Millimeter wave GSG high-frequency test probe and impedance self-matching method thereof

Abstract

The invention belongs to the technical field of communication, and particularly relates to a millimeter wave GSG high-frequency test probe and an impedance self-matching method thereof.The millimeter wave GSG high-frequency test probe comprises a probe base, a GSG probe body, a first-section conical CPW, an air bridge, a probe tip and an input transition unit; the GSG needle body is formed by arranging a signal needle and two grounding needles on a probe base in a GSG manner and fixing the signal needle and the two grounding needles in parallel; the first-section conical CPW is electrically connected with a signal pin of the GSG pin body; the probe tip and the front end of the head-section conical CPW are integrally formed; the input transition unit is coupled with the tail end of the GSG needle body and is matched with the contour to enable the GSG needle body and the input transition unit to keep transmission continuity; dynamic impedance self-matching of the probe structure is achieved, high-frequency reflection and modal coupling are effectively reduced, the bandwidth range, the signal stability and the repeated measurement consistency of millimeter wave testing are remarkably improved, meanwhile, high manufacturability and self-adaptive adjusting capacity are achieved, and the probe structure is suitable for popularization and application. The method is suitable for broadband test application of high-frequency chips, packaging interconnection and antenna arrays.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a millimeter-wave GSG high-frequency test probe and its impedance self-matching method. Background Technology

[0002] The rapid development of millimeter-wave communication and high-frequency testing technologies has placed significantly higher demands on the accuracy, stability, and bandwidth characteristics of RF probes. GSG (Ground-Signal-Ground) test probes have become one of the mainstream structures due to their ability to provide low parasitic inductance and capacitive coupling and achieve good signal integrity. In existing technologies, millimeter-wave GSG high-frequency test probes typically consist of a base, a GSG body, a transition line structure (such as a microstrip line or coplanar waveguide), a probe tip, and an input interface, used to establish a stable electrical connection between the chip under test (DUT) or high-frequency device and the test instrument. However, as test frequencies enter the gigahertz range, the influence of probe geometry, material distribution, and microstructure on impedance matching and energy transfer continuity increases dramatically, making it difficult for traditional structures to maintain stable matching across the entire bandwidth.

[0003] Most publicly available high-frequency GSG probes employ fixed geometric parameter designs, achieving matching within specific frequency bands by optimizing the pin spacing, the thickness ratio of the signal pin to the ground pin, the probe tip shape, and the metal layer thickness. For example, some technologies utilize a linear coplanar waveguide structure combined with parallel signal pins to reduce high-frequency reflections through a continuously tapered signal channel; other solutions incorporate a microbridge structure or dielectric transition layer above the ground pin to balance parasitic effects. While these structures exhibit good matching performance below 60 GHz, the electric field distribution between the probe tip and the transition section becomes extremely non-uniform at higher frequencies, where even minor geometric errors or manufacturing tolerances can cause significant shifts in port impedance. Because traditional probe designs primarily rely on static geometric optimization or empirical formula adjustments, lacking dynamic geometric inversion and adaptive shaping methods, automated impedance self-matching cannot be achieved for different test objects. Summary of the Invention

[0004] The main objective of this invention is to provide a millimeter-wave GSG high-frequency test probe comprising a probe base, a GSG needle body, a first-section tapered CPW, an air bridge, a probe tip, and an input transition unit. The GSG needle body consists of a signal needle and two grounding needles arranged in a GSG configuration and fixed side-by-side on the probe base. The first-section tapered CPW is electrically connected to the signal needle of the GSG needle body. The probe tip is integrally formed with the front end of the first-section tapered CPW. The input transition unit is coupled to the tail end of the GSG needle body. The final state of the probe tip and the front end of the first-section tapered CPW form a mating profile, which enables the GSG needle body, the first-section tapered CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching and maintains transmission continuity with the input transition unit.

[0005] Furthermore, the first conical CPW segment tapers continuously from wide to narrow along the test direction.

[0006] Furthermore, the first conical CPW has grounding channels on both sides, and an air bridge is used to bridge the grounding channels on both sides to form a return path.

[0007] Furthermore, the probe tip is used to establish a millimeter-wave contact area.

[0008] Furthermore, the contour design ensures a continuous transition between external power feeding and internal power transfer between the probe structure and the input transition unit.

[0009] An impedance self-matching method for a millimeter-wave GSG high-frequency test probe includes the following steps: Step 1: Establish a three-dimensional electromagnetic model including probe base, GSG needle body, first conical CPW, air bridge and probe tip. Acquire broadband port scattering data in an equally spaced sampling order and store them into a data sequence. At the same time, record the position trajectory of the port status point on the Smith circle to form the port status trajectory. Step 2: Use a matrix pencil to perform mode extraction on the data sequence, solve a set of complex exponential poles, and reconstruct the port scattering data based on the complex exponential poles to generate a list of characteristic modes. By analyzing the impulse response and field intensity peak position of each characteristic mode, the list of characteristic modes is divided into multiple response clusters belonging to specific components in the probe tip, the first conical CPW, and the air bridge, and response cluster identifiers are generated. Step 3: Perform probe tip geometry inversion based on the adjoint method, determine the candidate modification domain of the probe tip by calculating the geometric sensitivity map, and perform geometry update driven by the primitive library consisting of three primitive operations: cone surface micro-stretching, edge arcing and slope refinement within the candidate modification domain of the probe tip to form a geometry update path. Step 4: Using the geometric descent method on the Smith circle, port state point guided iteration is performed on the geometric update path. By executing combination primitives or adsorption primitives in different target neighborhoods, the port reflection index of the port state point reaches the preset matching level, and the matching profile of the probe tip final state and the front end of the first conical CPW is output.

[0010] Furthermore, in step two, the data sequence is divided into two groups of adjacent shifted data blocks of the same length according to the sampling order, forming two rectangular data structures; singular decomposition is performed on the first rectangular data structure to obtain the column space basis set, and the column space basis set is used to project the second rectangular data structure to form a system of linear equations for solving. The effective rank is determined based on the turning point of the difference between adjacent singular values ​​and the complex exponential poles are solved; the impulse response of each characteristic mode is reconstructed in the time domain and the peak arrival order is read along the direction from the probe tip to the input transition unit. The characteristic modes with the peak arrival order increasing in the direction are marked as propagation tags, and the characteristic modes with the peak arrival order decreasing in the direction are marked as radiation tags.

[0011] Furthermore, in step three, a forward excitation is applied to the port to obtain a forward field distribution, and a reverse phase equal-amplitude excitation is set at the port to obtain a companion field distribution. The forward field distribution and the companion field distribution are averaged on both sides of the grid surface, multiplied face by face, and the difference is obtained to obtain a geometric sensitivity map. After each primitive operation is completed, the set of poles of the complex exponential poles remains unchanged, and the modal coefficients are fitted with the minimum difference of two-segment sampling only on the new geometry to quickly reconstruct the port scattering data. If the angle between the port state point and the ray of the target point and the port state trajectory decreases, the current primitive operation is recorded and included in the geometric update path.

[0012] Furthermore, in step four, three target neighborhoods are set around the Smith circular target point from the outside to the inside. When the port state point is located in the outer target neighborhood, the first combination primitive, consisting of conical micro-stretching and synchronous convergence of the gap at the front end of the first conical CPW, is executed radially, with the two primitives alternating in a one-to-one ratio. When the port state point enters the middle target neighborhood, the second combination primitive, consisting of opening symmetrical micro-notches on both sides of the front end of the first conical CPW and slightly extending the bridging distance in the air bridge bridging area, is executed tangentially. When the port state point enters the inner target neighborhood, the adsorption primitive consisting of continuous edge arcing with the geometric sensitivity grid surface of the first position as the action surface is executed.

[0013] Furthermore, after each execution of the first combination primitive, the second combination primitive, or the adsorption primitive, the new position of the port state point is calculated in real time. When the reduction in arc length between the new position and the previous position reaches the preset matching level threshold, the geometric update path is fixed and the mating profile is output.

[0014] This invention discloses a millimeter-wave GSG high-frequency test probe and its impedance self-matching method, which has the following advantages: it can maintain stable transmission continuity and high repeatability in broadband millimeter-wave testing. By forming an integrated coupling structure of the GSG probe body, the first-segment tapered coplanar waveguide, and the air bridge, this invention effectively reduces parasitic coupling between the signal and grounding pins, and forms an adjustable fit profile between the probe tip and the front end of the first-segment tapered coplanar waveguide, enabling the probe to maintain a low-reflection impedance matching state in the high-frequency range. Compared with traditional fixed geometric probes, this invention generates a geometric sensitivity map through geometric inversion based on the adjoint method, which can automatically identify the local surface in the probe tip region that is most sensitive to impedance changes, and gradually perform geometric updates in a primitive-driven manner within the candidate modification domain of the probe tip, thereby establishing an accurate geometric update path. This update process is based on the mode decomposition of complex exponential poles, and can achieve synchronous convergence of electromagnetic response and geometric structure without external training or manual intervention. Furthermore, this invention employs a geometric descent method in the Smith circular space, closely linking the iterative movement of the port state point with geometric operations. Radial advancement, angular back-alignment, and edge adsorption are sequentially performed within the target neighborhood of the outer, middle, and inner layers, thereby achieving a preset matching level for the port reflection index within a finite number of steps. This method can stably reduce reflection loss across the entire frequency band, decrease multimode interference, and improve the phase consistency and amplitude linearity of signal transmission. Simultaneously, the dimensional changes of primitive operations are controlled within a manufacturable precision range, ensuring that the probe structure can be mass-produced using conventional microfabrication processes. Unlike traditional methods that rely on empirical adjustments or static parameter optimization, the self-matching algorithm of this invention performs real-time electromagnetic reconstruction in each round of geometric iteration, ensuring that the structural response remains dynamically consistent, greatly improving the convergence efficiency and reproducibility of the matching search. Attached Figure Description

[0015] Figure 1 This is a side view of the overall structure of the millimeter-wave GSG high-frequency test probe provided in an embodiment of the present invention; Figure 2 This is a detailed cross-sectional view of the mating contour of the probe tip and the front end of the first conical CPW provided in an embodiment of the present invention; Figure 3 A schematic diagram comparing the optimized trajectories of port states on a Smith chart, provided for embodiments of the present invention. Figure 4 This is a comparative schematic diagram showing the impact of an air bridge on the grounding current return path, provided for an embodiment of the present invention. Detailed Implementation

[0016] The method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0017] Example 1: A millimeter-wave GSG high-frequency test probe includes a probe base, a GSG needle body, a first-section tapered CPW, an air bridge, a probe tip, and an input transition unit. The GSG needle body consists of one signal needle and two grounding needles arranged in parallel on the probe base in a GSG configuration. The first-section tapered CPW is electrically connected to the signal needle of the GSG needle body. The probe tip is integrally formed with the front end of the first-section tapered CPW. The input transition unit is coupled to the tail end of the GSG needle body. The final state of the probe tip and the front end of the first-section tapered CPW form a mating profile. The mating profile allows the GSG needle body, the first-section tapered CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching and maintains transmission continuity with the input transition unit.

[0018] refer to Figure 1The millimeter-wave GSG high-frequency test probe of this invention includes, from left to right, an input transition unit (not shown in detail in the figure), a probe base, a ceramic support, a GSG needle body, a first-section tapered CPW, an air bridge, a probe tip, and a contact area with the test object. The probe base has a rectangular block structure, providing mechanical support and a fixing reference for the probe. The ceramic support is embedded in the right side of the probe base, and its ceramic material properties are represented by a cross-filled pattern, used to maintain dielectric stability in the area near the probe tip. The GSG needle body consists of three needles, represented by three parallel line segments in the figure, extending from left to right to the ceramic support area. The middle line segment represents the signal needle, represented by a thicker line width; the two line segments above and below represent the grounding needles, represented by relatively thinner line widths. The three needles are arranged in a GSG configuration and fixed side by side on the probe base, with the spacing between the signal needle and the grounding needle controlled within the range of 120 micrometers to 180 micrometers near the probe tip. The first tapered CPW is located on the upper surface of the ceramic support. Its tapering characteristic is represented by a trapezoidal outline. The wider end is located on the left and electrically connects to the signal pin of the GSG needle body, while the narrower end is located on the right and faces the probe tip. Grounding channels are provided on both sides of the first tapered CPW, represented by rectangular strips in the figure, arranged parallel to the main body of the first tapered CPW. The tapering length of the first tapered CPW is marked as 260 micrometers to 420 micrometers. An air bridge spans between the grounding channels on both sides of the first tapered CPW. It is represented by an arc-shaped bridge structure in the figure, located in the middle of the first tapered CPW to the area near the probe tip. The upper arc-shaped line of the air bridge represents the bridge body spanning the upper grounding channel, and the lower arc-shaped line represents the bridge body spanning the lower grounding channel. The two are connected by a dashed line to represent the three-dimensional structure of the air bridge in the direction perpendicular to the plane of the paper. The length of the air bridge is controlled between 80 micrometers and 160 micrometers, and the bridging height is controlled between 12 micrometers and 25 micrometers. The probe tip is integrally formed with the front end of the first tapered CPW, represented by a cone shape in the figure. The cone surface extends to the right from the narrow end of the first tapered CPW and gradually converges. The very tip of the probe tip is a contact microplane, represented by a small rectangle in the figure. This contact microplane is used to form physical contact with the metal pads of the device under test (DUT). The DUT is represented by a dashed rectangle in the figure, located to the right of the probe tip, and includes a schematic of the metal pads inside, illustrating the contact relationship between the contact microplane of the probe tip and the DUT pads. Figure 1 Two key dimensions are marked on the bottom: the tapered length of the first tapered CPW is 260 micrometers to 420 micrometers, and the overall length of the probe is 3 millimeters to 6 millimeters. Figure 1 The arrow on the right indicates the propagation direction, showing the propagation path of electromagnetic energy from the input transition unit through the GSG needle body, the first conical CPW, the probe tip, and finally to the object being tested.

[0019] In one specific embodiment, the probe base is constructed from a composite of a dimensionally stable metal body and a ceramic support. The metal body provides a fixation and heat dissipation channel, while the ceramic support maintains dielectric stability in the region adjacent to the probe tip. The metal body can be made of an alloy material with high hardness and a stable coefficient of thermal expansion, while the ceramic support can be made of a material with low dielectric loss. The surface of the metal body is finely ground in the mounting area near the GSG probe, with surface roughness controlled at the nanometer level to ensure that no perceptible gap effect is introduced in the gigahertz frequency band after assembly. The ceramic support is inserted into the stepped hole of the metal body with an interference fit controlled at the micrometer level. After insertion, it undergoes a stabilization and holding process at a temperature of 150 to 180 degrees Celsius for 30 to 45 minutes to ensure that the geometry remains constant during repeated contact cycles in a high-frequency environment.

[0020] The GSG needle body consists of one signal needle and two grounding needles arranged side-by-side on a probe base in a GSG configuration. The signal and grounding needles are made of a highly elastic material with stable conductivity. They undergo initial rough machining followed by microforming. Rough machining creates a needle blank with a uniform cross-section, the diameter of which can be selected from 80 to 120 micrometers. During the microforming stage, a gradual decrease in flexibility is created along the length, ensuring stable contact at the contact ends without permanent deformation under contact pressures of 0.15 to 0.30 Newtons. The center-to-center distance between the signal and grounding needles is controlled at 120 to 180 micrometers near the probe tip and 200 to 260 micrometers away from the probe tip. This gradual change concentrates the return flow path of the signal needle near the probe tip within the area defined by the air bridge. After the GSG needle body is installed into the probe base, it is constrained at three points by the positioning grooves on both sides and the clamping plate on the top. The constrained position is kept parallel to the axis of the signal needle and the grounding needle. The installation deviation is controlled to be no more than 5 micrometers within every 10 mm of length to avoid perceptible pattern tilt.

[0021] The first tapered CPW segment is electrically connected to the signal needle of the GSG needle body. The first tapered CPW segment tapers continuously from wide to narrow near the probe tip, with a taper length controlled between 260 and 420 micrometers. The linewidth at the wide end is controlled between 60 and 90 micrometers, and the linewidth at the narrow end is controlled between 20 and 35 micrometers. The gap between the grounding channels on both sides and the linewidth varies linearly throughout the entire length, with the gap variation and linewidth variation using the same linear proportion to maintain the symmetry of the lateral field distribution in space. The first tapered CPW segment achieves a low-resistance connection with the signal needle through a metal transition plate. The thickness of the metal transition plate is controlled between 5 and 12 micrometers, and the length of the transition plate covering the end of the signal needle is controlled between 60 and 90 micrometers, extending to the wide end region of the first tapered CPW segment. This arrangement aims to shorten the current diffusion path between different metals within the contact area, allowing the surface current density in the gigahertz band to be continuously distributed along the equivalent centerline of the first tapered CPW segment, thereby reducing reflections at the connection point between the first tapered CPW segment and the signal needle.

[0022] An air bridge is used to bridge the grounding channels on both sides of the first tapered CPW to form a return path. The air bridge is located in the region from the middle of the first tapered CPW to near the probe tip, with a length controlled between 80 and 160 micrometers and a bridging height controlled between 12 and 25 micrometers. The air bridge forms a suspended structure through a sacrificial layer, which is completely removed after development, ensuring that the area beneath the air bridge is filled with air. The air bridge design ensures that the grounding current, when traversing the tapered region of the first tapered CPW, no longer detours along the far-end grounding path, but is guided to an equipotential state within the air bridge area. This arrangement shortens the equivalent closed length of the grounding loop in the vicinity of the probe tip, suppresses asymmetric modes in the tapered geometry, and, together with the geometric arrangement of the GSG needle, establishes a stable return path in space. This allows the GSG needle, the first tapered CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching.

[0023] The probe tip is integrally formed with the front end of the first conical CPW. The probe tip is formed using a multi-segment geometric transition: first, a main conical surface is formed; then, a stepped convergence segment and a micro-arc transition segment are formed between the main conical surface and the front end of the first conical CPW; finally, a contact microplane is formed at the very front end. The cone length of the main conical surface is controlled between 90 and 140 micrometers, the height of the stepped convergence segment is controlled between 2 and 5 micrometers, the arc height of the micro-arc transition segment is controlled between 1 and 3 micrometers, and the side length of the contact microplane is controlled between 4 and 8 micrometers. This multi-segment geometric combination simultaneously satisfies two requirements: during contact, the contact microplane provides a stable and real contact area, reducing pressure fluctuations per unit area; during propagation, the stepped convergence segment and the micro-arc transition segment gradually change the equivalent edge in space, controlling the concentration of the electric field at the edge between the main conical surface and the front end of the first conical CPW, resulting in a more uniform current density distribution along the equivalent centerline when entering the first conical CPW. The probe tip surface undergoes secondary polishing after final shaping. The surface roughness after polishing is controlled at the nanometer level, and the polishing process lasts for 70 to 110 seconds to ensure wear uniformity during high-frequency contact cycles.

[0024] The mating profile is located between the final state of the probe tip and the front end of the first conical CPW. The mating profile consists of a conical extension section, edge micro-arcs, a contour-thinned area, and micro-notches on both sides. The conical extension section extends 20 to 35 micrometers along the direction of the first conical CPW. The edge micro-arcs form continuous arcs with radii of 2 to 3 micrometers on both sides. The contour-thinned area is located on the upper surface of the front end of the first conical CPW, with a thickness reduction of 0.5 to 1.2 micrometers and a length of 18 to 28 micrometers. The micro-notches on both sides are symmetrically arranged on both sides of the front end of the first conical CPW, with a depth of 0.8 to 1.6 micrometers and a length of 10 to 18 micrometers. The conical extension section gradually extends the equivalent electrical length of the main conical surface before entering the first conical CPW. The micro-arc at the edge reduces the peak of the electric field at the edge when entering the conical region. The equal-height thinning region locally reduces the equivalent gap between the conductor and the air, allowing near-field energy to be concentrated at the front end of the first conical CPW. The micro-notches on both sides introduce a controllable current shunt path near the grounding channel, allowing the grounding current to return to the equipotential state earlier under the action of the air bridge. Through the above geometric combination, the electric field and current density of the contact area are redistributed in space in conjunction with the contour, resulting in a significant reduction in equivalent reflection in the gigahertz frequency band. This allows the GSG needle body, the first conical CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching.

[0025] The input transition unit is coupled to the tail end of the GSG needle body. The input transition unit connects to the signal pin of the GSG needle body via a thickened metal transition section and to the grounding pin of the GSG needle body via grounding clamps on both sides. The thickened metal transition is a straight transition in the length direction, with a length of 1.2 mm to 1.8 mm and a thickness of 15 μm to 35 μm. The grounding clamps form surface contacts on both sides, with contact surface dimensions of 0.8 mm x 0.6 mm. The contact surfaces are broached in the same direction to improve the consistency of the surface contact. During assembly, the input transition unit forms two sets of positioning with the positioning reference of the probe base. The first set of positioning ensures consistency with the axis of the GSG needle body along the length direction, and the second set of positioning ensures consistency with the centerline of the first tapered CPW along the width direction. The combined deviation of the two sets of positioning is controlled within 8 μm. This connection method allows external energy to be stably transmitted along the direction of the first tapered CPW without introducing abrupt geometric changes after entering the GSG needle body, maintaining transmission continuity.

[0026] The manufacturing process begins with the bonding of the probe base and ceramic support, followed by the machining of the GSG probe body and the first conical CPW. The first conical CPW is formed on the upper surface of the ceramic support using patterned electroplating. A seed layer with a thickness of 0.2 to 0.5 micrometers is deposited first, followed by electroplating to form the main body layer with a thickness of 8 to 14 micrometers. The air bridge is formed using a sacrificial layer support electroplating method, with a sacrificial layer thickness of 10 to 18 micrometers. After air bridge electroplating, the sacrificial layer is slowly removed in a solution at 50 to 60 degrees Celsius for 8 to 14 minutes to ensure a complete air gap is formed beneath the air bridge and maintains a stable bridging height. The probe tip is integrally formed on the metal layer at the front end of the first conical CPW using a combination of laser micromachining and ion beam shaping, with the final cut completing the contact microplane. All metal surfaces are covered in the final stage with a coating thickness of 0.05 to 0.12 micrometers to improve corrosion resistance and contact stability.

[0027] refer to Figure 4As shown in the figure, this diagram uses a left-right contrast layout. The left side shows the ground current return path without an air bridge structure, while the right side shows the ground current return path with an air bridge, illustrating the technical role of the air bridge in shortening the grounding loop and suppressing asymmetric modes. The "no air bridge" section shows the current return state of the probe structure without an air bridge. This section includes the first conical CPW body, the upper and lower grounding channels, and a schematic diagram of the ground current return path. The first conical CPW body is represented by a rectangle and is located in the center. The upper and lower grounding channels are located above and below the CPW body, respectively, and are represented by narrow rectangular strips extending parallel to the CPW body. Together, these three elements constitute the basic transmission line structure of a coplanar waveguide. The ground current return path is represented by a dashed arrow, showing the actual current flow trajectory without air bridge constraints. Specifically, the ground current from a point on the CPW body needs to return to the equipotential state via the following path: first, it extends from a point on the ground channel to the far left end of the ground channel, then loops around to the opposite ground channel at the far end, and finally returns to the corresponding point at the initial position along the opposite ground channel. This return path forms a large closed loop in the figure, with a long projected length perpendicular to the propagation direction. The figure is labeled "long loop," indicating that the equivalent closed length of this return path is significantly larger than the local scale of the transmission line. Two lines of text are labeled at the bottom of the left side: "Long return path" and "Mode asymmetry." "Long return path" indicates that without an air bridge, the ground current must loop to the far end of the probe base to complete the return, resulting in an equivalent ground loop length on the order of approximately 800 micrometers. "Mode asymmetry" indicates that due to the spatial asymmetry of the return path, undesirable asymmetric transmission modes are easily excited in the tapered region of the first segment of the tapered CPW. These modes cause additional energy loss and reflections at high frequencies. (Includes sections with air bridge structure.) The right side of the diagram is labeled "with air bridge," indicating that this section shows the current return state of the probe structure after the air bridge is installed. The basic structure of this section is the same as the left side, including the first conical CPW body and grounding channels on the upper and lower sides, but an air bridge structure is added between the grounding channels. The air bridge is represented in the diagram as an arc-shaped bridge structure, located in the middle region of the first conical CPW. The upper arc curves downwards from the upper grounding channel, and the lower arc curves upwards from the lower grounding channel. The two arcs extend towards each other in the vertical direction but are not directly connected, indicating that the air bridge bridges the grounding channels on both sides in a direction perpendicular to the plane of the paper. The label "Air Bridge" points to this bridge-shaped structure. The return path of the grounding current is also indicated by a dashed arrow, but the path characteristics are significantly different from the left side. After the air bridge is installed, the grounding current can complete the return through the following short path: the grounding current from a certain point in the CPW body enters the adjacent grounding channel, then crosses the air bridge to the opposite grounding channel, and then returns along a short distance along the opposite grounding channel. This return path, constrained by the air bridge, forms a compact local closed loop, significantly shortening its equivalent closed length. The figure shows multiple dashed arrows pointing to the upper and lower ends of the air bridge, indicating that the grounding current is guided to an equipotential state within the air bridge's range. The bottom right side is labeled with two lines of text: "Short Loop" and "Fast Return to Equipotential." "Short Loop" indicates that the air bridge shortens the equivalent closed length of the grounding loop to approximately 180 micrometers, a reduction of about 77% compared to the case without the air bridge. "Fast Return to Equipotential" indicates that when the grounding current traverses the tapered region of the first tapered CPW, it no longer detours along the far-end grounding path but is rapidly guided to an equipotential state within the air bridge's range, thus maintaining the quasi-TEM mode characteristics of the transmission line.

[0028] During assembly, the GSG needles are arranged in a parallel configuration on the mounting area of ​​the probe base. Three reference lines are pre-set in the mounting area, corresponding to the axes of the signal needle and the two grounding needles, respectively. During assembly, the two grounding needles are fixed first, followed by the signal needle. A small amount of retainer is used for fixing, with the retainer covering 30% to 40% of the middle of each needle to avoid introducing additional media near the probe tip. After fixing, the signal needle is connected to the wide end of the first tapered CPW using a metal transition piece. The overlap length of the contact surface after connection is between 60 and 90 micrometers. The input transition unit is then installed, coupling it to the tail end of the GSG needle. The position of the input transition unit is adjusted using a secondary calibration in the assembly fixture. During calibration, the deviation between the centerline of the first tapered CPW and the centerline of the input transition unit is read in real time using an optical probe until the deviation is less than 8 micrometers. After assembly, the air bridge is inspected again under a microscope for its bridging height, ensuring it is within the range of 12 to 25 micrometers.

[0029] The calibration phase focuses on fine-tuning the mating profile and stabilizing contact repeatability. The mating profile between the probe tip and the front end of the first tapered CPW section, after initial machining, already includes the tapered extension section, edge micro-arcs, contour thinning zone, and micro-notches on both sides. Two types of fine-tuning are performed in the assembled state. The first type targets the depth of the micro-notches on both sides, increasing or decreasing the depth by 0.1 to 0.2 micrometers per single scan using an ion beam at 5 to 10 seconds. This aims to control the current initiation position in the air bridge return region, making the distribution of the grounding current along both ends of the air bridge more spatially symmetrical, thereby stabilizing the electric field distribution near the probe tip. The second type targets the thickness reduction of the contour thinning zone, adjusting the thickness by 0.1 to 0.3 micrometers through directional polishing for 6 to 12 seconds, followed by verification using a surface roughness meter. The reduction in thickness of the contour-thinning zone directly alters the equivalent edge relationship between the front end of the first conical CPW and the air, causing near-field energy to concentrate along the central region upon entering the first conical CPW, reducing energy leakage at the edges. Through these two types of fine-tuning, combined with the contour, a more precise field and flow distribution is achieved in space. This allows the GSG needle body, the first conical CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching, while maintaining transmission continuity in the direction of the input transition unit.

[0030] During testing, the probe tip applied a contact pressure of 0.15 to 0.30 Newtons to the metal pads of the test object, achieving stable contact across pad sizes ranging from 50 to 100 micrometers. After 10,000 repeated contact cycles, the average edge wear width of the contact microfacet was less than 1 micrometer, indicating stable contact. When the input transition unit operated continuously in an environment with temperatures between 20 and 30 degrees Celsius, no visible loosening or color change was observed at the connection between the metal transition plate and the signal pin, demonstrating stable transmission continuity during long-term operation.

[0031] In an optional embodiment, the number of air bridges can be one or two. When set to two, the two air bridges are spaced apart along the length of the first conical CPW, with a spacing of 60 to 100 micrometers. The arrangement of two air bridges further shortens the equivalent closed length of the grounding loop, allowing the grounding current to return to an equipotential state within a shorter path. In this optional embodiment, the depth of the micro-notches on both sides of the contour is selected in the range of 0.6 to 1.2 micrometers to avoid introducing excessive grounding current shunting in multi-air bridge scenarios. In another optional embodiment, the taper length of the first conical CPW is increased to 520 to 580 micrometers, while the rate of change of the taper linewidth is reduced, and the length of the conical extension section of the contour is correspondingly increased to 30 to 45 micrometers to maintain a slow geometric change in space, thereby allowing the equivalent edge to complete the transition over a longer distance, further reducing reflection when high-frequency energy enters the first conical CPW. A metal heat dissipation groove can also be added below the ceramic support of the probe base. The groove is 0.3 mm to 0.6 mm wide and 0.2 mm to 0.4 mm deep. This is used to reduce the temperature rise in the area near the probe tip during continuous operation and to avoid contact state drift caused by temperature changes.

[0032] Through the specific implementation process of manufacturing, assembly, and calibration described above, the mating profile formed between the final state of the probe tip and the front end of the first tapered CPW synchronously constrains the concentration of the edge electric field, the return position of the ground current, and the convergence of near-field energy in space. This allows the GSG needle body, the first tapered CPW, and the air bridge to work together to form a probe structure that achieves impedance self-matching. Simultaneously, the geometric coupling between the input transition unit and the tail end of the GSG needle body maintains consistency in both the length and width directions, thereby establishing a continuous and stable transmission channel between the measured object and the external instrument. The above implementation process provides a parameter range and process steps that can be directly processed and assembled. Based on this, those skilled in the art can complete the overall construction of the probe base, GSG needle body, first tapered CPW, air bridge, probe tip, and input transition unit, and achieve impedance self-matching and transmission continuity under the constraints of the mating profile.

[0033] Example 2: An impedance self-matching method for a millimeter-wave GSG high-frequency test probe, comprising the following steps: Step 1: Establish a three-dimensional electromagnetic model including the probe base, GSG needle body, first conical CPW, air bridge and probe tip. Acquire broadband port scattering data in an equally spaced sampling order and store them into a data sequence. At the same time, record the position trajectory of the port status point on the Smith circle to form the port status trajectory.

[0034] In one specific embodiment, the probe base is constructed as a single, integrated metal body, measuring 6.0 mm in length, 2.5 mm in width, and 1.2 mm in thickness. A ceramic support area is provided on the upper surface, consisting of a rectangular insert measuring 1.6 mm in length, 0.9 mm in width, and 0.20 mm in thickness. A 0.01 mm to 0.02 mm annular interference fit is provided between the metal and the ceramic. The GSG probe body consists of one signal pin and two ground pins arranged in a GSG configuration and fixed side-by-side. The total length of the pin shank is 3.0 mm, with a diameter of 0.10 mm near the probe tip and 0.12 mm away from the probe tip. The center-to-center distance between the signal pin and the adjacent ground pin near the probe tip is 0.15 mm, and the center-to-center distance away from the probe tip is 0.22 mm. The first tapered CPW is located on the upper surface of the ceramic support area, implemented with a metallic pattern. Its tapered length is 0.42 mm, with a wide end linewidth of 0.085 mm and a narrow end linewidth of 0.030 mm. The gap between the grounding channels on both sides and the linewidth varies linearly along the length direction, with a wide end gap of 0.070 mm and a narrow end gap of 0.025 mm. An air bridge bridging the grounding channels on both sides has a length of 0.12 mm, a bridging height of 0.018 mm, and a bridge width of 0.020 mm. The center position is 0.20 mm from the probe tip contact end. The probe tip is integrally formed with the front end of the first conical CPW. The main conical surface has a cone length of 0.12 mm. Between the main conical surface and the front end of the first conical CPW, there is a stepped convergence section with a height of 0.003 mm and a micro-arc transition section with an arc height of 0.002 mm. The front end forms a contact micro-plane with a side length of 0.006 mm. The mating profile is composed of a cone extension section with a length of 0.028 mm, a micro-arc radius of 0.0025 mm, a thickness reduction of 0.0009 mm in the equal-height thinning zone, and micro-notches on both sides with a depth of 0.0012 mm and a length of 0.014 mm. The thickness of the above metal pattern is uniformly 0.012 mm, and the thickness of the metal surface cover layer is 0.00008 mm. The ceramic support material is selected as alumina with low dielectric loss, which facilitates maintaining a stable field distribution in the gigahertz frequency band. The metal uses highly conductive electroplated copper with a cover layer, which can maintain a continuous surface current path in the millimeter-wave range and reduce unwanted fluctuations in port scattering data from the source.

[0035] To avoid the influence of external structures on port scattering data, an open-domain boundary is arranged around the model: a simulated enclosed space composed of air is formed in front of the probe tip, above and to both sides of the first conical CPW, and around the GSG needle body. The shortest distance from the enclosed space to the outer surface of any conductor is not less than 0.60 mm. An absorbing boundary is set outside the enclosed space to prevent radiated energy from being reflected back outside the enclosed space. The single port is located at the reference section at the tail end of the GSG needle body, with the reference plane located on a vertical section 0.80 mm back from the wide end of the first conical CPW. The reason for choosing to back the reference plane is that the geometry at this location still maintains a regular cross-section, and there are no sudden geometric changes along the propagation direction. This effectively reduces the interference of additional discontinuities near the port on the port scattering data, thus obtaining more repeatable port scattering data. The port polarization direction is in the same direction as the centerline of the first conical CPW. The lateral dimension of the port covers the projection area of ​​the signal needle and the two grounding needles, with a margin of 0.05 mm on each side to ensure that the port cross-section includes the main return path. The contact end face of the probe tip is not loaded with an external test object so that this step can focus on the broadband response of the structure itself; this setting allows the port scattering data to reflect the inherent characteristics of the structure itself, which is convenient for subsequent steps to stably separate the characteristic modes.

[0036] The mesh employs a three-dimensional unstructured mesh with an initial unit side length of 0.040 mm. Local refinement is applied to regions with concentrated electric fields: the minimum unit side length within the transition section between the probe tip contacting the microplane and the microarc is 0.0005 mm; the minimum unit side length near the narrow end and edge of the first conical CPW is 0.0010 mm; the minimum unit side length below and beside the air bridge is 0.0012 mm; and the minimum unit side length of the GSG needle near the reference plane is 0.005 mm. To suppress excessive stretching of the unit shape, the mesh anisotropic ratio is limited to no more than 6.0. To avoid numerical ill-conditioning caused by excessively dense local meshes, the size ratio between any two adjacent mesh layers does not exceed 2.0. During the adaptive process, the change in port scattering data between two adjacent iterations is used as the stopping criterion. Convergence is determined when the maximum change across the entire frequency band does not exceed 0.5%, and the significant change location no longer shifts forward or backward by more than 3 frequency points compared to the previous iteration. The advantage of this arrangement is that it simultaneously limits the drift of amplitude and position, so that convergence takes into account both the magnitude of the error and the region where the error occurs, thereby improving the consistency of full-band data under equal-interval sampling.

[0037] The bandwidth was set from 20 GHz to 110 GHz, with a sampling step of 0.25 GHz, resulting in 361 sampling points. This bandwidth was chosen because it covers commonly used millimeter-wave test ranges while fully revealing the impact of the matching profile on port scattering data at high frequencies. The sampling step was chosen because the 0.25 GHz interval allows for the resolution of rapid fluctuations introduced by the air bridge and the narrow end of the first conical CPW without significantly increasing computational load. To avoid endpoint bias, the sampling sequence was solved point-by-point, increasing from 20 GHz to 110 GHz in a fixed order. After each frequency point was completed, the port scattering data and its index were written to a cache table, and then sequentially written to the data file. To ensure order and integrity, three checks were performed during writing: first, the difference between adjacent frequency points must be equal to 0.25 GHz; second, the number of data entries must be equal to the current frequency index plus 1; and third, the timestamps were strictly incremented. If any condition is not met, the algorithm rolls back to the previous frequency point and recalculates that frequency point and the next two frequencies to prevent occasional solution jitter from disrupting the sequence continuity.

[0038] The data sequence is written row by row, with each row containing four columns: frequency index, frequency value, size of port scattering data, and orientation angle of port scattering data. The representation of size and orientation angle facilitates direct mapping of each data point to a coordinate point on the Smith circle, and avoids introducing complex complex number formats at the data sequence level. Quality self-checks intercept two types of anomalies: first, isolated spikes. If the size of any single point is simultaneously higher than the sizes of its immediate and next-to-immediate neighbors, and the difference between the two exceeds 0.10, and the orientation angles of the immediate and next-to-immediate neighbors differ by no more than 20 degrees, it is identified as an isolated spike, triggering a single recalculation for that point; second, cross-segment jumps. If the arc length of two adjacent points on the Smith circle exceeds 0.30, an intermediate frequency point is inserted between the two points for supplementary calculation, with the frequency taken as the median of the two points. After supplementary calculation, the original step size is resumed. Neither of these processing methods involves historical weights or multiple smoothing; only a minimal number of supplementary points are added when necessary to maintain the geometric continuity of the port state trajectory.

[0039] For each frequency point of port scattering data obtained, the corresponding magnitude and orientation angle are mapped to coordinates on a Smith circle, and these coordinates are appended to the trajectory list in the sampling order. To prevent misjudgment of trajectory wrapping when approaching the circumference, a continuous expansion rule from 0 degrees to 360 degrees is adopted for the orientation angle: when there is a jump from close to 360 degrees to close to 0 degrees, the latter is automatically added to 360 degrees in sequence for trajectory generation, and then normalized to the 0-360 degree range during final export. The trajectory is exported as two types of files: one is a complete trajectory file containing 361 trajectory points; the other is a key inflection point file, which is obtained by calculating the angle between three points on the trajectory and selecting points with an angle less than 150 degrees as inflection points, typically yielding 8 to 20 key inflection points. The key inflection point file is used for quickly locating segments of response change in the subsequent second step, while the complete trajectory file is used for rigorous mode extraction. This two-stage output approach can simultaneously balance subsequent calculation speed and result fidelity.

[0040] To suppress non-physical oscillations caused by localized high fields resulting from the extremely fine geometry of the probe tip, an air gap of 0.010 mm to 0.020 mm is maintained directly in front of the probe tip, providing a clear buffer zone between the contact microplane and the open domain boundary. To reduce mesh wrinkling at the edge of the air bridge, a 0.004 mm thick air pad is added below the air bridge. This pad is continuously connected to the surrounding air, does not alter the electromagnetic boundary, and is only used to improve mesh quality. These treatments do not change the physical meaning of the port scattering data but significantly reduce numerical errors caused by localized high curvature, thereby improving the stability of the equally spaced sampling sequence. To verify reproducibility, the solution is repeated three times under the same geometry and mesh rules, requiring that the magnitude difference at any frequency point does not exceed 0.02 and the directional angle difference does not exceed 5 degrees. If these values ​​are exceeded, the mesh is further refined by one level in the corresponding region, and the frequency range is recalculated.

[0041] In one optional implementation, the bandwidth is set to 24 GHz to 86 GHz, with a sampling step of 0.20 GHz, resulting in 311 sampling points. Other geometry, boundaries, ports, and mesh rules remain unchanged. This approach is suitable for process optimization in the mid-range millimeter-wave frequency band, enabling denser, equally spaced coverage of common test windows and reducing interpolation errors in the mid-frequency band. In another optional implementation, the frequency band is divided into two consecutive sub-segments: 20 GHz to 60 GHz and 60 GHz to 110 GHz. Each sub-segment uses equally spaced sampling with a step of 0.25 GHz, but three adjacent supplementary points are added at the 60 GHz boundary of the sub-segment, located at 59.75 GHz, 60.00 GHz, and 60.25 GHz respectively. This approach, while maintaining equally spaced sampling, locally densifies the boundary points where geometric resonance may occur, which helps improve the resolution of port state trajectories near key points.

[0042] Step 2: Use a matrix pencil to perform mode extraction on the data sequence, solve for a set of complex exponential poles, and reconstruct the port scattering data based on the complex exponential poles to generate a list of characteristic modes. By analyzing the impulse response and field intensity peak position of each characteristic mode, the list of characteristic modes is divided into multiple response clusters belonging to specific components in the probe tip, the first conical CPW, and the air bridge, and response cluster identifiers are generated.

[0043] The data sequence obtained in step one, with 361 sampling points, is arranged sequentially from index 1 to index 361. This data sequence is divided into two adjacent shifted rectangular data structures: the first block consists of a continuous segment from index 1 to index 320, arranged as a rectangle with 160 rows and 2 columns; the second block consists of a continuous segment from index 2 to index 321, also arranged as a rectangle with the same number of rows and columns. The adjacent shifting is used to explicitly encode the temporal progression relationship between adjacent sampling points into the linear constraint between the two data blocks; the number of rows is set to 160 to ensure that each column contains a sufficiently long historical segment to stably identify slowly decaying components; and the number of columns is set to 2 to reduce the impact of random jitter in the column direction and limit the computational scale, ensuring the numerical stability of subsequent singular decomposition.

[0044] Singularity decomposition is performed on the first rectangular data structure, resulting in a sequence of singular values ​​arranged in descending order of size. To determine the effective rank, a sequence of differences between adjacent singular values ​​is calculated, and a turning point is found within this difference sequence: when the difference between adjacent singular values ​​first exceeds 0.05, and the subsequent three consecutive difference values ​​are not less than 0.04, the index corresponding to the position preceding the turning point is taken as the effective rank. This "differential turning point plus continuous confirmation" rule has two advantages: first, it avoids single-point misjudgment when isolated noise spikes exist; second, it avoids missed detections due to excessive truncation when the number of true modes is slightly large. Taking the 361-point data in this embodiment as an example, the obtained singular value difference shows a significant increase for the first time at the 9th position, and then remains above 0.04 for the next three positions; therefore, the effective rank is taken as 8.

[0045] After determining the effective rank, a linear relationship is established using the first and second rectangular data structures. The column space basis of the first block is then projected onto the second block using minimum deviation to obtain a set of numerical solutions describing time progression. Eight complex exponential poles are directly read from these solutions. Each complex exponential pole corresponds to a pair of quantities: one representing the rate of increase or decrease, and the other representing the rate of directional angular progression along the Smith circle. To eliminate spurious numerical solutions, two screening criteria are set: the absolute value of the rate of increase or decrease does not exceed 0.15 per sampling point, and the rate of directional angular progression falls within the range of −8 degrees to 8 degrees per sampling point. If any pole exceeds these ranges, the number of rows is reconstructed in steps of 10 between 140 and 180. This process is repeated, using the most frequent poles as the standard, until all eight poles fall within the range. The purpose of this approach is to suppress the common problems of "overfitting" and "underfitting" with minimal structural changes, maintaining the stability of the pole set.

[0046] After fixing eight complex exponential poles, the corresponding amplitude coefficients are estimated. To avoid the spread of local bias caused by a one-time fitting of the entire frequency band, a "two-segment minimum difference fitting" method is adopted: 40 equally spaced points are selected in the 20 GHz to 60 GHz range, and 40 equally spaced points are selected in the 70 GHz to 110 GHz range. The amplitude coefficients are estimated independently for each of the two segments, and then the results of the two segments are averaged. The obtained eight complex exponential poles and the corresponding amplitude coefficients are combined to reconstruct port scattering data at 361 frequency points point by point. Two consistency checks are performed: first, the maximum deviation of the reconstructed magnitude and orientation angle from the original data in the entire frequency band does not exceed 0.04 and 6 degrees, respectively; second, the arc length error of the port state trajectory generated by the reconstructed data within any 50 consecutive points does not exceed 0.20. If these conditions are not met, a local fitting is added only within the 20 points where the error peak is located, and the corresponding amplitude coefficients are updated until the check criteria are met. The process of piecewise fitting and local correction avoids repeated oscillations that "affect the whole body when a small change is made", making the reconstruction results insensitive to local anomalies.

[0047] The eight complex exponential poles and their corresponding amplitude coefficients form a characteristic mode list. To facilitate subsequent sorting and filtering, three directly usable descriptive quantities are calculated for each characteristic mode: first, the dominant frequency band, determined by finding a continuous frequency range in the reconstruction results where the mode's contribution to magnitude exceeds 0.05, and recording the start and end frequencies of the range; second, the azimuth angle advancement direction, recorded as clockwise or counterclockwise according to the average contribution sign of the mode to the azimuth angle in the reconstruction results; and third, the energy concentration, recorded as a number between 0 and 1 based on the average contribution value of the mode to magnitude across the entire frequency band. Taking this embodiment as an example, among the eight characteristic modes, the main active frequency bands are concentrated in 26 GHz to 34 GHz, 38 GHz to 46 GHz, 52 GHz to 60 GHz, 61 GHz to 74 GHz, 78 GHz to 86 GHz, 90 GHz to 98 GHz, 100 GHz to 106 GHz, and a cross-band mode covering 24 GHz to 52 GHz.

[0048] A time-domain impulse response was generated for each characteristic mode, with a response length of 200 picoseconds and a sampling interval of 0.2 picoseconds. Six monitoring sections were set along the direction from the probe tip to the input transition unit in the three-dimensional electromagnetic model, with the monitoring sections located at distances of 0.05 mm, 0.10 mm, 0.20 mm, 0.40 mm, 0.80 mm, and 1.60 mm from the geometric center of the probe tip. The time of the first major peak of the impulse response was recorded at each monitoring section, and an arrival sequence was written according to the spatial order of the six monitoring sections. If the arrival sequence strictly increases from the monitoring section near the probe tip to the monitoring section near the input transition unit, it is a propagation tag; if the arrival sequence is reversed or a later major peak appears at the monitoring section near the probe tip, it is a radiation tag. The advantage of this determination method is that it directly corresponds to the propagation or return of energy along the geometric path, without relying on any statistical weights or historical samples. In this embodiment, for example, out of the eight characteristic modes, five were determined to be propagation tags and three were determined to be radiation tags.

[0049] For each characteristic mode, the field strength peak distribution in three regions was extracted in the 3D electromagnetic model using unit amplitude port excitation: the probe tip region, the front end region of the first conical CPW, and the air bridge bridging region. To avoid arbitrary region bounding values, specific spatial ranges were given. The probe tip region was defined as a cylinder with a radius of 0.06 mm and a height of 0.04 mm, centered on the geometric center of the probe tip contacting the microplane; the front end region of the first conical CPW was defined as a cuboid with a length of 0.20 mm, a width of 0.12 mm, and a height of 0.04 mm, centered on the centerline of the narrow end of the first conical CPW; and the air bridge bridging region was defined as a cuboid with a length of 0.16 mm, a width of 0.10 mm, and a height of 0.05 mm, centered on the geometric center of the air bridge. Within each region, the frequency and amplitude of peak occurrences were statistically analyzed using a uniform volume point grid, with a volume point spacing of 0.005 mm. For a given characteristic mode, the frequency of peak occurrences in the three regions is compared side-by-side, and the component corresponding to the region with the highest frequency is assigned to that mode. If the frequency is the same, the median of the peak amplitude is compared, and the higher one is assigned to the component. If they are still the same, the average distance from the peak position to the geometric center of the region is compared, and the smaller one is assigned to the component. This three-step decision-making process can provide a stable assignment without introducing weights. Taking this embodiment as an example, the statistical results of the assignments for the eight characteristic modes are: three in the probe tip region, three in the front end region of the first segment of the conical CPW, and two in the air bridge bridging region.

[0050] The characteristic mode list is grouped by the component to which it belongs, generating multiple response clusters, and a response cluster identifier is generated for each response cluster. The identifier format uses a combination of Chinese component name and serial number, such as "Probe Tip Response Cluster 1", "First Segment Conical CPW Response Cluster 1", "Air Bridge Response Cluster 1", etc. Each response cluster has a sorting rule: first sorted by energy concentration from high to low, then sorted by the center frequency of the main operating frequency band from low to high; the number of propagation tags and radiation tags in each response cluster is also recorded. Taking this embodiment as an example, "Probe Tip Response Cluster 1" contains 3 characteristic modes, of which 2 are propagation tags and 1 is a radiation tag; "First Segment Conical CPW Response Cluster 1" contains 3 characteristic modes, of which 3 are propagation tags; "Air Bridge Response Cluster 1" contains 2 characteristic modes, of which 1 is a propagation tag and 1 is a radiation tag. The above response cluster identifiers, along with the main operating frequency band, azimuth angle propagation direction, and energy concentration of each characteristic mode, are written into a list file. This list file serves as a direct index for the candidate shaping domain and priority verification region in subsequent step three.

[0051] After the complex exponential poles are found, two robustness checks are performed. The first is "recalculate after deleting a column": temporarily remove one column from the second rectangular data structure, repeat the pole finding process, and compare the difference in the direction angle advancement rate of the two pole sets. The average difference should not exceed 0.6 degrees per sampling point. If it exceeds the limit, increase the number of columns in the two rectangular data structures from 2 to 3 and recalculate. The second is "recalculate due to local perturbation": introduce a small perturbation of no more than one percent of the original value into the last 5 rows of the first rectangular data structure and recalculate. The average change in the growth or decay rate of the pole set should not exceed 0.02 per sampling point. After both checks pass, the stability of the characteristic mode list is confirmed, ensuring that the geometric sensitivity map and geometric update path in the subsequent step three will not frequently reverse due to mode jitter.

[0052] Using 361 data points as input, eight complex exponential poles were obtained. Three had dominant frequency bands between 20 GHz and 60 GHz, three between 60 GHz and 100 GHz, and two spanned different bands. The energy concentration ranged from 0.12 to 0.37. In terms of azimuth propagation direction, five were clockwise and three were counterclockwise. Based on impulse response and field strength peak position statistics, three characteristic modes were assigned to the probe tip region, three to the front end region of the first conical CPW, and two to the air bridge bridging region, ultimately forming three response clusters and generating corresponding response cluster identifiers. The manifest file records the propagation or radiation label, dominant frequency band, azimuth propagation direction, energy concentration, and assigned component for each characteristic mode; the file contains eight lines.

[0053] Step 3: Perform probe tip geometry inversion based on the adjoint method, determine the candidate modification domain of the probe tip by calculating the geometric sensitivity map, and perform geometry update driven by a primitive library consisting of three primitive operations: conical micro-stretching, edge arcing, and slope refinement within the candidate modification domain of the probe tip to form a geometry update path.

[0054] In one specific implementation, the forward field distribution is first obtained under single-port forward excitation, and then the accompanying field distribution is obtained by applying reverse phase equal-amplitude excitation at the same port. For the mesh surface covering the probe tip, the front end of the first conical CPW, and the neighborhood of the air bridge, the in-plane average values ​​of the forward field distribution and the accompanying field distribution are taken on both sides of the mesh surface. A face-by-face comparison operation is performed and the difference is calculated to obtain the geometric sensitivity map. To avoid local spikes affecting the ranking, the geometric sensitivity map is smoothed once only on adjacent surfaces, with the smoothing radius being one ring of the neighborhood of the cell. Then, the geometric sensitivity maps are sorted from largest to smallest absolute value, and the top 15% of the mesh surfaces are selected as the first batch of candidate sets.

[0055] Geometrically, the candidate modification domain for the probe tip is defined as the union of a cylinder with a radius of 0.08 mm and a height of 0.05 mm centered at the geometric center of the microplane contacting the probe tip, and a wedge-shaped band extending 0.22 mm backward from the front end of the first conical CPW. Topologically, the overlap ratio between the candidate mesh surface and this union must be no less than 50%. The first batch of candidate sets is mapped to the response cluster identifiers output in step two: when a response cluster identifier belongs to the probe tip region or the front end region of the first conical CPW, its corresponding mesh surface priority is increased by one level; when it belongs to the air bridge bridging region, only the field channel connecting the air bridge and the probe tip is increased by one level. Finally, the top 300 to 600 mesh surfaces are truncated from high to low as the action surface list of the candidate modification domain for the probe tip. The primitive library includes three primitive operations: conical micro-stretching, edge arcing, and slope refinement. The conical micro-stretching is performed along the probe tip axis to extend the conical segment containing the action surface at equal angles. The single-step extension is 0.2 to 0.6 micrometers, and the number of consecutive steps does not exceed 6. After extension, the collinear relationship between the main conical surface and the contact microplane is maintained, ensuring that the side length change of the contact microplane does not exceed 0.8 micrometers. Edge arcing is performed by establishing a continuous arc along the common edge of the action surface and the adjacent surface. The single-step arc height is 0.2 to 0.5 micrometers, and a maximum of 3 steps are allowed on the same edge. After implementation, the change in the normal angle between the intersection lines of the two sides should not exceed 5 degrees, thereby reducing the concentration of the electric field at the edge. Slope refinement involves inserting a linear transition segment between the main conical surface and the front end of the first conical CPW. The length of a single segment is 4 to 12 micrometers. After insertion, both ends maintain tangential continuity with the adjacent surface. If necessary, the transition segment is further edge-arcled, with an arc height not exceeding 0.3 micrometers.

[0056] refer to Figure 2The figure shows, from left to right, the main body of the first conical CPW, the components of the conforming profile, the main conical surface, the stepped convergence section, the micro-arc transition section, and the contact micro-plane. The main body of the first conical CPW is represented by a rectangle, with grounding channels above and below it, represented by narrow rectangular strips. The first conical CPW gradually converges from the wide end to the narrow end along the propagation direction, with the taper length ranging from 260 micrometers to 420 micrometers. The contour-thinning region is located on the upper surface of the front end of the first conical CPW, marked by a dashed rectangle, indicating that the metal layer thickness in this area is reduced relative to the surrounding area. The thickness reduction in the thinning region is controlled between 0.5 micrometers and 1.2 micrometers, with a length of 18 micrometers to 28 micrometers. Symmetrical micro-notches are located adjacent to the grounding channels on both sides of the front end of the first conical CPW, represented by solid black rectangles. The depth of the micro-notches ranges from 0.8 micrometers to 1.6 micrometers, with a length of 10 micrometers to 18 micrometers. These micro-notches are used to introduce a controlled current shunt path near the grounding channel. The conical extension, located between the narrow end of the first conical CPW and the main conical surface, is represented by a dashed trapezoidal outline in the figure, indicating that this section belongs to the transition region of the mating profile. The conical extension extends 20 to 35 micrometers along the direction of the first conical CPW, allowing the equivalent electrical length of the main conical surface to gradually extend before entering the first conical CPW. Edge micro-arcs, located at the connection between the conical extension and the front end of the first conical CPW, are represented by an arc curve in the figure, with a radius of 2 to 3 micrometers. The edge micro-arcs are symmetrically arranged on both sides, forming a continuous arc transition to reduce the peak concentration of the edge electric field. The main conical surface, represented by a larger trapezoidal outline, extends to the right from the mating profile region, with a cone length controlled between 90 and 140 micrometers. The main conical surface provides the main geometry of the probe tip and its contact guidance function. The stepped convergence section, located between the main conical surface and the contact microplane, is represented by two small rectangular steps in the figure, with a height ranging from 2 to 5 micrometers. This stepped convergence section creates a height difference in space, allowing the probe tip's geometry to gradually transition from the main conical surface to the contact microplane. The micro-arc transition section connects the stepped convergence section and the contact microplane, represented by an arc curve in the figure, with an arc height controlled between 1 and 3 micrometers. The micro-arc transition section further smooths the geometric transition, controlling the concentration of the edge electric field between the main conical surface and the leading edge of the first conical CPW. The contact microplane, located at the very tip of the probe tip, is represented by a rectangle in the figure, with a side length controlled between 4 and 8 micrometers. The contact microplane provides a stable, true contact area for forming reliable electrical contact with the metal pads of the measured object. Figure 2 Two key dimensions are marked at the bottom: the tapered region length of the first conical CPW is 260 to 420 micrometers, and the cone length of the main cone surface is 90 to 140 micrometers. These dimensions are indicated by bidirectional arrow segments, clearly indicating the spatial extent of each key geometric segment.

[0057] The geometric update follows a cycle of "surface scanning—primitive probing—rapid verification—admission recording." Specifically, starting from the first surface in the list, one of the following is sequentially probing: conical micro-stretching, edge arcing, or slope refinement, with only one primitive step performed at a time. After probing, the set of poles for complex exponential poles fixed in step two is called, and two-segment minimum difference fitting is performed on the modal coefficients only on the new geometry to quickly reconstruct the port scattering data from 20 GHz to 110 GHz, and calculate the new position of the port state point on the Smith circle. A "port state trajectory ray" is constructed, which is a line connecting the previous position to the target point; the angle between the new position and the ray is measured and compared with the angle before probing. If the ray angle decreases by at least 3 degrees and the maximum deviation of the reconstructed data across the entire frequency band does not exceed 0.05, the primitive step is considered valid, and the primitive step, along with the action surface number, primitive type, step size, and timestamp, is written into the geometric update path; otherwise, the geometric modification is revoked, and the next primitive type is switched on the same action surface to continue testing. After every 5 to 8 successfully recorded primitive steps, the action surface list is dynamically refreshed: the mesh surfaces that have already been acted upon are downweighted, and the adjacent mesh surfaces whose geometric sensitivity maps are still in the top 20% are upweighted, in order to promote the slow migration of the shaping front towards the front end of the first conical CPW.

[0058] To ensure geometric continuity and assembly manufacturability, three constraints are set: First, the cumulative change in the main cone length caused by any 10 consecutive primitive steps shall not exceed 16 micrometers; second, the side length of the contact microplane shall be maintained between 4 and 9 micrometers; third, the variation in the thickness reduction of the equal-height thinning zone at the front end of the first conical CPW shall be controlled within ±0.3 micrometers of the original value. Upon reaching any constraint boundary, further conical micro-stretching is paused, and edge arcing and slope refinement are prioritized to complete the current iteration.

[0059] When the action surface list has been traversed in one round or the geometric update path has accumulated 20 to 60 primitive steps, the current round ends and the geometric update path is output. Typically, within 1 to 3 rounds, the port state point can be advanced from the outermost region to the middle region, thus creating the initial path and starting neighborhood for the geometric descent in step four. The output also includes three types of supplementary data: the full-band deviation curve of the rapidly reconstructed port scattering data, the spatial heatmap of the action surface coverage, and a table of correspondence between primitive step sequences and response cluster identifiers, facilitating the direct location of priority verification regions in subsequent iterations.

[0060] In one alternative implementation, the candidate cutoff threshold is adjusted from the top 15% to the top 20%, and the single-step ray angle reduction criterion is adjusted from 3 degrees to 2 degrees. This is suitable for samples with relatively gentle initial mating contours and can obtain usable geometric update paths more quickly. For slope refinement, a "short-segment paired insertion" method is used, that is, symmetrically inserting transition segments of the same length on both sides of the same action surface, with a single segment length of 6 micrometers, to reduce the displacement of the transition segment relative to the centerline. This is suitable for situations where the port state point is already close to the middle layer region. Alternative implementation method three: Before edge arcing, "edge pre-cleaning" is added, using equal-height thinning and micro-polishing of 0.1 to 0.2 micrometers to remove processing burrs before arcing. This can increase the displacement of the port state point after single-step arcing by approximately 10% to 20%.

[0061] Step 4: Using the geometric descent method on the Smith circle, port state point guided iteration is performed on the geometric update path. By executing combination primitives or adsorption primitives in different target neighborhoods, the port reflection index of the port state point reaches the preset matching level, and the matching profile of the probe tip final state and the front end of the first conical CPW is output.

[0062] In one specific implementation, using the unit radius of the Smith circle as the calibration scale, three layers of target neighborhoods are set around the target point from the outside in: the outer target neighborhood has a radius of 0.35, the middle target neighborhood has a radius of 0.20, and the inner target neighborhood has a radius of 0.10. The initial position of the port state point is taken from the latest position at the end of step three. The reason for choosing layered neighborhoods is that the outer target neighborhood prioritizes amplitude convergence, the middle target neighborhood prioritizes angular correction, and the inner target neighborhood completes the final fitting with minimal geometric perturbation. This decouples the three types of actions: "inward pushing," "circumferential alignment," and "edge closing," avoiding mutual cancellation of single primitives at different stages.

[0063] When the port state point is located in the neighborhood of the outer target, the first combination primitive is executed radially. The first combination primitive consists of conical micro-stretching and synchronous convergence of the gap at the front end of the first conical CPW, which are implemented alternately in a one-to-one primitive step ratio. The single-step extrapolation of the conical micro-stretching is 0.3 μm to 0.6 μm, and does not exceed 2 consecutive steps; the single-sided convergence of the synchronous convergence of the gap at the front end of the first conical CPW is 0.2 μm to 0.4 μm, and the action length is 12 μm to 24 μm, also not exceeding 2 steps. After each pair of alternating implementations is completed, the minimum difference fitting of two sampling segments is performed on the new geometry using the pole set of complex exponential poles fixed in step two, reconstructing the port scattering data from 20 GHz to 110 GHz, and calculating the new position of the port state point. The admission criteria are that two conditions are met simultaneously: first, the radial distance relative to the target point decreases by no less than 0.03; second, the angle between the new position and the "port state trajectory ray" does not exceed 10 degrees. If the conditions are met, the pair of primitive steps is retained and the next pair of alternating steps continues; if not, the most recent pair of primitive steps is canceled, and the process switches to the next geometric sensitivity grid surface with a higher priority on the same action surface to continue the attempt. The reason for using this combination of primitives is that the conical micro-stretching extends the equivalent propagation path in the probe tip neighborhood, allowing energy to enter the equivalent centerline of the first conical CPW earlier. The gap at the front end of the first conical CPW converges synchronously to the electric field concentration at the balanced compression edges on both sides. The combined effect of these two factors causes the port state point to advance radially inward stably without excessive deflection of the direction angle.

[0064] When the port state point enters the neighborhood of the mid-layer target, the second combination primitive is executed tangentially. The second combination primitive consists of creating symmetrical micro-notches on both sides of the front end of the first conical CPW and slightly extending the bridging distance in the air bridge bridging area. These two primitives are executed alternately in a one-to-one primitive step ratio. The single-step depth of the symmetrical micro-notches is 0.1 to 0.2 micrometers, and the length is 8 to 12 micrometers; the single-step extension of the air bridge bridging distance is 1 to 3 micrometers. After each pair of alternating executions, the port scattering data is reconstructed, and the new position of the port state point is calculated. The admission criteria are that two conditions must be met simultaneously: first, the displacement along the circumferential direction is not less than 6 degrees; second, the radial distance does not increase by more than 0.01. If these conditions are met, the pair of primitive steps is retained; otherwise, it is canceled, and the position of the symmetrical micro-notches is shifted 4 to 6 micrometers along the edge of the first conical CPW before retrying. The reason for adopting this combination of primitives is that the symmetrical micro-notch introduces controlled edge delay on both sides of the front end of the first conical CPW, causing a slight difference in the relative propagation of energy on both sides, thereby producing angular alignment on the Smith circle; the slight extension of the air bridge bridging distance shortens the equivalent closed path change period of the grounding loop and suppresses excessive radial involution. The alternation of the two can complete the directional angular alignment without increasing the radial error.

[0065] When a port state point enters the inner target neighborhood, the adsorption primitive is executed. The adsorption primitive is a continuous edge arcing, selecting the geometric sensitivity grid surface with the highest position as the action surface. The arc height per step is 0.1 μm to 0.3 μm, and a maximum of 2 steps are performed on the same edge. After each step, the port scattering data is reconstructed and the new position of the port state point is calculated. If the arc length from the new position to the target point decreases by no less than 0.02, the step is recorded; otherwise, it is canceled and the process continues on the adjacent edge. The reason for using only edge arcing in the inner target neighborhood is that edge arcing has a continuous peak-shaving effect on the local edge electric field concentration, which can achieve the final adhesion with minimal geometric perturbation and avoid introducing new angular oscillations when approaching the target point.

[0066] The convergence and stopping rules employ a two-layer judgment mechanism. Layer 1 is an index judgment: the port reflection index must be no higher than 0.25 for at least 300 out of 361 sampling points, and no higher than 0.28 in the 30 GHz to 90 GHz range. Layer 2 is a geometric stability judgment: in the last 10 recorded primitive steps, the change in arc length from the port state point to the target point after any single step is no less than 0.01. Iteration stops when both judgments are simultaneously satisfied, and the matching profile of the probe tip final state and the first conical CPW front end is output. Layer 1 ensures performance meets the standards, while Layer 2 ensures the final state is insensitive to minor geometric perturbations, facilitating mass production replication. The rollback and switching rules apply to both the outer and middle target neighborhoods. If three consecutive alternating implementations on the same action surface fail to pass the admission criterion, the action surface is downgraded and switched to the next action surface. If more than six pairs of alternating implementations are revoked cumulatively on the same type of combinatorial primitive, a brief switch to another type of combinatorial primitive is made to execute one pair of alternating implementations before returning to the original combinatorial primitive. This switching can break the stalemate in a single geometric direction, allowing the port state point to first gain a small, beneficial displacement before returning to the main attack direction to continue advancing.

[0067] refer to Figure 3This figure uses the standard Smith chart coordinate system to characterize the distribution of the probe port reflection coefficient in the complex plane and its optimization process. The center of the Smith chart represents the perfectly matched state (reflection coefficient is zero), and the circumference represents the total reflection state (reflection coefficient amplitude is 1). The basic structure of the Smith chart includes an outer circle boundary, multiple sets of equal impedance circles, a real axis, a dashed axis, and coordinate labels. The outer circle boundary is represented by a solid line, with the radius corresponding to the position where the reflection coefficient amplitude is 1. The equal impedance circles are represented by dashed concentric circles, corresponding to different normalized impedance values ​​from the center outwards. The real axis is a horizontal straight line that passes through the center of the circle, with "1" at the right end indicating that the real part of the normalized impedance is 1; the dashed axis is a vertical straight line, with "+j" at the top indicating the inductive impedance component and "-j" at the bottom indicating the capacitive impedance component. The three-layer target neighborhood is represented by dashed rings to guide the optimization process of the geometric descent method. The radius of the outer target neighborhood is labeled 0.35, located on the outer edge of the graph; the radius of the middle target neighborhood is labeled 0.20, located in the middle; and the radius of the inner target neighborhood is labeled 0.10, located near the center. These three neighborhoods divide the Smith chart into different optimization segments, each corresponding to different combinatorial primitive operation strategies. The port state trajectory before optimization is represented by a dashed curve, starting at "20GHz," located in the upper right quadrant of the Smith chart, far from the center. This trajectory diverges outward with increasing frequency, passing through key frequency points such as 50GHz, 70GHz, and 90GHz, and finally remaining outside the outer target neighborhood at the 110GHz frequency point, indicating that the impedance matching performance of the probe before optimization was poor, and the port reflection coefficient was large. The port state trajectory after optimization is represented by a thick solid curve, also starting at "20GHz," but this trajectory develops along a path closer to the center. At the 50GHz frequency point, the optimized trajectory has entered the middle-layer target neighborhood; at the 70GHz and 90GHz frequency points, the trajectory continues to move closer to the center; at the 110GHz frequency point, the trajectory successfully enters the inner-layer target neighborhood, very close to the target matching point at the center. Key frequency points are marked on the trajectory with solid or hollow circles. Frequency points on the unoptimized trajectory are marked with hollow circles, while those on the optimized trajectory are marked with solid circles, making it easy to distinguish the different states of the two trajectories at the same frequency. Each key frequency point is marked with a frequency value and the text description "before optimization" or "after optimization". The target matching point is located at the center of the Smith chart, represented by concentric double circles, with the outer circle being solid black and the inner circle being hollow white, indicating that this point represents the ideal impedance matching state, i.e., the target location where the port reflection coefficient is zero. Figure 3A legend is provided at the bottom, using two different line segments to represent the "before optimization" (dashed line) and "after optimization" (solid line) trajectories, respectively, to help readers quickly identify the meaning of the two curves in the figure. This figure clearly shows the process by which the port state trajectory gradually converges from the outer layer to the inner layer to the target matching point through contour optimization, proving the technical effect of the present invention in achieving impedance self-matching in the 20GHz to 110GHz wideband. The optimized port state trajectory always remains within the target neighborhood of the middle or inner layer, indicating that the port reflection coefficient is effectively controlled and transmission continuity is maintained throughout the millimeter-wave band.

[0068] The cumulative change in the length of the main conical surface is limited to within 16 micrometers; the side length of the contact microplane remains between 4 and 9 micrometers; the minimum gap at the front end of the first conical CPW within the effective length range is not less than 12 micrometers; and the cumulative extension of the air bridge bridging distance does not exceed 8 micrometers. When any constraint becomes critical, the primitives associated with that constraint are suspended, and feasible steps are sought among the remaining two types of primitives to complete the target action in the current neighborhood until the constraint is released. The length of the conical extension segment is 24 to 38 micrometers; the radius of the edge micro-arc is 2.2 to 2.8 micrometers; the thickness reduction of the contour thinning zone is 0.7 to 1.1 micrometers, and the length is 18 to 28 micrometers; the depth of the micro-notches on both sides is 0.9 to 1.4 micrometers, and the length is 11 to 16 micrometers; the minimum gap after synchronous convergence of the front end gap of the first conical CPW is 90% to 95% of the original value; and the increase in the air bridge bridging distance relative to the initial value is 2 to 6 micrometers. The list of geometric elements and the geometric update path are archived together, and the port reflection index is confirmed to meet the aforementioned convergence and stopping rules during sample retesting.

[0069] In the example process, the port state point starts at a radius of approximately 0.31 in the outer target neighborhood. After four pairs of alternating primitive combinations, it radially advances to a radius of approximately 0.23. Upon entering the middle target neighborhood, three pairs of alternating primitive combinations are used, with a total directional angle of approximately 20 degrees and a radial distance maintained between a radius of approximately 0.22 and 0.21. Upon entering the inner target neighborhood, three consecutive edge arcing steps are performed, eventually reaching a range no more than 0.08 from the target point. The port reflection index is no higher than 0.25 in 312 out of 361 sampling points, and remains no higher than 0.28 in the 30 GHz to 90 GHz range, satisfying the stopping condition and outputting the mating profile.

[0070] In one alternative implementation, the radii of the three target neighborhoods are set to 0.40, 0.22, and 0.12, suitable for samples with initial port state points offset outwards and requiring longer radial advances. Within the middle target neighborhood, the single-step depth of the symmetrical micro-notch is reduced to 0.08 to 0.12 micrometers, while the single-step extension of the air bridge bridging distance is increased to 2 to 4 micrometers, suitable for samples with greater angular alignment requirements. Optionally, "intermittent adsorption" can be used within the inner target neighborhood, i.e., after applying one step of continuous edge arcing, a small, synchronous convergence action is inserted into the gap at the front end of the first conical CPW segment, with a convergence amount not exceeding 0.1 micrometers. This further compresses the micro-oscillations near the target point, improving the fit consistency during repeated assembly.

[0071] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these specific embodiments are merely illustrative. Those skilled in the art can omit, substitute, and modify the details of the above methods and systems in various ways without departing from the principles and essence of the present invention. For example, combining the above method steps to perform substantially the same function and achieve substantially the same result according to substantially the same method falls within the scope of the present invention. Therefore, the scope of the present invention is defined only by the appended claims.

Claims

1. A millimeter-wave GSG high-frequency test probe, comprising a probe base, a GSG needle body, a first-section tapered CPW, an air bridge, a probe tip, and an input transition unit; the GSG needle body consists of one signal needle and two grounding needles arranged side-by-side on the probe base in a GSG configuration; the first-section tapered CPW is electrically connected to the signal needle of the GSG needle body; the probe tip is integrally formed with the front end of the first-section tapered CPW; the input transition unit is coupled to the tail end of the GSG needle body; characterized in that... The final state of the probe tip and the front end of the first tapered CPW form a matching profile. The matching profile enables the GSG needle body, the first tapered CPW and the air bridge to work together to form a probe structure that completes impedance self-matching and maintains transmission continuity with the input transition unit.

2. The millimeter-wave GSG high-frequency test probe as defined in claim 1, characterized in that, The first segment of the tapered CPW tapers continuously from wide to narrow along the test direction.

3. The millimeter-wave GSG high-frequency test probe as defined in claim 1, characterized in that, The first conical CPW has grounding channels on both sides, and an air bridge is used to bridge the grounding channels on both sides to form a return path.

4. The millimeter-wave GSG high-frequency test probe as defined in claim 1, characterized in that, The probe tip is used to establish the millimeter-wave contact area.

5. The millimeter-wave GSG high-frequency test probe as defined in claim 1, characterized in that, The contour design ensures a continuous transition between external power feeding and internal power transfer between the probe structure and the input transition unit.

6. An impedance self-matching method for a millimeter-wave GSG high-frequency test probe, applied to the millimeter-wave GSG high-frequency test probe as defined in any one of claims 1 to 5, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional electromagnetic model including probe base, GSG needle body, first conical CPW, air bridge and probe tip. Acquire broadband port scattering data in an equally spaced sampling order and store them into a data sequence. At the same time, record the position trajectory of the port status point on the Smith circle to form the port status trajectory. Step 2: Use a matrix pencil to perform mode extraction on the data sequence, solve a set of complex exponential poles, and reconstruct the port scattering data based on the complex exponential poles to generate a list of characteristic modes. By analyzing the impulse response and field intensity peak position of each characteristic mode, the list of characteristic modes is divided into multiple response clusters belonging to specific components in the probe tip, the first conical CPW, and the air bridge, and response cluster identifiers are generated. Step 3: Perform probe tip geometry inversion based on the adjoint method, determine the candidate modification domain of the probe tip by calculating the geometric sensitivity map, and perform geometry update driven by the primitive library consisting of three primitive operations: cone surface micro-stretching, edge arcing and slope refinement within the candidate modification domain of the probe tip to form a geometry update path. Step 4: Using the geometric descent method on the Smith circle, port state point guided iteration is performed on the geometric update path. By executing combination primitives or adsorption primitives in different target neighborhoods, the port reflection index of the port state point reaches the preset matching level, and the matching profile of the probe tip final state and the front end of the first conical CPW is output.

7. The method according to claim 6, characterized in that, In step two, the data sequence is divided into two groups of adjacent shifted data blocks of the same length according to the sampling order, forming two rectangular data structures. Singular decomposition is performed on the first rectangular data structure to obtain the column space basis set. The column space basis set is then used to project the second rectangular data structure to form a system of linear equations for solving. The effective rank is determined based on the turning point of the difference between adjacent singular values, and the complex exponential poles are solved. The impulse response of each characteristic mode is reconstructed in the time domain, and the peak arrival order is read along the direction from the probe tip to the input transition unit. Characteristic modes with increasing peak arrival order along the direction are marked as propagation tags, and characteristic modes with decreasing peak arrival order along the direction are marked as radiation tags.

8. The method according to claim 6, characterized in that, In step three, a forward excitation is applied to the port to obtain the forward field distribution, and a reverse phase equal amplitude excitation is set at the port to obtain the adjoint field distribution. The forward field distribution and the adjoint field distribution are averaged on both sides of the grid surface, multiplied face by face, and the difference is obtained to obtain the geometric sensitivity map. After each primitive operation is completed, the set of poles of the complex exponential poles remains unchanged. Only the modal coefficients are subjected to two-segment minimum difference fitting on the new geometry to quickly reconstruct the port scattering data. If the angle between the port state point and the ray of the target point and the port state trajectory decreases, the current primitive operation is recorded and included in the geometric update path.

9. The method according to claim 6, characterized in that, In step four, three target neighborhoods are set around the Smith circular target point from the outside to the inside. When the port state point is located in the outer target neighborhood, the first combination primitive is executed radially, consisting of the conical micro-stretching and the synchronous convergence of the gap at the front end of the first conical CPW, with the two primitives alternating in a one-to-one ratio. When the port state point enters the middle target neighborhood, the second combination primitive is executed tangentially, consisting of opening symmetrical micro-notches on both sides of the front end of the first conical CPW and slightly extending the bridging distance in the air bridge bridging area, with the two primitives alternating in a one-to-one ratio. When the port state point enters the inner target neighborhood, the adsorption primitive consisting of continuous edge arcing with the geometric sensitivity grid surface of the first position as the action surface is executed.

10. The method according to claim 9, characterized in that, After each execution of the first combination primitive, the second combination primitive, or the adsorption primitive, the new position of the port state point is calculated in real time. When the reduction in arc length between the new position and the previous position reaches the preset matching level threshold, the geometric update path is fixed and the mating profile is output.

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