Very-low-frequency narrow-band antenna pre-distortion broadband transmitting method

Abstract

The invention discloses a very-low-frequency narrow-band antenna pre-distortion broadband transmitting method. The core of the very-low-frequency narrow-band antenna pre-distortion broadband transmitting method is composed of double-tuning network parameter calculation and pre-distortion waveform design. The method comprises the following steps: with a constraint condition that transmitter port equivalent impedance is equal to transmitter characteristic impedance under an antenna center frequency, adjusting a load current gain peak frequency to a working frequency by calculating an undetermined parameter so as to realize working frequency point tuning; changing parameters of the double-tuned network to design a low-Q-value target group, acquiring primary and secondary side currents under constant-amplitude excitation, importing the primary and secondary side currents into an actual network of an experimental group, and deducing corresponding excitation voltage; according to the method, tuning and resistance changing are achieved through the double-tuning network, transient current fluctuation suppression is achieved through the pre-distortion design, and the active power utilization rate and the very-low-frequency communication rate of the power amplifier are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of terminology information processing, and particularly to a method for predistortion broadband transmission of a very low frequency narrowband antenna. Background Technology

[0002] As countries deepen their exploration of deep-sea mineral and fishery resources, the demand for long-distance, high-reliability communication technologies is becoming increasingly urgent. Very low frequency (VLF) electromagnetic waves (also known as very long waves, with frequencies of 3kHz to 30kHz and wavelengths of 10km to 100km) propagate along the Earth's surface or through reflection from the ionosphere, exhibiting minimal attenuation in the air. These signals can penetrate seawater and reach deep into rock formations, exhibiting low attenuation, strong anti-interference capabilities, and long propagation distances. Therefore, they are increasingly widely used in deep-sea communication and geological exploration. Because the wavelength of VLF electromagnetic waves is on the order of 10-100 kilometers, to achieve high radiation efficiency, the size of the transmitting antenna element should be on the order of a quarter wavelength. In practice, VLF antennas are less than one-tenth the wavelength, possessing low radiation resistance and high series capacitance reactance, resulting in low radiation efficiency. To ensure stable and reliable reception of VLF signals by long-distance underwater targets, the VLF switching power amplifier needs to have sufficient capacity and fully utilize its output capability within the operating frequency band to ensure a sufficiently high final radiated power. However, the switching process of very low frequency (VLF) antennas generates a large transient current, which requires VLF switching power amplifiers to have a current threshold that exceeds the steady-state current by a significant proportion. This limits the active power utilization of VLF switching power amplifiers, making it a major factor restricting the development of VLF communication towards higher communication rates and higher transmission power.

[0003] Therefore, this invention proposes a predistortion broadband transmission method for very low frequency (VLF) narrowband antennas. A comprehensive evaluation model is established for active power utilization, transmitter-side voltage and current, and load-side voltage and current. The goal is to improve the power amplifier output power factor, reduce the response fluctuations of the antenna load current and the transmitter output power within the operating frequency band. Tuning at the operating frequency can be achieved through dual-tuned network parameter design, or by introducing a low-Q dummy load into the dual-tuned network to effectively suppress transient current overshoot after frequency switching. This method improves communication speed while ensuring increased active power utilization of the VLF switching power amplifier. This method is of great significance for improving the communication speed of VLF communication technology. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a predistortion broadband transmission method for very low frequency narrowband antennas.

[0005] A comprehensive evaluation model for the power amplifier output power factor, transmitter voltage and current response fluctuations, and load voltage and current fluctuations was derived. By adjusting the transmitter characteristic impedance and the virtual load Q value, the optimal solution for the component parameter combination was found, which effectively achieved broadband impedance matching of the very low frequency antenna and made the transmitter voltage circuit and load voltage and current response flatter.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems includes the following steps: A method for predistortion broadband transmission using a very low frequency narrowband antenna, characterized by comprising the following steps: Step 1: Construct a virtual dual-tuned network and input the known antenna load parameters; the known antenna load parameters include load resistance and capacitance values, primary-side self-inductance, secondary-side self-inductance, and tuning capacitor; Step 2: Set the transmitter characteristic impedance, i.e., the transmitter's inherent parameters, and adjust the load current gain peak value to the MSK operating frequency; Step 3: By writing the KVL equations for the primary and secondary loops of the double-tuned network, solve the mathematical model of the load current to obtain the first set of undetermined parameter values ​​for the double-tuned network; the first set of undetermined parameter values ​​includes the primary inductance of the double-tuned network. Primary tuning inductance value The sum represents the primary-side capacitance of the dual-tuned network. ; Step 4: Adjust the peak value of the secondary current to the MSK operating frequency to obtain the second set of undetermined parameter values ​​for the dual-tuned network; the second set of undetermined parameter values ​​includes the primary-side quality factor. Q 1 The mutual inductance M between the primary and secondary coupled inductors; Step 5: Simulate and verify whether the dual-tuned network achieves frequency modulation at the operating frequency. If yes, proceed to the next step; otherwise, repeat steps 2 to 4 until the simulation verifies that frequency modulation at the operating frequency has been achieved. Step Six: Modify the inductance and capacitance values ​​of the primary and secondary windings of the dual-tuned network to reduce the Q value of the dual-tuned network without changing the resonant frequency. Use the dual-tuned networks with lower Q values ​​as the target group. The Q value includes the secondary-side quality factor. and primary side parameters of the dual-tuned network ； Step 7: Calculate the primary and secondary current expressions of the target group with low Q value under constant amplitude MSK excitation by separating the steady-state and transient KVL equations. Obtain the primary and secondary currents of the target group. The primary and secondary currents of the target group are used as intermediate expressions to derive the predistortion excitation voltage of the real network. Step 8: Use the real dual-tuned network with high Q value as the experimental group; inject the primary and secondary currents of the target group into the experimental group to obtain the pre-distortion excitation voltage waveform of the experimental group, and obtain the transmitter port voltage waveform data of the real dual-tuned network. Step 9: Using the transmitter port voltage waveform data of the real network as the predistortion excitation signal, verify whether transient fluctuation suppression is achieved. If yes, save the corresponding predistortion excitation voltage; otherwise, do not save it. Step 10: Within the set range, modify the target group Q value with a preset step size, repeat steps 6 to 9, and take the Q value with the best transient fluctuation suppression effect as the optimal target group Q value; take the predistortion excitation voltage corresponding to the optimal target group Q value as the predistortion excitation signal of the real dual-tuned network.

[0007] A further improvement is made to the dual-tuned network, which includes a primary-side resistor (R1) connected at one end to the transmitter output voltage and at the other end to the power supply, and a primary-side capacitor (C1) connected at one end to the transmitter output voltage. The primary-side resistor (R1) of the dual-tuned network is further described as follows: R 1 The other end is electrically connected to the primary inductor of the dual-tuned network ( L T1 The same terminal of the dual-tuned network primary-side capacitor ( C 1 The other end is electrically connected to a third inductor ( L 3 One end of the third inductor ( L 3 The other end is electrically connected to the primary inductor of the dual-tuned network ( L T1 The opposite end of the dual-tuned network secondary inductor ( L T2 The same terminal of the dual-tuned network is connected to the secondary resistor of the dual-tuned network. R 2 One end of the double-tuned network secondary resistor ( R 2 The other end is electrically connected to the secondary capacitor of the dual-tuned network ( C 2 One end of the dual-tuned network secondary capacitor ( C 2 The other end is electrically connected to the fourth inductor ( L 4 One end of the fourth inductor ( L 4 The other end is electrically connected to the secondary inductor of the dual-tuned network ( L T2 () is an alternate name for the term.

[0008] Further improvements are made to step three, which includes the following steps: The KVL equations for the primary and secondary loops are: (3) in, The antenna's operating angular frequency. This indicates the transmitter output voltage. This represents the primary current of the double-tuned network. This represents the secondary current of a dual-tuned network. This represents the primary-side resistance of the dual-tuned network. Indicates the imaginary part. This represents the primary-side inductance of a dual-tuned network. This represents the primary-side capacitance of the dual-tuned network. C2 This represents the secondary capacitance of a double-tuned network, where M represents the mutual inductance between the primary and secondary coupled inductors. This indicates that the secondary resistance of the dual-tuned network is also the equivalent resistance of the antenna load. This indicates the secondary inductance of a dual-tuned network. The reflection impedance value of the secondary side to the primary side : (4) Indicates the total impedance of the secondary side; hour, ,have to in This is the angular frequency at the center frequency of the antenna; make , The mathematical model of the current is obtained from the KVL equations for the primary and secondary sides: (5) in, Q 1. Q 2 represents the quality factors of the primary and secondary loops, respectively; and These are all intermediate parameters; Secondary current magnitude for: (6) have to: (7) beg Extreme point, we get: , (8) in, Indicate intermediate variables The value obtained by solving the equation as the independent variable Indicate intermediate variables The value obtained by solving the equation as the independent variable; Mutual intuition M for: (9) To ensure that the mutually inductively coupled circuit simultaneously meets the requirements for both reflection impedance and peak current frequency, the following must be satisfied: (10) Summarized as follows: (11) Solving for: (12) Depend on Seeking , , ; This represents the primary-side self-inductance of the coupled inductor. This represents the value of the primary-side tuning inductance.

[0009] Further improvements are made to step four as follows: Adjust the peak value of the secondary current to the MSK operating frequency; Transmitter port impedance Zin for: (13) The total impedance of the primary side Z 11 is: (14) The primary edge quality factor Q1 is: (15) (16) Therefore, Z11 and Zin are simplified as follows: (17) (18) have to: (19) (20).

[0010] In a further improvement, the method for obtaining the low-Q dual-tuned network in step six is ​​as follows: Set a low Q-value secondary side quality factor ; Calculate the secondary capacitance of a low-Q dual-tuned network. : ( twenty one ) in f c is the center frequency of the antenna load; Low computation Q The value of the secondary inductance of the dual-tuned network, where L 2obj is the total inductance of the secondary side. L 4obj is the adjustable inductor on the secondary side, therefore: ( twenty two ) ( twenty three ) This represents the secondary self-inductance of the coupled inductor; Further obtain low Q Mutual inductance of a dual-tuned network for: ( twenty four ) Coupling coefficient of coupled inductor for: (25) Primary parameters of low Q-value dual-tuned networks for: (26) Calculate the total primary inductance of a dual-tuned network with low Q value. L 1obj and primary-side adjustable inductor L 3obj is: (27) (28) Primary capacitance of low Q-value target group C 1obj is: (29); This results in a dual-tuned network with a low Q value.

[0011] As a further improvement, step seven includes the following steps: First, the voltage and current equations for the dual-tuned network under constant amplitude excitation voltage are listed: (30) (31) in, Indicates the transmitter excitation voltage. t represents the voltage across the primary capacitor, and t represents time. This represents the voltage across the secondary capacitor. Primary and secondary capacitor voltages and Determining the attenuation parameter: (32) in , in, This represents the Laplace transform value of the secondary capacitor voltage. Describe the complex variable of the Laplace transform. Representing components d Damping ratio, Representing components d The undamped free oscillation angular frequency, Representing components e The undamped free oscillation angular frequency, This represents the undamped free oscillation angular frequency of component f. a and b All are intermediate coefficients; The transient response parameters of the antenna load with a dual-tuned network were analyzed analytically using the partial fraction method, and then calculated using WolframMathematica software. Where: the secondary capacitor voltage and transient voltage The decay angular frequency is ; in, Let represent the undamped free oscillation angular frequency of the k-th component, and let r represent the total number of transient components. This represents the damping ratio of the k-th component; This represents the magnitude of the k-th component. t represents the initial phase of the k-th component; t represents time. Primary capacitor voltage The response consists of two parts: transient response and steady-state response. (33) in, The sinusoidal coefficient representing the steady-state component of the primary capacitor voltage. The cosine coefficient representing the steady-state component of the primary capacitor voltage; This represents the angular frequency of the attenuation component 2. This represents the sinusoidal coefficient of the attenuation component 2. This represents the coefficient of the attenuation component 2 cosine. This represents the angular frequency of the attenuation component 1; Indicates the first a The undamped free oscillation angular frequency of the component Indicates the first a Damping ratio of the component; Indicates the first b Damping ratio of the component, Indicates the first bThe undamped free oscillation angular frequency of the component; The response is steady state. Secondary capacitor voltage The response also consists of two parts: transient response and steady-state parameters. f1 The sinusoidal coefficient representing the steady-state component of the secondary capacitor voltage. f2 The cosine coefficient representing the steady-state component of the secondary capacitor voltage; (34) The steady-state KVL equations for the circuit are as follows: (35) in, This represents the phasor value of the primary current. This indicates the phasor value of the secondary current; The transmitter output voltage is expressed as: (36) in EM Indicates the amplitude of the transmitter output voltage; Indicates the initial phase of the transmitter output voltage; Derived secondary steady-state current value I 2 is: (37) (38) This represents the phase angle of the intermediate variable. The phase angle of the intermediate variable; Transient response derivation: 1. The capacitor voltage remains unchanged before and after the symbol switching: (39) This represents the primary capacitor voltage at time t0. This represents the primary capacitor voltage at time t0+. This represents the secondary capacitor voltage at time t0. This represents the secondary capacitor voltage at time t0+; Assuming the capacitor voltage has reached a steady state before symbol switching, the formula for the capacitor voltage in the steady state is: (40) A1 represents the sinusoidal coefficient of the steady-state component of the primary capacitor voltage, and A2 represents the cosine coefficient of the steady-state component of the primary capacitor voltage. B1 represents the sinusoidal coefficient of the steady-state component of the secondary capacitor voltage, and B2 represents the cosine coefficient of the steady-state component of the secondary capacitor voltage. 2. The inductor current remains unchanged before and after the symbol switching: The primary inductor current of the dual-tuned network remains unchanged: (41) Similarly, the secondary inductor current of the double-tuned network remains unchanged: (42) 3. Steady-state and transient separation KVL equations L: (43) (44).

[0012] The advantages of this invention are as follows: This invention enables the tuning and resistance variation of the antenna load at the operating frequency. The predistortion design method based on the dual-tuned network can suppress transient current fluctuations after the antenna operating frequency is switched. By applying the above dual-tuned parameter design method and predistortion transmission method, the problem of large transient fluctuations of the very low frequency antenna load at high communication rates can be suppressed, the active power utilization rate of the power amplifier output can be improved, and the very low frequency communication rate can be increased.

[0013] The invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0014] Figure 1(a) is a diagram of the dual-tuned network structure designed by the method of the present invention.

[0015] Figure 1(b) is a T-type equivalent network structure diagram of the dual-tuned network designed by the method of the present invention.

[0016] Figure 2 This is a flowchart of a method for predistortion broadband transmission of a very low frequency narrowband antenna according to an embodiment of the present invention.

[0017] Figure 3(a) is the MSK excitation symbol diagram.

[0018] Figure 3(b) is a waveform of the load current of the MSK constant amplitude excitation antenna.

[0019] Figure 3(c) is a waveform diagram of the load current of the predistortion excitation antenna of the present invention. Detailed Implementation

[0020] Figure 1(a) is a cascaded structure diagram of the power amplifier, dual-tuned network, and antenna load designed by the method of the present invention. R 2. C 2 represents the equivalent resistance and equivalent capacitance of the very low frequency antenna load at the center frequency, respectively.L 4 is the secondary-side tuning inductor. L T2 The secondary self-inductance of the coupled inductor L T1 The primary-side self-inductance of the coupled inductor M For coupled inductors and mutual inductance, L 3 is the primary-side tuned inductor. ，C 1 is the primary-side tuning capacitor. R 1 represents the primary resistance. V AC This is the transmitter output voltage.

[0021] Figure 1(b) is a diagram of the power amplifier, dual-tuned T-type equivalent network, and antenna load cascade structure designed by the method of the present invention.

[0022] Figure 2 This is a flowchart of an embodiment of the impedance matching network design method of the present invention. The specific implementation steps are as follows: Step 1: Input antenna load parameters and some network parameters; Step 2: Write the steady-state KVL equations for the primary and secondary loops of the dual-tuned network, calculate the mathematical expression for the load current of the secondary loop of the dual-tuned network, find the angular frequency corresponding to the extreme point of the secondary current, adjust the angular frequency to the MSK operating frequency, realize the tuning of the antenna equivalent load at the operating frequency, and obtain the complete network parameters. Step 3: Reduce the Q value of the primary and secondary circuits of the dual-tuned network by modifying the inductance and capacitance values ​​of the primary and secondary circuits to obtain a low-Q target group. Write the KVL equations of the primary and secondary circuits of the low-Q target group under constant amplitude MSK excitation. Solve the mathematical model of the primary and secondary currents by separating steady-state and transient states. Step 4: Calculate the load voltage and current waveforms and power amplifier side voltage and current waveforms under the primary and secondary currents of the low Q-value target group, respectively. Establish a model of the fluctuation amplitude with respect to the reflection resistance and the Q value of the target group, and select the optimal parameter combination.

[0023] Figures 3(a)-3(c) show the simulation waveforms of the predistortion excitation voltage suppression effect in one embodiment of the present invention. During direct excitation, the excitation voltage is a constant amplitude MSK voltage. When the symbol is 0, it indicates that the transmitter MSK excitation voltage frequency is... f 1= f 0-Δ f When the symbol is 1, it indicates that the transmitter MSK excitation voltage frequency is... f 1= f 0+Δ f The transient current of the directly excited symbol fluctuates greatly. After adopting the pre-distortion excitation of the low-Q virtual load based on the dual-tuned network of the present invention, the fluctuation amplitude is greatly reduced, which verifies that the present invention has a good suppression effect on the transient current of the load end.

Claims

1. A method for predistortion broadband transmission using a very low frequency narrowband antenna, characterized in that, Includes the following steps: Step 1: Construct a virtual dual-tuned network and input the known antenna load parameters; the known antenna load parameters include load resistance and capacitance values, primary-side self-inductance, secondary-side self-inductance, and tuning capacitor; Step 2: Set the transmitter characteristic impedance, i.e., the transmitter's inherent parameters, and adjust the load current gain peak value to the MSK operating frequency; Step 3: By writing the KVL equations for the primary and secondary loops of the double-tuned network, solve the mathematical model of the load current to obtain the first set of undetermined parameter values ​​for the double-tuned network; the first set of undetermined parameter values ​​includes the primary inductance of the double-tuned network. Primary tuning inductance value The sum represents the primary-side capacitance of the dual-tuned network. ; Step 4: Adjust the peak value of the secondary current to the MSK operating frequency to obtain the second set of undetermined parameter values ​​for the dual-tuned network; the second set of undetermined parameter values ​​includes the primary-side quality factor. Q 1 The mutual inductance M between the primary and secondary coupled inductors; Step 5: Simulate and verify whether the dual-tuned network achieves frequency modulation at the operating frequency. If yes, proceed to the next step; otherwise, repeat steps 2 to 4 until the simulation verifies that frequency modulation at the operating frequency has been achieved. Step 6: Modify the inductance and capacitance values ​​of the primary and secondary loops of the double-tuned network to reduce the Q value of the double-tuned network without changing the resonant frequency. Use the double-tuned network with the low Q value as the target group. The Q value includes the secondary side quality factor. and primary side parameters of the dual-tuned network ； Step 7: Calculate the primary and secondary current expressions of the target group with low Q value under constant amplitude MSK excitation by separating the steady-state and transient KVL equations. Obtain the primary and secondary currents of the target group. The primary and secondary currents of the target group are used as intermediate expressions to derive the predistortion excitation voltage of the real network. Step 8: Use a real dual-tuned network with a high Q value as the experimental group; Inject the primary and secondary currents of the target group into the experimental group to obtain the predistorted excitation voltage waveform of the experimental group and acquire the transmitter port voltage waveform data of the real dual-tuned network. Step 9: Using the transmitter port voltage waveform data of the real network as the predistortion excitation signal, verify whether transient fluctuation suppression is achieved. If yes, save the corresponding predistortion excitation voltage; otherwise, do not save it. Step 10: Within the set range, modify the target group Q value with a preset step size, repeat steps 6 to 9, and take the Q value with the best transient fluctuation suppression effect as the optimal target group Q value. The predistortion excitation voltage corresponding to the optimal target group Q value is used as the predistortion excitation signal of the real dual-tuned network.

2. The very low frequency narrowband antenna predistortion broadband transmission method as described in claim 1, characterized in that, The dual-tuned network includes a primary-side resistor (R1) connected at one end to the transmitter output voltage and at the other end to the power supply, and a primary-side capacitor (C1) connected at one end to the transmitter output voltage. R 1 The other end is electrically connected to the primary inductor of the dual-tuned network ( L T1 The same terminal of the dual-tuned network primary-side capacitor ( C 1 The other end is electrically connected to a third inductor ( L 3 One end of the third inductor ( L 3 The other end is electrically connected to the primary inductor of the dual-tuned network ( L T1 The opposite end of the dual-tuned network secondary inductor ( L T2 The same terminal of the dual-tuned network is connected to the secondary resistor of the dual-tuned network. R 2 One end of the double-tuned network secondary resistor ( R 2 The other end is electrically connected to the secondary capacitor of the dual-tuned network ( C 2 One end of the dual-tuned network secondary capacitor ( C 2 The other end is electrically connected to the fourth inductor ( L 4 One end of the fourth inductor ( L 4 The other end is electrically connected to the secondary inductor of the dual-tuned network ( L T2 () is an alternate name for the term.

3. The very low frequency narrowband antenna predistortion broadband transmission method as described in claim 1, characterized in that, The steps in step three are as follows: The KVL equations for the primary and secondary loops are: ( 3 ) in, The antenna's operating angular frequency. This indicates the transmitter output voltage. This represents the primary current of the double-tuned network. This represents the secondary current of a dual-tuned network. This represents the primary-side resistance of the dual-tuned network. Indicates the imaginary part. This represents the primary-side inductance of a dual-tuned network. This represents the primary-side capacitance of the dual-tuned network. C2 This represents the secondary capacitance of a double-tuned network, where M represents the mutual inductance between the primary and secondary coupled inductors. This indicates that the secondary resistance of the dual-tuned network is also the equivalent resistance of the antenna load. This indicates the secondary inductance of a dual-tuned network. The reflection impedance value of the secondary side to the primary side : ( 4 ) Indicates the total impedance of the secondary side; hour, ,have to ; in This is the angular frequency at the center frequency of the antenna; make , The mathematical model of the current is obtained from the KVL equations for the primary and secondary sides: ( 5 ) in, Q 1. Q 2 represents the quality factors of the primary and secondary loops, respectively; and These are all intermediate parameters; Secondary current magnitude for: ( 6 ) have to: ( 7 ) beg Extreme point, we get: ， ( 8 ) in, Indicate intermediate variables The value obtained by solving the equation as the independent variable Indicate intermediate variables The value obtained by solving the equation as the independent variable; Mutual intuition M for: ( 9 ) To ensure that the mutually inductively coupled circuit simultaneously meets the requirements for both reflection impedance and peak current frequency, the following must be satisfied: ( 10 ) Summarized as follows: ( 11 ) Solving for: ( 12 ) Depend on Seeking , , ; This represents the primary-side self-inductance of the coupled inductor. This represents the value of the primary-side tuning inductance.

4. The very low frequency narrowband antenna predistortion broadband transmission method as described in claim 3, characterized in that, The steps in step four are as follows: Adjust the peak value of the secondary current to the MSK operating frequency; Transmitter port impedance Zin for: ( 13 ) The total impedance of the primary side Z 11 is: ( 14 ) The primary edge quality factor Q1 is: ( 15 ) ( 16 ) Therefore, Z11 and Zin are simplified as follows: ( 17 ) ( 18 ) have to: ( 19 ) ( 20 )。 5. The very low frequency narrowband antenna predistortion broadband transmission method as described in claim 1, characterized in that, In step six, the method for obtaining the low-Q dual-tuned network is as follows: Set a low Q-value secondary side quality factor ; Calculate the secondary capacitance of a low-Q dual-tuned network. : ( 21 ) in f c is the center frequency of the antenna load; Low computation Q The value of the secondary inductance of the dual-tuned network, where L 2obj is the total inductance of the secondary side. L 4obj is the adjustable inductor on the secondary side, therefore: ( 22 ) ( 23 ) This represents the secondary self-inductance of the coupled inductor; Further obtain low Q Mutual inductance of a dual-tuned network for: ( 24 ) Coupling coefficient of coupled inductor for: ( 25 ) Primary parameters of low Q-value dual-tuned networks for: ( 26 ) Calculate the total primary inductance of a dual-tuned network with low Q value. L 1obj and primary-side adjustable inductor L 3obj is: ( 27 ) ( 28 ) Primary capacitance of low Q-value target group C 1obj is: ( 29 )； This results in a dual-tuned network with a low Q value.

6. The very low frequency narrowband antenna predistortion broadband transmission method as described in claim 1, characterized in that, Step seven includes the following steps: First, the voltage and current equations for the dual-tuned network under constant amplitude excitation voltage are listed: ( 30 ) ( 31 ) in, Indicates the transmitter excitation voltage. t represents the voltage across the primary capacitor, and t represents time. This represents the voltage across the secondary capacitor. Primary and secondary capacitor voltages and Determining the attenuation parameter: ( 32 ) in , ; in, This represents the Laplace transform value of the secondary capacitor voltage. Describe the complex variable of the Laplace transform. Representing components d Damping ratio, Representing components d The undamped free oscillation angular frequency, Representing components e The undamped free oscillation angular frequency, Representing components f The undamped free oscillation angular frequency, a and b All are intermediate coefficients; The transient response parameters of the antenna load with a dual-tuned network were analyzed analytically using the partial fraction method, and then calculated using WolframMathematica software. Where: the secondary capacitor voltage and transient voltage The decay angular frequency is ; in, Let represent the undamped free oscillation angular frequency of the k-th component, and let r represent the total number of transient components. This represents the damping ratio of the k-th component; This represents the magnitude of the k-th component. t represents the initial phase of the k-th component; t represents time. Primary capacitor voltage The response consists of two parts: transient response and steady-state response. (33) in, The sinusoidal coefficient representing the steady-state component of the primary capacitor voltage. The cosine coefficient representing the steady-state component of the primary capacitor voltage; This represents the angular frequency of the attenuation component 2. This represents the sinusoidal coefficient of the attenuation component 2. This represents the coefficient of the attenuation component 2 cosine. This represents the angular frequency of the attenuation component 1; Indicates the first a The undamped free oscillation angular frequency of the component Indicates the first a Damping ratio of the component; Indicates the first b Damping ratio of the component, Indicates the first b The undamped free oscillation angular frequency of the component; The response is steady state. Secondary capacitor voltage The response also consists of two parts: transient response and steady-state parameters. ； f1 The sinusoidal coefficient representing the steady-state component of the secondary capacitor voltage. f2 The cosine coefficient representing the steady-state component of the secondary capacitor voltage; (34) The steady-state KVL equations for the circuit are as follows: ( 35 ) in, This represents the phasor value of the primary current. This indicates the phasor value of the secondary current; The transmitter output voltage is expressed as: ( 36 ) in EM Indicates the amplitude of the transmitter output voltage; Indicates the initial phase of the transmitter output voltage; Derived secondary steady-state current value I 2 is: ( 37 ) ( 38 ) This represents the phase angle of the intermediate variable. The phase angle of the intermediate variable; Transient response derivation:

1. The capacitor voltage remains unchanged before and after the symbol switching: ( 39 ) This represents the primary capacitor voltage at time t0. This represents the primary capacitor voltage at time t0+. This represents the secondary capacitor voltage at time t0. This represents the secondary capacitor voltage at time t0+; Assuming the capacitor voltage has reached a steady state before symbol switching, the formula for the capacitor voltage in the steady state is: ( 40 ) A1 represents the sinusoidal coefficient of the steady-state component of the primary capacitor voltage, and A2 represents the cosine coefficient of the steady-state component of the primary capacitor voltage. B1 represents the sinusoidal coefficient of the steady-state component of the secondary capacitor voltage, and B2 represents the cosine coefficient of the steady-state component of the secondary capacitor voltage.

2. The inductor current remains unchanged before and after the symbol switching: The primary inductor current of the dual-tuned network remains unchanged: ( 41 ) Similarly, the secondary inductor current of the double-tuned network remains unchanged: ( 42 ) 3. Steady-state and transient separation KVL equations L: ( 43 ) ( 44 )。

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