Broadband Wilkinson power divider optimization design method

Abstract

The invention provides an optimization design method for a broadband Wilkinson power divider, relates to the technical field of mobile communication, and solves the problems that when a broadband or multi-frequency power divider is optimized in the prior art, a particle swarm algorithm possibly has a local optimum condition, the performance is very good in a certain narrow band, but the overall bandwidth does not reach the standard, and in the later stage of iteration, the overall bandwidth is not up to the standard. The positions and speeds of all particles tend to be consistent, and the ability of the whole population to explore a new area is exhausted. According to the technical scheme, the risk of falling into local optimum is reduced by adding a mutation operator, a crossover operator and selection operation. According to the invention, the power divider can maintain excellent performance in a wider frequency band.

Description

Technical Field

[0001] This invention relates to the field of mobile communication technology, specifically to an optimized design method for a broadband Wilkinson power divider. Background Technology

[0002] A power divider is a microwave component (such as the classic Wilkinson power divider) that distributes an input signal to multiple output ports according to a specific ratio and phase. It typically performs optimally at a center frequency or within a very narrow frequency band. With the rapid development of modern wireless communication technology, there is an urgent need for communication systems that support high data rates. To meet this requirement, the design of broadband compact circuits has become a current research hotspot. The design of broadband power dividers essentially transforms from a relatively simple, low-parameter circuit into a complex, multi-parameter circuit synthesis problem, with a dramatic increase in design parameters. The application background of PSO (Particle Swarm Optimization) stems from the high-dimensional, highly nonlinear, and multi-objective optimization challenges brought about by broadband design.

[0003] When optimizing a broadband or multi-frequency power divider, the particle swarm optimization algorithm may encounter a "local optimum": it performs well within a narrow band, but the overall bandwidth is insufficient. Furthermore, in the later stages of iteration, the positions and velocities of all particles tend to be consistent, and the entire swarm's ability to explore new regions becomes exhausted. Summary of the Invention

[0004] Therefore, this invention provides a broadband Wilkinson power divider optimization design method to solve the above problems; this invention provides a particle swarm optimization algorithm that integrates genetic algorithm, and by adding mutation operator, crossover operator and selection operation, the risk of getting trapped in local optima is reduced, so that the power divider can maintain excellent performance in a wider frequency band.

[0005] This invention provides a broadband Wilkinson power divider optimization design method, comprising the following steps:

[0006] Step 1: Considering the dissipation effect, the Wilkinson power divider is transformed into an odd-mode equivalent circuit and an even-mode equivalent circuit by combining odd-mode analysis techniques, and its scattering matrix is ​​calculated.

[0007] Step 2: Construct the fitness function F based on the scattering matrix;

[0008] Step 3: Parameter initialization and population generation, including algorithm parameter setting, solution space definition, population initialization, and initialization of historical bests;

[0009] Step 4: Begin iterative optimization and update standard PSO parameters;

[0010] Step 5: Combine the fitness function to update the individual and global optimum, add the crossover operation from the genetic algorithm, and determine whether the particles should be replaced; then select mutation, and similarly determine whether the particles should be replaced; obtain the optimal fitness of this generation according to the fitness function, and increment it by 1 iteratively, then return to step 4 to determine whether the convergence condition is met or whether the maximum number of iterations has been reached based on the fitness value. If yes, output the optimal parameters of the power divider; otherwise, continue iterating.

[0011] Step 6: Record the global optimal fitness of this generation for plotting, and finally record and output the numerical values.

[0012] Furthermore, in step 2: F = |maxS 11 -0.04|+|maxS 23 -0.03|, where maxS 11 and maxS 23 S in the required frequency domain 11 and S 23 The maximum amplitude.

[0013] Furthermore, in step 4, the update formula for the standard PSO parameters is as follows:

[0014] ;

[0015] in, Let be the position of particle n at time t. Let n be the position of particle n at time t+1. Let n be the velocity of particle n at time t+1. The particle's velocity determines its direction and step size in the search space. The velocity is updated using the current velocity, the individual optimal solution, and the global optimal solution.

[0016] ;

[0017] in, Inertial weights control the inertia that allows particles to maintain their current state of motion. and These are acceleration factors, referred to as individual learning factors and social learning factors, used to control the particle's path towards the individual optimal solution. and the group optimal solution The speed at which they approach; and It is a random number between [0, 1]; It is the optimal position for particle n. It is the globally optimal position.

[0018] Furthermore, in step 1, the power divider consists of N segments with different characteristic impedances. ,width and length It consists of microstrip lines, and the isolation between the output ports is achieved by N isolation resistors. The input and output impedances are represented by Z0=50Ω.

[0019] Furthermore, the width of the microstrip line and length These are the parameters that need to be optimized; the formula is used to calculate a given effective constant. and characteristic impedance As shown below; here (0) indicates that dispersion and dissipation effects are not considered, where f is the operating frequency;

[0020] .

[0021] Furthermore, in the effective constant Based on this, an effective constant is proposed. The dispersion formula is shown below:

[0022] ;

[0023] In the formula, Indicates the effective dielectric constant in relation to frequency; It is the relative permittivity of the substrate; It is the effective dielectric constant of the microstrip line under DC conditions; ,in , Where Z0 is in Ω, f is in GHz, and d is in cm.

[0024] Furthermore, in step 2, the fitness function is constructed based on the power divider scattering matrix, and functions are defined for the widths W1 and W2 of the two transmission lines, the physical lengths L1 and L2 of the transmission lines at both ends, and the isolation resistors R1 and R2, for subsequent calls.

[0025] The present invention has the following advantages over the prior art:

[0026] 1. The present invention provides a broadband Wilkinson power divider optimization design method, which provides a particle swarm optimization algorithm that integrates genetic algorithm. By adding mutation operator, crossover operator and selection operation, the risk of getting trapped in local optima is reduced, so that the power divider can maintain excellent performance in a wider frequency band.

[0027] 2. This invention provides a broadband Wilkinson power divider optimization design method. To predict the actual circuit performance, it considers the dispersion and dissipation effects of microstrip lines and derives the power divider's scattering matrix from the odd-even mode equivalent circuit. This algorithm integrates the selection, crossover, and mutation operations of a genetic algorithm, reducing the risk of the standard particle swarm optimization algorithm getting trapped in local optima. The power divider optimized based on the genetic-particle swarm optimization algorithm avoids the drawbacks of traditional power divider design processes, such as cumbersome procedures, low accuracy, and high computational load in simulation, significantly improving design efficiency and accuracy.

[0028] 3. This invention provides a broadband Wilkinson power divider optimization design method. Based on simulation data, compared with the standard particle swarm optimization algorithm, it achieves superior circuit performance over a wider continuous frequency band. The designed power divider has a size of only 0.6cm*0.7cm, far smaller than the size of current mainstream designs. Attached Figure Description

[0029] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] Figure 1 The even-mode equivalent circuit diagram of a Wilkinson power divider;

[0031] Figure 2 The odd-mode equivalent circuit diagram of a Wilkinson power divider;

[0032] Figure 3 Here is a flowchart of the genetic-particle swarm optimization algorithm;

[0033] Figure 4 For example S 11 S 23 And VSWR simulation curves;

[0034] Figure 5 For example S 21 and S 31 The simulation curve. Detailed Implementation

[0035] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] The design of broadband power dividers essentially transforms from a relatively simple, low-parameter circuit into a complex, multi-parameter circuit synthesis problem, leading to a dramatic increase in design parameters. The application of Particle Swarm Optimization (PSO) stems from the high-dimensional, highly nonlinear, and multi-objective optimization challenges presented by broadband design. PSO is a global optimization algorithm that employs parallel computation. The core advantage of the Genetic Particle Swarm Optimization algorithm lies in its introduction of genetic operations (selection, mutation, crossover), which effectively solves the inherent problems of premature convergence and loss of population diversity in power divider optimization using ordinary PSO algorithms. This transforms it from a fast "local optimizer" into a powerful "global explorer."

[0037] The broadband Wilkinson power divider optimization design method provided in this embodiment specifically includes the following steps:

[0038] Step 1: Considering the dissipation effect, the Wilkinson power divider is transformed into an odd-mode equivalent circuit and an even-mode equivalent circuit by combining odd-mode analysis techniques, and its scattering matrix is ​​calculated.

[0039] Based on the dispersive microstrip line model and specular reflection characteristics, the scattering parameters of the Wilkinson power divider were calculated using the even-odd mode analysis method. The equally divided broadband Wilkinson power divider consists of N segments with different characteristic impedances. ,width and length It consists of microstrip lines, with isolation between the output ports achieved by N isolation resistors, and the input and output impedance is represented by Z0 = 50Ω. The width of the microstrip line... and length These are the parameters that need to be optimized; the formula can be used to calculate a given effective constant. and characteristic impedance As shown below. Here (0) indicates that dispersion and dissipation effects are not considered, where f is the operating frequency.

[0040]

[0041] In the above effective constants Based on this, an effective constant was proposed. The dispersion formula is shown below.

[0042]

[0043] In the formula, Indicates the effective dielectric constant in relation to frequency; It is the relative permittivity of the substrate; It is the effective dielectric constant of the microstrip line under DC conditions; ,in , (Where Z0 is in Ω, f is in GHz, and d is in cm). From the above formula, we can see that... When f=0, it simplifies to the DC value. And it increases to as the frequency increases. .

[0044] In addition, the losses caused by dielectric loss and conductor loss are shown below.

[0045]

[0046]

[0047] in and These are the relative permittivity and loss tangent of the medium, respectively. Since the conductivity of the metal is given, the complex transport constant of the dissipative microstrip line model can be expressed as follows.

[0048]

[0049] For even-mode excitation, equal-amplitude, zero-phase-difference waves are incident on ports 2 and 3 respectively. No current flows through the isolation resistor, so it can be ignored. Thus, the Wilkinson power divider can be divided into two symmetrical two-port networks. The equivalent circuit of the upper part is as follows: Figure 1 As shown.

[0050] Based on the dispersion dissipation effect, the transmission matrix of the i-th microstrip line is shown in the following equation.

[0051]

[0052] A two-port network transmission matrix can be represented as the product of N cascaded transmission matrices, as shown in the following equation.

[0053]

[0054] Therefore, some scattering parameters of the even mode can be expressed as:

[0055]

[0056]

[0057] For odd-mode excitation, waves of equal amplitude and with a 180° phase difference are incident on ports 2 and 3, respectively. The upper part of the equivalent circuit is as follows: Figure 2 As shown, the transfer matrix of the i-th parallel isolation resistor can be expressed as:

[0058]

[0059] Therefore, the transfer matrix under odd modes is expressed as:

[0060]

[0061] For odd-mode excitation, the impedance of port 1 is zero. Therefore, the scattering parameters of the odd-mode are as follows.

[0062]

[0063] Finally, the scatter matrix of the Wilkinson power divider can be expressed as:

[0064] ;

[0065] Step 2: Construct the fitness function F based on the scattering matrix; F = |maxS 11 -0.04|+|maxS 23 -0.03|, where maxS 11 and maxS 23 S in the required frequency domain 11 and S 23 The maximum amplitude; define functions for the widths W1 and W2 of the two transmission lines, the physical lengths L1 and L2 of the transmission lines at both ends, and the isolation resistors R1 and R2, for subsequent calls.

[0066] Step 3: Parameter initialization and population generation, including algorithm parameter setting, solution space definition, population initialization, and initialization of historical bests;

[0067] Step 4: Begin iterative optimization and update standard PSO parameters;

[0068] ;

[0069] in, Let be the position of particle n at time t. Let n be the position of particle n at time t+1. Let n be the velocity of particle n at time t+1. The particle's velocity determines its direction and step size in the search space. The velocity is updated using the current velocity, the individual optimal solution, and the global optimal solution.

[0070] ;

[0071] in, Inertial weights control the inertia that allows particles to maintain their current state of motion. and These are acceleration factors, referred to as individual learning factors and social learning factors, used to control the particle's path towards the individual optimal solution. and the group optimal solution The speed at which they approach; and It is a random number between [0, 1]; It is the optimal position for particle n. It is the globally optimal position.

[0072] Step 5: Combine the fitness function to update the individual and global optimum, add the crossover operation from the genetic algorithm, and determine whether the particles should be replaced; then select mutation, and similarly determine whether the particles should be replaced; obtain the optimal fitness of this generation according to the fitness function, and increment it by 1 iteratively, then return to step 4 to determine whether the convergence condition is met or whether the maximum number of iterations has been reached based on the fitness value. If yes, output the optimal parameters of the power divider; otherwise, continue iterating.

[0073] Step 6: Record the global optimal fitness of this generation for plotting, and finally record and output the numerical values.

[0074] like Figure 3The diagram shows the flowchart of the broadband Wilkinson power divider based on the genetic-particle swarm optimization (GSO) algorithm of this invention. The first stage involves parameter initialization and population generation, designing the algorithm parameters: C1, C2: learning factors of the PSO, controlling the step size of particles towards individual and swarm optima; Wmax, Wmin: maximum and minimum values ​​of the inertia weight, used for a linear decreasing strategy to balance global search and local exploitation; D: particle dimension, here 6, corresponding to W1, L1, R1, W2, L2, R2, indicating a second-order Wilkinson power divider design; PC, PM: crossover and mutation probabilities of the genetic algorithm, set to 0.8 and 0.1 respectively in this paper. The solution space is defined as follows: POmax and POmin: define the physical value range of each optimization variable (e.g., microstrip line length, width, resistance); Vmax and Vmin: define the particle velocity boundary as ±10%, preventing the search step size from being too large or too small. The population is initialized as follows: POP: Population position matrix, each particle represents a power divider design scheme; V: Population velocity matrix; F: Fitness value corresponding to each particle, calculated by calling the previously defined function. The smaller the fitness value, the better the scheme performance. The initial population optimum is as follows: Gbest: The best position that each particle has experienced; Zbest: The globally optimal position found by the entire population so far. Second stage: Iterative optimization main loop. Standard PSO update, update weight: linearly decreases with iteration; update particle velocity: update velocity according to its own best and the population optimum, and perform velocity boundary processing; update particle position: move particles according to velocity, and perform position boundary processing; evaluate new position: call the function to calculate the fitness value of the new position. Compare the fitness of each particle's new position with its individual historical best and update; compare the best fitness of all particles with the population optimum and update. Genetic Algorithm Crossover Operation: A crossover pool is selected, and the top 80% of particles are chosen based on fitness. Two parents are randomly selected from the pool, and a offspring is generated through a weighted average. The offspring replaces the replaced particle only if its fitness is better, ensuring the population quality does not decline. Gaussian Mutation Operation: 10% of individuals are randomly selected for mutation. A small random perturbation following a Gaussian distribution is added to the selected particle's current position. The low-probability, high-probability mutations generated by the Gaussian distribution help escape local optima. Only mutations that produce better solutions are retained. After the genetic algorithm operation, the individual and population optima of all particles are checked and updated again. The global optimal fitness value of the current generation is recorded, and progress information is displayed every 10 generations. After the algorithm ends, a fitness convergence curve is plotted, and the parameter values ​​of the optimal solution are output, providing statistical information: optimal fitness, average fitness, and fitness standard deviation.

[0075] In summary, for the bandwidth optimization design of the power divider, this design adopts a second-order quarter-wavelength transmission line structure to extend the bandwidth. An optimization strategy based on the genetic-particle swarm optimization algorithm is proposed: it combines the fast convergence of the particle swarm optimization algorithm, the global search capability of the genetic algorithm through hybridization, the local escape capability of Gaussian mutation, multiple boundary treatments to ensure the feasibility of the solution, and adaptive inertia weights to balance exploration and utilization. Simulation tests are conducted on the second-order broadband power divider. This scheme, through reasonable technical trade-offs, enables the power divider to achieve optimal bandwidth within the required frequency band. Figure 4 , Figure 5 As shown, the power divider loss is less than 3.3dB, the isolation is greater than 20dB, the return loss is better than 20dB, and a relatively good bandwidth is obtained. This verifies that the power divider under this strategy has advantages such as high isolation, wide bandwidth, and miniaturization, and has high potential for practical applications.

[0076] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A broadband Wilkinson power divider optimization design method, characterized in that, Includes the following steps: Step 1: Considering the dissipation effect, the Wilkinson power divider is transformed into an odd-mode equivalent circuit and an even-mode equivalent circuit by combining odd-mode analysis techniques, and its scattering matrix is ​​calculated. Step 2: Construct the fitness function F based on the scattering matrix; Step 3: Parameter initialization and population generation, including algorithm parameter setting, solution space definition, population initialization, and initialization of historical bests; Step 4: Begin iterative optimization and update standard PSO parameters; Step 5: Combine the fitness function to update the individual and global optimum, add the crossover operation from the genetic algorithm, and determine whether the particles should be replaced; then select mutation, and similarly determine whether the particles should be replaced; obtain the optimal fitness of this generation according to the fitness function, and increment it by 1 iteratively, then return to step 4 to determine whether the convergence condition is met or whether the maximum number of iterations has been reached based on the fitness value. If yes, output the optimal parameters of the power divider; otherwise, continue iterating. Step 6: Record the global optimal fitness of this generation for plotting, and finally record and output the numerical values.

2. The broadband Wilkinson power divider optimization design method according to claim 1, characterized in that, In step 2: F = |maxS 11 -0.04|+|maxS 23 -0.03|, where maxS 11 and maxS 23 S in the required frequency domain 11 and S 23 The maximum amplitude.

3. The broadband Wilkinson power divider optimization design method according to claim 2, characterized in that, In step 4, the update formula for the standard PSO parameters is as follows: ； in, Let be the position of particle n at time t. Let n be the position of particle n at time t+1. Let n be the velocity of particle n at time t+1. The particle's velocity determines its direction and step size in the search space. The velocity is updated using the current velocity, the individual optimal solution, and the global optimal solution. ； in, Inertial weights control the inertia that allows particles to maintain their current state of motion. and These are acceleration factors, referred to as individual learning factors and social learning factors, used to control the particle's path towards the individual optimal solution. and the group optimal solution The speed at which they approach; and It is a random number between [0, 1]; It is the optimal position for particle n. It is the globally optimal position.

4. The broadband Wilkinson power divider optimization design method according to claim 3, characterized in that, In step 1, the power divider consists of N segments with different characteristic impedances. ,width and length It consists of microstrip lines, and the isolation between the output ports is achieved by N isolation resistors. The input and output impedances are represented by Z0=50Ω.

5. The broadband Wilkinson power divider optimization design method according to claim 4, characterized in that, The width of the microstrip line and length These are the parameters that need to be optimized; the formula is used to calculate a given effective constant. and characteristic impedance As shown below; here (0) indicates that dispersion and dissipation effects are not considered, where f is the operating frequency; 。 6. The broadband Wilkinson power divider optimization design method according to claim 5, characterized in that, In effective constant Based on this, an effective constant is proposed. The dispersion formula is shown below: ； In the formula, Indicates the effective dielectric constant in relation to frequency; It is the relative permittivity of the substrate; It is the effective dielectric constant of the microstrip line under DC conditions; ,in , Where Z0 is in Ω, f is in GHz, and d is in cm.

7. The broadband Wilkinson power divider optimization design method according to claim 6, characterized in that, In step 2, the fitness function is constructed based on the power divider scattering matrix, defining a function containing the widths W1 and W2 of the two transmission lines; the physical lengths L1 and L2 of the transmission lines at both ends; and the isolation resistors R1 and R2.

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