Electromagnetic wave wideband frequency shift preserving transmission method based on double constitutive parameter time-varying circuit

Abstract

This invention discloses a broadband frequency-shifting conformal transmission method for electromagnetic waves based on a time-varying circuit with dual constitutive parameters, belonging to the fields of microwave radio frequency, time metamaterials, and frequency domain transformation technology. The method is implemented using a frequency-shifting transmission circuit, which includes a microstrip transmission line and a periodically loaded inductor branch. The inductor branch includes switches, series inductors, and parallel inductors. When all switches in the frequency-shifting transmission circuit are open, an input pulse signal is sent to the circuit. When the pulse signal has fully entered the microstrip transmission line, all switches close simultaneously. Due to the wavenumber conservation of the microstrip transmission line, frequency shift occurs, achieving frequency-shifting transmission. This method does not rely on a complex local oscillator system, does not increase circuit complexity excessively, and theoretically does not generate harmonics. It achieves broadband frequency shifting, reflection-free, high-efficiency transmission, and waveform distortion-free conformal transmission, providing a new technical path for broadband, low-distortion signal processing in the microwave radio frequency field.

Description

Technical Field

[0001] This invention belongs to the fields of microwave radio frequency, time metamaterials and frequency domain transformation technology, and specifically relates to a broadband frequency-shifting conformal transmission method for electromagnetic waves based on a time-varying circuit with dual constitutive parameters. Background Technology

[0002] In fields such as microwave radio frequency communication, radar detection, and radio frequency measurement, frequency conversion is a core component of signal processing. It is necessary to shift the frequency of the input signal to the target frequency band while ensuring the integrity, wide bandwidth adaptability, and low loss of signal transmission.

[0003] Traditional frequency conversion mainly relies on mixers, which are technologically mature. However, in recent years, they have gradually revealed insurmountable shortcomings, such as narrowband adaptability, harmonic generation due to nonlinear characteristics, waveform distortion, significant signal reflection, structural dependence on the local oscillator signal, and limited system compatibility. Therefore, addressing these issues is of great significance when designing frequency shifting circuits.

[0004] To address the shortcomings of traditional mixers, existing technologies have made some attempts. Subharmonic mixers improve isolation by reducing the local oscillator frequency requirement, but still fail to overcome the "narrowband frequency shifting" bottleneck, and the waveform distortion problem remains unresolved. Microwave photonic mixers, while capable of achieving ultra-wideband, are complex, expensive, and bulky, making them unsuitable for miniaturized, low-cost terminal devices. Existing research on time metamaterials, such as time-quarter-wave impedance converters, attempts to reduce reflections through time boundary manipulation, but has failed to achieve a synergistic effect of broadband frequency shifting and waveform preservation.

[0005] In summary, existing frequency conversion technologies cannot simultaneously achieve broadband frequency shifting, reflection-free operation, waveform preservation, harmonic elimination, and low system complexity. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a broadband frequency-shifting conformal transmission method for electromagnetic waves based on a time-varying circuit with dual constitutive parameters.

[0007] The technical problem addressed by this invention is solved as follows:

[0008] A broadband frequency-shifting conformal transmission method for electromagnetic waves based on a time-varying circuit with dual constitutive parameters is proposed. The method is implemented using a frequency-shifting transmission circuit, which includes a microstrip transmission line and a periodically loaded inductor branch.

[0009] A microstrip transmission line includes a dielectric substrate, a microstrip line, and a ground plane, with the microstrip line and ground plane located on the upper and lower surfaces of the dielectric substrate, respectively. Inductor branches of a set length are periodically applied to the microstrip transmission line, which is divided into N segments, where N is a positive integer. The inductor branches include switches, series inductors, and parallel inductors. One end of the switch is connected to the starting end of the microstrip line in each segment, and the other end of the switch is connected to one end of the series inductor, which is then connected to the ground plane. One end of the parallel inductor is connected to the connection point between the switch and the series inductor. When n∈[1,N-1], the other end of the parallel inductor corresponding to the nth segment of the microstrip transmission line is connected to the connection point between the switch and the series inductor corresponding to the (n+1)th segment. When n=N, the other end of the parallel inductor corresponding to the nth segment is connected to the end of the microstrip line in the nth segment via an end switch.

[0010] The characteristic impedance of the microstrip transmission line is denoted as Z1. With all switches closed, the characteristic impedance of the frequency shift transmission line is the Bloch impedance Z2, which satisfies the condition Z2 = Z1.

[0011] When all switches in the frequency shift transmission circuit are open, an input pulse signal is sent to the frequency shift transmission circuit; when the pulse signal has fully entered the microstrip transmission line, all switches are closed at the same time, and frequency shift occurs due to the conservation of wavenumber of the microstrip transmission line, thus realizing frequency shift transmission.

[0012] Furthermore, the electrical length of the segmented microstrip transmission line is less than one-eighth of the wavelength corresponding to the center frequency of the input pulse signal.

[0013] Furthermore, before and after the switching moments from open to closed in all switches, the following time boundary conditions exist:

[0014] ;

[0015] in, The time of switch switching and These represent the moments before and after the switch switching, respectively, and z represents the transmission distance; and They are respectively Time and The voltage of the microstrip transmission line at position z along the transmission distance. and They are respectively Time and The current in the microstrip transmission line at position z at any given moment;

[0016] According to the telegraph equations of a microstrip transmission line, the incident wave, the time-reflected wave, and the time-transmitted wave are respectively represented as:

[0017] Incident wave: ;

[0018] Time-reflected wave: ;

[0019] Time-transmitted waves: ;

[0020] in, and These are the voltage and current of the incident wave, respectively. It is a time variable; The frequency of the frequency shift transmission circuit when all switches are open. The frequency of the frequency shift transmission circuit is when all switches are closed; k is the wave number. and R and T are the voltage and current of the time-reflected wave, respectively; R and T are the time reflection coefficient and time transmission coefficient, respectively. and These represent the voltage and current of the time-transmitted wave, respectively.

[0021] Substituting the incident wave, time-reflected wave, and time-transmitted wave into the above time boundary conditions, we obtain the time transmission coefficient T and the time reflection coefficient R as follows:

[0022] ;

[0023] From the above equation, it can be seen that, under the condition that Z2=Z1, the time reflection coefficient R of the time boundary generated at all switch switching moments from open to closed is 0.

[0024] Furthermore, when all switches are open, the constitutive parameters of the frequency shift transmission circuit are:

[0025] ;

[0026] in, and These represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are open; and These are the equivalent distributed capacitance and inductance per unit length of a microstrip transmission line, respectively. At the speed of light, is the equivalent dielectric constant of the microstrip transmission line;

[0027] When all switches are closed, the constitutive parameters of the frequency shift transmission circuit are:

[0028] ;

[0029] in, and Let represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are closed, respectively, and ω be the frequency;

[0030] Frequency mobility for:

[0031] .

[0032] Furthermore, the relative permittivity of the dielectric substrate is =4.4, thickness is =1.575 The width of the microstrip line is =2.9 The characteristic impedance of the microstrip transmission line is Z1 = 51.37 Ω.

[0033] Furthermore, in the inductor branch, the series inductor is =62.4 Parallel inductors are =99.84 .

[0034] The beneficial effects of this invention are:

[0035] The method described in this invention is based on a broadband frequency-shift transmission circuit, utilizing time boundary conditions and the wavenumber conservation law to achieve frequency shifting. Through precise design, time reflection is theoretically eliminated, thus achieving reflection-free and efficient frequency-shift transmission over a wide frequency band. It exhibits advantages such as broadband coverage, waveform preservation, and low reflection, effectively overcoming the shortcomings of traditional solutions in terms of frequency band adaptability and signal integrity. It has potential applications in various scenarios, including long-distance communication, broadband radar detection, and RF test instruments. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the frequency shift transmission circuit in the method described in this invention;

[0037] Figure 2 This is an equivalent schematic diagram of the switch closure in the frequency shift transmission circuit of the method described in this invention;

[0038] Figure 3 This is a schematic diagram of the dispersion curve results for states 1 and 2 in the method described in the embodiment;

[0039] Figure 4 This is a schematic diagram of the characteristic impedance results for states 1 and 2 in the method described in the embodiment;

[0040] Figure 5 This is a schematic diagram of the time-domain results of the input port voltage and the output port voltage in the method described in the embodiment;

[0041] Figure 6This is a schematic diagram illustrating the shape-preserving effect of the input port voltage and output port voltage in the method described in the embodiment.

[0042] Figure 7 This is a schematic diagram of the frequency domain results of the input port voltage and the output port voltage in the method described in the embodiment;

[0043] Figure 8 This is a schematic diagram of the temporal reflection coefficient amplitude result at the time boundary in the method described in the embodiment. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] This embodiment provides a broadband frequency shift and conformal transmission method for electromagnetic waves based on a time-varying circuit with dual constitutive parameters. Without relying on a complex local oscillator system or increasing circuit complexity, it achieves broadband frequency shifting, high-efficiency transmission without reflection, and waveform distortion-free conformal transmission. This breaks through the performance bottleneck of traditional mixers and provides a new technical path for broadband, low-distortion signal processing in the microwave radio frequency field.

[0046] The method described in this embodiment is based on a frequency shift transmission circuit, the structural diagram of which is shown below. Figure 1 As shown, it includes a microstrip transmission line and a periodically loaded inductor branch;

[0047] A microstrip transmission line includes a dielectric substrate, a microstrip line, and a ground plane, with the microstrip line and ground plane located on the upper and lower surfaces of the dielectric substrate, respectively.

[0048] In this embodiment, the relative permittivity of the dielectric substrate is: =4.4, thickness is =1.575 The width of the microstrip line is =2.9 The characteristic impedance of the microstrip transmission line is Z1 = 51.37. .

[0049] According to the field-circuit equivalence principle, the equivalent distributed capacitance per unit length of a microstrip transmission line is... and inductor They are respectively:

[0050] ;

[0051] in, At the speed of light, is the equivalent dielectric constant of the microstrip transmission line.

[0052] On the microstrip transmission line at a set length =40 For a periodically loaded inductor branch, the microstrip transmission line is divided into N segments, where N is a positive integer. The inductor branch includes a switch, a series inductor, and a parallel inductor. One end of the switch is connected to the starting end of the microstrip line in the segmented microstrip transmission line, and the other end of the switch is connected to one end of the series inductor, which is connected to the ground plane. One end of the parallel inductor is connected to the connection point between the switch and the series inductor. When n∈[1,N-1], the other end of the parallel inductor corresponding to the nth segment of the microstrip transmission line is connected to the connection point between the switch and the series inductor corresponding to the (n+1)th segment of the microstrip transmission line. When n=N, the other end of the parallel inductor corresponding to the nth segment of the microstrip transmission line is connected to the end of the microstrip line in the nth segment of the microstrip transmission line through an end switch.

[0053] In this embodiment, the series inductor in the inductor branch is =62.4 Parallel inductors are =99.84 .

[0054] With all switches closed, the characteristic impedance of the frequency shift transmission line is the Bloch impedance Z2.

[0055] Before and after the switching moments of all switches from open to closed, the following two time boundary conditions exist:

[0056] ;

[0057] in, The time of switch switching and These represent the moments before and after the switch switching, respectively, and z represents the transmission distance; and They are respectively Time and The voltage of the microstrip transmission line at position z along the transmission distance. and They are respectively Time and The current in the microstrip transmission line at position z at any given moment;

[0058] According to the telegraph equations of microstrip transmission lines, the incident wave, time-reflected wave, and time-transmitted wave can be expressed as follows:

[0059] Incident wave: ;

[0060] Time-reflected wave: ;

[0061] Time-transmitted waves: ;

[0062] in, and These are the voltage and current of the incident wave, respectively. It is a time variable; The frequency of the frequency shift transmission circuit when all switches are open. For all switches closed, the frequency of the frequency shift transmission circuit is such that, since the wave number and LC are the same, it satisfies... k is the wave number; and R and T are the voltage and current of the time-reflected wave, respectively; R and T are the time reflection coefficient and time transmission coefficient, respectively. and These represent the voltage and current of the time-transmitted wave, respectively.

[0063] Substituting the incident wave, time-reflected wave, and time-transmitted wave into the above time boundary conditions, we obtain the analytical solutions for the time transmission coefficient T and the time reflection coefficient R, respectively:

[0064] ;

[0065] From the above equation, we can see that, when satisfying... Under these conditions, at all switching moments from open to closed, the time reflection coefficient R of the resulting time boundary is 0, eliminating time reflection waves and enhancing frequency shift and shape preservation effects.

[0066] When all switches in the frequency shift transmission circuit are open, an input pulse signal is sent to the frequency shift transmission circuit; when the pulse signal has fully entered the microstrip transmission line, all switches are closed at the same time, and frequency shift occurs due to the conservation of wavenumber of the microstrip transmission line, thus realizing broadband frequency shift transmission.

[0067] The equivalent principle diagram of the switch changing from open to closed in the frequency shift transmission circuit in the method described in this embodiment is as follows: Figure 2 As shown.

[0068] The constitutive parameters before and after the switch switching are obtained based on the field-circuit equivalence principle.

[0069] When all switches are open, the constitutive parameters of the frequency shift transmission circuit are:

[0070] ;

[0071] in, and These represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are open; and These are the equivalent distributed capacitance and inductance per unit length of a microstrip transmission line, respectively. At the speed of light, is the equivalent dielectric constant of the microstrip transmission line;

[0072] When all switches are closed, the constitutive parameters of the frequency shift transmission circuit are:

[0073] ;

[0074] in, and Let represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are closed, respectively, and ω be the frequency;

[0075] Frequency mobility for:

[0076] ;

[0077] in, The frequency of the frequency shift transmission circuit when all switches are open. This is the frequency of the frequency shift transmission circuit when all switches are closed.

[0078] To achieve better frequency shift performance, it is also necessary to ensure that the spectrum of the input pulse signal is within the impedance matching region. The electrical length of the segmented microstrip transmission line is less than one-eighth of the wavelength corresponding to the center frequency of the input pulse signal.

[0079] In this embodiment, the voltages at the input and output ports of the microstrip transmission line are measured, and the spectra of the input and output voltages are calculated respectively, comparing the theoretical and simulation solutions. To obtain more complete and accurate frequency shift information, the dispersion curves for both the open and closed states of the switch also need to be calculated.

[0080] According to the transmission matrix theory of microwave networks, the transmission matrix of a microstrip transmission line when all switches are open... for:

[0081] = ;

[0082] in, , The phase velocity of the frequency shift transmission circuit when all switches are open. = j is the symbol for the imaginary part;

[0083] Loaded series inductor The corresponding transmission matrix for:

[0084] = ;

[0085] Based on the transformation relationship between the transfer matrix and the admittance matrix, the transfer matrix is ​​obtained. corresponding admittance matrix and transmission matrix corresponding admittance matrix Admittance matrix of a microstrip transmission line after adding a series inductor This leads to the transmission matrix obtained after loading a series inductor onto the microstrip transmission line. ;

[0086] Loaded parallel inductor The corresponding transmission matrix for:

[0087] = ;

[0088] The final transmission matrix of the frequency shift transmission circuit when all switches are closed is:

[0089] ;

[0090] The formula for calculating Bloch impedance Let A and B be the elements in the first row and first column of A0, and the elements in the first row and second column of A0, respectively; the characteristic impedance of the frequency shift transmission circuit after the switch is closed can be obtained. Then, by selecting an appropriate frequency range, the impedance before and after the switching described in step 2 can be equalized, so that the time reflection coefficient is zero.

[0091] Similarly, the dispersion relation in periodic structures is expressed as:

[0092] ;

[0093] Where D is the element in the second row and second column of A0;

[0094] From the above equation, the dispersion curves of the frequency shift transmission circuit when all switches are closed are obtained as follows: β is the wave number, and the dispersion relation of the microstrip transmission line when all switches are open is: They are all functions of frequency.

[0095] It can be seen that when an appropriate frequency range is selected so that the Bloch impedance and the characteristic impedance of the microstrip transmission line are matched, the corresponding frequency shift information can be found on the dispersion curve that varies with frequency. This achieves broadband frequency shift transmission with a time reflection coefficient of 0, perfectly solving the problems of frequency bandwidth and waveform distortion in existing technologies.

[0096] This embodiment simulates and verifies the above process, with the open state of the switch recorded as 1 and the closed state of the switch recorded as 2. Figure 3 This is a schematic diagram of the theoretical results of the dispersion curves of the frequency shift transmission circuit in state 1 and state 2 in the method described in this invention; Figure 4This is a schematic diagram of the characteristic impedance theoretical results of the frequency shift transmission circuit in states 1 and 2 in the method of the present invention. Under the parameter design described in this embodiment, a Gaussian pulse with a main frequency component in the range of 470~670MHz is input into the microstrip transmission line. While achieving approximately impedance matching in the range of 470~670MHz, the dispersion relationship also maintains good linearity.

[0097] A schematic diagram of the time-domain results of the input port voltage and output port voltage in the method described in this invention is shown below. Figure 5 As shown, the input voltage is the time-domain waveform of the input port voltage in the frequency shift transmission circuit. The switch is closed when the input signal has fully entered the circuit, resulting in the output voltage being the time-domain waveform of the output port voltage in the frequency shift transmission circuit. To further verify the conformal performance of the frequency shift transmission circuit described in this embodiment, the input port signal is shifted in time to coincide with the output port signal, as shown... Figure 6 As shown. By observation Figure 5 and Figure 6 As can be seen from the time-domain waveform, the frequency shift transmission circuit of the method described in this embodiment effectively solves the waveform distortion problem while realizing frequency shift and basically eliminating reflection due to the switching, and achieves a good shape preservation effect.

[0098] Simultaneously, Fourier transforms are performed on the time-domain waveforms of the voltages at ports 1 and 2, i.e., the input voltage waveform and the output voltage waveform, respectively, to obtain the incident spectrum and the transmission spectrum, as follows: Figure 7 As shown, a good frequency shift effect has been achieved. Further calculations yielded the frequency mobility of the center frequency. Frequency mobility corresponding to the dispersion curve and the frequency mobility calculated based on the field-path equivalent. All meet the good standard.

[0099] Based on the above results, we can further obtain Figure 8 The time reflection coefficient spectrum shown reveals an extremely low reflection coefficient, verifying the anti-reflection effect of the frequency shift transmission circuit described in this embodiment.

[0100] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications made thereon, shall fall within the scope of protection of the present invention.

Claims

1. A method for electromagnetic wave broadband frequency-shifting conformal transmission based on a double-constitutive-parameter time-varying circuit, characterized in that, It is implemented based on a frequency-shifting transmission circuit, which includes a microstrip transmission line and a periodically loaded inductor branch; A microstrip transmission line includes a dielectric substrate, a microstrip line, and a ground plane, with the microstrip line and ground plane located on the upper and lower surfaces of the dielectric substrate, respectively. Inductor branches of a set length are periodically applied to the microstrip transmission line, which is divided into N segments, where N is a positive integer. The inductor branches include switches, series inductors, and parallel inductors. One end of the switch is connected to the starting end of the microstrip line in each segment, and the other end of the switch is connected to one end of the series inductor, which is then connected to the ground plane. One end of the parallel inductor is connected to the connection point between the switch and the series inductor. When n∈[1,N-1], the other end of the parallel inductor corresponding to the nth segment of the microstrip transmission line is connected to the connection point between the switch and the series inductor corresponding to the (n+1)th segment. When n=N, the other end of the parallel inductor corresponding to the nth segment is connected to the end of the microstrip line in the nth segment via an end switch. The characteristic impedance of the microstrip transmission line is denoted as Z1. With all switches closed, the characteristic impedance of the frequency shift transmission line is the Bloch impedance Z2, which satisfies the condition Z2 = Z1. When all switches in the frequency shift transmission circuit are open, an input pulse signal is sent to the frequency shift transmission circuit; when the pulse signal has fully entered the microstrip transmission line, all switches are closed at the same time, and frequency shift occurs due to the conservation of wavenumber of the microstrip transmission line, thus realizing frequency shift transmission.

2. The method for broadband frequency-shifting conformal transmission of electromagnetic waves based on a time-varying circuit with dual constitutive parameters according to claim 1, characterized in that, The electrical length of the segmented microstrip transmission line is less than one-eighth of the wavelength corresponding to the center frequency of the input pulse signal.

3. The method for broadband frequency-shifting conformal transmission of electromagnetic waves based on a time-varying circuit with dual constitutive parameters according to claim 1, characterized in that, Before and after the switching moments of all switches from open to closed, the following time boundary conditions exist: ； in, The time of switch switching and These represent the moments before and after the switch switching, respectively, and z represents the transmission distance; and They are respectively Time and The voltage of the microstrip transmission line at position z along the transmission distance. and They are respectively Time and The current in the microstrip transmission line at position z at any given moment; According to the telegraph equations of a microstrip transmission line, the incident wave, the time-reflected wave, and the time-transmitted wave are respectively represented as: Incident wave: ; Time-reflected wave: ; Time-transmitted waves: ; in, and These are the voltage and current of the incident wave, respectively. It is a time variable; The frequency of the frequency shift transmission circuit when all switches are open. The frequency of the frequency shift transmission circuit is when all switches are closed; k is the wave number. and R and T are the voltage and current of the time-reflected wave, respectively; R and T are the time reflection coefficient and time transmission coefficient, respectively. and These represent the voltage and current of the time-transmitted wave, respectively. Substituting the incident wave, time-reflected wave, and time-transmitted wave into the above time boundary conditions, we obtain the time transmission coefficient T and the time reflection coefficient R as follows: ； From the above equation, it can be seen that, under the condition that Z2=Z1, the time reflection coefficient R of the time boundary generated at all switch switching moments from open to closed is 0.

4. The method for broadband frequency-shifting conformal transmission of electromagnetic waves based on a time-varying circuit with dual constitutive parameters according to claim 1, characterized in that, When all switches are open, the constitutive parameters of the frequency shift transmission circuit are: ； in, and These represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are open; and These are the equivalent distributed capacitance and inductance per unit length of a microstrip transmission line, respectively. At the speed of light, is the equivalent dielectric constant of the microstrip transmission line; When all switches are closed, the constitutive parameters of the frequency shift transmission circuit are: ； in, and Let represent the dielectric constant and permeability of the frequency shift transmission circuit when all switches are closed, respectively, and ω be the frequency; Frequency mobility for: 。 5. The method for broadband frequency-shifting conformal transmission of electromagnetic waves based on a time-varying circuit with dual constitutive parameters according to claim 1, characterized in that, The relative permittivity of the dielectric substrate is =4.4, thickness is =1.575 The width of the microstrip line is =2.9 The characteristic impedance of the microstrip transmission line is Z1 = 51.37 Ω.

6. The method for broadband frequency-shifting conformal transmission of electromagnetic waves based on a time-varying circuit with dual constitutive parameters according to claim 1, characterized in that, In the inductor branch, the series inductor is =62.4 Parallel inductors are =99.84 .

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