A Design Method of Wideband Reflection Amplification Circuit Based on Real Frequency Matching Method

Abstract

The present invention discloses a design method for a broadband reflection amplification circuit based on the real-frequency matching method. First, the reflection amplification circuit is designed, and the real-frequency matching network is designed based on the real-frequency matching method. Finally, the real-frequency matching network is inserted at the input end of the reflection amplification circuit to construct a broadband reflection amplification circuit based on the real-frequency matching method. The method of the present invention tests the input impedance of the reverse amplification circuit through the load-pull technology, then calculates the parameter characteristics of the matching network using an optimization algorithm, and finally obtains the structure and parameter values of the matching network through the circuit synthesis method. It is not limited by a specific matching network architecture, can greatly improve the performance of the matching network, solves the broadband matching problem between the transceiver antenna and the reflection amplification circuit, enables the reflection amplification circuit to achieve high gain at different input powers and input frequencies, thereby broadening the working bandwidth of the reflection amplification circuit and achieving the purpose of expanding the application scenarios of the reflection amplification circuit.

Description

Technical Field

[0001] The present invention belongs to the technical field of reflection amplification radio frequency circuits, and particularly relates to a design method of a broadband reflection amplification circuit based on the real-frequency matching method. Background Art

[0002] In the application field of the Internet of Things, in order to reduce the power consumption of terminals, the RFID technology based on backscatter communication is often adopted. Its passive terminals (tags) achieve self-power supply through energy harvesting, and send data through the backscatter method without transmitting energy, greatly reducing the power consumption of the terminals. However, in a system using backscatter communication, its reflected power is very low, which greatly limits the communication distance of the system's reflection link. To solve this problem, the existing method is to use reflection amplification technology to increase the reflected power, which is mainly based on the negative resistance characteristics of triodes or tunnel diodes. However, the backscatter circuit has only one port, which serves as both input and output. The communication bandwidth of the reflection amplification system directly implemented through the backscatter circuit is very narrow, seriously affecting the application field of the reflection amplification terminal.

[0003] The existing method for improving the bandwidth of the reflection amplification circuit is to add a matching network at the input of the reverse amplification circuit. However, the method of using the existing fixed structure to achieve the input matching of the reflection amplification circuit limits the working bandwidth of the system and cannot achieve the optimal matching. The existing reflection amplification circuit uses the method of the existing fixed matching circuit structure, and its structure mainly includes L-type, T-type, and π-type. The role of the matching network is to achieve the matching of the load impedance and the source impedance, reduce signal reflection, and improve the system performance. The existing matching network is used to achieve the matching of the reflection amplification circuit. Due to the diversity of the input impedance and the load impedance, and the fact that the gain of the reflection amplification circuit is greatly affected by the frequency and power of the antenna received signal, it is difficult for the fixed matching structure to achieve the optimal matching in various application situations, thus limiting the performance of the reflection amplification circuit.

[0004] In summary, the existing matching network can only select a fixed matching circuit structure, with poor adaptability, and cannot change the circuit architecture according to application requirements. Especially for a narrowband circuit such as reflection amplification, the fixed-structure matching network is even more difficult to meet the actual application requirements. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a design method of a broadband reflection amplification circuit based on the real-frequency matching method. The load pulling technology is used to obtain the reflection amplification input impedance and the antenna input impedance at different powers and frequencies, and the optimal matching in various situations is realized through an optimization algorithm, so as to achieve the purpose that the reflection amplification circuit has high gain at different input powers and frequencies.

[0006] The technical solution adopted by the present invention is: a design method of a broadband reflection amplification circuit based on the real-frequency matching method, and the specific steps are as follows:

[0007] S1. Design a reflection amplification circuit and, based on the real-frequency matching method, design a real-frequency matching network;

[0008] First, obtain the circuit structure of the real-frequency matching network according to the least squares optimization algorithm and network synthesis method, and set the use of S-parameters (S 11 、S 12 、S 21 、S 22 ) to characterize the characteristics of the matching network.

[0009] Among them, the real-frequency matching network includes two ports. Port 1 is the input port, and port 2 is the output port; S 11 represents the reflection coefficient of the input port of the matching network, S 22 represents the reflection coefficient of the output port of the matching network, S 12 represents the reflection coefficient from the output port to the input port of the matching network, and S 21 represents the reflection coefficient from the input port to the output port of the matching network.

[0010] Then, the S-parameter characterization expression of the real-frequency matching network is as follows:

[0011]

[0012] Among them, σ represents a variable, s = jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, and h(s), f(s) represent arbitrary real coefficient polynomials, and satisfy the following constraints:

[0013] g(s)g(-s) = f(s)f(-s) + h(s)h(-s) (2)

[0014] Obtain the antenna impedance Z in in the real-frequency matching network through actual testing, and then adjust the corresponding values in the S-parameters to transform the load impedance Z L to the impedance value required for the input impedance.

[0015] The expression of the reflection coefficient Γ in of port 1 is as follows:

[0016]

[0017] Among them, Z s represents the source impedance, and Z in represents the input impedance.

[0018] From equations (3) and the definition of S-parameters, the relationship between the reflection coefficient and the S-parameters can be known, and the expression is as follows:

[0019] S 11 = Γin (4)

[0020] Then, from the lossless characteristic of the matching network, it can be known that S 21 and S 11 The relationship is as follows:

[0021]

[0022] In the process of implementing the matching network, let T0 represent the desired transmission gain, and ω i (i = 1, 2…, n…, N) represents the frequency points of each discrete point selected within the working frequency band, and N represents the total number of discrete points selected. Then, the expression of the optimized cost function is as follows:

[0023]

[0024] where ΔT represents the sum of the squares of the differences between the actual transmission gain and the desired transmission gain at each discrete point, and T represents the current transmission gain.

[0025] When the network function that meets the matching requirements is calculated through the least squares optimization algorithm, the expression of the single-port driving-point impedance function of the load matching network is as follows:

[0026]

[0027] where λ represents a variable, R S represents the impedance of the input source, g(λ) represents the Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial.

[0028] Then, the rational fraction form expression of Equation (7) is as follows:

[0029]

[0030] where n and m represent the highest degrees of s in the calculated numerator and denominator; a i and b i respectively represent the coefficients of the numerator and denominator polynomials of the impedance function.

[0031] The cost function expression based on the impedance error function is as follows:

[0032]

[0033] where ΔZ represents the impedance fluctuation value, and Z in (ω i ) represents the input impedance of the input port at the frequency point ω i , and Z opt (ω i ) represents the optimal impedance at the frequency point ω i .

[0034] Finally, the least squares optimization algorithm is used to minimize ΔZ and obtain Z. in (ω i ) expression, and then through the network synthesis method, a real-frequency matching network is obtained.

[0035] S2. Insert the real-frequency matching network designed in step S1 at the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real-frequency matching method.

[0036] The broadband reflection amplifier circuit based on the real-frequency matching method includes: a reflection amplifier circuit, a real-frequency matching network, and an antenna; the reflection amplifier circuit is connected to port 1 of the real-frequency matching network, and port 2 of the real-frequency matching network is connected to the antenna.

[0037] Furthermore, in step S1, the circuit structure of the real-frequency matching network is obtained according to the least squares optimization algorithm and the network synthesis method, specifically as follows:

[0038] A1. Initialize the polynomial h(s), that is, through the normalized frequency point ω a , the real part and imaginary part of the reflection load, to generate the initial value h0 of the polynomial h(s).

[0039] First, load-pull measurement is used to measure the input and output impedances of the reflection amplifier circuit at different frequency points and perform normalization processing.

[0040] Then, according to the impedance values corresponding to the measured discrete frequency points, calculate the correlation coefficients of the initial value g0 of the denominator polynomial g(s), specifically as follows:

[0041] Let ω a represent the normalized frequency point corresponding to the impedance, set the variable x = ω 2 = -s 2 , define the array of the linear regression of the auxiliary polynomial P a (x) as Xd, that is, Xd = ω a * ω a ′, generate the data point set Pd of P a (x), and its calculation expression is as follows:

[0042]

[0043] Among them, ω a ′ represents the conjugate value of ω a , S RL and S RX respectively represent the real part and imaginary part corresponding to the impedance value, Pd is the polynomial coefficient corresponding to P a (x), k represents the total number of DC transmission zeros of the equalizer, and pk represents the kth data point in the data point set Pd.

[0044] Perform polynomial fitting on the data of Xd and Pd for the selected number of times nr = n / 2, and use the polyfit function in MATLAB to generate the polynomial P a (x), that is, P a = polyfit(Xd, Pd, nr), then P a (x) = P1x nr + P2x nr-1 +…+ P nr+1 coefficients of.

[0045] Then directly use the MATLAB function G = conv(P a , P a ) to generate the strictly positive polynomial G(x) = P a 2 (x)>0, and obtain the convolution result vector G corresponding to the coefficients of P a (x).

[0046] Then use the MATLAB function X r = roots(G) to find the roots of G(x) = P a 2 (x)>0, and set the intermediate variable Use the MATLAB function P r = sqrt(-X r ) to first generate the right half-plane roots RHP; then set the intermediate variable P r m = -P r to find the left half-plane LHP roots, and construct the polynomial g(s) accordingly.

[0047] Finally, based on the LHP roots P r m, use the MATLAB function C = poly(P r m) to construct the polynomial C(s), and then through obtain the vector g0.

[0048] After calculating g0, use the polyfit function in MATLAB to generate the polynomials A(x) and B(x), and obtain the polynomial coefficients A d and B d , specifically as follows:

[0049] Let S RLa and S RXa represent the real and imaginary parts of the load impedance after normalization. For each sampling frequency point ω i , let S RL = S RLa (ω i ) and S RX = S RXa (ωi ), then A can be obtained d (ω i ) = g R *S RL +g X *S RX and B d (ω i ) = (g X *S RL +g R *S RX ) / ω.

[0050] where g R , g X i.e., the intermediate variable obtained by g0 through the MATLAB function polyval(g0, s), ω represents the value of ω a at the frequency point ω i , i.e., ω = ω a (ω i ).

[0051] Then use the MATLAB functions A = polyfit(Xd, A d , na) and B = polyfit(Xd, B d , nb) to find the polynomials A(x) and B(x).

[0052] where, if the given n is even, na = n / 2, nb = (n - 2) / 2; if n is odd, then na = nb = (n - 1) / 2.

[0053] Finally, calculate the initial value h0 of the polynomial h(s), and the calculation expression is as follows:

[0054] h(s) = A(-s 2 ) + sB(s 2 ) (11)

[0055] A2. Based on step A1, use nonlinear least squares coefficient optimization for the polynomial h(s);

[0056] Call the lsqnonlin function of MATLAB and perform multiple iterations to calculate all the optimized coefficients of the polynomial h(s), and the expression is as follows:

[0057]

[0058] where ε nopt represents the minimum error optimized at the nth discrete point.

[0059] Then solve the optimization objective. First, set the unknown vector x = [.] and set the coefficient vector h = x, and assign the h0 obtained in step A1 to the vector x;

[0060] Obtain the values of polynomials g(s) and h(s) at a given s, namely g val and h val . Then, the normalized value of the driving-point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ).

[0061] Based on Equation (9), call the lsqnonlin function to minimize the cost function value, obtain the optimization vector x, and finally generate the optimal polynomial h(s).

[0062] A3. Based on Step A2, generate a strictly Hurwitz polynomial g(s);

[0063] Based on the optimal polynomial h(s) generated in Step A2, let U = [h n h n-1 ... h0], V = [(-1) n h n (-1) n- 1 h n-1 ... h0]. The following expression can be obtained from the convolution of U and V:

[0064] H(-s 2 ) = h(s)h(-s) = H0 + H1s +... + H n s n (13)

[0065] where h n represents the coefficient corresponding to the nth discrete point, and H n represents the coefficient corresponding to each term of H(-s 2 ).

[0066] Then, generate an even polynomial G(-s 2 ), and the expression is as follows:

[0067] G(-s 2 ) = H(-s 2 ) + (-1) k s 2k = G0 + G1s 2 +... + G n s 2n (14)

[0068] where G n represents the coefficient corresponding to each term of G(-s 2 ), and k represents a variable, that is, the coefficient between 0 and n.

[0069] Store the row vector X again, and the expression is as follows:

[0070] X = [(-1) n G n (-1) n-1 G n-1 ...G0] (15)

[0071] Calculate the roots pk and pkm of G(-s 2 ) in the right half-plane and the left half-plane, and the expression is as follows:

[0072] pk = sqrt(-Xk) (16)

[0073] pkm = -pk (17)

[0074] Finally, generate a monic polynomial Through the MATLAB function Generate the strict Hurwitz polynomial g(s).

[0075] Among them, gc = {g n g n-1 ...g0} represents an (n + 1)-order row vector, that is, the coefficients of g(s) = g0 + g1s +... + gnsn.

[0076] A4. Based on step A3, calculate the current transmission gain T;

[0077] First, define the complex variable s = jω; j = sqrt(-1), then s = sqrt(-1)*ω.

[0078] Use h and g to calculate the polynomials g val = polyval(g, s) and h val = polyval(h, s), and obtain g val = g0s n + g1s n-1 +…+ g n-1 s + g n , h val = h0s n + h1s n-1 +…+ h n-1 s + h n .

[0079] Obtain the current transmission gain T through the input impedance (g val + h val ) / (g val - h val ), and through g val = polyval(g, s), h val = polyval(h, s), f val= s k and L 11 = h val / g val , we can get Weight = f val conj(f val )(1 - L 11 conj(L 11 )) and D = h val conj(h val )(1 + L 11 conj(L 11 )) + f val conj(f val ) - 2real(L 11 h val conj(g val )) Then, the transmission gain T = Weight / D can be obtained.

[0080] Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, L 11 represents the load reflection coefficient.

[0081] A5. Based on steps A1 - A4, use the network synthesis method to obtain the real - frequency matching network circuit structure;

[0082] Through the optimized h(s) and g(s) and long division, obtain the component parameters and the starting component types of the matching network. Calculate the values of each item of the input matching by the network synthesis formula (18) to obtain the normalized values of each device of the input matching.

[0083]

[0084] Among them, Z L represents the load impedance, X ns represents the margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, inductance C n represents the capacitance at the n - th discrete point, L n represents the inductance at the n - th discrete point.

[0085] Finally, according to the impedance of the tested reflection amplifier circuit, calculate the optimal matching network characteristics and synthesize the corresponding matching circuit to design a broadband reflection amplifier circuit.

[0086] Advantages of the present invention: The method of the present invention first designs a reflection amplification circuit, designs a real-frequency matching network based on the real-frequency matching method, and finally inserts the real-frequency matching network at the input end of the reflection amplification circuit to construct a broadband reflection amplification circuit based on the real-frequency matching method. The method of the present invention tests the input impedance of the reverse amplification circuit through the load-pulling technology, then calculates the parameter characteristics of the matching network by using an optimization algorithm, and finally obtains the structure and parameter values of the matching network through the circuit synthesis method. It is not limited by a specific matching network architecture, can greatly improve the performance of the matching network, solves the broadband matching problem between the transceiver antenna and the reflection amplification circuit, enables the reflection amplification circuit to achieve high gain at different input powers and input frequencies, thereby broadening the working bandwidth of the reflection amplification circuit and achieving the purpose of expanding the application scenarios of the reflection amplification circuit.

[0087] Description of the drawings

[0088] Figure 1 It is a flowchart of a design method for a broadband reflection amplification circuit based on the real-frequency matching method of the present invention.

[0089] Figure 2 It is a structural diagram of a broadband reflection amplification circuit based on the real-frequency matching method in an embodiment of the present invention.

[0090] Figure 3 It is a schematic diagram for characterizing the characteristics of the matching network using S parameters in an embodiment of the present invention.

[0091] Figure 4 It is a flowchart of the least squares optimization algorithm and the network synthesis method in an embodiment of the present invention. Detailed implementation manners

[0092] The following further describes the embodiments of the present invention with reference to the drawings.

[0093] As Figure 1 shown, a flowchart of a design method for a broadband reflection amplification circuit based on the real-frequency matching method of the present invention is as follows:

[0094] S1. Design a reflection amplification circuit and design a real-frequency matching network based on the real-frequency matching method;

[0095] The structure of the broadband reflection amplification circuit based on the real-frequency matching method proposed in this embodiment is as Figure 2 shown. The real-frequency matching network is used to achieve the optimal matching between the reflection amplification circuit and the antenna at different powers and frequencies. First, the circuit structure of the real-frequency matching network is obtained according to the least squares optimization algorithm and the network synthesis method. It is set to use S parameters (S 11 、S 12 、S 21 、S 22 ) to characterize the characteristics of the matching network, thenFigure 3 The characteristics of the matching network are characterized by the S-parameters shown below.

[0096] Among them, the real-frequency matching network includes two ports. Port 1 is the input port, and Port 2 is the output port; S 11 represents the reflection coefficient of the input port of the matching network, and S 22 represents the reflection coefficient of the output port of the matching network, and S 12 represents the reflection coefficient from the output port to the input port of the matching network, and S 21 represents the reflection coefficient from the input port to the output port of the matching network.

[0097] Then the S-parameter characterization expression of the real-frequency matching network is as follows:

[0098]

[0099] Among them, σ represents a variable, s = jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, and h(s), f(s) represent arbitrary real-coefficient polynomials, and satisfy the following constraints:

[0100] g(s)g(-s) = f(s)f(-s) + h(s)h(-s) (2)

[0101] The antenna impedance Z in the real-frequency matching network is obtained through actual testing in , and then by adjusting the corresponding values in the S-parameters, the load impedance Z L is transformed to the impedance value required for the input impedance.

[0102] From Figure 3 it can be seen that the expression of the reflection coefficient Γ in of Port 1 is as follows:

[0103]

[0104] Among them, Z s represents the source impedance, and Z in represents the input impedance.

[0105] From Equation (3) and the definition of S-parameters, the relationship between the reflection coefficient and the S-parameters can be known, and the expression is as follows:

[0106] S 11 = Γ in (4)

[0107] Then, from the lossless characteristics of the matching network, the relationship between S 21 and S 11 can be known, and the expression is as follows:

[0108]

[0109] In the real-frequency matching method, only the S 21 value needs to be optimized to be as large and flat as possible within the working frequency band, and the better the performance of the designed matching network will be.

[0110] In the process of implementing the matching network, let T0 represent the desired transmission gain, and ω i (i = 1, 2…, n…, N) represent the frequency points of each discrete point selected within the working frequency band, and N represent the total number of discrete points selected. Then the expression of the optimized cost function is as follows:

[0111]

[0112] where ΔT represents the sum of the squares of the differences between the actual transmission gain and the desired transmission gain at each discrete point, and T represents the current transmission gain.

[0113] When the network function meeting the matching requirements is calculated through the least squares optimization algorithm, the expression of the single-port driving point impedance function of the load matching network is as follows:

[0114]

[0115] where λ represents a variable, R S represents the impedance of the input source, g(λ) represents a Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial.

[0116] Then the rational fraction form expression of Equation (7) is as follows:

[0117]

[0118] where n and m represent the highest degrees of s in the calculated numerator and denominator; a i and b i represent the coefficients of the numerator and denominator polynomials of the impedance function respectively.

[0119] Furthermore, the load matching network can obtain the types (resistors, capacitors, and inductors) and values of each component through network synthesis.

[0120] Since the S-parameters are mainly used for power matching and cannot reflect the efficiency characteristics of the reflection amplifier circuit, and when considering the harmonic impedance, the form of the transmission gain cannot reflect the fluctuations of the harmonic matching state. On the other hand, according to load pulling, the optimal impedance of each circuit module can be easily obtained. Then, the output power and efficiency and other characteristics of the reflection amplifier circuit can be directly reflected through the error of the impedance function. Then the expression of the cost function based on the impedance error function is as follows:

[0121]

[0122] where, ΔZ represents the impedance fluctuation value, and Z in (ω i ) represents the input impedance of the input port at the frequency point ω i , and Z opt (ω i ) represents the optimal impedance at the frequency point ω i . Of course, the smaller ΔZ is, the closer the impedance function Z in is to the target impedance function. By using the optimization algorithm to minimize ΔZ, the expression of Z in (ω i ) is obtained. Further, through the network synthesis method, a real-frequency matching network can be obtained, and then a reflection amplifier circuit with broadband and high-efficiency characteristics can be designed.

[0123] S2. Insert the real-frequency matching network designed in step S1 at the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real-frequency matching method;

[0124] As Figure 2 , 3 shown, the broadband reflection amplifier circuit based on the real-frequency matching method includes: a reflection amplifier circuit, a real-frequency matching network, and an antenna; the reflection amplifier circuit is connected to port 1 of the real-frequency matching network, and port 2 of the real-frequency matching network is connected to the antenna.

[0125] In the broadband reflection amplifier circuit based on the real-frequency matching method, it is necessary to first generate polynomials h(s) and g(s), then calculate the transmission gain of the actual matching network at each frequency point, and finally comprehensively calculate the component types and coefficients of the matching network.

[0126] As Figure 4 shown, in this embodiment, in step S1, the circuit structure of the real-frequency matching network is obtained according to the least squares optimization algorithm and the network synthesis method, specifically as follows:

[0127] A1. Initialize the polynomial h(s), that is, generate the initial value h0 of the polynomial h(s) through the normalized frequency point ω a , the real part and the imaginary part of the reflection load.

[0128] First, use load-pull measurement to measure the input and output impedances of the reflection amplifier circuit at different frequency points and perform normalization processing.

[0129] Then, according to the impedance values corresponding to the measured discrete frequency points, calculate the correlation coefficients of the initial value g0 of the denominator polynomial g(s), specifically as follows:

[0130] Let ω a represent the normalized frequency point corresponding to the impedance, set the variable x = ω 2 = -s 2 , and define the auxiliary polynomial P a(x) The array for linear regression is Xd, i.e., Xd = ω a *ω a ′, generating P a (x) The data point set Pd, and its calculation expression is as follows:

[0131]

[0132] Where, ω a ′ represents the conjugate value of ω a , S RL and S RX respectively represent the real part and the imaginary part corresponding to the impedance value. Pd is the coefficients of each polynomial corresponding to P a (x). k represents the total number of DC transmission zeros of the equalizer (set according to the actual situation), and pk represents the k-th data point in the data point set Pd.

[0133] Perform polynomial fitting on the data given by Xd and Pd with the selected degree nr = n / 2, and use the polyfit function in MATLAB to generate the polynomial P a (x), i.e., P a = polyfit(Xd, Pd, nr), then we can get P a (x) = P1x nr + P2x nr-1 + … + P nr+1 Coefficients.

[0134] Then directly use the MATLAB function G = conv(P a , P a ) to generate the strictly positive polynomial G(x) = P a 2 (x) > 0, and obtain the convolution result vector G corresponding to the coefficients of P a (x).

[0135] Then use the MATLAB function X r = roots(G) to find the roots of G(x) = P a 2 (x) > 0, and set the intermediate variable Use the MATLAB function P r = sqrt(-X r ) to first generate the right half plane roots (Right Half Plane, RHP); then set the intermediate variable P r m = -P r to find the left half plane (Left Half Plane, LHP) roots, and construct the polynomial g(s) based on this.

[0136] Finally, based on the LHP roots P rm, construct the polynomial C(s) through the MATLAB function C = poly(P r m), and then through obtain the vector g0.

[0137] After calculating g0, use the polyfit function in MATLAB to generate the polynomials A(x) and B(x), and obtain the polynomial coefficients A d and B d , specifically as follows:

[0138] Let S RLa and S RXa represent the real and imaginary parts of the load impedance obtained after normalization. For each sampling frequency point ω i , let S RL = S RLa (ω i ) and S RX = S RXa (ω i ), then we can get A d (ω i ) = g R * S RL + g X * S RX and B d (ω i ) = (g X * S RL + g R * S RX ) / ω.

[0139] Among them, g R , g X are the intermediate variables obtained by the MATLAB function polyval(g0, s). ω represents the value of ω a at the frequency point ω i , that is, ω = ω a (ω i ).

[0140] Then use the MATLAB functions A = polyfit(Xd, A d , na) and B = polyfit(Xd, B d , nb) to find the polynomials A(x) and B(x).

[0141] Among them, if the given n is even, na = n / 2, nb = (n - 2) / 2; if n is odd, then na = nb = (n - 1) / 2.

[0142] Finally, calculate the initial value h0 of the polynomial h(s), and the calculation expression is as follows:

[0143] h(s) = A(-s2 ) + sB(s 2 ) (11)

[0144] A2. Based on step A1, use non - linear least - squares coefficient optimization for the polynomial h(s);

[0145] Call the lsqnonlin function in MATLAB to calculate all the optimized coefficients of the polynomial h(s) through multiple iterations. The expression is as follows:

[0146]

[0147] where ε nopt represents the minimum error optimized at the nth discrete point.

[0148] Then solve the optimization objective. First, set the unknown vector x = [.] and set the coefficient vector h = x, and assign h0 obtained in step A1 to the vector x;

[0149] Obtain the values of the polynomials g(s) and h(s) at the given s, g val and h val , and the normalized value of the driving - point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ).

[0150] Based on equation (9), call the lsqnonlin function to minimize the cost - function value, obtain the optimized vector x, and finally generate the optimal polynomial h(s).

[0151] A3. Based on step A2, generate a strictly Hurwitz polynomial g(s);

[0152] Based on the optimal polynomial h(s) generated in step A2, set U = [h n h n-1 ...h0], V = [(-1) n h n (-1) n- 1 h n-1 ...h0]. The convolution of U and V can obtain the following expression:

[0153] H(-s 2 ) = h(s)h(-s) = H0 + H1s+... + H n s n (13)

[0154] where h n represents the coefficient corresponding to the nth discrete point, and H n represents H(-s2 ) The corresponding coefficients of each item.

[0155] Then generate an even polynomial \(G(-s)\) 2 ), and the expression is as follows:

[0156] \(G(-s)\) 2 ) = \(H(-s)\) 2 ) + \((-1)\) k \(s\) 2k = \(G_0 + G_1s\) 2 +... + \(G\) n \(s\) 2n (14)

[0157] Where, \(G\) n represents the corresponding coefficients of each item of \(G(-s)\) 2 ), \(k\) represents a variable, that is, the coefficients between 0 and \(n\).

[0158] Then store the row vector \(X\), and the expression is as follows:

[0159] \(X = [(-1)\) n \(G\) n \((-1)\) n-1 \(G\) n-1 ... \(G_0]\) (15)

[0160] Calculate the roots \(p_k\) and \(p_{km}\) of \(G(-s)\) 2 ) in the right half-plane and the left half-plane, and the expression is as follows:

[0161] \(p_k = \sqrt{-X_k}\) (16)

[0162] \(p_{km} = -p_k\) (17)

[0163] Finally, generate a monic polynomial through the MATLAB function to generate a strictly Hurwitz polynomial \(g(s)\).

[0164] Where, \(g_c=\{g\) n \(g\) n-1 ... \(g_0\}\) represents an \((n + 1)\)-order row vector, that is, the coefficients of \(g(s)=g_0 + g_1s+...+g_ns^n\).

[0165] A4. Based on step A3, calculate the current transmission gain \(T\);

[0166] First, define the complex variable \(s = j\omega\); \(j=\sqrt{-1}\), then \(s=\sqrt{-1}\times\omega\).

[0167] Use \(h\) and \(g\) to calculate the polynomials \(g\) val = polyval(\(g,s\)) and \(h\) val= polyval(h, s), obtaining g val = g0s n + g1s n-1 + … + g n-1 s + g n , h val = h0s n + h1s n-1 + … + h n-1 s + h n .

[0168] Through the input impedance (g val + h val ) / (g val - h val ), the current transmission gain T is obtained. Through g val = polyval(g, s), h val = polyval(h, s), f val = s k and L 11 = h val / g val , it can be obtained that Weight = fvalconj(fval)(1 - L 11 conj(L 11 )) and D = h val conj(h val )(1 + L 11 conj(L 11 )) + f val conj(f val ) - 2real(L 11 h val conj(g val ))), then the transmission gain T = Weight / D can be obtained.

[0169] Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, and L 11 represents the load reflection coefficient.

[0170] A5. Based on steps A1 - A4, use the network synthesis method to find the real - frequency matching network circuit structure;

[0171] Through the optimized h(s) and g(s) and long division, the component parameters and the starting component types of the matching network are obtained. The values of each item of the input matching are calculated by the network synthesis formula (18), so as to obtain the normalized values of each device of the input matching.

[0172]

[0173] Among them, ZL represents the load impedance, X ns represents the margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, inductance C n represents the capacitance at the nth discrete point, L n represents the inductance at the nth discrete point.

[0174] Finally, based on the impedance of the tested reflection amplifier circuit, the optimal matching network characteristics are calculated, and the corresponding matching circuit is synthesized, thereby designing a broadband reflection amplifier circuit.

[0175] In summary, in view of the problem of narrow bandwidth of the existing reflection amplifier matching circuit, the method of the present invention proposes a design method of a broadband reflection amplifier circuit based on the real-frequency matching method. It uses the load-pulling technology to obtain the input impedance of the reflection amplifier and the input impedance of the antenna at different powers and frequencies, and realizes the optimal matching in various situations through an optimization algorithm. It can be used to solve the broadband matching problem between the transceiver antenna and the reflection amplifier circuit, so that the reflection amplifier circuit can achieve high gain at different input powers and input frequencies, broaden the working bandwidth of the reflection amplifier circuit, adapt to the application environment of different input powers and frequencies, and achieve the purpose of expanding the application scenario of the reflection amplifier circuit.

[0176] Those of ordinary skill in the art will realize that the above embodiments are for helping readers understand the principles of the present invention and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A broadband reflection amplifier circuit design method based on real frequency matching method, the specific steps are as follows: S1. Design the reflection amplifier circuit and design the real frequency matching network based on the real frequency matching method; First, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and network synthesis method, and the S parameters (S 11 , S 12 , S 21 , S 22 ) to characterize the characteristics of the matching network; in, The real frequency matching network includes two ports, S 11 is the reflection coefficient of the matching network input port, S 22 is the reflection coefficient of the matching network output port, S 12 It represents the reflection coefficient from the output port to the input port of the matching network, S 21 It represents the reflection coefficient from the input port to the output port of the matching network; Then the S parameter characterization expression of the real frequency matching network is as follows: Where σ represents a variable, s=jω, j represents an imaginary number, ω represents a frequency point, * represents a conjugate operation, g(s) represents a Hurwitz polynomial, h(s), f(s) represent arbitrary real coefficient polynomials, and satisfy the following constraints: g(s)g(-s)=f(s)f(-s)+h(s)h(-s) (2) The antenna impedance Z in the real frequency matching network is obtained through actual testing in , and then adjust the corresponding value in the S parameter to make the load impedance Z L The impedance value required to transform to the input impedance; Input port reflection coefficient Γ in The expression is as follows: Among them, Z s represents the source impedance, Z in represents input impedance; From formula (3) and the definition of S parameters, we can know the relationship between reflection coefficient and S parameters, which is expressed as follows: S 11 =C in (4) According to the lossless characteristics of the matching network, S 21 With S 11 The relationship is expressed as follows: In the process of realizing the matching network, let T0 represent the desired transmission gain, ω i (i=1,2…,n…,N) represents the frequency of each discrete point selected in the working frequency band, and N represents the total number of discrete points selected. The expression of the optimized cost function is as follows: Wherein, ΔT represents the sum of the squares of the differences between the actual transmission gain and the expected transmission gain at each discrete point, and T represents the current transmission gain; After the network function that meets the matching requirements is calculated through the least squares optimization algorithm, the single-port driving point impedance function expression of the load matching network is as follows: Among them, λ represents a variable, R S represents the impedance of the input source, g(λ) represents the Hurwitz polynomial, and h(λ) represents an arbitrary real coefficient polynomial; Then the rational fraction form of formula (7) is as follows: Where n and m represent the highest power of the numerator and denominator s calculated; a i and b i Respectively represent the coefficients of the numerator and denominator polynomials of the impedance function; The cost function expression based on the impedance error function is as follows: Among them, ΔZ represents the impedance fluctuation value, Z in (ω i ) indicates that the input port is at the frequency point ω i The input impedance, Z opt (ω i ) indicates that at the frequency point ω i The optimal impedance at Finally, the least squares optimization algorithm is used to minimize ΔZ and calculate Z in (ω i ) expression, and then obtain the real frequency matching network through the network synthesis method; S2, inserting the real frequency matching network designed in step S1 into the input end of the reflection amplifier circuit to construct a broadband reflection amplifier circuit based on the real frequency matching method; The broadband reflection amplifier circuit based on the real frequency matching method comprises: a reflection amplifier circuit, a real frequency matching network, and an antenna; the reflection amplifier circuit is connected to the input port of the real frequency matching network, and the output port of the real frequency matching network is connected to the antenna.

2. The method for designing a broadband reflection amplifier circuit based on a real frequency matching method according to claim 1, characterized in that: In step S1, the real frequency matching network circuit structure is obtained according to the least squares optimization algorithm and the network synthesis method, which is specifically as follows: A1. Initialize the polynomial h(s), that is, by normalizing the frequency point ω a , the real and imaginary parts of the reflected load, generating the initial value h0 of the polynomial h(s); Firstly, load-pull is used to measure the input and output impedance of the reflection amplifier circuit at different frequencies, and then normalized. Then, according to the impedance values ​​corresponding to the discrete frequency points tested, the correlation coefficient of the initial value g0 of the denominator polynomial g(s) is calculated as follows: Let ω a Indicates the normalized frequency corresponding to the impedance, set the variable x = ω 2 =-s 2 , define the auxiliary polynomial P a (x) The array of linear regression is Xd, that is, Xd = ω a *ω a ′, generate P a The data point set Pd of (x) is calculated as follows: Among them, ω a ′ represents ω a The conjugate value, S RL and S RX Respectively represent the real and imaginary parts of the impedance value, Pd is P a (x) The corresponding polynomial coefficients, k represents the total number of DC transmission zeros of the equalizer, and pk represents the kth data point in the data point set Pd; Perform polynomial fitting on the data given by Xd and Pd with the selected order nr = n / 2, and use the polyfit function of MATLAB to generate the polynomial P a (x), that is, P a =polyfit(Xd,Pd,nr), then we can get P a (x) = P1x nr +P2x nr-1 +…+P nr+1 The coefficient of Then directly through the MATLAB function G = conv (P a ,P a ) Generate a strictly positive polynomial G(x) = P a 2 (x)>0, get P a (x) The convolution result vector G corresponding to each coefficient; Then through the MATLAB function X r =roots(G) to find G(x)=P a 2 (x)>0 root and set the intermediate variable Through the MATLAB function P r =sqrt(-X r ) First generate the right half plane root RHP; then set the intermediate variable P r m=-P r Find the left half plane LHP root and construct the polynomial g(s) based on it; Finally, based on the LHP root P r m, through the MATLAB function C = poly(P r m) Construct the polynomial C(s), and then pass Get vector g0; After calculating g0, use MATLAB's polyfit function to generate polynomials A(x) and B(x), and get the polynomial coefficients A d and B d , as follows: Let S RLa and S RXa Represents the real and imaginary parts of the load impedance obtained after normalization. For each sampling frequency ω i , let S RL =S RLa (ω i ) and S RX =S RXa (ω i ), then we can get A d (ω i ) = g R *S RL +g X *S RX and B d (ω i )=(g X *S RL +g R *S RX ) / ω; Among them, g R , g X That is, g0 is the intermediate variable obtained by the MATLAB function polyval(g0,s), and ω represents ω a At frequency ω i The value of ω=ω a (ω i ); Then use the MATLAB function A=polyfit(Xd,A d ,na) and B = polyfit(Xd,B d ,nb) Find the polynomials A(x) and B(x); Wherein, if the given n is an even number, na=n / 2, nb=(n-2) / 2; if n is an odd number, na=nb=(n-1) / 2; Finally, the initial value h0 of the polynomial h(s) is calculated, and the calculation expression is as follows: h(s)=A(-s 2 )+sB(s 2 ) (11) A2, based on step A1, using nonlinear least squares coefficients to optimize the polynomial h(s); Call MATLAB's lsqnonlin function and iterate multiple times to calculate all the optimization coefficients of the polynomial h(s). The expression is as follows: Among them, ε nopt Represents the minimum error of the optimization of the nth discrete point; Then solve the optimization target, first set the unknown vector x = [.] and set the coefficient vector h = x, assign h0 obtained in step A1 to vector x; Get the value g of the polynomial g(s) and h(s) at a given point s val and h val , the normalized value of the driving point impedance can be obtained: Z in =(g val +h val ) / (g val -h val ); Based on formula (9), the lsqnonlin function is called to minimize the cost function value, the optimization vector x is obtained, and finally the optimal polynomial h(s) is generated; A3. Based on step A2, generate a strict Hurwitz polynomial g(s); Based on the optimal polynomial h(s) generated in step A2, let U = [h n h n-1 ...h0], V=[(-1) n h n (-1) n-1 h n- 1...h0], the convolution of U and V gives the following expression: H(-s 2 )=h(s)h(-s)=H0+H1s+...+H n s n (13) Among them, h n Represents the coefficient corresponding to the nth discrete point, H n Indicates H(-s 2 )The coefficients corresponding to each item; Then generate an even-degree polynomial G(-s 2 ), the expression is as follows: G(-s 2 )=H(-s 2 )+(-1) k s 2k =G0+G1s 2 +...+G n s 2n (14) Among them, G n Indicates G(-s 2 ) The coefficients corresponding to each item, k represents the variable, that is, the coefficient between 0 and n; Then store the row vector X, the expression is as follows: X=[(-1) n G n (-1) n-1 G n-1 ...G0] (15) Calculate G(-s 2 ) The roots pk and pkm in the right and left half planes are expressed as follows: Finally, the first polynomial is generated Through MATLAB function Generate strict Hurwitz polynomial g(s); Where gc = {g n g n-1 ...g0} represents the (n+1)th order row vector, that is, g(s) = g0+g1s+...+g n s n The coefficient of A4. Based on step A3, calculate the current transmission gain T; First, define the complex variable s = jω; j = sqrt(-1), then s = sqrt(-1)*ω; Calculate the polynomial g using h and g val =polyval(g,s) and h val =polyval(h,s), find g val =g0s n +g1s n-1 +…+g n-1 s+g n ,h val =h0s n +h1s n-1 +…+h n-1 s+h n ; Through the input impedance (g val +h val ) / (g val -h val ) obtain the current transmission gain T, through g val =polyval(g,s),h val =polyval(h,s),f val =s k and L 11 =h val / g val , we can get Weight = f val conj(f val )(1-L 11 conj(L 11 )) and D=h val conj(h val )(1+L 11 conj(L 11 ))+f val conj(f val )-2real(L 11 h val conj(g val )), then we can get the transmission gain T = Weight / D; Among them, Weight and D represent the set intermediate variables, f val represents the frequency variable, L 11 represents the load reflection coefficient; A5. Based on steps A1-A4, use a network synthesis method to find the real frequency matching network circuit structure; The component parameters and starting component types of the matching network are obtained by using the optimized h(s) and g(s) and long division method. The values ​​of each input matching item are calculated by the network comprehensive formula (18), and the normalized input matching component values ​​are obtained. Among them, Z L represents the load impedance, X ns Indicates margin, capacitance f0 represents the center frequency, R0 represents the characteristic impedance, and inductance C n Represents the capacitance at the nth discrete point, L n represents the inductance at the nth discrete point; Finally, based on the tested impedance of the reflection amplifier circuit, the optimal matching network characteristics are calculated, and the corresponding matching circuit is synthesized to design a broadband reflection amplifier circuit.

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