A microwave network-aided automatic synthesis method for arbitrary-tapped T-coil

Abstract

The application discloses a microwave network assisted arbitrary-tap T-coil automatic synthesis method, comprising the following steps: firstly, using a microwave network to obtain the limit performance and the optimal topological structure of a circuit under the action of non-ideal factors; then, using the microwave network to consider the change range of the optimal inductance value when the quality factor and the coupling coefficient of the T-coil change in a reasonable range and to take the change range as an optimization area; then, according to the set index and process, combining the extended Wheeler formula and Latin hypercube sampling to obtain initial samples; then, using a Gaussian process regression to establish a proxy model of the concerned index and the parameters; finally, performing global optimization through a multi-path global optimization algorithm to obtain a target T-coil layout. It is verified that the method can efficiently synthesize the optimal T-coil.

Description

Technical Field

[0001] This invention belongs to the field of radio frequency integrated circuit design, and particularly relates to an automatic synthesis method for arbitrary tap T-type coils assisted by microwave networks. Background Technology

[0002] T-coils are widely used in bandwidth extension applications. In electrostatic discharge (ESD) scenarios, the current discharge path is typically capacitive, which severely impacts high-speed signals. Therefore, T-coils are needed to make the signal invisible to the ESD load. Typically, a T-coil has only one tap, and while there are well-established theoretical calculations for its parameters, these methods are based on idealized scenarios and are practically unusable in real-world engineering. Furthermore, a single-tap T-coil can only connect to one ESD load. In practice, multi-level ESD protection is often used to ensure the chip's ESD protection capability. Using a separate T-coil for each ESD level would consume a significant amount of chip area. Therefore, using multi-tap T-coils instead of multiple T-coils is essential. Summary of the Invention

[0003] The purpose of this invention is to provide an automatic synthesis method for arbitrary tap T-coils assisted by microwave networks, so as to solve the technical problem that using a T-coil for each level of electrostatic protection would consume a large amount of chip area.

[0004] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0005] A microwave network-assisted automatic synthesis method for arbitrary tapped T-type coils, comprising the following steps:

[0006] Step S1: Set indicators and process constraints;

[0007] Step S2: Under the premise of the indicators and process constraints set in step S1, the optimal circuit topology is determined using microwave network analysis methods, such as the number of taps and load type. This step is optional.

[0008] Step S3: Based on the optimal circuit topology obtained in step S2, the microwave network optimization method is used to consider the range of change of each inductance value and the total inductance value of the T-coil when the quality factor and coupling coefficient of the T-coil vary within a reasonable range.

[0009] Step S4: Use the extended Wheeler formula and Latin hypercube sampling to obtain a certain number of initial samples;

[0010] Step S5: First, based on the initial sample obtained in step S4, the Gaussian process regression machine learning method is used to train the model on the index and the low-frequency inductance value of each inductor in T-coil, and finally the surrogate model is obtained.

[0011] Step S6: Optimize the surrogate model using a global optimization algorithm. Depending on the direction of the index optimization, the lower confidence bound (LCB) or upper confidence bound (UCB) method is used to explore potential points and obtain multiple sets of optimal target values ​​and corresponding input parameter combinations.

[0012] Step S7: Perform full-wave simulation on the input parameter combinations obtained in step S6, output the optimal set of parameter combinations and their simulation results, and update the sample set to determine whether the simulation results meet the design specifications. If not, repeat steps S5 to S7 until the loop stops.

[0013] Furthermore, the number of T-coil taps is an integer greater than 1, and T-coil can be stretched or compressed to fit any rectangular area, thereby improving chip space utilization.

[0014] Furthermore, the indicators include the indicators of the T-coil itself or the circuit indicators; the indicators of the T-coil itself include inductance value, quality factor, and coupling coefficient, while the circuit indicators include S-parameters and their derived parameters, including S21, S11, and group delay.

[0015] Furthermore, in step S1, the process constraints include geometric parameter constraints, which specifically include: maximum external width, maximum external height, maximum line width, minimum line width, maximum spacing, minimum spacing, maximum number of turns, minimum number of turns, maximum scaling factor, and minimum scaling factor.

[0016] Furthermore, in step S2, this method adaptively adjusts the number of taps in each T-coil and the load connected to each tap within an allowable range, and uses microwave network analysis methods to obtain the connection method with the best limiting performance as the optimal circuit topology without affecting the circuit function.

[0017] Furthermore, in step S3, the reasonable range of the quality factor and coupling coefficient of T-coil needs to be determined according to the process. The quality factor range is [0, 99], and the coupling coefficient range is [0, -0.9]. The optimal inductance value range of T-coil refers to the set of inductance values ​​when multiple sets of circuit indicators are optimal, obtained by using the optimization method of microwave network when the quality factor and coupling coefficient change within a reasonable range. The upper and lower limits of this set are taken as the range of inductance value variation.

[0018] Furthermore, in step S4, a portion of the obtained initial samples satisfy the extended Wheeler formula constraint, which is expressed as:

[0019] (1-ε)×min(L sum ) < L E <(1+ε)×max(L) sum )

[0020] Among them, L E To calculate the inductance value using the extended Wheeler formula, L sum ε is the range of total inductance value determined in step S3, and ε is the tolerance. Since the maximum deviation of low-frequency inductance value estimated by the extended Wheeler formula is 30%, ε is taken as 30%.

[0021] Furthermore, in step S4, the Wheeler formula is extended, which is specifically expressed as:

[0022]

[0023] in,

[0024]

[0025] Among them, D outw D is the outer diameter width. outh For outer diameter and height, D inw For inner diameter width, D inh Where is the inner diameter and height, N is the number of turns, K1, K2, and K3 are constant coefficients, μ0 is the magnetic permeability in vacuum, and P represents the duty cycle of the metal part.

[0026] Furthermore, in step S5, during training, a surrogate model is obtained by learning the relationship between the geometric parameters of the T-coil and the set indices and the low-frequency inductance value.

[0027] Furthermore, in step S6, the fitness function used in the method of employing a constant lower confidence bound (LCB) is expressed as follows:

[0028]

[0029] The fitness function used in the method employing the constant upper bound of the confidence bound UCB is expressed as follows:

[0030]

[0031] Where x represents the geometric parameters optimized by the algorithm, y(x) is the predicted mean under this set of geometric parameters, and CB i Let be the i-th CB value, s(x) be the prediction variance under this set of geometric parameters, and n be the total number of CB values.

[0032] The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils of the present invention has the following advantages:

[0033] 1. According to claim 4, the method of the present invention can be used to design a variable T-shaped coil, which can be adapted to any rectangular area by adjusting the expansion rate of the T-shaped coil to optimize the circuit layout and improve the area utilization rate.

[0034] 2. This invention utilizes microwave networks to analyze the optimal performance of circuits under non-ideal conditions, and can identify the optimal circuit topology during the design phase;

[0035] 3. This invention combines microwave network optimization to obtain the variation range of each inductor and the total inductance of T-coil, which can greatly reduce the optimization area and improve the overall success rate;

[0036] 4. This invention uses machine learning to assist in optimization, which has better adaptability than methods such as equivalent circuits and analytical formulas, and can maintain good accuracy even at high frequencies;

[0037] 5. This invention uses multiple LCB values ​​for multi-path optimization to avoid problems such as failure to converge or getting trapped in local optima due to improper LCB value settings;

[0038] 6. According to claim 1, the present invention is not only applicable to low frequencies, but also applicable to millimeter wave bands, and can be adapted to any form of circuit structure. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of a traditional distributed ESD circuit.

[0040] Figure 2 This is the equivalent circuit diagram of the T-coil with arbitrary taps according to the present invention;

[0041] Figure 3 This is the simplified equivalent circuit diagram of the arbitrary tap T-coil of this invention;

[0042] Figure 4 This is the equivalent circuit diagram of the arbitrary tap T-coil after decoupling according to the present invention;

[0043] Figure 5 This is a schematic diagram illustrating the splitting of the T-coil network and the load network in this invention;

[0044] Figure 6 These are two sub-networks split from the T-coil network of this invention;

[0045] Figure 7 This is a schematic diagram of the T-coil network cascading of the present invention;

[0046] Figure 8 The parasitic capacitance curves of all diodes used in the embodiments of the present invention are shown below.

[0047] Figure 9 This paper compares the convergence results of the present invention with those of the traditional method when the load is a set of F6 diodes.

[0048] Figure 10 This is a comparison of the convergence results of the present invention's method with those of the traditional method when the load is two sets of F3 diodes;

[0049] Figure 11 This is a comparison of the convergence results of the present invention and the traditional method when the load is three sets of F2 diodes;

[0050] Figure 12 This invention compares the convergence results of its method with those of a traditional method when the load consists of six groups of F1 diodes.

[0051] Figure 13 Circuit topology diagram Figure 1 ;

[0052] Figure 14 Circuit topology diagram Figure 2 ;

[0053] Figure 15 A schematic diagram of the breakdown of a microwave network for a circuit with arbitrary topology;

[0054] Figure 16 Comparison of S-parameters calculated by the microwave network method with those obtained by SPECTRE simulation 1;

[0055] Figure 17 Comparison of S-parameters calculated by the microwave network method with those obtained by SPECTRE simulation 2;

[0056] Figure 18 Comparison of S-parameters calculated by the microwave network method with those obtained by SPECTRE simulation 3;

[0057] Figure 19 Flowchart of an automatic synthesis method for arbitrary tap T-type coils assisted by microwave networks;

[0058] Figure 20 Prioritize and optimize multiple optimization objectives;

[0059] Figure 21 This section compares the performance of different circuit topologies optimized using microwave networks in the case study.

[0060] Figure 22 The T-coil layout obtained by synthesizing circuit topology 1 in the case study;

[0061] Figure 23 The T-coil layout obtained by synthesizing circuit topology 2 in the case study;

[0062] Figure 24 A comparison of the circuit performance obtained by combining two different circuit topologies in the case study; Detailed Implementation

[0063] To better understand the purpose, structure, and function of this invention, the following detailed description, in conjunction with the accompanying drawings, provides an automatic synthesis method for arbitrary tap T-type coils assisted by a microwave network.

[0064] Generally, a T-coil has only one tap. However, in many scenarios, a single-level ESD system lacks sufficient ESD protection. On the other hand, connecting each level of a multi-level ESD system to a T-coil would consume a significant amount of space. A diagram of a traditional distributed ESD system is shown below. Figure 1 As shown, it distributes a large ESD load evenly across multiple smaller ESD loads, maximizing RF performance while ensuring ESD protection capabilities.

[0065] In traditional distributed ESD systems, each inductor stage is implemented using a separate transmission line, and the inductance value of each inductor segment is...

[0066]

[0067] Where ω0 is the bandwidth, Z0 is the characteristic impedance, and C is the parasitic capacitance of the ESD load after cutting. However, the traditional approach of having multiple inductors operating independently and connecting each stage of a multi-stage ESD circuit to a T-coil occupies a large area, which is difficult to implement on space-constrained chips. But if multiple taps can be led out from the T-coil, with each tap connected to a single ESD load, distributed ESD can be achieved on a single coil, saving a significant amount of area.

[0068] For a multi-tap T-coil, N-1 taps divide the coil into N parts, each segment of the inductor is coupled to every other segment, and each tap is connected to a load, such as... Figure 2 As shown.

[0069] If we consider the circuit above, the coupling between inductors makes the circuit analysis too complex. Therefore, we simplify it to consider only the coupling between adjacent inductors, such as... Figure 3 As shown.

[0070] In this case, the circuit can be decoupled, assuming the inductance of each segment of the T-coil is L. i The quality factor is Q. i L i With L i+1 The coupling coefficient between them is ki If the angular frequency is ω, then the mutual inductance between adjacent inductors is

[0071]

[0072] If the coupling coefficient is less than 0, it indicates negative coupling between inductors, and the mutual inductance is also negative; otherwise, it is positive. Given the inductance value and quality factor, the impedance of each coil segment can be calculated. Decouple it

[0073]

[0074] The circuit after decoupling is as follows Figure 4 As shown.

[0075] Directly analyzing the circuit described above is too complex; therefore, it will be disassembled and analyzed using microwave networks. The T-coil network with a load can be decomposed into T-coil network A and load network B, which have N+1 and N-1 ports respectively. It's important to note that this decomposition means the T-coil section and the load section can be completely or almost decoupled, which is achievable in most cases. The network decomposition is as follows: Figure 5 As shown.

[0076] For the T-coil network, it can be further broken down into, for example... Figure 6 The two components are shown. It's easy to see that regardless of the number of taps in a T-coil, it consists of one component 1 and N components 2. Analyzing these two components individually, their admittance matrices can be obtained as follows:

[0077]

[0078] Its corresponding scattering matrix is ​​S part1 S part2 .

[0079] When a T-coil has only one tap, one component 1 and one component 2 need to be cascaded. When a T-coil has two taps, one component 1 and two components 2 need to be cascaded, i.e., a single-tap T-coil cascaded with one component 2. When a T-coil has three taps, one component 1 and three components 2 need to be cascaded, i.e., a double-tap T-coil cascaded with one component 2. And so on. When a T-coil has N taps, component 1 and N components 2 need to be cascaded, i.e., an N-1 tap T-coil cascaded with one component 2.

[0080] Therefore, regardless of the number of taps, a T-coil is always constructed by cascading an N-1 tap T-coil with a component 2. Thus, starting with a zero-tap T-coil network A (i.e., component 1), each additional tap is cascaded with a component 2 network B. The cascaded network becomes the new T-coil network A, which is then cascaded with component 2 network B, as follows. Figure 7 As shown, the parameters of an arbitrary N-tap T-coil network can be obtained by iterating repeatedly.

[0081] Assume the scattering matrices of network A and network B are as follows:

[0082]

[0083]

[0084] in,

[0085]

[0086]

[0087]

[0088] The cascaded T-coil scattering matrix is

[0089] S T-coil =S pp +S pc (Γ-S cc )S cp #(Formula 7)

[0090] in,

[0091]

[0092] r = J2

[0093] Thus, the scattering matrix of a single T-coil is obtained.

[0094] For a load network, its scattering matrix can be obtained through measurement and simulation. The scattering matrix of an N-tap load network is: Similarly, the scattering matrix of the loaded T-coil network can be obtained using Equation 7, where,

[0095]

[0096] Γ=J N-2 ,

[0097] In this context,

[0098]

[0099]

[0100]

[0101] This allows us to establish the relationship between the T-coil electrical parameters and the final link S-parameters. Optimizing the link parameters will yield the optimal T-coil electrical parameters.

[0102] The calculation of electrical parameters of a T-coil based on an ideal load is a well-established theoretical framework. For a single-tap T-coil with a coupling coefficient of -0.5, Razavi's formula is as follows:

[0103]

[0104] Among them, C p R is the ideal capacitance value of the load. T This represents the terminating resistance value. For distributed ESD, without considering coupling between inductors, Ito specifies that the inductance value for each inductor segment should be...

[0105]

[0106] Where ω0 is the bandwidth, z0 is the characteristic impedance, and C is the parasitic capacitance of the ESD load after cutting.

[0107] The following examines the performance comparison between the traditional method and the microwave network optimization method under ideal conditions, where the inductance quality factor is infinite and the inductance and coupling coefficient are constant. The parasitic capacitance values ​​of all loads are as follows: Figure 8 As shown.

[0108] When the load consists of only one set of F6 diodes, the optimal T-coil electrical parameter values ​​are calculated using the formula given by Razavi. Under the same conditions, the optimal T-coil electrical parameter values ​​are obtained using a microwave network optimization method. The performance of both methods is obtained through SPECTRE simulation, and the results are as follows: Figure 9 As shown, the microwave network optimization results in better performance.

[0109] When the load consists of two groups of F3 diodes, three groups of F2 diodes, and six groups of F1 diodes, the optimal inductance value is calculated using the formula given by Ito when there is no coupling between the inductors. The optimal performance under these conditions is then obtained using SPECTRE simulation. Alternatively, the optimal inductance value is obtained when there is coupling between the inductors using microwave network optimization methods, with the coupling coefficient uniformly set to -0.5. The optimal performance under this condition is then obtained using SPECTRE simulation, and the results are as follows: Figure 10, Figure 11 , Figure 12 As shown, regardless of the number of taps, the performance obtained using the microwave network optimization method is always better than that of the traditional design method.

[0110] In summary, microwave network optimization methods can more comprehensively consider non-ideal characteristics, leading to better theoretical solutions. Traditional methods have overly simplistic equivalents for active components, resulting in significant deviations at high frequencies and bandwidths. Furthermore, they fail to consider the effects of inductance losses, inductance fluctuations, coupling coefficient fluctuations, and load capacitance fluctuations, making them overly idealistic and unusable in practical engineering.

[0111] The previous section introduced T-coil synthesis in a simple scenario, considering only the case of a tapped diode load. This scenario is based on a highly idealized premise and is far more complex in real-world engineering. Therefore, the following section will combine all the methods introduced above with various factors in actual engineering to generalize and extend T-coil synthesis, realizing concrete engineering value.

[0112] In actual engineering, the scenarios and frameworks of circuits vary greatly. Figure 13 and Figure 14 Two scenarios, a TX scenario and an RX scenario, are shown respectively. As can be seen, the circuit architectures of the different scenarios are quite different. In addition to the different number of T-coils on each link, the number of taps on each T-coil may also be different. Moreover, the circuit form may be a differential circuit or a single-ended circuit. Depending on the scenario, the load may be connected to the taps of the T-coil or to the input / output port of the T-coil.

[0113] Given a load, the optimal electrical parameters of the T-coil are related to the load, the current quality factor, and the current coupling coefficient. Therefore, considering non-ideal conditions, microwave network optimization can be used to obtain a better initial theoretical solution, thereby greatly narrowing the optimization range and accelerating the optimization speed. However, it is necessary to consider how to apply microwave network optimization to determine the optimization region. Generally, microwave networks are divided according to the function of the circuit, which best conforms to physical understanding. However, different circuits carry different functions, and the different circuit forms lead to significant limitations of this method. Each new scenario requires network decomposition and network cascading derivation, which consumes a lot of time.

[0114] While dividing networks based on circuit function is more intuitive, it hinders the uniformity of network topology. From another perspective, for any circuit framework, the entire link can always be divided into a backbone network and a T-coil network. The T-coil network can be viewed as branches of the backbone network; regardless of how the branches change, the backbone network remains constant. Figure 15 As shown.

[0115] For a T-coil with arbitrary taps, its scattering matrix can be obtained from the inductance value, quality factor, and coupling coefficient using the methods described above. For the backbone network, its scattering matrix can be obtained using SPECTRE simulation.

[0116] Assume there are n in total tcoil There are t T-coils, each with t taps. i If the number of channels in the circuit is m (1 for single-ended and 2 for differential), then the total number of ports in the backbone network is . Assume the scattering matrix of each T-coil is The scattering matrix of the cascaded link is then:

[0117]

[0118] Among them, S pp S pc S cc S cp Γ are respectively

[0119]

[0120]

[0121]

[0122]

[0123] This leads to a method for calculating the link scattering matrix under any circuit. Figure 16 , 17 Section 18 compares several sets of S-parameters calculated using the microwave network cascade method with those obtained from SPECTRE simulations. The dashed lines are from SPECTRE simulations, while the solid lines are from microwave network calculations. It is evident that their results are nearly identical, further demonstrating the accuracy of the microwave network methodology. Therefore, microwave network calculations can replace SPECTRE, significantly saving simulation time, but the performance is limited to S-parameters and their derived parameters.

[0124] Combining the methods mentioned above, a flowchart of an automatic synthesis method for arbitrary tap T-type coils assisted by microwave networks is shown below. Figure 19 As shown, it includes the following steps.

[0125] Step 1: Initialize the algorithm.

[0126] Specifically, this step requires setting the chip manufacturing process, the metal layers used, and the target circuit netlist. In addition, it requires inputting the desired circuit performance and geometric constraints, including the maximum external width D.outwmm Maximum external height D outhm Maximum line width W max Minimum line width W min Maximum spacing S max Minimum spacing S min Maximum number of laps N max、 Minimum number of laps N min Maximum elongation γ max and minimum stretching ratio γ min .

[0127] Step 2: Optimize the circuit topology (optional).

[0128] Specifically, this step adaptively adjusts the number of T-coil taps in the netlist and uses microwave networking methods to explore the topology with optimal circuit performance when the quality factor is 20 and the coupling coefficient is -0.5.

[0129] Step 3: Explore optimization opportunities.

[0130] Specifically, this step first automatically calls SPECTRE to perform simulation based on the netlist input in step 1 or the optimal topology determined in step 2, extracting the S-parameters of the backbone network. Then, using parameter scanning, it takes into account the variation range of the inductance value of each inductor and the total inductance when the quality factor varies in the range of [0, 99], the coupling coefficient varies in the range of [0, -0.9], and the inductance value and coupling coefficient fluctuate in the range of [0%, 50%].

[0131] Step 4: Collect initial samples.

[0132] Specifically, this step involves collecting a certain number of initial samples using the Latin hypercube within the set constraints. The number of initial samples is ten times the number of variables. To provide a better starting point for global optimization, half of the initial samples need to satisfy the extended Wheeler formula constraints, i.e.

[0133] (1-ε)×min(L sum ) < L E <(1+ε)×max(L) sum )#(Formula 11)

[0134] Among them, L E To calculate the inductance value using the extended Wheeler formula, L sum ε represents the range of total inductance value determined in step 3, and ε is the tolerance. Since the maximum deviation of the low-frequency inductance value estimated by the extended Wheeler formula is 30%, ε is taken as 30%. The other half of the sample is completely randomly selected.

[0135] Step 5: Train a Gaussian process regression (GPR) surrogate model that incorporates prior knowledge.

[0136] Specifically, this step uses GPR to establish a proxy model between the geometric parameters of the T-coil and each set index and each low-frequency inductance value.

[0137] Step 6: Global optimization of multipaths.

[0138] Specifically, this step includes: Predicting all the surrogate models established in step 5, and exploring potential points using either LCB or UCB methods depending on the optimization direction of the metrics. For the minimum optimization problem, the fitness function is set using the confidence lower bound method:

[0139]

[0140] For the maximum value optimization problem, the fitness function is set using the confidence upper bound method as follows:

[0141]

[0142] Among them, CB i Let y(x) be the i-th CB value, y(x) be the predicted mean, and s(x) be the predicted standard deviation.

[0143] After obtaining all predicted values, the indicators are categorized into constraint indicators and extreme value indicators. For constraint indicators, meeting the conditions is sufficient; for extreme value indicators, it is necessary to pursue the maximum or minimum value of the indicator. Specifically, the normalized relative error of all predicted values ​​needs to be calculated, then they are categorized, and after certain transformations, a constraint target value and an extreme value target value are obtained. For constraint target values, the value can be positive or negative, and a value less than zero means that the target is met; for extreme value target values, the value is always negative and the smaller the better. In addition, the inductance value constraint obtained from microwave network optimization also needs to be met. The priority of all objectives is as follows: Figure 20 As shown.

[0144] Step 7: Verification and Output.

[0145] Specifically, this step will model and simulate the optimal geometric parameters for different paths in step 6, add the optimization results of all paths to the sample set, and determine whether any samples meet the objective. If not, return to step 5 to retrain the surrogate model; otherwise, output the geometric parameters and model that meet the objective.

[0146] The above is a detailed flowchart of an automatic synthesis method for an arbitrary tap T-type coil assisted by a microwave network provided in this embodiment. In order to more clearly illustrate the method and prove the advancement and correctness of the method in this embodiment, the following specific case is provided.

[0147] Case Study:

[0148] Design a T-coil circuit with a bandwidth of 80 GHz, requiring |S 11 | < -10dB, and within the bandwidth |S 21 |As large as possible. This case provides two possible topologies: a single-tap T-coil with one group of F3 loads and a three-tap T-coil with three groups of F1 loads. The parasitic capacitance of the diode is as follows: Figure 8 As shown.

[0149] As can be seen from the indicators, there are two indicators in this case, namely |S 11 |This is a constraint indicator; it only needs to be satisfied.|S 21 This is an extremum index, requiring the search for its extreme value under satisfied constraints. First, the limiting performance of two circuit topologies is analyzed using microwave network methods, with comparisons shown below. Figure 21 As shown, the limiting performance of both structures can satisfy |S 11 |Indicator, but for single taps|S 21 The worst value of -1.083dB was observed at 80.1GHz, while at three taps |S 21 The worst value of -0.902dB was observed at 78.1GHz, indicating that the three-tap topology is superior to the single-tap topology. Therefore, the three-tap topology is used as the benchmark.

[0150] Subsequently, using a microwave network method, the inductance value variation ranges for each inductor in the three-tap configuration were optimized to be L1 & L4 ∈ [10, 30.6] pH, L2 & L3 ∈ [10, 66.4] pH, and the total inductance value variation range was L sum ∈[40.6,128.5]pH. Table 1 shows the final synthesized T-coil geometry parameters and synthesis time. For comparison, this case study synthesized two topologies simultaneously. Figure 22 The layout of a single-tap T-coil is shown. Figure 23 The layout of the three-tap T-coil was displayed. Figure 24 The results of the T-coil synthesis are shown in the comparison. It can be seen that the final performance of the three-tap T-coil is almost consistent with the extreme performance obtained by the microwave network method, and it is indeed better than the single-tap T-coil.

[0151] Table 1

[0152] Topology Single tap T-coil Three-tap T-coil T-coil structure Single-ended octagon Single-ended octagon <![CDATA[Area (um 2 )]]> 36.90×30.15 28.51×27.63 Maximum line width (um) 5.00 2.37 Minimum line width (µm) 2.06 2.37 Spacing (um) 0.57 0.34 Number of laps 2 2 elongation 0.50 0.86 Tap position 0.53 0.4,0.55,0.73 Inner diameter width (um) 19.02 15.62 Total time (h) 2.20 2.92

[0153] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A microwave network-assisted automatic synthesis method for arbitrary tap T-type coils, characterized in that, The method includes the following steps: Step S1: Set indicators and process constraints; Step S2: Under the premise of the indicators and process constraints set in step S1, the optimal circuit topology is determined using microwave network analysis methods. Step S3: Based on the optimal circuit topology obtained in step S2, the optimization method of microwave network is used to consider the range of change of each inductance value and the total inductance value of T-coil when the quality factor and coupling coefficient of T-coil change within a reasonable range. Step S4: Obtain the initial sample using the extended Wheeler formula and Latin hypercube sampling; Step S5: First, based on the initial sample obtained in step S4, the Gaussian process regression machine learning method is used to train the model on the index and the low-frequency inductance value of each inductor in T-coil, and finally the surrogate model is obtained. Step S6: Optimize the surrogate model using a global optimization algorithm. Depending on the direction of the index optimization, the lower confidence bound (LCB) or upper confidence bound (UCB) method is used to explore potential points and obtain multiple sets of optimal target values ​​and corresponding input parameter combinations. Step S7: Perform full-wave simulation on the input parameter combinations obtained in step S6, output the optimal set of parameter combinations and their simulation results, and update the sample set to determine whether the simulation results meet the design specifications. If not, repeat steps S5 to S7 until the loop stops. In step S4, a portion of the obtained initial samples satisfy the extended Wheeler formula constraint, which is expressed as: ； in, The inductance value is calculated using the extended Wheeler formula. The range of total inductance value variation determined in step S3. To account for tolerance, since the maximum deviation of the low-frequency inductance value estimated by the extended Wheeler formula is 30%, Take 30%; In step S4, the Wheeler formula is extended, and its specific expression is as follows: ； in, ； in, The outer diameter width, For outer diameter and height, For inner diameter width, Inner diameter height For the number of laps, The constant coefficients, Permeability in vacuum This indicates the duty cycle of the metal portion.

2. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, The number of T-coil taps is an integer greater than 1, and the T-coil can be stretched or compressed to fit any rectangular area, thereby improving chip space utilization.

3. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, The aforementioned indicators include those of the T-coil itself or those of the circuitry. The specifications of T-coil itself include inductance, quality factor, and coupling coefficient, while the circuit specifications include S-parameters and their derived parameters.

4. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, In step S1, the process constraints include geometric parameter constraints, which specifically include: maximum external width, maximum external height, maximum line width, minimum line width, maximum spacing, minimum spacing, maximum number of turns, minimum number of turns, maximum scaling factor, and minimum scaling factor.

5. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, In step S2, this method adaptively adjusts the number of taps in each T-coil and the load connected to each tap of the T-coil within an allowable range. Without affecting the circuit function, it uses microwave network analysis methods to obtain the connection method with the best limiting performance as the optimal circuit topology.

6. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, In step S3, the reasonable ranges for the quality factor and coupling coefficient of T-coil need to be determined based on the process, and the range of variation for the quality factor is as follows: The coupling coefficient varies within the range of The optimal inductance range of T-coil refers to the set of inductance values ​​obtained by using microwave network optimization methods when the quality factor and coupling coefficient vary within a reasonable range, and the upper and lower limits of the set are taken as the range of inductance value variation.

7. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, In step S5, during training, a surrogate model is obtained by learning the relationship between the geometric parameters of T-coil and the set indices and the low-frequency inductance value.

8. The microwave network-assisted automatic synthesis method for arbitrary tap T-type coils according to claim 1, characterized in that, In step S6, the method of using a constant lower confidence bound (LCB) value is employed, and the fitness function used is expressed as follows: ； The fitness function used in the method employing the constant upper bound of the confidence bound UCB is expressed as follows: ； in, Geometric parameters for algorithm optimization The predicted mean under geometric parameters, For the first One CB value, The prediction variance under geometric parameters, This represents the total number of CBs.

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