless charging.

[0006] The first technical solution adopted by the present application is a double-sided LCC compensation topology control system suitable for unmanned aerial vehicle wireless charging, which comprises an FPGA controller, the FPGA controller is connected with an alternating current voltage signal conditioning circuit, a full-bridge inverter driving circuit, a transmitting side LCC compensation topology structure respectively, the transmitting side LCC compensation topology structure is connected with a receiving side LCC compensation topology structure through a wireless signal, and the receiving side LCC compensation topology structure is connected with a signal verification circuit.

[0007] The first technical solution of the present application is also characterized in that: The transmitting side LCC compensation topology structure comprises a wireless communication transmitting module I, further comprises a transmitting side switch capacitor driving circuit, and the transmitting side switch capacitor driving circuit is connected with a transmitting side resonance circuit.

[0008] The receiving side LCC compensation topology structure comprises a wireless communication receiving module I, the wireless communication receiving module I is connected with a signal conditioning circuit, a receiving side switch capacitor driving circuit and a receiving side resonance circuit in sequence, and the wireless communication transmitting module I is connected with the wireless communication receiving module I through a wireless signal.

[0009] The signal verification circuit comprises a wireless communication transmitting module II, the wireless communication transmitting module II is connected with a direct current voltage signal conditioning circuit, the direct current voltage signal conditioning circuit is connected with a direct current voltage sensor and a direct current sensor respectively, the direct current voltage sensor is connected with a battery equivalent load in parallel, the battery equivalent load is connected with a filter capacitor and a non-controlled rectifier bridge in parallel, the wireless communication transmitting module II is connected with a wireless communication receiving module II through a wireless signal, and the wireless communication receiving module II is connected with the FPGA controller.

[0010] The second technical solution adopted by the present application is a parameter design method of a double-sided LCC compensation topology control system suitable for unmanned aerial vehicle wireless charging, and the design process of the coupling mechanism is as follows: The coupling mechanism comprises a transmitting coil L 1, L 2 and mutual inductance M According to formula (1) and (2), the self-inductance of the transmitting coil L 1 and the receiving coil L 2 is calculated: (1) (2) Wherein, μ 0 is the vacuum permeability, N 1, D 1 and l1 is a transmitting coil L 1, diameter, axial length of N 2, D 2 and l 2 is a receiving coil L 2, diameter, axial length of 1 is a transmitting coil L 1 and receiving coil L 2 is completely aligned, mutual inductance M is maximum, denoted as M max , the calculation formula is: (3) wherein, r 1 and r 2 are the radii of the corresponding coils, d is the vertical distance between the two coils; transmitting coil L 1 and receiving coil L 2 is not aligned, at this time, the mutual inductance correction coefficient K is introduced: (4) wherein, s is the horizontal offset ratio when the transmitting coil L 1 and receiving coil L 2 maximum offset; minimum mutual inductance M min denoted as: (5) Maximum coupling coefficient k max and minimum coupling coefficient k min is: (6) (7).

[0011] The design process of constant current and constant voltage resonance frequency is as follows: constant current resonance frequency f c and constant voltage resonance frequency f v The functional relationship is expressed as: (8) wherein, f c , f v ∈(80kHz, 200kHz).

[0012] The design process of the transmitting side LCC compensation topology parameters is as follows: according to the transmitting coil self-inductance L 1 and the maximum coupling coefficient k max and the constant-current resonant frequency f c and the constant-voltage resonant frequency f v , the transmitting side compensation inductance L f1 is: (9) the transmitting side compensation capacitance C f1 and C 1 is: (10) (11).

[0013] The design process of the receiving side LCC compensation topology parameters is as follows: according to the transmitting coil self-inductance L 1, the receiving coil self-inductance L 2 and the maximum coupling coefficient k max , the constant-current resonant frequency f c and the constant-voltage resonant frequency f v , the transmitting side compensation capacitance C f1 and C 1, the receiving side compensation inductance L f2 is represented as: (12) the receiving side compensation capacitance C f2 and C 2 is: (13) (14).

[0014] The design process of the transmission gain verification is as follows: the minimum transmission gain of the constant-current mode and the constant-voltage mode g c and g v is: (15) (16).

[0015] The beneficial effects of the present application are as follows: 1) In order to solve the problem that the system resonance frequency deviates due to the coupling coefficient fluctuation caused by the coil deviation, the parameter optimization design method is provided, the constant resonance frequency of the constant current and constant voltage output mode is realized under the coupling coefficient and equivalent resistance fluctuation, the tracking control of the resonance frequency is omitted, the control system is simplified, and the adverse effects caused by the load change and the coil deviation are significantly reduced.

[0016] 2) In order to solve the problem that the system transmission efficiency is reduced due to the coupling coefficient and equivalent resistance fluctuation, the switch capacitor is used for impedance matching in the two modes, so that the minimum reactive current and ZVS are realized; in addition, the current phase flowing through the switch capacitor is not affected by the load or the coupling coefficient, which means that the switch capacitor can be used without the current phase detection circuit, and the circuit design is simplified. 3) The constant current and constant voltage output accurate control are realized through the traditional phase shift control, and the decoupling of the phase shift angle and the switch capacitor control angle is realized, that is, the phase shift angle only adjusts the output voltage and the output current, and the switch capacitor control angle only adjusts the input impedance, so that the control system is simplified, and the two variables do not need to be cooperatively controlled through a complex algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a power supply structure schematic diagram of the parameter design method and control system suitable for the unmanned aerial vehicle wireless charging double-sided LCC compensation topology of the application; Figure 2 is a parameter design flow chart of the parameter design method and control system suitable for the unmanned aerial vehicle wireless charging double-sided LCC compensation topology of the application; Figure 3 is a constant current / constant voltage, minimum reactive current and ZVS control principle block diagram of the parameter design method and control system suitable for the unmanned aerial vehicle wireless charging double-sided LCC compensation topology of the application; Fig. 4 (a) is the waveform of the output current, the output voltage, the input current and the input voltage when the coupling coefficient k =0.12 and the load R L =33Ω in the constant current mode; Fig. 4 (b) is the waveform of the output current, the output voltage, the input current and the input voltage when the coupling coefficient k =0.12 and the load R L =55Ω in the constant current mode; Fig. 5 (a) is the waveform of the output current, the output voltage, the input current and the input voltage when the coupling coefficient k =0.2 and the load R L =33Ω in the constant current mode; Fig. 5 (b) is the waveform of the output current, the output voltage, the input current and the input voltage when the coupling coefficient k= 0.2 with load R L waveforms of output current, output voltage, input current and input voltage when = 55Ω. Figure 6(a) is the coupling coefficient k = 0.12 with load R L waveforms of output current, output voltage, input current and input voltage when = 55Ω. Figure 6(b) is the coupling coefficient k = 0.12 with load R L waveforms of output current, output voltage, input current and input voltage when = 33Ω. Figure 6(c) is the coupling coefficient k = 0.2 with load R L waveforms of output current, output voltage, input current and input voltage when = 33Ω. Figure 7(a) is the coupling coefficient k = 0.12 with load R L waveforms of output current, output voltage, input current and input voltage when = 55Ω.

[0018] Figure 7(b) is the coupling coefficient k = 0.12 with load R L waveforms of output current, output voltage, input current and input voltage when = 110Ω.

[0019] Figure 8(a) is the coupling coefficient k = 0.2 with load R L waveforms of output current, output voltage, input current and input voltage when = 55Ω.

[0020] Figure 8(b) is the coupling coefficient k = 0.2 with load R L waveforms of output current, output voltage, input current and input voltage when = 110Ω.

[0021] Figure 9(a) is the coupling coefficient k = 0.2 with load R L waveforms of output current, output voltage, input current and input voltage when = 55Ω.

[0022] Fig. 9(b) is a coupling coefficient k =0.2 and load R L Fig. 9(b) is a coupling coefficient

[0023] Fig. 9(c) is a coupling coefficient k =0.12 and load R L Fig. 9(c) is a coupling coefficient

[0024] Fig. 10(a) is a coupling coefficient k =0.12 constant current-constant voltage mode switching waveform diagram.

[0025] Fig. 10(b) is a coupling coefficient k =0.17 constant current-constant voltage mode switching waveform diagram.

[0026] Fig. 10(c) is a coupling coefficient k =0.2 constant current-constant voltage mode switching waveform diagram.

[0027] In the figure, 1. DC power supply, 2. Full-bridge inverter circuit, 3. AC current sensor, 4. AC voltage sensor, 5. Transmit side resonant circuit, 6. Receive side resonant circuit, 7. Uncontrolled rectifier bridge, 8. Filter capacitor, 9. Battery equivalent load, 10. DC current sensor, 11. DC voltage sensor, 12. AC current and voltage signal conditioning circuit, 13. DC current and voltage signal conditioning circuit, 14. Full-bridge inverter drive circuit, 15. FPGA controller, 16. Transmit side switched capacitor drive circuit, 17. Receive side switched capacitor drive circuit, 18. Wireless communication transmit module I, 19. Wireless communication receive module I, 20. Wireless communication receive module II, 21. Wireless communication transmit module II, 22. Signal conditioning circuit. DETAILED DESCRIPTION

[0028] The following will be described in detail in conjunction with the specific embodiments.

[0029] Example 1 The present application is suitable for the bilateral LCC compensation topology control system of unmanned aerial vehicle wireless charging, and the structural schematic diagram is as Figure 1As shown, including direct current power supply 1, full-bridge inverter circuit 2, alternating current sensor 3, alternating voltage sensor 4, transmitting side resonance circuit 5, receiving side resonance circuit 6, uncontrolled rectifier bridge 7, filter capacitor 8, battery equivalent load 9, direct current sensor 10, direct voltage sensor 11, alternating current voltage signal conditioning circuit 12, direct current voltage signal conditioning circuit 13, full-bridge inverter drive circuit 14, FPGA controller 15, transmitting side switch capacitor drive circuit 16, receiving side switch capacitor drive circuit 17, wireless communication transmitting module I 18, wireless communication receiving module I 19, wireless communication receiving module II 20, wireless communication transmitting module II 21, signal conditioning circuit 22.

[0030] Direct current power supply 1, full-bridge inverter circuit 2, transmitting side resonance circuit 5 constitute the transmitting end (ground charging platform) main circuit, wherein the full-bridge inverter circuit 2 is composed of four MOSFETs (S1-S4), the transmitting side resonance circuit 5 is composed of a compensation inductor L f1 , parallel compensation capacitor C f1 , series compensation capacitor C 1 and transmitting side switch capacitor, transmitting coil L 1, the transmitting side switch capacitor is composed of a capacitor C c and two source connected MOSFET (S a -S b ) in parallel; receiving side resonance circuit 6, uncontrolled rectifier bridge 7, filter capacitor 8, battery equivalent load 9 constitute the receiving end (mounted on unmanned aerial vehicle) main circuit, wherein the receiving side resonance circuit 6 is composed of a receiving coil L 2, series compensation capacitor C 2, receiving side switch capacitor, parallel compensation capacitor C f2 and compensation inductor L f2 , the receiving side switch capacitor is composed of a capacitor C v and two source connected MOSFET (S c -S d ) in parallel.

[0031] Under the coupling coefficient and load fluctuation, the system realizes the constant current and constant voltage charging modes and switching by controlling the phase shift angle of the full-bridge inverter circuit 2. At the same time, under the constant current and constant voltage charging modes, the system input impedance is adjusted in real time by controlling the transmitting side switch capacitor and the receiving side switch capacitor respectively, so that the system can realize minimum reactive current and ZVS in the "constant current pre-charging-constant voltage floating charging" two stages.

[0032] Embodiment 2 The whole bilateral LCC compensation WPT charging system adopts a single controller structure of FPGA, mainly realizing the switching of constant current resonant frequency and constant voltage resonant frequency, current control, voltage control, minimum reactive current control and ZVS control functions f c f v The EP4CE6F17C8 chip of Altera Company is connected with the alternating current voltage signal conditioning circuit 12, the direct current voltage signal conditioning circuit 13, the full-bridge inverter driving circuit 14, the transmitting side switch capacitor driving circuit 16, the wireless communication transmitting module I 18 and the wireless communication receiving module II 20 respectively. The full-bridge inverter driving circuit 14, the transmitting side switch capacitor driving circuit 16 and the receiving side switch capacitor driving circuit 17 adopt the optical coupling chip TLP250H of Toshiba Company, and the 0-3.3V PWM control signal sent by the FPGA controller 15 is isolated and amplified to the voltage square wave driving signal of-7.5V-+15V, which is used for driving the full-bridge inverter circuit 2, the transmitting side switch capacitor and the receiving side switch capacitor to work.

[0033] Embodiment 3 In the bilateral LCC compensation WPT charging system of the application, the sensor is responsible for collecting the voltage and current signals of the power supply, and the conditioning circuit adjusts and transforms the amplitudes of the signals to meet the input signal requirements of the controller, so as to provide accurate data basis for the control and operation of the subsequent controller. The alternating current sensor 3, the alternating voltage sensor 4, the direct current sensor 10 and the direct voltage sensor 11 all adopt Hall sensors (the output signals are current signals), which realize the isolated sampling of the input current U in , the input voltage I in , the load current I R and the load voltage U R The alternating current voltage signal conditioning circuit 12 and the direct current voltage signal conditioning circuit 13 are mainly composed of sampling resistors and operational amplifiers (LF353), which realize the operational amplification of the sampling signals of the input current U in , the input voltage I in , the load current I R and the load voltage U R , so as to ensure that they meet the input signal requirements of the controller.

[0034] Embodiment 4 ​The AC current voltage signal conditioning circuit 12 is connected with the AC current sensor 3, the AC voltage sensor 4 and the FPGA controller 15, and the DC current voltage signal conditioning circuit 13 is connected with the DC current sensor 10, the DC voltage sensor 11 and the wireless communication transmitting module II 21. The specific connection relationship between the AC current sensor 3 and the AC current voltage signal conditioning circuit 12 is that the output port of the AC current sensor 3 is connected with the input port of the AC current voltage signal conditioning circuit 12, the current signal output by the AC current sensor 3 is converted into a voltage signal through a sampling resistor first, then the voltage signal is amplified by one stage of inverse proportional and one stage of inverse comparison through the operational amplifier (LF353) in the AC current voltage signal conditioning circuit 12, so as to adjust the output signal of the AC current sensor 3 into a voltage square wave signal of 0-3.3V, which is sent to the FPGA controller 15 for processing. The specific connection relationship between the AC voltage sensor 4 and the AC current voltage signal conditioning circuit 12 is that the output port of the AC voltage sensor 4 is connected with the input port of the AC current voltage signal conditioning circuit 12, the current signal output by the AC voltage sensor 4 is converted into a voltage signal through a sampling resistor first, then the voltage signal is amplified by one stage of inverse proportional and one stage of inverse comparison through the operational amplifier (LF353) in the AC current voltage signal conditioning circuit 12, so as to adjust the output signal of the AC voltage sensor 4 into a voltage square wave signal of 0-3.3V, which is sent to the FPGA controller 15 for processing. The specific connection relationship between the DC current sensor 10 and the DC current voltage signal conditioning circuit 13 is that the output port of the DC current sensor 10 is connected with the input port of the DC current voltage signal conditioning circuit 13, the current signal output by the DC current sensor 10 is converted into a voltage signal through a sampling resistor first, then the voltage signal is amplified by two stages of inverse proportional through the operational amplifier (LF353) in the DC current voltage signal conditioning circuit 13, so as to adjust the output signal of the DC current sensor 10 into a DC voltage signal of 0-3.3V, which is converted into a digital signal and then sent to the wireless communication transmitting module II 21 for processing. The specific connection relationship between the DC voltage sensor 11 and the DC current voltage signal conditioning circuit 13 is that the output port of the DC voltage sensor 11 is connected with the input port of the DC current voltage signal conditioning circuit 13, the current signal output by the DC voltage sensor 11 is converted into a voltage signal through a sampling resistor first, then the voltage signal is amplified by two stages of inverse proportional through the operational amplifier (LF353) in the DC current voltage signal conditioning circuit 13, so as to adjust the output signal of the DC voltage sensor 11 into a DC voltage signal of 0-3.3V, which is converted into a digital signal and then sent to the wireless communication transmitting module II 21 for processing.The wireless transceiver in the application mainly realizes the information interaction function of the transmitting end and the receiving end. The wireless communication transmitting module I 18, the wireless communication receiving module I 19, the wireless communication receiving module II 20 and the wireless communication transmitting module II 21 all adopt the wireless transceiver NRF24L01+ of the Norwegian Nordic Semiconductor Company. The specific information transmission mode is as follows: the FPGA controller 15 writes the driving signal of the receiving side switch capacitor into the sending buffer area of the wireless communication transmitting module I 18, converts the digital signal into a 2.4GHz radio frequency signal through the internal radio frequency circuit after verification, and radiates out by the antenna. The wireless communication receiving module I 19 continuously monitors the specified frequency channel, filters and demodulates the received radio frequency signal first, restores it into a digital signal, and after verifying that the data is correct, transmits the data to the signal conditioning circuit 22. The signal conditioning circuit 22 analyzes, processes and converts the data into a 0-3.3V PWM control signal, and transmits it to the receiving side switch capacitor driving circuit 17. The direct current voltage and current signal conditioning circuit 13 writes the information of the load current and the load voltage into the sending buffer area of the wireless communication transmitting module II 21, converts the digital signal into a 2.4GHz radio frequency signal through the internal radio frequency circuit after verification, and radiates out by the antenna. The wireless communication receiving module I 21 continuously monitors the specified frequency channel, filters and demodulates the received radio frequency signal first, restores it into a digital signal, and after verifying that the data is correct, transmits the data to the FPGA controller 15.

[0035] Example 5 The flow chart of the anti-offset double-sided LCC compensation WPT system design method of the application is shown in Figure 2 The specific steps are as follows: Step 1, design of the coupling mechanism; The coupling mechanism in the WPT system is generally composed of a transmitting coil L 1, L 2 and mutual inductance M . The application is mainly used for multi-rotor unmanned aerial vehicles for aerial photography, agricultural plant protection, power inspection and small material transportation. In order to reduce the load of the unmanned aerial vehicle side and improve the charging reliability, the diameter of the transmitting coil is generally greater than that of the receiving coil, and a magnetic core is not added on the coil. Therefore, according to formulas (1) and (2), the self-inductance of the transmitting coil L 1 and the receiving coil L 2 can be calculated.

[0036] (1) (2) Wherein, μ 0 is the vacuum permeability, N 1, D 1 and l 1 are the transmitting coil LThe number of turns, diameter, axial length (distance between the two ends of the coil) of the receiving coil 2, N 2, D 2 and l 2 is the receiving coil L 2.

[0037] For the WPT charging system, the offset of the receiving coil and the transmitting coil will cause the mutual inductance M to change, thereby causing the coupling coefficient k to fluctuate. Therefore, it is necessary to estimate the offset boundary of the receiving coil and the transmitting coil, thereby estimating the mutual inductance range, calculating the maximum coupling coefficient k max and the minimum coupling coefficient k min . Generally, the offset range of the transmitting coil and the receiving coil does not exceed the radius of the transmitting coil, so the present application uses the simplified correction coefficient method in engineering to estimate the mutual inductance range. When the centers of the transmitting coil L 1 and the receiving coil L 2 are completely aligned, the mutual inductance value is the maximum, denoted as M max , and the calculation formula is: (3) wherein r 1 and r 2 are the radii of the corresponding coils, d is the vertical distance between the two coils.

[0038] When the centers of the transmitting coil L 1 and the receiving coil L 2 are not aligned, the mutual inductance correction coefficient K is introduced as: (4) wherein, s is the horizontal offset ratio when the transmitting coil L 1 and the receiving coil L 2 are maximally offset.

[0039] The minimum mutual inductance M min can be represented as: (5) The maximum coupling coefficient k max and the minimum coupling coefficient k min are: (6) (7) From step 1, the self-inductance of the transmitting coil can be calculated L 1. The self-inductance of the receiving coil L 2. The maximum coupling coefficient k max and the minimum coupling coefficient k min .

[0040] Step 2, constant current and constant voltage resonance frequency design; In order to realize the constant resonance frequency in two output modes, the constant current resonance frequency f c and the constant voltage resonance frequency f v in the present application can be expressed as: (8) The working frequency of the unmanned aerial vehicle wireless charging system is approximately 80kHz-200kHz. Therefore, when designing the constant current and constant voltage resonance frequencies, the present application needs to f c , f v ∈(80kHz, 200kHz).

[0041] Step 3, design of the transmitting side LCC compensation topology parameters; According to the self-inductance of the transmitting coil L 1 in step 1, the maximum coupling coefficient k max and the constant current resonance frequency f c and the constant voltage resonance frequency f v in step 2, the transmitting side compensation inductance L f1 is: (9) The transmitting side compensation capacitance C f1 and C 1 is: (10) (11) Step 4, design of the receiving side LCC compensation topology parameters; according to the self-inductance of the transmitting coil L 1, the self-inductance of the receiving coil L 2, the maximum coupling coefficient k max , the constant current resonance frequency f c and the constant voltage resonance frequency f vTransmit side compensation capacitor in step 3 C f1 And C 1, receive side compensation inductance L f2 Can be expressed as: (12) Receive side compensation capacitor C f2 And C 2 is: (13) (14) Step 5, transmission gain verification; in constant current mode, the output current decreases with the decrease of coupling coefficient; in constant voltage mode, the output voltage increases with the decrease of coupling coefficient. Therefore, it is necessary to verify whether the minimum transmission gain of the system in two output modes meets the charging requirements.

[0042] According to the parameters calculated in steps 1-4, the minimum transmission gain of constant current mode and constant voltage mode g c And g v For: (15) (16) When the minimum transmission gain in two output modes can meet the charging requirements of the unmanned aerial vehicle, the system design is completed, if not, the constant current resonance frequency needs to be reselected f c And constant voltage resonance frequency f v .

[0043] The constant current / constant voltage control method of the bilateral LCC compensation WPT system for wireless charging of the unmanned aerial vehicle mainly includes four stages: the first stage, initialization. After pressing the start key, the system line is initialized, then the load voltage is detected, if the load voltage is less than the reference value, the system enters the constant current mode; if the load voltage is greater than or equal to the reference value, the system enters the constant voltage mode. The second stage, constant current output mode. If it is judged as constant voltage mode in initialization, skip this stage, and directly enter the constant voltage mode soft start step of the third stage. First, the system performs soft start, and the phase shift angle of the full-bridge inverter is controlled, so that the load current gradually increases according to the soft start time. At the same time, in order to ensure that the MOSFET of the full-bridge inverter maintains ZVS during soft start, the control angle of the transmit side switching capacitor β c Always keep 90 degrees, and the MOSFET of the receive side switching capacitor always keeps on, so that the capacitor Cv A short circuit is used to prevent the constant current resonant frequency from shifting. Next, the phase shift angle is adjusted in real time according to the load current to achieve constant current output. Simultaneously, the control angle of the transmitting-side switched capacitor is adjusted according to the phase difference between the load voltage and current. β c This achieves minimum reactive current and ZVS control. The third stage involves switching from constant current mode to constant voltage mode. First, when the load voltage is greater than or equal to the reference value, the system operating frequency switches from the constant current resonant frequency to the constant voltage resonant frequency. Then, by controlling the phase shift angle of the full-bridge inverter, the load voltage is gradually increased according to the soft-start time. Simultaneously, to ensure that the MOSFETs of the full-bridge inverter maintain ZVS during soft start, the control angle of the receiving-side switched capacitor is adjusted. β v Always maintained at 90°, the MOSFET of the emitter-side switched capacitor remains on, keeping the capacitor... C c Short circuit to prevent constant voltage resonant frequency deviation. Fourth stage: Constant voltage output mode. First, constant voltage output is achieved by adjusting the phase shift angle in real time according to the load voltage. Then, the control angle of the receiving-side switched capacitor is adjusted according to the phase difference between the load voltage and current. β v This achieves minimum reactive current and ZVS control.

[0044] Example 6 The control flow of the bilateral LCC compensation WPT system for wireless charging of drones is as follows: Figure 3 As shown, please follow these steps: This method mainly consists of four stages, with the first stage being initialization, including steps 1 and 2, as detailed below: Step 1: Parameter initialization, load current reference value. I ref Load voltage reference value U ref Constant current resonant frequency f c Constant voltage resonant frequency f v .

[0045] Step 2: Detect the load voltage to determine the output mode.

[0046] After pressing the start key, the load voltage detection conditioning code is encoded (the voltage is converted into a 0-3.3V DC voltage signal through a two-stage inverting proportional circuit, and the signal is encoded), and then the encoded information is written into the transmission buffer of the wireless communication transmission module II 20. After verification, the digital signal is converted into a 2.4GHz radio frequency signal by the internal radio frequency circuit, and is radiated by the antenna. The wireless communication receiving module II 21 continuously monitors the designated frequency channel, and after receiving the radio frequency signal, it is first filtered and demodulated to restore it to a digital signal. After verification (using the self-checking function of the NRF24L01+ communication module), the data is confirmed to be correct, and then the data is transmitted to the FPGA controller 15. Finally, the FPGA controller 15 compares the load voltage U R with the load voltage reference value U ref If U R < U ref , the system operating frequency is the constant current resonance frequency f c , and the system enters the constant current mode; if U R ≥ U ref , the system operating frequency is the constant voltage resonance frequency f v , and the system enters the constant voltage mode.

[0047] The second stage is the constant current output mode, which includes steps 3-5. If the first stage determines that the system is in the constant voltage mode, it will skip this stage and directly enter the third stage step 7. The details are as follows: Step 3, soft start in constant current mode.

[0048] The DSP controller 15 sets the phase shift angle θ , and the FPGA controller 15 sends a PWM enable signal to start with the minimum charging current, reducing the risk of damage to devices such as MOSFET and capacitor in the WPT system due to overcurrent and overvoltage. For the WPT system, the current value of the soft start in the constant current mode is generally 10% of the rated value, so the setting method of the soft start phase shift angle θ is as follows: (17) wherein U d is the output voltage of the DC power supply 1.

[0049] In addition, the FPGA controller 15 sets the control angle β cThe phase shift angle is always 90°, and the PWM signal is sent to the transmitting side switch capacitor drive circuit 16, so that the system input impedance angle α c is greater than 0 and keeps the maximum value, always working in inductive state, ensuring that the inverter MOSFET keeps ZVS during soft start. At the same time, the FPGA controller 15 sets the receiving side switch capacitor MOSFET to always keep on, encodes the PWM signal, writes it into the transmission buffer of the wireless communication transmission module I18, and after verification, converts the digital signal to a 2.4GHz radio frequency signal through the internal radio frequency circuit, which is radiated by the antenna. The wireless communication receiving module I19 continuously monitors the designated channel, and after receiving the radio frequency signal, it is first filtered and demodulated to restore it to a digital signal. After verifying that the data is correct, the data is transmitted to the signal conditioning circuit 22. The signal conditioning circuit 22 analyzes, processes and converts the data into a 0-3.3V PWM control signal, and transmits it to the receiving side switch capacitor drive circuit 17, so that the capacitor C v is short-circuited to avoid constant current resonance frequency deviation.

[0050] Step 4, constant current charging control.

[0051] The load current detection conditioning encoding is written into the wireless communication transmission module II21 by the DC current sensor 10 and the DC current voltage signal conditioning circuit 13, and then radiated by the antenna. The wireless communication receiving module II20 continuously monitors the designated channel, and after receiving the radio frequency signal, it is first filtered and demodulated, and the data is transmitted to the FPGA controller 15. Finally, the FPGA controller 15 compares the load current I R with the load voltage reference value I ref If I R < 0 I ref , the phase shift angle θ = θ - Δθ ; if I R > 0 I ref , the phase shift angle θ = θ + Δθ . Wherein Δθ is the adjustment amount of the phase shift angle, which can be expressed as: (18) Wherein k p is the proportional coefficient, k i is the integral coefficient.

[0052] Step 5, minimum reactive current and ZVS control in constant current mode: the input current and input voltage signals of the double-sided LCC compensation topology are collected by the alternating current sensor 3 and the alternating voltage sensor 4 respectively, and then the input current and input voltage signals of the double-sided LCC compensation topology are converted into 0-3.3V voltage square wave signals by the alternating current and voltage signal conditioning circuit 12 (inverted proportional circuit + inverted comparison circuit based on LF353 operational amplifier) and input to the FPGA controller 15.

[0053] Then, the input current and input voltage signals of the double-sided LCC compensation topology are phase-detected to obtain the phase difference between them. The FPGA controller 15 first obtains the rising edges of the input voltage and the input current by the XOR method, and the logic operation formula for obtaining the rising edges is: (19) wherein, I r and V r are the rising edges of the input current and the input voltage respectively, I (k) and V (k) are the current load current level and the current load voltage level respectively, I (k-1) and V (k-1) are the previous input current level and the previous input voltage level respectively.

[0054] counting from the input voltage rising edge V r to the input current rising edge I r , and the counting value is recorded as m, that is, the counting value of the phase difference between the input voltage and the input current. Counting from the input voltage rising edge to the next input voltage rising edge, and the counting value is recorded as n, that is, the counting value of the input voltage period, then the counting value of the phase difference between the input voltage and the input current is converted into the phase difference: (20) wherein, m is the counting value of the phase difference between the input voltage and the input current, n is the counting value of the input voltage period, A c is the phase difference between the input current and the input voltage of the double-sided LCC compensation topology in constant current mode.

[0055] Finally, the current phase shift angle θ is compared with the phase difference between the input current and the input voltage A c by the FPGA controller 15, if θ > A cThe control angle of the transmitting side switching capacitor β c =β c - Δβ c The control angle of the transmitting side switching capacitor θ < A c The control angle of the transmitting side switching capacitor β c =β c + Δβ c The minimum reactive current and ZVS control in constant current mode are realized. Wherein Δβ c The adjustment amount of the control angle of the transmitting side switching capacitor is the same as the proportional coefficient and the integral coefficient, and the specific design is consistent with formula (18).

[0056] The third stage is the switching from constant current output mode to constant voltage output mode, including steps 6-7, as follows: Step 6, whether to switch the working frequency.

[0057] The load voltage detection conditioning code is obtained through the DC voltage sensor 11 and the DC current voltage signal conditioning circuit 13, and then the encoded load voltage signal is radiated out by the wireless communication transmitting module II 21. The wireless communication receiving module II 20 continuously monitors the designated channel, receives the data, and transmits it to the FPGA controller 15. The FPGA controller 15 compares the load voltage U R with the load voltage reference value U ref , if U R < U ref , the system working frequency is unchanged; if U R= U ref , the system working frequency is switched from the constant current resonance frequency f c to the constant voltage resonance frequency f v .

[0058] Step 7, soft start in constant voltage output mode.

[0059] The DSP controller 15 resets the phase shift angle θ according to formula (20), and sends a PWM enable signal to the FPGA controller 15 to switch and start the constant voltage charging mode with the minimum charging voltage.

[0060] (21) In addition, the FPGA controller 15 sets the control angle of the receiving side switched capacitor β v is always 90°, and the PWM signal is encoded and radiated by the antenna of the wireless communication transmission module I18. After the data is received by the wireless communication receiving module I19, it is transmitted to the signal conditioning circuit 22, which converts it into a 0-3.3V PWM control signal and transmits it to the receiving side switched capacitor drive circuit 17, so that the system input impedance angle α c is greater than 0 and maintains the maximum value, always working in an inductive state, ensuring that the inverter MOSFET maintains ZVS during soft start. At the same time, the FPGA controller 15 sets the MOSFET of the transmitting side switched capacitor to always be on and sends a PWM signal to the transmitting side switched capacitor drive circuit 16, so that the capacitor C c is short-circuited, avoiding the constant voltage resonance frequency shift.

[0061] The fourth stage is the constant voltage output mode, which includes steps 8-9, as follows: Step 8, constant voltage charging control.

[0062] The load voltage signal is transmitted to the FPGA controller 15 through the DC voltage sensor 11, the DC current voltage signal conditioning circuit 13, the wireless communication transmission module I21, and the wireless communication receiving module I20. The FPGA controller 15 compares the load voltage U R with the load voltage reference value U ref If U R < 0 U ref , the phase shift angle θ = θ - Δθ is increased; if U R > 0 U ref , the phase shift angle θ = θ + Δθ is decreased.

[0063] Step 9, minimum reactive current and ZVS control in constant voltage mode The input current and input voltage signals of the double-sided LCC compensation topology are converted into 0-3.3V voltage square wave signals and input to the FPGA controller 15 through the AC current sensor 3, the AC voltage sensor 4, and the AC current voltage signal conditioning circuit 12. The FPGA controller 15 also calculates the phase difference between the input current and the input voltage in the constant voltage mode of the double-sided LCC compensation topology using the XOR method in step 5 A v , and compares it with the current phase shift angle θIf a comparison is made, θ > A v The control angle of the receiving-side switched capacitor. β v =β v - Δβ v ;like θ < A v The control angle of the receiving-side switched capacitor. β v =β v + Δβ v This enables the achievement of minimum reactive current and ZVS control in constant voltage mode. Δβ v The adjustment amount of the switching capacitor control angle on the receiving side is the same as that in equation (18).

[0064] The bilateral LCC compensation topology parameter design method and control method of the present invention are applied to, for example... Figure 1 In the illustrated UAV WPT charging system, parameter design allows the system to maintain constant current and constant voltage resonant frequencies under varying coupling coefficients and load fluctuations, eliminating the need for resonant frequency tracking control. Furthermore, the output current remains constant with load changes at the constant current resonant frequency, and the output voltage remains constant with load changes at the constant voltage resonant frequency. In addition, this design method can achieve constant phase of the input current of the transmitting-side switched capacitor at the constant current resonant frequency and constant phase of the input current of the receiving-side switched capacitor at the constant voltage resonant frequency, eliminating the need for an input current phase detection module in the switched capacitor control system. Therefore, the parameter design method of this invention can significantly simplify the control system.

[0065] After parameter design, fluctuations in the coupling coefficient of the UAV WPT charging system only alter the transmission gain of the constant current and constant voltage output modes, allowing the system to achieve constant current and constant voltage output using only traditional phase-shift control. Furthermore, this invention introduces switched capacitors to ensure the system consistently achieves minimum reactive current and ZVS under varying coupling coefficients and load fluctuations.

[0066] Figures 4 and 5 show the coupling coefficients. k =0.12 and k Load current under different loads when =0.2 U R Load voltage I R Input current I in and input voltage U inwaveforms. According to Fig. 4(a) and Fig. 4(b), when the coupling coefficient k = 0.12 and the operating frequency is 81 kHz, the load current remains at 1.1 A when the load increases from 33 Ω to 55 Ω, and the phase-shift angle is only adjusted by 5°. Similarly, according to Fig. 5(a) and Fig. 5(b), when the coupling coefficient k = 0.2 and the operating frequency is 81 kHz, the phase-shift angle is only adjusted by 3° before and after the load changes, and the load current remains unchanged. Comparing Fig. 4(a) and Fig. 5(a), when the coupling coefficient decreases from 0.2 to 0.12, the load current remains at 1.1 A by reducing the phase-shift angle from 27° to 0° while the load remains at 55 Ω. As can be seen from Fig. 4(b) and Fig. 5(b), when the load is 33 Ω, constant current can also be achieved by adjusting the phase-shift angle when the coupling coefficient changes. In summary, by using the design method of the present application, the constant-current resonant frequency is independent of the coupling coefficient, and the system can achieve load-independent constant-current output characteristics at the resonant frequency, so that the system can achieve constant-current output only by phase-shift control.

[0067] Fig. 6 is the input current of the transmitting side switch capacitor under different coupling coefficients and loads when the constant-current mode is output I 1. Transmitting side switch capacitor drive U sa , input current I in , input voltage U in waveforms. Comparing Fig. 6(a) and Fig. 6(b), when the coupling coefficient k = 0.12, the control angle β c is reduced from 133° to 93° when the load is adjusted from 55 Ω to 33 Ω, so as to maintain the minimum reactive current and ZVS. As can be seen from Fig. 6(b) and Fig. 6(c), when the load is 33 Ω, the coupling coefficient k is reduced from 0.2 to 0.12, and the control angle β c only needs to be adjusted from 117° to 133° to achieve ZVS under the minimum reactive current. As can be seen from Fig. 6(a), Fig. 6(b) and Fig. 6(c), the phase of the input current of the transmitting side switch capacitor I 1 is not affected by the changes in load and coupling coefficient, and always remains constant. It can also be seen that, in the constant-current mode, adjusting the control angle β c of the transmitting side switch capacitor does not affect the control of the phase-shift angle, and the control angle of the transmitting side switch capacitor and the phase-shift angle are decoupled.

[0068] Fig. 7 and Fig. 8 are the input current of the transmitting side switch capacitor when the coupling coefficient k = 0.12 and kLoad current under different loads when =0.2 U R Load voltage I R Input current I in and input voltage U in The waveform. Based on Figures 7(a) and 7(b), the coupling coefficient... k =0.12, operating frequency 90kHz, when the load increases from 55Ω to 110Ω, the load voltage remains at 60V, and the phase shift angle remains almost unchanged before and after the load change. Similarly, according to Figures 8(a) and 8(b), the coupling coefficient... k With a coupling coefficient of 0.2, the system maintains a constant load voltage at 90kHz. Comparing Figures 7(a) and 8(a), with the load constant at 55Ω, when the coupling coefficient decreases from 0.2 to 0.12, the load voltage remains constant at 60V by increasing the phase shift angle from 0° to 33°. Figures 7(b) and 8(b) show that even with a load of 110Ω, a constant voltage can be achieved by adjusting the phase shift angle when the coupling coefficient changes. In summary, through the design method of this invention, the constant voltage resonant frequency is independent of the coupling coefficient, and the system can achieve load-independent constant voltage output characteristics at the resonant frequency, enabling the system to achieve constant voltage output solely through phase shift control.

[0069] Figure 9 shows the input current of the emitter-side switched capacitor under different coupling coefficients and loads during constant current mode output. I 2. Transmitter-side switched capacitor drive U sc Input current I in Input voltage U in The waveform. Comparing Figure 9(a) and Figure 9(b), when the coupling coefficient... k When the resistance is 0.2, the load can be adjusted from 55Ω to 110Ω by adjusting the control angle. β v The angle is reduced from 137° to 116° to maintain minimum reactive current and ZVS. As shown in Figures 9(b) and 9(c), when the load is 110Ω, the coupling coefficient... k To reduce it from 0.2 to 0.12, simply... β v Adjusting the angle from 116° to 90° enables ZVS with minimal reactive current. Figures 9(a), 9(b), and 9(c) show the input current of the switched capacitor on the receiving side. I Phase 2 remains constant regardless of load and coupling coefficient changes. Similarly, it can be seen that in constant voltage mode, adjusting the control angle of the receiving-side switched capacitor... βv The control of the phase shift angle is not affected, and the decoupling of the switch capacitor control angle and the phase shift angle on the receiving side is realized.

[0070] Figure 10 is an experimental waveform of constant current-constant voltage conversion under different coupling coefficients. k As shown in Figure 10 (a), Figure 10 (b) and Figure 10 (c), the coupling coefficients are 0.12, 0.17 and 0.2 respectively, the constant current-constant voltage conversion process is about 20ms, and the load voltage before and after switching U R The load current I R is basically kept constant, and the change rate is less than 2%.

[0071] In summary, the parameter design method and the control method proposed by the application have significant advantages in many aspects. The constant current resonance frequency and the constant voltage resonance frequency are always kept constant and are not affected by the load and the coupling coefficient fluctuation, so that the system does not need to track the resonance frequency control; under the constant current resonance frequency, the output current is independent of the load, and under the constant voltage resonance frequency, the output voltage is independent of the load, which significantly reduces the regulation range of the phase shift angle; the phase of the transmitting side switch capacitor input current is constant in the constant current mode, and the phase of the receiving side switch capacitor input current is constant in the constant voltage mode, so that the phase detection module of the switch capacitor control system is saved; the decoupling of the phase shift angle and the switch capacitor control angle is realized in the two output modes, the cooperative control of the two variables is avoided, and the complexity of the control system is reduced.

[0072] The application is suitable for a bilateral LCC compensation topology control system for unmanned aerial vehicle wireless charging, and has the following advantages: 1) Compared with other parameter design methods of bilateral LCC compensation topology, the application has the following advantages: the constant resonance frequency is realized in the constant current and constant voltage output modes, the tracking control of the resonance frequency is saved, the control system is simplified, and the adverse effects of load changes and coil deviation are significantly reduced; the output current under the constant current resonance frequency and the output voltage under the constant voltage resonance frequency are independent of the load, and the regulation range of the phase shift angle is greatly reduced.

[0073] 2) The application realizes the minimum reactive current and ZVS in the whole charging process in the two modes by adjusting the transmitting side and receiving side switch capacitors; in addition, the input current phase of the switch capacitor is not affected by the load and the coupling coefficient, which means that the regulation of the switch capacitor control angle can be realized without a current phase detection circuit, and the circuit design is simplified. 3) The application realizes the decoupling of the phase shift angle and the switch capacitor control angle, that is, the phase shift angle only regulates the output voltage and the output current, and the switch capacitor control angle only regulates the input impedance, which simplifies the control system and eliminates the need for complex algorithms to cooperatively control the two variables.

Claims

1. A bilateral LCC compensation topology control system suitable for unmanned aerial vehicle wireless charging, characterized in that: The FPGA controller (15) is connected with the AC current voltage signal conditioning circuit (12), the full-bridge inverter drive circuit (14), the transmitting side LCC compensation topology structure, the receiving side LCC compensation topology structure and the signal verification circuit respectively. 2.The double-sided LCC compensation topology control system for wireless charging of UAVs of claim 1, wherein: The transmitting side LCC compensation topology structure comprises a wireless communication transmitting module I (18) and a transmitting side switched-capacitor drive circuit (16) connected with the transmitting side resonant circuit (5). 3.The double-sided LCC compensation topology control system for wireless charging of UAVs of claim 2, wherein: The receiving side LCC compensation topology structure comprises a wireless communication receiving module I (19) connected with a signal conditioning circuit (22), a receiving side switched-capacitor drive circuit (17) and a receiving side resonant circuit (6) in sequence.

4. The double-sided LCC compensation topology control system suitable for wireless charging of drones of claim 3, wherein: The signal verification circuit comprises a wireless communication transmitting module II (21) connected with a direct current voltage signal conditioning circuit (13) connected with a direct current voltage sensor (11) and a direct current sensor (10) respectively, the direct current voltage sensor (11) is connected with a battery equivalent load (9) in parallel, the battery equivalent load (9) is connected with a filter capacitor (8) and a non-controlled rectifier bridge (7) in parallel, the wireless communication transmitting module II (21) is connected with a wireless communication receiving module II (20) through wireless signal, and the wireless communication receiving module II (20) is connected with the FPGA controller (15).

5. A parameter design method for a double-sided LCC compensation topology control system suitable for wireless charging of a UAV, characterized in that: The design process of the coupling mechanism is as follows:

6. The parameter design method of the double-sided LCC compensation topology control system suitable for the wireless charging of the UAV according to claim 5, characterized in that: ​ The coupling mechanism comprises a transmitting coil L 1. A receiving coil L 2 and mutual inductance M According to equations (1) and (2), the self-inductance of the transmitting coil L 1 and the receiving coil L 2 is calculated: （1） （2） wherein ​ 0 is the vacuum permeability, N 1, D 1 and l 1 are the number of turns, diameter, axial length of the transmitting coil L 1, N 2, D 2 and l 2 are the number of turns, diameter, axial length of the receiving coil L 2. Transmit coil L 1 and the receive coil L 2 are in perfect alignment, the mutual inductance M is maximum and is denoted by M max The formula for calculating it is: （3） wherein, r 1 and r 2 are the radii of the respective coils, d is the vertical distance between the two coils; the transmitting coil L 1 is not aligned with the center of the receiving coil L 2, in which case a mutual inductance correction factor K is introduced: （4） wherein s is a transmit coil L 1 and a receive coil L 2 horizontal offset ratio at maximum offset; minimum mutual inductance M min is represented as: （5） maximum coupling coefficient k max and minimum coupling coefficient k min is: （6） （7）。 7. The parameter design method of the double-sided LCC compensation topology control system suitable for the wireless charging of the UAV according to claim 6, wherein: The design process of the constant current and constant voltage resonant frequency is as follows: constant current resonant frequency f c The function relationship with constant voltage resonant frequency f v is represented as: （8） wherein f c , f v ∈ (80 kHz, 200 kHz).

8. The parameter design method of the double-sided LCC compensation topology control system suitable for the wireless charging of the UAV according to claim 7, wherein: The transmit side LCC compensation topology parameter design process is as follows: according to the self-inductance of the transmit coil in step 1 L 1 and the maximum coupling coefficient k max and the constant current resonance frequency in step 2 f c and the constant voltage resonance frequency f v , the transmit side compensation inductance L f1 is: （9） Transmit side compensation capacitor C f1 And C 1 is: （10） （11）。 9. The parameter design method of the double-sided LCC compensation topology control system suitable for the wireless charging of the UAV according to claim 8, wherein: The receiving side LCC compensation topology parameter design process is as follows: according to the transmitting coil self-inductance in step 1 L 1, the receiving coil self-inductance L 2 and the maximum coupling coefficient k max , the constant current resonance frequency in step 2 f c and the constant voltage resonance frequency f v , the transmitting side compensation capacitor in step 3 C f1 and C 1, the receiving side compensation inductance L f2 is represented as: （12） Receive side compensation capacitor C f2 and C 2 is: （13） （14）。 10. The parameter design method of the double-sided LCC compensation topology control system suitable for the wireless charging of the UAV according to claim 9, wherein: The transmission gain check design process is as follows: minimum transmission gain of constant current mode and constant voltage mode g c and g v is: （15） （16）。

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