Antenna impedance matching optimization method and system based on rectangular coordinate system

Abstract

The application discloses an antenna impedance matching optimization method and system based on a rectangular coordinate system and belongs to the technical field of wireless communication. The method maps a complex impedance point into a point in a rectangular coordinate system, defines a series reactance to make the point vertically translate and defines a parallel reactance to make the point rotate along an impedance circle with a specific diameter. Through the geometric rule, the complex impedance matching design is converted into an intuitive path planning problem. In the design, a path of translation and rotation alternation is planned in the rectangular coordinate system according to source and load impedances, and element parameters are inversely deduced according to geometric relations; in the solution, the input impedance is obtained by reversely tracing the movement of the point. The system realizes the method and contains a visualization module. The application overcomes the defects of Smith chart, such as difficult understanding and non-intuitive design, and provides a new tool for impedance matching design, which is regular, uniform, highly visible and especially convenient for wideband optimization and software implementation.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a design and analysis method for antenna impedance matching networks, and more particularly to an impedance matching optimization method and system based on a planar rectangular coordinate system. Background Technology

[0002] The Smith chart has long been a classic tool in the design and analysis of antenna matching networks. While it represents the reflection coefficient in polar coordinates, it has significant drawbacks: First, its theory is based on complex complex plane mappings, resulting in a steep learning curve and difficulty in understanding. Second, when designing on the chart, the trajectories for series and parallel components differ (requiring movement along circles of equal resistance or equal reactance), making the derivation process complex and prone to errors. Third, the points on the chart have a weak correlation with actual circuit component parameters (inductance, capacitance values), requiring formula conversion and making the design less intuitive. Finally, for optimization designs such as broadband matching, the Smith chart offers limited guidance and often relies on experience. Therefore, there is an urgent need for a more intuitive, understandable, and standardized method for impedance matching design and analysis that clearly demonstrates the relationship between component parameters and performance. Summary of the Invention

[0003] The technical problem to be solved by this invention is to overcome the technical defects of the existing Smith chart method, such as difficulty in understanding, lack of intuitiveness in the design process, weak correlation with component parameters, and complexity of broadband optimization, and to provide an impedance matching optimization method and system based on a rectangular coordinate system, which is visual and has clear geometric relationships.

[0004] The technical solution adopted by the present invention to solve its technical problem is: an antenna impedance matching optimization method based on a rectangular coordinate system. Its core is to regard the complex impedance point (Z=R+jX) as a point in a plane rectangular coordinate system, where the horizontal axis is the resistance R and the vertical axis is the reactance X, and the changes in capacitance and inductance are transformed into the geometric movement of this point.

[0005] Specifically, the following steps are included:

[0006] Step S1, Basic Operation Definition: Define the vertical translation of the impedance point corresponding to the series reactance operation; define the clockwise rotation of the impedance point corresponding to the parallel reactance operation along a specific impedance circle, the diameter of which is equal to the pure resistance value of the parallel circuit.

[0007] Step S2, Matching Network Design: For the given source impedance and load impedance, determine their corresponding points in the rectangular coordinate system; by alternately performing geometric operations of "translation" and "rotation", plan a path from the source impedance point to the conjugate point of the load impedance point; based on the geometric trajectory traversed by the path, calculate the parameter values ​​of the required series and parallel reactance components in reverse.

[0008] Step S3, Complex Network Decomposition: For T-type, Π-type, or multi-level matching networks, decompose them into multiple cascaded Γ-type networks and introduce virtual resistors as intermediate nodes; in the coordinate system, complete the path planning and parameter calculation of the complex network through multiple impedance circles of different diameters and continuous translation-rotation operations.

[0009] Step S4, Impedance Calculation: For a network with known topology and component parameters, starting from the load end, perform reverse geometric operations in the coordinate system according to the rules of step S1 (translate when encountering series connections, rotate along a circle when encountering parallel connections) to gradually trace the movement trajectory of the impedance points and finally obtain the impedance value at the input end.

[0010] An antenna impedance matching optimization system based on a Cartesian coordinate system, used to implement the above method, includes:

[0011] (1) Coordinate modeling module, used to establish the mapping relationship between impedance points and circuit states in a Cartesian coordinate system;

[0012] (2) Geometric operation rule library, storing the rules for vertical translation corresponding to series connection and rotation along the circle corresponding to parallel connection, as well as the impedance circle generation algorithm;

[0013] (3) Path planning and calculation module, used to perform geometric path planning in the coordinate system according to the input impedance requirements, and calculate the component parameters based on the geometric relationship;

[0014] (4) Visualization module, used to dynamically display the moving path of the impedance point, the impedance circle, and the corresponding circuit topology and component parameters.

[0015] The beneficial effects of this invention are:

[0016] 1. Intuitive and easy to understand: It transforms abstract complex number operations into intuitive geometric movements of points, lines, and circles, with unified rules (serial connection means vertical translation, parallel connection means rotation along a circle), which greatly reduces the learning and usage threshold.

[0017] 2. Clear design: Component parameters (such as reactance values) are directly represented in the graphics as line segment lengths or coordinates on a circle. The design process is like geometric drawing, clear and concise, avoiding tedious formula derivation.

[0018] 3. Optimized Visualization: For broadband matching, the relationship between the quality factor Q (path slope) and bandwidth can be intuitively observed through the geometric diagram of multi-level Γ network cascade, which facilitates optimization by selecting virtual resistors and the number of stages.

[0019] 4. Simple solution: When solving the network impedance in reverse, each step has a clear geometric operation, the process is simple and not prone to errors.

[0020] 5. Easy to implement in software: The method has clear logic and fixed rules, making it very suitable for programming and implementation into computer-aided design (CAD) software to improve design efficiency. Attached Figure Description

[0021] Figure 1 This is a schematic diagram showing the complex impedance of the RC and RL series circuit in a rectangular coordinate system in an embodiment of the present invention.

[0022] Figure 2 This is a geometric analysis diagram of the complex impedance of the RC and RL parallel circuits and their series-parallel equivalents in an embodiment of the present invention.

[0023] Figure 3 The diagram shows the geometric analysis of four basic Γ-type matching networks and their matching processes in the embodiments of the present invention.

[0024] Figure 4 This is a diagram illustrating the decomposition and matching process of the T-type matching network in an embodiment of the present invention.

[0025] Figure 5 This is a diagram illustrating the decomposition and matching process of the Π-type matching network in an embodiment of the present invention.

[0026] Figure 6 This is a visual analysis diagram of the impedance matching process of a multi-level Γ network (broadband matching) in an embodiment of the present invention.

[0027] Figure 7 This is an example diagram illustrating the geometric steps of the known network input impedance solution process in an embodiment of the present invention. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that the following embodiments are for illustrative purposes only and are not intended to limit the invention.

[0029] Example 1: See Figure 1 and Figure 2 This explains the basic operating rules. Figure 1 In the middle, the resistor R is connected in series with the inductive reactance X. LS The corresponding point A(R, X) LS It moves vertically along the straight line x=R in the first quadrant. Let the impedance angle be θ1, then the quality factor of the circuit is Q=tanθ1=X. LS / R. Similarly, resistor R is connected in series with capacitive reactance X. CS The corresponding point is B(R, -X). CS The circuit moves perpendicularly along the straight line x=R in the fourth quadrant. Let the impedance angle be θ², then the quality factor of the circuit is Q=tanθ²=X. CS / R.

[0030] exist Figure 2 In the first quadrant, resistor R is connected in parallel with inductive reactance X. LP It can be equivalent to resistance r1 and inductive reactance X. LS If the circuit is connected in series, then the coordinates of the complex point A representing the complex impedance are (r1, X). LS Since parallel circuits and series circuits are equivalent, we have:

[0031] Taking the real part of both sides of the equation, we have:

[0032] After sorting, we can obtain:

[0033] Therefore, we can conclude that the trajectory of point A is a path starting from point (…). With 0 as the center, and A circle with radius R, i.e.: R / / X LP At time, point A(r1, X) LS The trajectory of ) is the upper half of a circle with OR as its diameter.

[0034] Intercept +R on the imaginary axis and draw a line parallel to the real axis. This line intersects the extension of OA at point A'. Let the impedance angle be θ1, then ∠+RA'O = θ1. The quality factor of the circuit is Q = tanθ1 = X. LS / r1=R / X LP Therefore, the length of line segment + RA' represents X. LP The size of point A' is given by (X). LP As the parallel inductance L gradually increases, point A' moves horizontally to the right, while point A starts from point O and rotates clockwise along the impedance circle.

[0035] Similarly, in Figure 2 In the fourth quadrant, resistor R is connected in parallel with capacitive reactance X. CP Complex impedance point B(r2, -X) CS The trajectory of line segment X is the lower half of a circle with OR as its diameter. The length of line segment -RB' represents X. CP The size of point B' is given by (X). CPAs the parallel capacitor C gradually increases, point B' moves horizontally to the left, causing point B to rotate clockwise along the impedance circle from point R.

[0036] Since both ΔOAR and ΔOBR are right triangles, conversely, once the impedance r+jX of the series circuit is known... S This allows us to determine the diameter OR of the impedance circle, and based on geometric relationships, we can calculate the parallel R / / jX. P Circuit parameters.

[0037] Figure 2 In essence, it visualizes all parameters of the equivalent circuit of RC and RL series and parallel connections.

[0038] Example 2: See Figure 3 Taking one type of Γ-shaped network as an example (a large resistor R connected in parallel with a capacitor and then in series with an inductor, matched by a small resistor r). In the design, first mark R and r on the real axis. R is connected in parallel with the capacitor, and its corresponding point is rotated clockwise from point R along a circle of diameter OR to point B. r is connected in series with the inductor, and its corresponding point is moved vertically upwards from point r to point A. A and B are symmetrical about the real axis (conjugate), completing the matching. Based on the geometric relationships of a right triangle, the following can be directly calculated:

[0039] Q is the path-determined quality factor. Parallel capacitive reactance X CP = R / Q, series inductive reactance X LS = r * Q.

[0040] Example 3: See Figure 4 and Figure 5 The T-shaped and Π-shaped networks are shown respectively.

[0041] The T-network can be viewed as two cascaded Γ-networks, introducing a virtual resistance R. V (R) V >R), and X C = X C1 / / X C2 There is only one "vertical arm" element in the network, therefore it corresponds to one element named OR. V The impedance circle is the diameter of the network. The matching path of the T-network is: point r → (series X) L1 Move up) → Point A → (Parallel X) C1 (Rotation along the circle) → R V Point → (Parallel X) C2 (Rotating along the circle) → point B; simultaneously point R → (series X) L2 Move upwards) → point C (conjugate with B). All component values ​​can be calculated using geometric similarity relationships:

[0042] In particular, when R V When =R+r, we have:

[0043] This is a T-type 90° phase-shift network. At this point, Figure 4 The fact that OA⊥OB indicates that the phase angle difference between the input and output voltage (or current) is 90°.

[0044] Similar to the Π network, R V <r,X L = X L1 +X L2 The path involves two circles of different diameters. The matching path of the Π network is: point r → (parallel X) C1 (Rotate along circle r) → Point A → (Series X) L1 (Move upwards) → R V Point → (Serial X) L2 Move upwards) → point B; simultaneously, point R → (parallel X) C2 (Rotate along circle R) → Point C (conjugate with B). All component values ​​can be calculated using geometric similarity relationships:

[0045] In particular, when R V When =R / / r= Rr / (R+r), we have:

[0046] This is a Π-type 90° phase-shift network. At this point, Figure 5 The fact that OA⊥OB indicates that the phase angle difference between the input and output voltage (or current) is 90°.

[0047] Example 4: See Figure 6 This demonstrates how a multi-level Γ network achieves broadband matching. This is achieved by introducing multiple virtual resistors R. V1 ,R V2,..., the matching path is decomposed into multiple gentler "translation - rotation" sequences. On the geometric graph, the overall slope of the path (i.e., the Q value) decreases, corresponding to a wider bandwidth. The designer can intuitively optimize the bandwidth performance by adjusting the number of stages and the R V value. The specific matching process is analyzed as follows:

[0048] The two - stage Γ - type network can also be called the ΠΓ - type network. The r of this network is < R V < R. Since there are two vertical - arm elements, there are two impedance circles. The matching process is briefly described as follows: Looking from left to right, R is in parallel with X C1 , the R point rotates clockwise to the A point, in series with X L1 , the A point is translated upward to the virtual resistance R V point, in parallel with X C2 , the R V point rotates clockwise to the B point, in series with X L2 , the B point is translated upward to the r point.至此, the impedance matching from R to r is completed.

[0049] In the matching analysis diagram of the two - stage Γ - type network, OA and OB can be made collinear. Let the angle between this line and the real axis be θ. According to the geometric relationship, there are:

[0050] For the three - stage inverse - Γ - type network, r < R V1 < R V2 < R. Since there are three vertical - arm elements, there are three impedance circles corresponding to them. The matching process is briefly described as follows: Looking from left to right, r is in series with X L1 , the r point is translated upward to the A point, in parallel with X C1 , the A point rotates clockwise to the virtual resistance R V1 point, in series with X L2 , the R V1 point is translated upward to the B point, in parallel with X C2 , the B point rotates clockwise to the virtual resistance R V2 point, in series with X L3 , the R V2 point is translated upward to the C point, and finally in parallel with X C3 , the C point rotates clockwise to the R point.至此, the impedance matching from r to R is completed.

[0051] For the three - stage inverse - Γ - type network, OA, OB, and OC can be made collinear. Let the angle between this line and the real axis be θ. According to the geometric relationship, there are:

[0052] Example 5: See Figure 7 This demonstrates the reverse solution for input impedance. Starting from a known load impedance point, geometric operations are performed step-by-step from left to right (or right to left) according to the actual network structure (translation for series connections, finding circles and rotation for parallel connections) to finally obtain the coordinates of the input impedance point E, i.e., the input impedance value. The specific process is as follows:

[0053] (1) After a 1Ω resistor is connected in series with a 1Ω inductive reactance, the coordinates of point A are (1, 1). Points O and A can determine an impedance circle with a diameter of 2Ω. It is easy to see that 1+1j is equivalent to 2 / / 2j, that is, the coordinates of point A' are (2, 2). This also shows that the inductive admittance of the equivalent parallel circuit is 0.5S.

[0054] (2) After adding a 0.3S inductance in parallel, the total inductance is 0.8S, which means the total inductive reactance is 1.25Ω. Therefore, point A' shifts to the left to point B', with coordinates (1.25, 2). This causes the impedance point to rotate counterclockwise from point A along the 2Ω impedance circle to point B. The coordinates of point B can be calculated as (0.5618, 0.8989).

[0055] (3) With a 1.4Ω capacitive reactance connected in series, point B is shifted downwards by 1.4Ω to point C. It is easy to know that the coordinates of point C are (0.5618, -0.5011). Points O and C can determine an impedance circle with a diameter of approximately 1Ω. It can be seen that a 0.5618Ω resistor connected in series with a 0.5011Ω capacitor is equivalent to a 1Ω resistor connected in parallel with a 1.12Ω capacitor (capacitating approximately 0.9S), that is, the coordinates of point C' are (1.12, -1).

[0056] (4) With a parallel capacitance of 1.1S, the total capacitance is 2S, which means the capacitive reactance is 0.5Ω. Therefore, point C' shifts to the left to point D', and the coordinates of point D' are (0.5, -1). This causes the impedance point to rotate clockwise from point C along the 1Ω impedance circle to point D. The coordinates of point D can be calculated as (0.2, -0.4).

[0057] (5) Finally, connect a 0.9Ω inductive reactance in series. Move point D upward by 0.9Ω to point E. It is easy to know that the coordinates of point E are (0.2, 0.5), that is, the impedance value of point E is Z = 0.2 + j0.5Ω. This completes the process.

[0058] The method described in this invention is not only applicable to antenna matching, but also to the core idea of ​​visualizing impedance transformation as a geometric problem. It can also be applied to RF circuit design fields that require impedance transformation, such as filter design and amplifier matching.

Claims

1. An antenna impedance matching optimization method based on a Cartesian coordinate system, characterized in that, Includes the following steps: (1) Establish a mapping in a plane rectangular coordinate system, where the horizontal axis represents resistance R, the vertical axis represents reactance X, and the complex impedance Z = R + jX corresponds to a point in the coordinate system; (2) Define the basic geometric operation rules: connect a reactor element in series to make the impedance point translate in a direction perpendicular to the horizontal axis; connect a reactor element in parallel to make the impedance point rotate clockwise along a predetermined impedance circle, the diameter of which is equal to the pure resistance value in the parallel branch. (3) Determine the corresponding start and end points in the coordinate system based on the source impedance and load impedance to be matched; (4) By alternately applying the geometric operations of translation and rotation, plan a geometric path from the starting point to the conjugate point of the ending point; (5) Based on the translation distance and the parameters of the impedance circle involved in the rotation in the geometric path, the type and parameter value of each reactance element required in the matching network are deduced.

2. The method according to claim 1, characterized in that, The method for determining the impedance circle is as follows: for a resistor R and a reactance X P In a parallel circuit, the trajectory of the equivalent series impedance point is a circle with the center coordinates (R / 2, 0) and the radius R / 2. When the parallel reactance is inductive, the trajectory is the upper semicircle; when the parallel reactance is capacitive, the trajectory is the lower semicircle.

3. The method according to claim 1, characterized in that, When planning the matching path, for a Γ-type matching network, the path consists of one rotation operation and one translation operation; for a T-type, Π-type, or multi-stage matching network containing virtual resistance, the path is decomposed into a series of consecutive rotation-translation operations connected by impedance circles of different diameters.

4. The method according to claim 3, characterized in that, The method further includes a broadband matching optimization step: by increasing the number of levels of the matching network, multiple virtual resistance points are introduced in the coordinate system, thereby decomposing the geometric path into more segments to reduce the slope of the overall path, that is, to reduce the overall quality factor Q of the network, thereby achieving a wider matching bandwidth.

5. An antenna impedance matching optimization system based on a rectangular coordinate system, used to implement the method according to any one of claims 1-4, characterized in that, include: (1) Coordinate modeling module, used to establish the mapping relationship between impedance points and circuit states in a Cartesian coordinate system; (2) Geometric rule library, which stores the geometric operation rules corresponding to vertical translation in series and rotation along a circle in parallel; (3) Path planning and calculation module, which is used to perform geometric path planning in the coordinate system based on the input source impedance and load impedance, and calculate the topology of the matching network and the parameter values ​​of each component based on the geometric relationship. (4) Visual interface, used to display the rectangular coordinate system, the moving path of the impedance point, the impedance circle and the final generated circuit schematic.

6. The system according to claim 5, characterized in that, The system also includes an impedance calculation module, which receives the known matching network topology and component parameters, starts from the load impedance point, performs the corresponding geometric operations in reverse in the coordinate system, and gradually derives and displays the position and value of the input impedance point.

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