Four-coupled stacked transformer, automated design method, and millimeter-wave bidirectional variable gain amplifier

Abstract

The application discloses a four-coupling stacked transformer, an automatic design method and a millimeter wave bidirectional variable gain amplifier, relates to the technical field of on-chip transformers, and solves the technical problems of poor flexibility of the topological shape of a stacked transformer winding designed manually in a rectangular coordinate system, low electromagnetic coupling efficiency in multi-coupling matching, and large undesired coupling between the windings of the two groups of transformers. The four-coupling stacked transformer comprises a first coupling group, a first 8-shaped inner circle winding surrounded by first outer circle folded line windings with irregular topological shapes, a second coupling group, and a second 8-shaped inner circle winding surrounded by second outer circle folded line windings with irregular topological shapes. The first outer circle folded line windings and the second outer circle folded line windings form a first transformer, and the first 8-shaped inner circle winding and the second 8-shaped inner circle winding form a second transformer.

Description

Technical Field

[0001] This invention relates to the field of on-chip transformer technology, and more particularly to a four-coupled stacked transformer, an automated design method, and a millimeter-wave bidirectional variable gain amplifier. Background Technology

[0002] In millimeter-wave phased array communication and sensing systems, the transmit and receive links typically need to implement transmit / receive switching, gain adjustment, and beam control within the same RF front-end. Traditional solutions usually employ separate transmit and receive links, using a transmit / receive switch to switch the transmit / receive path and achieve operational direction switching. However, separate transmit and receive links require redundant configuration of active and passive matching networks, increasing chip area. Furthermore, using a transmit / receive switch introduces additional insertion loss, reducing transmit output power, receive noise performance, and system efficiency. A better approach is to independently configure transformers in the passive matching networks of the transmit and receive links. These transformers achieve link impedance matching to reduce reflection loss and provide signal isolation to improve system stability.

[0003] Related technologies attempt to reduce chip area by physically stacking the circuit structures of the transmit and receive links, requiring the transformers of the two links to be designed as four-coupled stacked transformers. Typically, the stacked transformer architecture is modeled manually using a Cartesian coordinate system. Even with numerous design parameters, the topology of the transformer windings is limited to octagons, resulting in poor topology flexibility. Under tight on-chip space requirements, electromagnetic coupling efficiency is low during multi-coupling matching, and significant undesirable coupling can easily exist between the windings of the two sets of transformers, preventing the bidirectional variable gain amplifier from achieving excellent bidirectional performance.

[0004] In the process of realizing this invention, the inventors discovered at least the following problems in the prior art: The topology of stacked transformer windings designed in the existing Cartesian coordinate system has poor flexibility, low electromagnetic coupling efficiency during multi-coupling matching, and large undesirable coupling can easily exist between the windings of the two sets of transformers. Summary of the Invention

[0005] The purpose of this invention is to provide a four-coupled stacked transformer, an automated design method, and a millimeter-wave bidirectional variable gain amplifier to solve the technical problems of poor topological flexibility of stacked transformer windings designed manually in the existing Cartesian coordinate system, low electromagnetic coupling efficiency during multi-coupling matching, and large undesirable coupling between the windings of two sets of transformers. The various technical effects of the preferred solutions provided by this invention are detailed below.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The present invention provides a four-coupled stacked transformer, comprising: a first coupling group, including a first outer loop winding with an irregular topological shape formed by sequentially connecting multiple conductive segments, and a first figure-eight-shaped inner loop winding spaced apart by the first outer loop winding; and a second coupling group, located below the first coupling group, including a second outer loop winding with an irregular topological shape formed by sequentially connecting multiple conductive segments, and a second figure-eight-shaped inner loop winding spaced apart by the second outer loop winding; the first outer loop winding and the second outer loop winding are mounted on a substrate. The orthographic projections of the surfaces completely or partially overlap, and the orthographic projections of the first figure-eight inner winding and the second figure-eight inner winding completely or partially overlap on the substrate plane; the number of conductive lines in both the first outer winding and the second outer winding is greater than 8, and both the first and second figure-eight inner windings include two local loop traces with different topological shapes; the first outer winding and the second outer winding form a first transformer; the first figure-eight inner winding and the second figure-eight inner winding form a second transformer.

[0007] Preferably, the ports of the first outer loop winding and the second outer loop winding are arranged opposite to each other, and the ports of the first figure-eight inner loop winding and the second figure-eight inner loop winding are arranged opposite to each other.

[0008] Preferably, the first coupling group is mirror-symmetric, and the second coupling group is mirror-symmetric.

[0009] Preferably, the first figure-eight inner winding includes a first partial loop trace, a second partial loop trace, and a first center bridging trace and a second center bridging trace intersecting on the orthographic projection of the figure-eight inner winding onto the substrate plane; the second figure-eight inner winding includes a third partial loop trace, a fourth partial loop trace, and a third center bridging trace and a fourth center bridging trace intersecting on the orthographic projection of the figure-eight inner winding onto the substrate plane; the first outer winding, the first partial loop trace, the second partial loop trace, and the first center bridging trace are formed on the first metal layer, and the first center bridging trace is used to connect the first… A first partial loop trace and a second partial loop trace; a second outer loop winding, the third partial loop trace, the fourth partial loop trace, and a second center bridging trace are formed on a second metal layer, the second center bridging trace connecting the first partial loop trace and the second partial loop trace via vias; a third center bridging trace is formed on a third metal layer, connecting the third partial loop trace and the fourth partial loop trace via vias; a fourth center bridging trace is formed on a fourth metal layer, connecting the third partial loop trace and the fourth partial loop trace via vias.

[0010] This invention also provides an automated design method for a four-coupled stacked transformer, used in the four-coupled stacked transformer provided by this invention. The method includes: constructing a polar coordinate system with the geometric center point of the first coupling group as the origin, setting N polar angles, where N is a positive integer; constructing design parameters, the design parameters including the orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, and the polar radii of the orthographic projections of the second figure-eight inner loop winding in the polar coordinate system at the N polar angles, and also including the linewidths of the first outer loop winding, the first figure-eight inner loop winding, the second outer loop winding, the second figure-eight inner loop winding, and the offset of the geometric center point of the second coupling group relative to the geometric center point of the first coupling group; minimizing the value of the objective function. The objective is to find the optimal combination of design parameters within the design parameter constraint space. The calculation process for the objective function of each design parameter combination includes: generating a layout file of a four-coupled stacked transformer based on the design parameter combination; performing a geometric constraint check on the layout file; performing electromagnetic simulation on the layout file that passes the geometric constraint check to obtain electromagnetic simulation data; obtaining a four-port differential impedance matrix based on the electromagnetic simulation data; and calculating the objective function based on the four-port differential impedance matrix. The objective function includes at least one of five items: differential winding inductance error, main coupling error, undesired coupling between the outer loop winding and the figure-eight inner loop winding, Q-value penalty, and layout file exceeding boundary penalty. The differential winding includes the first outer loop winding, the second outer loop winding, the first figure-eight inner loop winding, and the second figure-eight inner loop winding.

[0011] Preferably, when both the first coupling group and the second coupling group are mirror-symmetrical, in the polar angle interval A total of N / 2 polar angles are set, and the polar angle range is obtained based on the mirror axis symmetry relationship. The remaining N / 2 polar angles, where N is an even number greater than or equal to 2.

[0012] Preferably, Bayesian optimization, genetic algorithm, particle swarm optimization, random search algorithm, or local search algorithm are used to find the optimal combination of design parameters within the design parameter constraint space with the goal of minimizing the value of the objective function.

[0013] Preferably, the step of generating the layout file of the four-coupled stacked transformer based on the design parameter combination includes: obtaining N layout generation points of the first outer loop winding, N layout generation points of the first figure-eight inner winding, N layout generation points of the second outer loop winding, and N layout generation points of the second figure-eight inner winding in a rectangular coordinate system based on the design parameter combination and N polar angles; sequentially connecting the N layout generation points of the first outer loop winding and the second outer loop winding according to the 45° routing rule; and connecting the N layout generation points of the first figure-eight inner winding according to the first preset connection order and the 45° routing rule to obtain the first local loop routing and the second... Two local loop traces are used; the first and second local loop traces are connected by crossing the first and second center jumper traces, and a hidden metal layer and via connection are used in the conflict area of ​​the first and second center jumper traces; the N layout generation points of the second figure-eight inner winding are connected according to the second preset connection sequence and 45° routing rule to obtain the third and fourth local loop traces; the third and fourth local loop traces are connected by crossing the third and fourth center jumper traces, and a hidden metal layer and via connection are used in the conflict area of ​​the third and fourth center jumper traces.

[0014] Preferably, for two adjacent map generation points located in the first and second quadrants of the rectangular coordinate system , The process of executing the 45° routing rule includes: if the layout generation point and map generation points If the angle between the line connecting the two points is a multiple of 45° with the positive x-axis, then directly connect the two adjacent plot generation points. , If the map generation point and map generation points If the angle between the line connecting the points is not a multiple of 45° and the positive x-axis, then from the point where the layout is generated... Starting from the map generation point, first follow a diagonal line at a positive or negative 45° angle, then follow the axial line to obtain diagonal candidate transition points. Starting from the axis, first follow the axis line, then follow a positive 45° or negative 45° diagonal line to obtain candidate transition points along the axis; if two adjacent map generation points... , If the candidate transition points are located in the first quadrant and the second quadrant respectively, then the candidate transition point furthest from the x-axis of the rectangular coordinate system among the oblique candidate transition points and the axial candidate transition points is taken as the transition point. If two adjacent layout generation points are located in the first quadrant and the second quadrant respectively, then the candidate transition point is taken as the transition point. , If the candidate transition points are located in the same quadrant, the one furthest from the y-axis of the rectangular coordinate system among the oblique candidate transition points and the axial candidate transition points is taken as the transition point; the layout generation points are then connected sequentially. Transition points and map generation points ;in, This indicates the index of the point where the map was generated.

[0015] This invention also provides a millimeter-wave bidirectional variable gain amplifier, comprising a first RF port, a first three-coupled balun, a first bidirectional fixed gain stage, a first four-coupled stacked transformer, a bidirectional variable gain amplification stage, a second four-coupled stacked transformer, a second bidirectional fixed gain stage, a second three-coupled balun, and a second RF port connected in sequence; the first four-coupled stacked transformer and the second four-coupled stacked transformer are both the four-coupled stacked transformers provided by this invention; or, the first four-coupled stacked transformer and the second four-coupled stacked transformer are both obtained according to the automated design method of the four-coupled stacked transformers provided by this invention.

[0016] Implementing one of the above-described technical solutions of the present invention has the following advantages or beneficial effects: On the one hand, by physically stacking the first and second coupling groups, the first figure-eight inner winding is surrounded by the first outer zigzag winding at intervals, and the second figure-eight inner winding is surrounded by the second outer zigzag winding at intervals, making the overall structure of the four-coupled stacked transformer compactly stacked within the passive region. On the other hand, the first and second outer zigzag windings have the same winding shape, both being irregular topological shapes, and both containing more than 8 conductive segments. This allows their topological shapes to be not limited to octagons, increasing the degree of freedom in electromagnetic coupling, which is beneficial for energy coupling and improves their coupling efficiency. While the first and second figure-eight inner windings have the same winding shape, to facilitate energy coupling, the two local loop traces included in both are set with different topological shapes, further improving electromagnetic coupling. The first figure-eight inner winding and the second figure-eight inner winding have opposite local loops, which generate induced magnetic fluxes of opposite polarity when the outer loop winding is excited. This approximately cancels out the induced magnetic fluxes, thereby reducing the unwanted energy coupling between the outer loop winding and the figure-eight inner winding and enhancing the isolation between the transformers of the transmit and receive links. Therefore, the first outer loop winding and the second outer loop winding are used as the first transformer to transmit a signal flow in one direction, and the first figure-eight inner winding and the second figure-eight inner winding are used as the second transformer to transmit a signal flow in another direction, so that the bidirectional variable gain amplifier has excellent bidirectional operating performance. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a schematic diagram of the layout file of the four-coupled stacked transformer in Embodiment 1 of the present invention; Figure 2 This is a flowchart illustrating the automated design method for a four-coupled stacked transformer in Embodiment 2 of the present invention. Figure 3 This is a schematic diagram of the parametric modeling of the four-coupled stacked transformer in polar coordinates in Embodiment 2 of the present invention; Figure 4 This is a schematic diagram illustrating the objective function calculation process for each combination of design parameters in Embodiment 2 of the present invention; Figure 5 This is a schematic diagram of the layout file generation process in Embodiment 2 of the present invention; Figure 6 This is a schematic diagram showing the connection sequence of the first outer ring broken line winding, the second outer ring broken line winding, the first figure-eight inner ring winding, and the second figure-eight inner ring winding in different layout generation points in Embodiment 2 of the present invention. Figure 7 These are two adjacent layout generation points in the first and second quadrants in Embodiment 2 of the present invention. , A schematic diagram illustrating the process of connecting traces according to the 45° routing rule; Figure 8 This is a schematic diagram of the bridging window and chamfer avoidance when routing the second figure-eight inner winding in Embodiment 2 of the present invention; Figure 9 This is the inductance simulation result of the four differential windings of the four-coupled stacked transformer in Embodiment 2 of the present invention; Figure 10 These are the simulation results of the Q values ​​of the four differential windings of the four-coupled stacked transformer in Embodiment 2 of the present invention; Figure 11 This is the simulation result of the coupling coefficient between the four differential windings of the four-coupled stacked transformer in Embodiment 2 of the present invention; Figure 12 This is a schematic diagram of the structure of the millimeter-wave bidirectional variable gain amplifier in Embodiment 3 of the present invention; Figure 13 This is a photograph of the millimeter-wave bidirectional variable gain amplifier chip in Embodiment 3 of the present invention; Figure 14 This is the curve showing the relationship between the input signal frequency and S-parameters of the millimeter-wave bidirectional variable gain amplifier chip during forward signal flow in Embodiment 3 of the present invention; Figure 15 This is the curve showing the relationship between the input signal frequency and the S21 parameter when the millimeter-wave bidirectional variable gain amplifier chip is in the forward signal flow state in Embodiment 3 of the present invention. Figure 16 This is the curve showing the relationship between the input signal frequency and the relative phase when the millimeter-wave bidirectional variable gain amplifier chip is in the forward signal flow state in Embodiment 3 of the present invention. Figure 17 These are the curves showing the relationship between the input signal frequency and the root mean square gain error and root mean square phase error of the millimeter-wave bidirectional variable gain amplifier chip during forward signal flow in Embodiment 3 of the present invention. Figure 18 This is the curve showing the relationship between the input signal frequency and S-parameters when the millimeter-wave bidirectional variable gain amplifier chip is used for reverse signal flow in Embodiment 3 of the present invention. Figure 19 This is the curve showing the relationship between the input signal frequency and the S21 parameter when the millimeter-wave bidirectional variable gain amplifier chip is used for reverse signal flow in Embodiment 3 of the present invention. Figure 20 This is the curve showing the relationship between the input signal frequency and the relative phase when the millimeter-wave bidirectional variable gain amplifier chip is used for reverse signal flow in Embodiment 3 of the present invention. Figure 21 These are curves showing the relationship between the input signal frequency and the root mean square gain error and root mean square phase error when the millimeter-wave bidirectional variable gain amplifier chip is in reverse signal flow in Embodiment 3 of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the present invention clearer, various exemplary embodiments described below will be referenced to the accompanying drawings, which form part of the exemplary embodiments, illustrating various exemplary embodiments that may be used to implement the present invention. Unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. It should be understood that they are merely examples of processes, methods, and apparatuses consistent with some aspects of the present invention disclosed as detailed in the appended claims, and other embodiments may be used, or structural and functional modifications may be made to the embodiments listed herein without departing from the scope and spirit of the present invention.

[0019] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," etc., indicate the orientation or positional relationship based on the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the referred element must have a specific orientation, or be constructed and operated in a specific orientation. The terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. The term "multiple" means two or more. The terms "connected" and "linked" should be interpreted broadly, for example, they can be fixed connections, detachable connections, integral connections, mechanical connections, electrical connections, communication connections, direct connections, indirect connections through an intermediate medium, and can be the internal connection of two elements or the interaction relationship between two elements. The term "and / or" includes any and all combinations of one or more of the related listed items. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0020] To illustrate the technical solution described in this invention, specific embodiments are described below, showing only the parts related to the embodiments of this invention.

[0021] Example 1: like Figure 1 As shown, the present invention provides a four-coupled stacked transformer, comprising: The first coupling group includes a first outer loop winding with an irregular topological shape formed by connecting multiple conductive lines in sequence, and a first figure-eight inner loop winding that is spaced and surrounded by the first outer loop winding. The second coupling group, located below the first coupling group, includes a second outer loop winding with an irregular topological shape formed by connecting multiple conductive lines in sequence, and a second figure-eight inner loop winding that is spaced apart by the second outer loop winding; the orthographic projections of the first outer loop winding and the second outer loop winding on the substrate plane overlap completely or partially, and the orthographic projections of the first figure-eight inner loop winding and the second figure-eight inner loop winding on the substrate plane overlap completely or partially. The number of conductive segments in both the first outer loop winding and the second outer loop winding is greater than 8. Both the first figure-eight inner loop winding and the second figure-eight inner loop winding include two local loop traces with different topological shapes. The first outer loop winding and the second outer loop winding constitute the first transformer; the first figure-eight inner loop winding and the second figure-eight inner loop winding constitute the second transformer.

[0022] like Figure 1As shown, both the first and second outer loop windings have more than 8 conductive segments, which is not a standard topology. Their topology can be customized to meet coupling requirements, offering high flexibility. The first and second figure-eight inner loop windings each have different topologies, including two local loop traces, to facilitate energy coupling and further enhance flexibility.

[0023] from Figure 1 It can be seen that the first and second figure-eight inner windings are not strictly limited to a standard figure-eight shape. The figure-eight inner winding mainly includes two local loops with opposite winding directions, and two center bridging lines connecting the two local loops with opposite winding directions. The two center bridging lines intersect in the orthographic projection of the substrate plane, but are not actually connected to ensure that the two local loops have opposite winding directions. The outer rings (first outer loop zigzag winding and second outer loop zigzag winding) generate an approximately unidirectional magnetic field in the figure-eight inner winding region. The two local loops of the figure-eight inner winding generate induced magnetic fluxes of opposite polarities due to their opposite winding directions. The two can approximately cancel each other out, thereby reducing the energy coupling between the outer rings (first outer loop zigzag winding and second outer loop zigzag winding) and the inner rings (first figure-eight inner winding and second figure-eight inner winding), and enhancing the isolation of the first and second transformers used for signal flow paths in different directions. Meanwhile, the first outer loop winding and the second outer loop winding have the same winding shape and are stacked, and the first figure-eight inner loop winding and the second figure-eight inner loop winding have the same winding shape and are stacked, which is conducive to the energy coupling of the first transformer and the second transformer.

[0024] An opening is provided in a local loop of the figure-eight inner winding as the port of the figure-eight inner winding. It can be understood that both the first and second outer loop windings are irregular semi-enclosed structures formed by sequentially connecting multiple conductive segments. The openings in these semi-enclosed structures, serving as ports for the first and second outer loop windings, do not have a standard topological shape, such as a standard octagon, thus providing more degrees of freedom for electromagnetic coupling.

[0025] In this embodiment, to enhance signal flow anti-interference capabilities and facilitate chip testing and packaging, the ports of the first outer loop winding and the second outer loop winding are oriented differently, as are the ports of the first figure-eight inner loop winding and the second figure-eight inner loop winding. Preferably, the ports of the first outer loop winding and the second outer loop winding are positioned opposite each other, as are the ports of the first figure-eight inner loop winding and the second figure-eight inner loop winding. For example, as shown... Figure 1In the first outer loop winding (comprising terminals 1 and 2) and the first figure-eight inner loop winding (comprising terminals 3 and 4) face to the left, while the second outer loop winding (comprising terminals 5 and 6) and the second figure-eight inner loop winding (comprising terminals 7 and 8) face to the right, in order to enhance the signal flow's anti-interference capability.

[0026] In this preferred embodiment of Example 1, to simplify the design and improve the electromagnetic coupling between the ports of the first outer loop winding and the second outer loop winding, the first figure-eight inner loop winding, and the second figure-eight inner loop winding, the first coupling group is mirror-axis symmetrical, and the second coupling group is mirror-axis symmetrical. Mirror-axis symmetry means that the topological shape of the winding is symmetrical on both sides of the horizontal axis of the substrate surface.

[0027] In the preferred embodiment of this first example, as Figure 6 As shown, the first figure-eight inner winding includes a first partial loop trace, a second partial loop trace, and a first center bridging trace and a second center bridging trace that intersect in the orthographic projection onto the substrate plane; the second figure-eight inner winding includes a third partial loop trace, a fourth partial loop trace, and a third center bridging trace and a fourth center bridging trace that intersect in the orthographic projection onto the substrate plane; combined with Figure 1 As can be seen, the first outer loop winding, the first partial loop trace, the second partial loop trace, and the first center bridging trace are formed on the first metal layer (M9). The first center bridging trace is used to connect the first partial loop trace and the second partial loop trace. The second outer loop winding, the third partial loop trace, the fourth partial loop trace, and the second center bridging trace are formed on the second metal layer (M8). The second center bridging trace connects the first partial loop trace and the second partial loop trace using vias. The third center bridging trace is formed on the third metal layer (M7) and connects the third partial loop trace and the fourth partial loop trace using vias. The fourth center bridging trace is formed on the fourth metal layer (M6) and connects the third partial loop trace and the fourth partial loop trace using vias.

[0028] In this preferred embodiment, orthographic projection crossing refers to the intersection of two orthographic projections on the substrate plane. The four-coupled stacked transformer adopts a multi-layer metal three-dimensional cross-connection layout. The vertical stacking of the two windings of the same transformer enhances electromagnetic coupling and has the advantages of low loss, strong anti-interference, and good high-frequency characteristics.

[0029] This embodiment enables the implementation of two originally independent transformers within the same on-chip region, thereby supporting the physical stacking of the forward and reverse links in a bidirectional variable gain amplifier. Compared to the conventional scheme of directly stacking two transformers, the figure-eight inner winding reduces the undesired mutual inductance between the outer loop winding and the figure-eight inner winding through flux cancellation of the two local loop traces on the left and right. This allows the two signal links to maintain good electrical isolation even when physically close, thereby reducing the passive network area of ​​the bidirectional variable gain amplifier, which is of great significance for reducing the millimeter-wave front-end area.

[0030] Example 2: In existing technologies, the design of multi-coupled stacked transformers typically employs a manual design approach, modeling the transformer architecture using a Cartesian coordinate system. This involves, for example, directly moving the coordinates of certain vertices, endpoints, or corners. While this method is intuitive, simple, and aligns with manual design habits, the transformer winding topology is a standardized octagon, resulting in poor flexibility and limiting the degrees of freedom in electromagnetic coupling. Under tight on-chip space requirements, this leads to low electromagnetic coupling efficiency during multi-coupled matching, and significant undesirable coupling can easily exist between the windings of the two transformer sets, preventing the bidirectional variable gain amplifier from achieving excellent bidirectional performance.

[0031] Furthermore, multi-coupled stacked transformer models in Cartesian coordinates have a high-dimensional parameter space, making manual tuning exceptionally difficult, challenging to find the optimal solution, and time-consuming. For example, a four-coupled stacked transformer typically requires attention to 15 performance indicators (4 winding inductances + 6 coupling coefficients + 4 Q values ​​+ area). The mapping between the parameter space and the indicators is 26 × 15 = 390, meaning that designers have 390 possible scenarios to consider when tuning parameters. This makes it difficult for designers to decide which parameter to adjust to achieve the desired result. For instance, changing the line width of a coil not only affects its own winding inductance and Q value but also indirectly affects the inductance of other coils through the coupling coefficient. Simultaneously, design rule checking (DRC) issues must be considered, leading to long design times, typically measured in weeks.

[0032] Based on this, this embodiment provides an automated design method for a four-coupled stacked transformer, used in the four-coupled stacked transformer of Embodiment 1. For example... Figure 2 As shown, the method includes: Step S1, using the coordinates of the geometric center point of the first coupling group in the rectangular coordinate system Construct a polar coordinate system with the origin, and set N polar angles, where N is a positive integer; in the polar coordinate system, the polar angle is defined as horizontal to the right. The direction of the polar axis is also the positive x-axis direction in a Cartesian coordinate system. The N polar angles can be set at equal or unequal intervals. The N polar angles are distributed within the polar angle range. Inside.

[0033] Preferably, when both the first coupling group and the second coupling group are mirror-symmetrical about the polar axis, then both the first coupling group and the second coupling group are mirror-symmetrical about both sides of the polar axis, within the polar angle range. A total of N / 2 polar angles are set, and the polar angle range is obtained based on the mirror axis symmetry relationship. The remaining N / 2 polar angles, where N is an even number greater than or equal to 2, simplify the design and reduce the amount of computation.

[0034] In one example, both the first coupling group and the second coupling group are mirror-symmetric, such as... Figure 3 As shown, N is 8, and each coupling group actually generates 8 polar angles. Each polar angle is represented as: ; For polar angle indexing, eight polar angles are set at equal intervals. Among them, to These are 22.5°, 67.5°, 112.5°, and 157.5° respectively, located above the x-axis (polar axis), i.e., the polar angle range. Located below the x-axis, i.e., within the polar angle range. within to The angles are 202.5°, 247.5°, 292.5°, and 337.5° respectively. to Obtained by mirroring.

[0035] Step S2: Construct design parameters, which include the orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, the polar radii of the second figure-eight inner loop winding in the polar coordinate system at N polar angles, and the linewidth of the first outer loop winding. Line width of the first figure-eight inner winding Line width of the second outer loop winding Line width of the second figure-eight inner winding The offset of the geometric center point of the second coupling group relative to the geometric center point of the first coupling group .

[0036] In this embodiment, the first outer loop winding is in the... The polar radius of each polar angle is expressed as The first figure-eight inner winding is in the first The polar radius of each polar angle is expressed as The second outer loop winding is in the first... The polar radius of each polar angle is expressed as The second figure-eight inner winding is in the first... The polar radius of each polar angle is expressed as , Therefore, under normal circumstances, especially when the first coupling group and the second coupling group are not mirror-symmetric, a total of 4N+5 design parameters are included.

[0037] Preferably, when both the first coupling group and the second coupling group are mirror-symmetrical, the orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, and the orthographic projection of the second figure-eight inner loop winding in the polar coordinate system, are placed in the polar angle interval. The polar radii of the N / 2 polar angles within the layout file are used as design parameters. During layout file generation, based on the mirror axis symmetry relationship, the orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, as well as the orthographic projection of the second figure-eight inner loop winding in the polar coordinate system within the polar angle intervals, are automatically obtained according to the following polar radius transformation relationship. The polar radius is calculated using N / 2 polar angles within the range, thus reducing the number of design parameters to 2N+5. The polar radius conversion relationship is as follows: ; ; in, Indicates polar angle interval Polar index within; of N polar angles, the first... The polar angle and the first Each polar angle is mirror-symmetric. This indicates that the first outer loop winding is in the... The polar radius of each polar angle, This indicates that the first figure-eight inner winding is in the... The polar radius of each polar angle, This indicates that the orthographic projection of the second outer loop winding in the polar coordinate system is at the _th The polar radius of each polar angle, This indicates that the orthographic projection of the second figure-eight inner winding in the polar coordinate system is at the _th The polar radius of each polar angle. This indicates that the first outer loop winding is in the... The polar radius of each polar angle, This indicates that the first figure-eight inner winding is in the... The polar radius of each polar angle, This indicates that the orthographic projection of the second outer loop winding in the polar coordinate system is at the _th The polar radius of each polar angle, This indicates that the orthographic projection of the second figure-eight inner winding in the polar coordinate system is at the _th The polar radius of each polar angle.

[0038] In this embodiment, the layout file is not limited to GDS (Graphic Data System) layout file, GDSII (Graphic Data System II) layout file, OASIS (Open Artwork System Interchange Standard) layout file, or LEF (Library Exchange Format) layout file.

[0039] In the above example, both the first coupling group and the second coupling group are mirror-symmetric, and N is 8. The orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, and the orthographic projection of the second figure-eight inner loop winding in the polar coordinate system, are plotted at the polar angle. polar angle polar radius , , , , , , , , , , , , , , , There are a total of 21 design parameters, which can be combined and expressed as follows: : .

[0040] In this embodiment, since the first coupling group and the second coupling group are stacked vertically, to simplify the design, an independent polar coordinate system is no longer set for the second coupling group. Instead, an offset is introduced based on the polar coordinate system of the first coupling group. Therefore, the geometric center of the second coupling group is: .

[0041] Therefore, in the layout file generation, based on the orthographic projection of the second outer loop winding in the polar coordinate system and the orthographic projection of the second figure-eight inner loop winding in the polar coordinate system, the polar radius and offset at each polar angle are calculated. It can convert and obtain the polar radii of the second outer loop winding and the second figure-eight inner loop winding in the polar coordinate system of the second coupling group at N polar angles.

[0042] In this embodiment, the polar radius variable of the outer loop winding can be used to control the main outline, coverage area, and outer loop-outer loop main coupling of the first and second outer loop windings; the polar radius variable of the figure-eight inner loop winding can be used to control the local loop trace size, left and right local loop trace area, and inner loop-inner loop main coupling of the two figure-eight inner loops. arrive The optimizer controls the metal losses, Q-value, and manufacturability of different groups and windings; the offset controls the relative position between the first and second coupling groups, thus affecting outer-to-outer-coil coupling, inner-to-inner-coil coupling, and undesired outer-to-inner-coil coupling. Compared to directly optimizing Cartesian coordinate vertices, these variables have clear physical meanings and are more suitable as optimizer inputs.

[0043] Step S3 involves finding the optimal combination of design parameters within the design parameter constraint space, with the goal of minimizing the objective function value. The design parameter constraint space refers to the numerical constraint range of all design parameters, defined by the upper and lower limits of their values. Specifically, multiple design parameter combinations are randomly generated within the constraint space, or multiple combinations are generated by iterating through the constraint space step by step. A layout file for a four-coupled stacked transformer is generated based on each design parameter combination. Geometric constraints are checked on the layout files, and electromagnetic simulation is performed on the layout files that pass the geometric constraint check to obtain electromagnetic simulation data. The objective function value is calculated based on the electromagnetic simulation data. The design parameter combination with the minimum objective function value is selected as the optimal design parameter combination.

[0044] In this embodiment, the geometric constraints include: ; ; ; ; ; in, , These represent the minimum and maximum pole radii of the outer loop winding, respectively. , This indicates that the first outer loop winding or the second outer loop winding is in the... The polar radius of each polar angle. , These represent the minimum and maximum pole radii of the figure-eight inner winding, respectively. , This indicates that the first figure-eight inner winding or the second figure-eight inner winding is in the... The polar radius of each polar angle. This indicates the minimum pole radius deviation between the outer loop winding and the figure-eight inner loop winding. This indicates the maximum line width of the outer loop winding. This indicates the minimum line width of the figure-eight inner winding. , This indicates the lower limit and upper limit of the metal trace width. Indicating the fourth in a four-coupled stacked transformer The line width of each differential winding Indicates the winding index. . This indicates the minimum spacing between processes within the same metal layer. Indicates the adjacent first and second layers in the same metal layer The first differential winding and the first The actual spacing between the boundaries of the differential windings .

[0045] In this embodiment, to improve the accuracy of the optimal design parameter combination, automated iteration is used to obtain a four-coupled stacked transformer that meets the comprehensive performance requirements of a millimeter-wave bidirectional variable gain amplifier. Preferably, in step S3, Bayesian optimization, genetic algorithm, particle swarm optimization, random search algorithm, or local search algorithm is used to find the optimal design parameter combination within the design parameter constraint space with the goal of minimizing the value of the objective function.

[0046] For example, when using a random search algorithm, a combination of design parameters is randomly generated within the design parameter constraint space and taken as the current optimal solution. The objective function of the four-coupled stacked transformer using the current optimal solution's design parameters is calculated, and this value is taken as the current optimal value. The design parameter constraint space is cyclically sampled. For each sampled design parameter combination, the objective function of the four-coupled stacked transformer using the sampled design parameter combination is calculated. The calculated objective function value is compared with the current optimal value, and the smaller one is selected as the new current optimal value, thus updating the current optimal solution. After reaching a preset number of iterations, the current optimal solution is output as the optimal design parameter combination. When using a local search algorithm, a greedy strategy can be adopted, searching only within the neighborhood of the current optimal solution. Similarly, the objective function value is taken as the current optimal value. The specific process is existing technology and will not be elaborated here.

[0047] For example, when using a genetic algorithm, multiple combinations of design parameters are randomly generated as individuals within the design parameter constraint space to obtain an initial population. The objective function is used as the fitness function, and selection, crossover, mutation, and generation of the next generation are performed according to the existing genetic algorithm execution process. This process is iterated until the population converges, and the individual with the lowest fitness is selected as the optimal combination of design parameters. Similarly, when using a particle swarm optimization algorithm, a combination of design parameters is used as a particle, and the objective function is used as the fitness function. The optimal combination of design parameters is obtained according to the existing particle swarm optimization algorithm process, which will not be elaborated further here.

[0048] Preferably, this embodiment uses a Bayesian optimization method to obtain the optimal combination of design parameters. Specific steps include: Step 1: Generate M combinations of design parameters within the design parameter constraint space using Latin hypercube sampling or uniform random sampling methods, and use them as the initial training set, where M is a positive integer.

[0049] Step 2: Generate the layout file corresponding to the four-coupled stacked transformer based on each design parameter combination in the training set. Perform geometric constraint checks on the layout files. Perform electromagnetic simulation on the layout files that pass the geometric constraint check to obtain electromagnetic simulation data. Obtain the four-port differential impedance matrix based on the electromagnetic simulation data. If the layout file fails the geometric constraint check and the Design Rule Check (DRC), remove the design parameter combination from the training set to save simulation time.

[0050] Step 3: Calculate the objective function based on the four-port differential impedance matrix for each design parameter combination in the training set. The objective function includes at least one of five factors: differential winding inductance error, main coupling error, undesired coupling between the outer loop winding and the figure-eight inner winding, Q-value penalty, and layout file boundary violation penalty. The differential winding includes a first outer loop winding, a second outer loop winding, a first figure-eight inner winding, and a second figure-eight inner winding. The objective function is used as the optimization target to meet the comprehensive millimeter-wave performance requirements, such as wideband gain flatness, minimum noise figure, and port matching.

[0051] Step 4: Construct a Gaussian Process (GP) regression surrogate model. The regression surrogate model outputs the predicted mean and predicted variance of the objective function for the unknown combination of design parameters. Specifically, the covariance function of the Gaussian process can use the Matrn kernel function to accommodate possible nonlinear abrupt changes in the electromagnetic simulation results.

[0052] Step 5: Construct the acquisition function, prioritizing the Expected Improvement (EI) acquisition function. By globally maximizing this function (using a multi-starting-point gradient ascent algorithm), the parameter points that maximize the improvement in the predicted mean and variance of the objective function are obtained. These are the next set of design parameter combinations for electromagnetic simulation. This combination is added as a sample to the training set, and steps 2 through 5 are returned for execution until the termination iteration condition is met. The termination iteration condition is not limited to reaching the preset maximum number of iterations. The design parameter combination that minimizes the objective function value is selected from the training set as the optimal design parameter combination.

[0053] In this embodiment, as Figure 4 As shown, the calculation process for the objective function value of each design parameter combination includes: Step S31: Generate the layout file of the four-coupled stacked transformer based on the combination of design parameters.

[0054] Preferred, such as Figure 5 As shown, when both the first coupling group and the second coupling group are mirror-symmetric, step S31 includes: Step S311: Based on the design parameter combination and N polar angles, obtain N layout generation points for the first outer ring broken line winding, N layout generation points for the first figure-eight inner ring winding, N layout generation points for the second outer ring broken line winding, and N layout generation points for the second figure-eight inner ring winding in the rectangular coordinate system.

[0055] In the process of generating layout files from design parameters, it is necessary to first convert all polar radius variables and their corresponding polar angles into layout generation points in a Cartesian coordinate system. It should be noted that the layout generation points are not additional optimization variables, but rather intermediate geometric points calculated from the N polar angles and polar radii of the first outer loop winding, the second outer loop winding, the first figure-eight inner loop winding, and the second figure-eight inner loop winding. These points are used to determine the critical positions of the winding (metal wire) centerlines.

[0056] For example, when N is 8, for the first coupling group, the first outer loop winding and the first figure-eight inner loop winding are... Each map generation point is represented as follows: and : ; ; For the second coupling group, the second outer loop winding and the second figure-eight inner loop winding are... Each map generation point is respectively and for: ; ; in, polar radius , , , Determined by the mirror axis symmetry relationship. Represents the cosine function. This represents the sine function. This represents the coordinates of the geometric center point of the first coupling group in a rectangular coordinate system. This represents the coordinates of the geometric center point of the second coupling group in a rectangular coordinate system.

[0057] Step S312: Connect the N layout generation points of the first outer ring zigzag winding and the second outer ring zigzag winding in sequence according to the 45° routing rule to obtain the metal routing of the first outer ring zigzag winding and the second outer ring zigzag winding.

[0058] For example, four differential windings are positioned at pole angles. polar angle Eight map generation points in the direction are used simultaneously to Indicates. For example... Figure 6 As shown, for the second coupling group with the port on the right, the second outer loop broken winding is connected in ascending order of polar angle to obtain the layout generation point connection order (i.e., point sequence) of the second outer loop broken winding. for: ; For the first coupling group with the port located on the left, the connection order (i.e., point sequence) of the first outer loop broken-line winding layout generation points. Through the Obtained by cyclic translation, as follows: .

[0059] Step S313: Connect the N layout generation points of the first figure-eight inner winding according to the first preset connection sequence and 45° routing rule to obtain the first local loop routing and the second local loop routing; connect the first local loop routing and the second local loop routing using the intersecting first center bridging routing and the second center bridging routing, and use the under-hole metal layer and via connection method in the conflict area of ​​the first center bridging routing and the second center bridging routing.

[0060] Step S314: Connect the N layout generation points of the second figure-eight inner winding according to the second preset connection sequence and 45° routing rule to obtain the third local loop routing and the fourth local loop routing; connect the third local loop routing and the fourth local loop routing using the intersecting third center bridging routing and the fourth center bridging routing, and use the under-mount metal layer and via connection method in the conflict area of ​​the third center bridging routing and the fourth center bridging routing.

[0061] In this embodiment, as Figure 6 As shown, the figure-eight inner windings are not connected in a single circumferential sequence, but rather the layout connection points are rearranged to form two local loop traces on the left and right sides and two center bridging traces. For the second coupling group with the port on the right, the second preset connection sequence of the second figure-eight inner winding corresponds to the point sequence... It can be written as: ; For the first coupling group with the port on the left, the point sequence corresponding to the first preset connection order of the first figure-eight inner winding. It can be written as: ; in, , The connecting section that spans the upper and lower half-planes, i.e., the center bridging cable, for example... and This is the source of the central bridging region of the figure-eight inner winding. When the actual layout file is generated, the connection points between any two adjacent layouts are still generated as polylines according to the 45° routing rule. Therefore, the final routing of the two figure-eight inner windings may have more than 8 sides (segments), while maintaining the topology of the left and right local loop routing and the central bridging routing of the two figure-eight inner windings.

[0062] like Figure 8 As shown, a local bridging avoidance structure is set for the cross-bridge area of ​​the figure-eight inner winding. The purpose is not to introduce new circuit modules, but to solve local design rule checking (DRC) issues such as cross-layer connection of the center jumper trace of the figure-eight inner winding, vias close to corners, and center jumper traces close to the slant side of the outer winding when generating the layout file. Figure 8 The central bridging section and local chamfers in the diagram can both be understood as the representation of the bridging and avoidance structure in the specific layout.

[0063] Suppose that the section of the figure-eight inner winding that needs to be bridged is generated from the layout point. Connect to the layout generation point The center of the coupling group is , The x-axis coordinate of the coupling group center is given by [x], and the half-width of the bridging window is D. The bridging window displays the intersection of two center-bridging traces. D is determined by the trace width, via size, and minimum process spacing, and is not used as a design parameter. To avoid center-bridging traces directly passing through the center area, the original traces can be connected. Replace with the following bridging path: ; in: auxiliary points ; auxiliary points ; auxiliary points ; auxiliary points ; Represents a symbolic function used for extraction. The sign of the internal variable. , Represents the map generation point The x-coordinate and y-coordinate in a rectangular coordinate system. , Represents the map generation point The x-coordinate and y-coordinate in a rectangular coordinate system.

[0064] The above bridging path starts from the original map generation point. Enter the bridging window boundary laterally, complete the bridging along the vicinity of the bridging window boundary, and finally return laterally to the target layout generation point. . The central bridging route (third central bridging route) can be connected by a submerged metal layer and vias according to the interlayer conflict situation, thereby geometrically forming a cross bridge at the center of the figure-eight inner winding without introducing additional optimization variables.

[0065] To avoid the right-angle bend in the bridging path being close to the hypotenuse of the outer loop winding, and to avoid the current congestion effect caused by the right-angle bend, the right-angle bend is replaced with a 45° or 135° chamfer segment, i.e., execution... Figure 8 The chamfer avoidance shown is illustrated. Let the original right-angle bend be auxiliary point B1, and cut equal lengths from the two metal wires forming the bend. (Chamfer length) forms the chamfer, and the two endpoints after chamfering are written as: Original path Replace with Since the original angle is horizontal / vertical on both sides, the resulting sections are cut to the same length. This refers to a 45° or 135° chamfered section.

[0066] The chamfer length is determined by the safety distance between the bridging section and the hypotenuse of the adjacent broken-line outer winding. Safety distance for: ; in, , These represent the line widths of the inner figure-eight winding segment and the outer zigzag winding segment in the coupling group, respectively. This represents the minimum spacing between processes within the same metal layer. Chamfer length. satisfy: ; ; in, This indicates the maximum available length for chamfering near the bend. Indicates the chamfer length. The bridging center line of the figure-eight inner winding (i.e.) Figure 8 (Center line of the bridge window). This indicates the center line of the outer loop winding adjacent to the figure-eight inner loop winding. This represents the minimum distance between two centerlines. When actually generating the layout file, the smallest distance that satisfies the above safety distance is selected first. This reduces disturbances to the original bridging path, current path length, and local parasitic parameters.

[0067] Meanwhile, cross-layer vias are not placed directly at the chamfer tip or right-angle bend, but rather offset a certain distance along the bridging path to avoid insufficient local spacing between the via surrounding layer and the metal of the bend or outer loop winding. The aforementioned bridging, chamfering, and via offset are all determined by the layout generation point, linewidth, process spacing, and the position of adjacent outer loops, ensuring the correctness of the generated layout file without adding additional optimization variables.

[0068] In this preferred embodiment of the first example, for two adjacent map generation points in the first and second quadrants of the rectangular coordinate system... , The process of implementing the above 45° routing rule for wiring connections is as follows: Figure 7 As shown, it includes: If the map generation point and map generation points If the angle between the line connecting the two points and the positive x-axis is a multiple of 45°, then directly connect the two adjacent plot generation points. Map generation point Map generation point Coordinates are Map generation point Coordinates are .

[0069] If the map generation point and map generation points If the angle between the line connecting the points is not a multiple of 45° and the positive x-axis, then from the point where the layout is generated... Starting from the map generation point, first follow a diagonal line at a positive or negative 45° angle, then follow the axial line to obtain diagonal candidate transition points. Starting by traversing the axis and then following a 45° or -45° diagonal line, candidate transition points along the axis are obtained. Both of these methods of constructing candidate transition points can guarantee... To the oblique candidate transition point / axial candidate transition point, and from the oblique candidate transition point / axial candidate transition point to... All are line segments in directions that are multiples of 45°.

[0070] Specifically, determine the map generation point. and map generation points The method to determine whether the angle between the line connecting the x-axis and the positive x-axis is a multiple of 45° is as follows: Calculate the map generation point and map generation points x-axis coordinate deviation and y-axis coordinate deviation , ;like , or Then the map generation point and map generation points The angle between the line connecting these points and the positive x-axis is already a multiple of 45°, so a direct connection is sufficient. If the above condition is not met, it indicates that the layout generation point... and map generation points The angle between the line connecting the two axes and the positive x-axis is not a multiple of 45°, so a transition point needs to be inserted between them. This transition point is not a new optimization variable; it is determined by... , And the derived geometric points determined by the angular interval in which they are located.

[0071] Specifically: Obtain symbols , symbols Calculate the minimum deviation And constructing oblique candidate transition points according to the above method. and axial candidate transition points : ; ; ; .

[0072] If two adjacent map generation points , Located in the first quadrant and the second quadrant respectively, such as Figure 3 In the 67.5° and 112.5° directions, the candidate transition point that is furthest from the x-axis of the rectangular coordinate system among the oblique and axial candidate transition points is taken as the transition point. Connect the map generation points in sequence Transition point and map generation points Since the polar x-axis of both the first and second coupling groups is parallel to the global x-axis of the rectangular coordinate system, and the ordinate of their origins is 0, let the first distance... ,therefore: ; The function represents the transition point from the oblique direction. and axial candidate transition points In the middle, filter out those that make the first distance The candidate transition point that is maximized is taken as the transition point. This rule prioritizes moving the top bridging segment away from the x-axis, avoiding the formation of inwardly concave sharp corners between the two upper half-zone layout generation points, and even causing short circuits in the figure-eight inner winding and outer loop winding.

[0073] If two adjacent map generation points , Located in the same quadrant, for example Figure 3 In the middle, at the 22.5° and 67.5° directions, or at the 112.5° and 157.5° directions, the candidate transition point will be obliquely oriented. and axial candidate transition points The point furthest from the y-axis in the Cartesian coordinate system is used as the transition point. Connect the layout generation points sequentially. Transition point and map generation points ;in, This indicates the index of the point where the map was generated.

[0074] For the first coupling group, let the second distance be... For the second coupling group, let the second distance be... ,therefore: transition point ,at this time, The function represents the transition point from the oblique direction. and axial candidate transition points In the middle, filter out those that make the second distance The candidate transition point that is maximized is selected as the transition point. This rule prioritizes outward expansion of polylines within the same quadrant, preventing local polylines from contracting towards the center. The lower half of the path is generated by mirroring the upper half; using the absolute value of the distance from the coordinate axis ensures consistency between the upper and lower mirror images.

[0075] The aforementioned transition point rule applies to all outer loop windings and all figure-eight inner loop windings. Although the transition point causes the winding traces to exceed eight segments and makes the outer loop winding an irregular loop shape, while the figure-eight inner loop winding consists of two local loop traces on the left and right, forming a current path resembling the number "eight" through a bridging / crossover (center bridging trace) in the middle, the induced magnetic flux generated by the two local loop traces on the outer loop winding is approximately canceled out. Therefore, even with the introduction of the transition point, it can still be called a figure-eight inner loop winding. This treatment satisfies the DRC check according to design rules while effectively achieving higher degrees of freedom in the irregular loop winding shape through changes in the polar radius in the design parameters, while the number of design parameters remains unchanged.

[0076] Step S32: Perform a geometric constraint check on the layout file. For layout files that pass the geometric constraint check, perform electromagnetic simulation to obtain electromagnetic simulation data. Based on the electromagnetic simulation data, obtain the four-port differential impedance matrix. Layout files that fail the geometric constraint check are not subjected to electromagnetic simulation.

[0077] In this embodiment, the design parameters are dimensional parameter vectors. The optimization process involves embedding an electromagnetic closed-loop. The optimization goal is not to achieve strong coupling of all four differential windings, but rather to simultaneously satisfy the following three conditions: First, the coupling between the two outer loop windings satisfies the energy transfer and impedance transformation requirements of the first transformer; second, the coupling between the two figure-eight inner windings satisfies the energy transfer and impedance transformation requirements of the second transformer; third, the coupling between the outer loop windings and the figure-eight inner windings is limited to a small range to ensure that the forward and reverse links, although physically stacked, are as electrically independent as possible.

[0078] Electromagnetic simulation results can be read in two ways. The first method involves setting single-ended ports at both ends of the four differential windings (first outer loop winding, second outer loop winding, first figure-eight inner winding, and second figure-eight inner winding), for a total of eight single-ended ports, resulting in an S8P file (eight-port scattering parameter data file). The S8P file is then converted into an eight-port single-ended admittance matrix. Then, through the differential port transformation matrix The four-port differential admittance matrix is ​​obtained. Finally, the four-port differential impedance matrix is ​​obtained. : ; .

[0079] The second method involves directly setting up four differential ports in the electromagnetic simulator, obtaining an S4P file (four-port scattering parameter data file), and then directly converting it into a four-port differential impedance matrix. Both methods ultimately yield a four-port differential impedance matrix defined under the same port. At the target frequency f, let the angular frequency... Differential impedance matrix elements Indicates the first The first differential winding and the first Mutual impedance between differential windings Indicates the first The self-impedance of each differential winding The first outer loop winding, the second outer loop winding, the first figure-eight inner loop winding, and the second figure-eight inner loop winding are all differential windings. Calculate the following parameters: No. The equivalent inductance of each differential winding: ; No. Quality factor (Q value) of each differential winding: ; No. The first differential winding and the first Magnetic coupling coefficient between the differential windings: ; in, Indicates the first The imaginary part of the self-impedance of each differential winding. Indicates the first The real part of the self-impedance of each differential winding; Indicates the first The self-impedance of each differential winding; This indicates taking the geometric mean. The sign of the inductance is determined by the polarity of the differential port. For broadband designs, the equivalent inductance can be calculated at multiple frequency points. Quality Factor and magnetic coupling coefficient The average, maximum error, or minimum value.

[0080] Step S33: Calculate the value of the objective function based on the four-port differential impedance matrix. The objective function includes the differential winding inductance error. Main coupling error Undesired coupling between the outer loop winding and the figure-eight inner winding Q-value penalty Penalty for map files exceeding boundaries At least one of the five items is required, and the differential winding includes a first outer loop winding, a second outer loop winding, a first figure-eight inner loop, and a second figure-eight inner loop.

[0081] Preferably, the objective function ; ; in, This represents the average error of the equivalent inductance of each differential winding deviating from its respective target inductance value; This indicates the main coupling between the first outer loop winding and the second outer loop winding. The error deviating from the target value of the main coupling, and the main coupling between the first figure-eight inner winding and the second figure-eight inner winding. The sum of errors deviating from the main coupling target value; This indicates the undesired coupling between the outer loop winding and the figure-eight inner loop winding; This represents the penalty for a Q value falling below the target Q value; the penalty size can be customized. Indicates area or offset The penalty for causing the layout file to exceed the preset layout boundary can be customized in size. This represents the magnetic coupling coefficient between the a-th outer loop winding and the b-th figure-eight inner loop winding, where a is the index of the outer loop winding and b is the index of the figure-eight inner loop winding. , These represent the first outer loop winding and the second outer loop winding, respectively. , These represent the first figure-eight inner winding and the second figure-eight inner winding, respectively. , , , , These represent the first, second, third, fourth, and fifth weights, respectively, and represent the objective function's weights on... , , , , The level of attention can be customized according to your needs.

[0082] This embodiment provides a polar coordinate modeling method for a four-coupled stacked transformer, which... Figure 1 The layout structure shown and Figure 3The design parameter variable system shown is directly transformed into optimizable parameters. When the first coupling group and the second coupling group are mirror-symmetric, the N fixed directions are composed of N / 2 independent polar angles in the upper half-plane and their x-axis mirror images, used to define the key polar coordinate directions of the outer loop winding and the figure-eight inner loop. The outer loop winding is generated according to the circumferential point sequence, and the figure-eight inner loop winding is generated by rearranging the point sequence to produce left and right local loop traces and center bridging traces, resulting in a non-intuitive shape topology that is difficult to directly draw by hand, with higher flexibility, more electromagnetic coupling degrees of freedom, improved main coupling efficiency, and suppression of undesirable coupling. Therefore, this modeling method neither restricts the final inner and outer coils to standard octagons nor arbitrarily moves the Cartesian coordinate vertices, but provides a continuous, manufacturable, and physically meaningful parameter space for electromagnetic closed-loop optimization while maintaining the figure-eight topology of the inner loop winding, port relationships, and DRC constraints checked by design rules.

[0083] Electromagnetic closed-loop simulation was performed on the layout file generated by the optimal combination of design parameters to obtain the electromagnetic closed-loop optimization results. Figure 9 The equivalent inductance curves of four differential windings (first outer loop winding, second outer loop winding, first figure-eight inner winding, and second figure-eight inner winding) as a function of frequency are shown. Figure 10 The curves showing the quality factor (Q value) as a function of frequency for four differential windings (first outer loop winding, second outer loop winding, first figure-eight inner winding, and second figure-eight inner winding) are presented. Both the equivalent inductance and the quality factor (Q value) meet the target requirements. Figure 11 The electromagnetic coupling coefficients between different differential windings are shown. It can be seen that the electromagnetic coupling coefficients of two differential windings belonging to the same transformer ( Figure 11 The K13 and K24 windings are relatively high. The electromagnetic coupling coefficient between the outer loop winding and the figure-eight inner winding is ( ). Figure 11 The values ​​of K14, K23, K34, and K12 are all less than 0.05, achieving a high degree of decoupling.

[0084] This embodiment establishes a continuous geometric parameterization and electromagnetic closed-loop optimization process. Through automated optimization algorithms such as automatic layout generation, electromagnetic simulation, extraction of equivalent inductance L / quality factor / electromagnetic coupling coefficient, and Bayesian optimization, the computer is allowed to handle high-dimensional problems. This makes it easier to automatically iterate and find the optimal four-coupled transformer structure that meets the requirements of the target circuit in a short time. This reduces the difficulty of manually designing stacked four-coupled transformers and improves the quality factor and design efficiency of passive structures.

[0085] The automated design method for four-coupled stacked transformers provided in this embodiment can improve the design efficiency and repeatability of four-coupled stacked transformers. It utilizes polar coordinate parameters to convert the outer loop winding, figure-eight inner loop, center distance, line width, spacing, ports, and bridging bridges into continuous geometric variables. Transition points are automatically generated using deterministic 45° routing rules to satisfy the layout file for DRC (Design Rule Check) inspection. This eliminates the need for repeated manual movement of layout points and for resetting port and bridging relationships each time.

[0086] This embodiment can improve the effective proportion of optimized samples. Since constraints such as minimum linewidth, minimum spacing, 45° transition points, local bridging avoidance, and chamfers can be checked during the design parameter generation stage, design parameter combinations that do not meet geometric constraints will not be included in electromagnetic simulation, saving simulation time. Compared with directly searching using rectangular coordinate points, this method generates fewer invalid structures such as self-intersections, short circuits, and unreachable ports.

[0087] This embodiment achieves superior overall circuit performance compared to the hand-crafted structure. The optimization objective is not merely to compare the equivalent inductance L, Q value, or electromagnetic coupling coefficient K of individual differential windings to empirically derived values, but also to consider outer-ring main coupling, inner-ring main coupling, outer-inner-ring isolation, Q value, area, and the gain, bandwidth, and phase parameters of the bidirectional variable gain amplifier circuit stage. Therefore, even if the equivalent inductance L or electromagnetic coupling coefficient K values ​​of some differential windings in the final optimized structure differ from those in the hand-crafted structure, as long as the Q value and circuit-level performance are superior, it should be considered a beneficial effect of the closed-loop optimization of this embodiment.

[0088] Example 3: This embodiment provides a millimeter-wave bidirectional variable gain amplifier, the circuit schematic of which is shown below. Figure 12 As shown, the corresponding chip layout diagram is as follows: Figure 13 As shown, the millimeter-wave bidirectional variable gain amplifier includes a first RF port, a first three-coupled balun, a first bidirectional fixed gain stage, a first four-coupled stacked transformer, a bidirectional variable gain amplification stage, a second four-coupled stacked transformer, a second bidirectional fixed gain stage, a second three-coupled balun, and a second RF port connected in sequence. Both the first and second four-coupled stacked transformers are four-coupled stacked transformers provided in Embodiment 1; or, both the first and second four-coupled stacked transformers are designed according to the automated design method for four-coupled stacked transformers provided in Embodiment 2.

[0089] Among them, the first three-coupled balun, the first four-coupled stacked transformer, and the second three-coupled balun are passive modules. The first bidirectional fixed-gain stage, the bidirectional variable-gain amplifier stage, and the second bidirectional fixed-gain stage are active modules. The first RF port and the second RF port are in the forward signal flow ( Figure 12 (green part) and reverse signal flow ( Figure 12It is used in the blue part. Figure 12 The forward and reverse signal flows represent the RF transmit and receive link signals, respectively. Except for the first RF port, the first triple-coupled balun, the second triple-coupled balun, and the second RF port, the processing circuits for the forward and reverse signal flows are completely independent in the first bidirectional fixed gain stage, the first quadruple-coupled stacked transformer, the bidirectional variable gain amplifier stage, the second quadruple-coupled stacked transformer, and the second bidirectional fixed gain stage, each with its own flow path.

[0090] This embodiment introduces a first four-coupling stacked transformer and a second four-coupling stacked transformer, comprising an outer loop winding and a figure-eight inner loop winding, into a millimeter-wave bidirectional variable gain amplifier. This allows the two sets of transformers required for the forward and reverse links to be physically stacked within the same compact passive region, while maintaining electrical isolation between the two signal links. It also improves the bandwidth, gain adjustment, and phase consistency of the bidirectional variable gain amplifier (VGA). The bidirectional variable gain amplifier (VGA) chip designed using this scheme has completed tape-out testing, proving the feasibility of the present invention.

[0091] When the millimeter-wave bidirectional variable gain amplifier in this embodiment processes a forward signal stream, its specific working principle is as follows: (1) First radio frequency port Used to receive single-ended radio frequency signals to be amplified.

[0092] (2) First three-coupling baron It is used to convert a single-ended radio frequency signal to be amplified into a differential signal with equal amplitude and opposite phase.

[0093] (3) First bidirectional fixed gain stage like Figure 12 As shown, transistors M1, M2, and M3 of the N-channel used for forward signal flow are turned on, with the source of transistor M3 grounded to form a tail current source. Transistors M30, M28, and M29 of the N-channel used for reverse signal flow are turned off.

[0094] The first and second terminals of the differential signal output coil of the first triple-coupled balun output differential signals V1+ and V1- with equal amplitude and opposite phase, respectively. The first terminal of the differential signal output coil of the first triple-coupled balun is connected to the gate of transistor M1 and the first terminal of the second capacitor C2, respectively. The second terminal of the differential signal output coil of the first triple-coupled balun is connected to the gate of transistor M2 and the first terminal of the first capacitor C1, respectively. The drain of transistor M1 is connected to the second terminal of the first capacitor C1 and terminal 1 of the first quadruple-coupled stacked transformer (the first terminal of the first outer loop winding of the first transformer), respectively. The source of transistor M1 is connected to the drain of transistor M3 and the source of transistor M2, respectively. The drain of transistor M2 is connected to the second terminal of the second capacitor C2 and terminal 2 of the first quadruple-coupled stacked transformer (the second terminal of the first outer loop winding of the first transformer), respectively.

[0095] Specifically, when the differential signal V1+ increases, the gate voltage of transistor M1 increases, the source-drain conduction capability of transistor M1 is enhanced, and the drain current of transistor M1 increases. Simultaneously, when the differential signal V1- decreases, the gate voltage of transistor M2 decreases, the source-drain conduction capability of transistor M2 weakens, and the drain current of transistor M2 decreases. Transistor M3 is the tail current source, and its drain current is constant, being the sum of the drain currents of transistors M1 and M2. Therefore, the increase in the drain current of transistor M1 equals the decrease in the drain current of transistor M2, resulting in an increase in the drain voltage of transistor M1 (terminal 1 of the first four-coupled stacked transformer) and a decrease in the drain voltage of transistor M2 (terminal 2 of the first four-coupled stacked transformer).

[0096] Conversely, when the differential signal V1+ decreases, the gate voltage of transistor M1 decreases, the source-drain conduction capability of transistor M1 weakens, and the drain current of transistor M1 decreases. Simultaneously, when the differential signal V1- increases, the gate voltage of transistor M2 increases, the source-drain conduction capability of transistor M2 strengthens, and the drain current of transistor M2 increases. The decrease in the drain current of transistor M1 is equal to the increase in the drain current of transistor M2, resulting in a decrease in the drain voltage of transistor M1 (terminal 1 of the first four-coupled stacked transformer) and an increase in the drain voltage of transistor M2 (terminal 2 of the first four-coupled stacked transformer).

[0097] Finally, an amplified differential voltage signal is output between terminals 1 and 2 of the first four-coupled stacked transformer.

[0098] (3) First four-coupled stacked transformer The differential voltage signal output from the first bidirectional fixed gain stage is input from terminals 1 and 2 of the first quad-coupled stacked transformer (i.e., the first outer loop winding of the first quad-coupled stacked transformer), and the isolated and amplified differential voltage signal is output from terminals 5 and 6 of the first quad-coupled stacked transformer (i.e., the second outer loop winding of the first quad-coupled stacked transformer).

[0099] (4) Bidirectional variable gain amplifier like Figure 12 As shown, transistors M8, M4, M5, M6, M7, M9, M10, M11, and M12 of the N-channel transistors used for forward signal flow are turned on, and the source of transistor M8 is grounded, forming a tail current source. Transistors M19, M20, M21, M22, M23, M24, M25, M26, and M27 of the N-channel transistors used for reverse signal flow are turned off.

[0100] Terminal 5 of the first four-coupling stacked transformer is connected to the first terminal of the third capacitor C3 and the first terminal of the fifth capacitor C5, respectively. The second terminal of the third capacitor C3 is connected to the gate of transistor M4, the bias power supply AVA, the gate of transistor M9, and the drain and source of transistor M10, respectively. The source of transistor M4 is connected to the drain of transistor M8, the source of transistor M5, the source of transistor M6, and the source of transistor M7, respectively. The drain of transistor M4 is connected to the drain of transistor M5 and terminal 5 of the second four-coupling stacked transformer (i.e., the first terminal of the second outer loop winding of the first four-coupling stacked transformer). The source and drain of transistor M9, the drain of transistor M10, the gate of transistor M5, and the first terminal of the fourth capacitor C4 are all connected to the first terminal of the third resistor R3. The second terminal of the third resistor R3 is connected to the bias power supply AVb. The second terminal of the fourth capacitor C4 is connected to the first terminal of the sixth capacitor C6 and terminal 6 of the first four-coupled stacked transformer. The second terminal of the sixth capacitor C6 is connected to the gate of transistor M7, the bias power supply AVA, the gate of transistor M11, and the drain and source of transistor M12. The drain and source of transistor M11, the gate of transistor M12, the second terminal of the fifth capacitor C5, and the gate of transistor M6 are all connected to the first terminal of the fourth resistor R4. The second terminal of the fourth resistor R4 is connected to the bias power supply AVb. The drains of transistors M6 and M7 are both connected to terminal 6 of the second four-coupled stacked transformer (i.e., the second terminal of the second outer loop winding of the first four-coupled stacked transformer).

[0101] Transistors M9, M10, M11, and M12 are transistors used as capacitors, such as... Figure 12As shown, the source and drain of the transistor are shorted together to serve as capacitor plates, and the gate serves as another capacitor plate. These are connected to bias power supplies AVA and AVb, respectively. Therefore, the capacitance value changes with the bias power supplies AVA and AVb.

[0102] Specifically, a bias voltage is set for the gate of transistor M8 to conduct its source and drain, with the source grounded to form a tail current source. The bias power supply AFa is set to be greater than the bias power supply AVb, making the source-drain conduction degree of transistor M4 greater than that of transistor M6, and making the source-drain conduction degree of transistor M7 greater than that of transistor M5.

[0103] Let the output voltage at terminal 5 of the first four-coupled stacked transformer be V2+, and the output voltage at terminal 6 be V2-. The AC component of the voltage signal V2+ reaches the gate of transistor M4 through the third capacitor C3, and reaches the gate of transistor M6 through the fifth capacitor C5.

[0104] When the AC component of the voltage signal V2+ increases, the source-drain conduction of transistor M4 and transistor M6 both increase. The increase in drain current of transistor M4 is greater than that of transistor M6. Therefore, at this time, the drain of transistor M4 draws more current from terminal 5 of the second four-coupled stacked transformer, significantly pulling down the voltage of terminal 5 of the second four-coupled stacked transformer. The drain of transistor M6 slightly pulls down the voltage of terminal 6 of the second four-coupled stacked transformer. At this point, the AC component of the voltage signal V2- reaches the gate of transistor M5 through the fourth capacitor C4 and the gate of transistor M7 through the sixth capacitor C6. Its AC component decreases, weakening the source-drain conduction of both transistor M5 and M7. However, the reduction in leakage current of transistor M7 is greater than that of transistor M5. Consequently, the pull-down effect of transistor M7's drain on terminal 6 of the second quad-coupled stacked transformer is significantly reduced, while the pull-down effect of transistor M5's drain on terminal 5 of the second quad-coupled stacked transformer is slightly reduced. Under these combined effects, the voltage at terminal 5 of the second quad-coupled stacked transformer is pulled down, and the voltage at terminal 6 of the second quad-coupled stacked transformer is raised, thus inverting and amplifying the differential voltage signals V2+ and V2-.

[0105] Similarly, when the AC component of the voltage signal V2+ decreases, the source-drain conduction of transistor M4 and transistor M6 both weaken. However, the decrease in the drain current of transistor M4 is greater than the decrease in the drain current of transistor M6. Therefore, at this time, the drain of transistor M4 draws less current from terminal 5 of the second quad-coupled stacked transformer, raising the voltage of terminal 5 of the second quad-coupled stacked transformer. The drain of transistor M6 also draws less current from terminal 6 of the second quad-coupled stacked transformer, raising the voltage of terminal 6 of the second quad-coupled stacked transformer, but the increase is less than the previous increase in the voltage of terminal 5 of the second quad-coupled stacked transformer. At this time, the AC component of the voltage signal V2- reaches the gate of transistor M5 through the fourth capacitor C4 and the gate of transistor M7 through the sixth capacitor C6. Its AC component increases, enhancing the source-drain conduction of both transistor M5 and M7. However, the increase in leakage current of transistor M7 is greater than that of transistor M5. Consequently, the pull-down effect of transistor M7's drain on terminal 6 of the second four-coupled stacked transformer is significantly enhanced, while the pull-down effect of transistor M5's drain on terminal 5 of the second four-coupled stacked transformer is only slightly enhanced. Under these combined effects, the voltage at terminal 5 of the second four-coupled stacked transformer is raised, and the voltage at terminal 6 of the second four-coupled stacked transformer is pulled down, thus inverting and amplifying the differential voltage signals V2+ and V2-.

[0106] Bias power supplies AVA and AVb are voltage values ​​representing the gate control voltages of the variable gain amplifier stage in forward signal flow mode. Bias power supply AVA is the gate control voltage for transistors M5 and M6, and bias power supply AVb is the gate control voltage for transistors M4 and M7. The gain in forward signal flow mode is positively correlated with |AVa-AVb|; adjusting |AVa-AVb| allows for gain amplification and reduction.

[0107] (5) Second and fourth coupled stacked transformer The differential voltage signals V3- and V3+ output from the bidirectional variable gain amplifier are input from terminals 5 and 6 of the second quad-coupled stacked transformer (i.e., the second outer loop winding of the second quad-coupled stacked transformer), and the isolated and amplified differential voltage signals V4- and V4+ are output from terminals 1 and 2 of the second quad-coupled stacked transformer (i.e., the first outer loop winding of the second quad-coupled stacked transformer).

[0108] (6) Second bidirectional fixed gain stage like Figure 12As shown, transistors M13, M15, and M14 of the N-channel used for forward signal flow are turned on, and the source of transistor M15 is grounded, forming a tail current source. Transistors M16, M17, and M18 of the N-channel used for reverse signal flow are turned off.

[0109] The second quad-coupled stacked transformer outputs differential signals V4- and V4+ with equal amplitude and opposite phase from terminals 1 and 2. Terminal 1 of the second quad-coupled stacked transformer is connected to the gate of transistor M13 and the first terminal of the eighth capacitor C8, respectively. The drain of transistor M13 is connected to the first terminal of the seventh capacitor C7 and the first terminal of the single-ended output coil of the second tri-coupled balun, respectively. Terminal 2 of the second quad-coupled stacked transformer is connected to the second terminal of the seventh capacitor C7 and the gate of transistor M14, respectively. The drain of transistor M14 is connected to the second terminal of the eighth capacitor C8 and the second terminal of the single-ended output coil of the second tri-coupled balun, respectively. The source of transistor M13 is connected to the drain of transistor M15 and the source of transistor M14, respectively.

[0110] Specifically, when the differential signal V4- increases, the gate voltage of transistor M13 increases, the source-drain conduction capability of transistor M13 strengthens, and the drain current of transistor M13 increases. Simultaneously, when the differential signal V4+ decreases, the gate voltage of transistor M2 decreases, the source-drain conduction capability of transistor M2 weakens, and the drain current of transistor M14 decreases. Transistor M15 is the tail current source, and its drain current is constant, being the sum of the drain currents of transistors M13 and M14. Therefore, the increase in the drain current of transistor M13 equals the decrease in the drain current of transistor M14. Consequently, the drain voltage of transistor M13 (at the first terminal of the differential signal output coil of the second triple-coupled balun) increases, while the drain voltage of transistor M14 (at the second terminal of the differential signal output coil of the second triple-coupled balun) decreases.

[0111] Conversely, when the differential signal V4- decreases, the gate voltage of transistor M13 decreases, the source-drain conduction capability of transistor M13 weakens, and the drain current of transistor M13 decreases. Simultaneously, when the differential signal V4+ increases, the gate voltage of transistor M14 increases, the source-drain conduction capability of transistor M14 strengthens, and the drain current of transistor M14 increases. The decrease in the drain current of transistor M13 equals the increase in the drain current of transistor M14. Therefore, the drain voltage of transistor M13 (at the first terminal of the differential signal output coil of the second triple-coupled balun) decreases, while the drain voltage of transistor M14 (at the second terminal of the differential signal output coil of the second triple-coupled balun) increases.

[0112] Finally, the amplified differential voltage signal is obtained at the first and second ends of the differential signal output coil of the second and third coupled balun.

[0113] (7) Second and third coupling Baron The differential voltage signals at the first and second ends of the differential signal output coil of the second triple-coupled balun are converted into single-ended radio frequency signals using a single-ended output coil.

[0114] (8) Second radio frequency port Output the single-ended radio frequency signal of the single-ended output coil of the second and third coupled balun.

[0115] When the millimeter-wave bidirectional variable gain amplifier of this embodiment processes the reverse signal flow, it uses Figure 12 The blue part of the circuit.

[0116] The single-ended RF signal to be amplified is input from the second RF port and converted into a differential signal through the second triple-coupled balun.

[0117] In the second bidirectional fixed-gain stage, transistors M13, M15, and M14 of the N-channel used for the forward signal flow are turned off, while transistors M16, M17, and M18 of the N-channel used for the reverse signal flow are turned on. The source of transistor M18 is grounded, forming a tail current source. Transistor M16... In the second four-coupled stacked transformer, the second transformer is working, and the first transformer is not working, meaning ports 3, 4, 7, and 8 are working, isolating and acquiring the differential signal and inputting it into the bidirectional variable-gain amplifier stage for amplification.

[0118] In the bidirectional variable gain amplifier stage, transistors M8, M4, M5, M6, M7, M9, M10, M11, and M12 of the N-channel used for the forward signal flow are turned off. Transistors M19, M20, M21, M22, M24, M25, M26, and M27 of the N-channel used for the reverse signal flow are turned on. The source of transistor M23 is grounded, forming a tail current source.

[0119] The differential signal, after being amplified in reverse phase by the bidirectional variable gain amplifier stage, is isolated and output to the first bidirectional fixed gain stage through the first four-coupled stacked transformer. The second transformer of the first four-coupled stacked transformer is working, while the first transformer is not working, i.e., ports 3, 4, 7, and 8 are working.

[0120] In the first bidirectional fixed gain stage, transistors M1, M2, and M3 of the N-channel used for forward signal flow are turned off, while transistors M30, M28, and M29 of the N-channel used for reverse signal flow are turned on. The source of transistor M30 is grounded, forming a tail current source.

[0121] The first bidirectional fixed gain stage amplifies the differential signal output from the first four-coupled stacked transformer, and converts the amplified differential signal into a single-ended radio frequency signal through the first three-coupled balun. The single-ended radio frequency signal is then output through the first radio frequency port.

[0122] The reverse signal flow processing circuits in the first bidirectional fixed gain stage, the bidirectional variable gain amplification stage, and the second bidirectional fixed gain stage have the same structure as the forward signal flow processing circuits, and their working principle is the same as that of the forward signal flow amplification principle, so they will not be described again here.

[0123] In reverse signal stream processing, such as Figure 12 As shown, the gain can be adjusted by regulating the bias power supplies BVa and BVb of the bidirectional variable gain amplifier stage (gain and...). (Positive correlation). The first and second bidirectional fixed gain stages, located on either side, provide base gain, input / output isolation, and drive capability.

[0124] When operating with a forward signal flow, the bidirectional variable gain amplifier stage employs an active cross-coupling structure. The gate signals of transistors M4 and M5 are differential signals, but their outputs are combined into a single path. Therefore, the currents on their gate-drain parasitic capacitances Cgd cancel each other out. Similarly, the currents on the gate-drain parasitic capacitances Cgd of transistors M6 and M7 cancel each other out, thus eliminating the phase degradation caused by the gate-drain parasitic capacitance Cgd. Likewise, when operating with a reverse signal flow, the currents flowing through the gate-drain parasitic capacitances Cgd of transistors M19 and M20, and transistors M21 and M22, achieve the same cancellation effect.

[0125] The millimeter-wave bidirectional variable gain amplifier provided in this embodiment achieves excellent bidirectional performance not only by completely separating the main bodies of the forward and reverse signal flow paths and shutting off the tail current source tubes of the other path when one path is working, but also by relying on the first and second quad-coupled stacked transformers. By decoupling the figure-eight inner winding and the outer broken-line winding controlled by polar coordinates, it achieves high coupling of energy in the same path, suppresses leakage of energy in different paths, and further isolates the coupling between the forward and reverse directions, thereby achieving excellent bidirectional performance.

[0126] After fabricating the millimeter-wave bidirectional variable gain amplifier into a chip, the chip's performance under forward and reverse signal flow was tested. Figure 14 The curves showing the relationship between the input signal frequency and S-parameters during forward signal flow are presented. Figure 15 The curve showing the relationship between the input signal frequency and the S21 parameter during forward signal flow is displayed. Figure 16 The curve showing the relationship between the input signal frequency and the relative phase during a forward signal flow is displayed. Figure 17The curves showing the relationship between the input signal frequency and the root mean square gain error and root mean square phase error during forward signal flow are presented. Figure 18 The curve showing the relationship between the input signal frequency and S-parameters during reverse signal flow is displayed. Figure 19 The curve showing the relationship between the input signal frequency and the S21 parameter during reverse signal flow is displayed. Figure 20 The curve showing the relationship between the input signal frequency and the relative phase during reverse signal flow is displayed. Figure 21 The curves showing the relationship between the input signal frequency and the root mean square gain error and root mean square phase error during reverse signal flow are illustrated. It can be seen that the millimeter-wave bidirectional variable gain amplifier chip in this embodiment exhibits excellent phase error performance within the gain adjustment range.

Claims

1. A four-coupled stacked transformer, characterized in that, include: The first coupling group includes a first outer loop winding with an irregular topological shape formed by connecting multiple conductive lines in sequence, and a first figure-eight inner loop winding that is spaced and surrounded by the first outer loop winding. The second coupling group, located below the first coupling group, includes a second outer loop winding with an irregular topological shape formed by connecting multiple conductive lines in sequence, and a second figure-eight inner loop winding that is spaced apart by the second outer loop winding; the orthographic projections of the first outer loop winding and the second outer loop winding on the substrate plane overlap completely or partially, and the orthographic projections of the first figure-eight inner loop winding and the second figure-eight inner loop winding on the substrate plane overlap completely or partially. The number of conductive lines in both the first outer loop winding and the second outer loop winding is greater than 8. Both the first figure-eight inner loop winding and the second figure-eight inner loop winding include two local loop traces with different topological shapes. The first outer loop winding and the second outer loop winding constitute the first transformer; The first figure-eight inner winding and the second figure-eight inner winding constitute the second transformer; The first figure-eight inner winding includes a first partial annular trace, a second partial annular trace, and a first center bridging trace and a second center bridging trace that intersect on the orthographic projection of the substrate plane. The second figure-eight inner winding includes a third partial annular trace, a fourth partial annular trace, and a third center bridging trace and a fourth center bridging trace that intersect on the orthographic projection of the substrate plane; The first outer loop winding, the first partial loop trace, the second partial loop trace, and the first center bridging trace are formed on the first metal layer, and the first center bridging trace is used to connect the first partial loop trace and the second partial loop trace. The second outer loop winding, the third partial loop trace, the fourth partial loop trace, and the second center bridging trace are formed on the second metal layer. The second center bridging trace is connected to the first partial loop trace and the second partial loop trace by means of a via. The third center bridging trace is formed on the third metal layer and is connected to the third local loop trace and the fourth local loop trace via vias; The fourth center bridging trace is formed on the fourth metal layer and is connected to the third local loop trace and the fourth local loop trace via vias.

2. The four-coupled stacked transformer according to claim 1, characterized in that, The ports of the first outer loop winding and the second outer loop winding are arranged opposite to each other, and the ports of the first figure-eight inner loop winding and the second figure-eight inner loop winding are arranged opposite to each other.

3. The four-coupled stacked transformer according to claim 2, characterized in that, The first coupling group is mirror-symmetric, and the second coupling group is mirror-symmetric.

4. An automated design method for a four-coupled stacked transformer, used for the four-coupled stacked transformer as described in any one of claims 1-3, characterized in that, The method includes: A polar coordinate system is constructed with the geometric center point of the first coupling group as the origin, and N polar angles are set, where N is a positive integer. The design parameters include the orthographic projections of the first outer loop winding, the first figure-eight inner loop winding, and the second outer loop winding in the polar coordinate system, the polar radii of the orthographic projections of the second figure-eight inner loop winding in the polar coordinate system at N polar angles, and also include the linewidths of the first outer loop winding, the first figure-eight inner loop winding, the second outer loop winding, the second figure-eight inner loop winding, and the offset of the geometric center point of the second coupling group relative to the geometric center point of the first coupling group; The goal is to minimize the value of the objective function by finding the optimal combination of design parameters within the design parameter constraint space. The calculation process for the objective function value of each design parameter combination includes: Layout files for a four-coupled stacked transformer are generated based on a combination of design parameters. The layout file is subjected to geometric constraint checks, and electromagnetic simulation is performed on the layout file that passes the geometric constraint checks to obtain electromagnetic simulation data. Based on the electromagnetic simulation data, a four-port differential impedance matrix is ​​obtained. The objective function is calculated based on the four-port differential impedance matrix. The objective function includes at least one of the following five items: differential winding inductance error, main coupling error, undesired coupling between the outer loop winding and the figure-eight inner loop winding, Q-value penalty, and layout file exceeding boundary penalty. The differential winding includes the first outer loop winding, the second outer loop winding, the first figure-eight inner loop winding, and the second figure-eight inner loop winding.

5. The automated design method for a four-coupled stacked transformer according to claim 4, characterized in that, By employing Bayesian optimization, genetic algorithms, particle swarm optimization, random search algorithms, or local search algorithms, the optimal combination of design parameters is found within the design parameter constraint space with the goal of minimizing the value of the objective function.

6. The automated design method for a four-coupled stacked transformer according to claim 4, characterized in that, When both the first coupling group and the second coupling group are mirror-symmetrical, in the polar angle interval A total of N / 2 polar angles are set, and the polar angle range is obtained based on the mirror axis symmetry relationship. The remaining N / 2 polar angles, where N is an even number greater than or equal to 2.

7. The automated design method for a four-coupled stacked transformer according to claim 6, characterized in that, The layout file for generating a four-coupled stacked transformer based on a combination of design parameters includes: Based on the design parameter combination and N polar angles, N layout generation points of the first outer ring broken line winding, N layout generation points of the first figure-eight inner ring winding, N layout generation points of the second outer ring broken line winding, and N layout generation points of the second figure-eight inner ring winding are obtained in the rectangular coordinate system. Connect the N layout generation points of the first outer ring broken line winding and the second outer ring broken line winding in sequence according to the 45° routing rule; The first local loop trace and the second local loop trace are obtained by connecting the N layout generation points of the first figure-eight inner ring winding according to the first preset connection sequence and 45° routing rule; the first local loop trace and the second local loop trace are connected by using the intersecting first center bridging trace and the second center bridging trace, and the under-hole metal layer and via connection method are used in the conflict area of ​​the first center bridging trace and the second center bridging trace. The second local loop trace and the fourth local loop trace are obtained by connecting the N layout generation points of the second figure-eight inner winding according to the second preset connection sequence and the 45° routing rule; the third local loop trace and the fourth local loop trace are connected by the intersecting third center bridging trace and the fourth center bridging trace, and the under-mount metal layer and via connection method are used in the conflict area of ​​the third center bridging trace and the fourth center bridging trace.

8. The automated design method for a four-coupled stacked transformer according to claim 7, characterized in that, For two adjacent map generation points located in the first and second quadrants of the rectangular coordinate system , The process of implementing the 45° routing rule includes: If the map generation point and map generation points If the angle between the line connecting the two points is a multiple of 45° with the positive x-axis, then directly connect the two adjacent plot generation points. , ; If the map generation point and map generation points If the angle between the line connecting the points is not a multiple of 45° and the positive x-axis, then from the point where the layout is generated... Starting from the map generation point, first follow a diagonal line at a positive or negative 45° angle, then follow the axial line to obtain diagonal candidate transition points. Start by following the axis and then follow a positive 45° or negative 45° diagonal line to obtain candidate transition points along the axis; If two adjacent map generation points , If the candidate transition points are located in the first quadrant and the second quadrant respectively, then the candidate transition point furthest from the x-axis of the rectangular coordinate system among the oblique candidate transition points and the axial candidate transition points is taken as the transition point. If two adjacent layout generation points are located in the first quadrant and the second quadrant respectively, then the candidate transition point is taken as the transition point. , If they are located in the same quadrant, the candidate transition point that is furthest from the y-axis of the rectangular coordinate system among the oblique candidate transition points and the candidate transition points of the axial direction will be taken as the transition point. Connect the layout generation points sequentially Transition points and map generation points ;in, This indicates the index of the point where the map was generated.

9. A millimeter-wave bidirectional variable gain amplifier, characterized in that, It includes a first RF port, a first three-coupled balun, a first bidirectional fixed gain stage, a first four-coupled stacked transformer, a bidirectional variable gain amplifier stage, a second four-coupled stacked transformer, a second bidirectional fixed gain stage, a second three-coupled balun, and a second RF port, which are connected in sequence. Both the first four-coupled stacked transformer and the second four-coupled stacked transformer are four-coupled stacked transformers as described in any one of claims 1-3; or, both the first four-coupled stacked transformer and the second four-coupled stacked transformer are obtained according to the automated design method for four-coupled stacked transformers as described in any one of claims 4-8.

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