Accelerated Microwave Design Optimization With Tuning Space Mapping

We introduce a tuning space-mapping technology for microwave design optimization. The general tuning space-mapping algorithm is formulated, which is based on a so-called tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant updates of the design variables. The tuning model is developed in a fast circuit-theory based simulator and typically includes the fine model data at the current design in the form of the properly formatted scattering parameter values. It also contains a set of tuning parameters, which are used to optimize the model so that it satisfies the design specification. The calibration process may involve analytical formulas that establish the dependence of the design variables on the tuning parameters. If the formulas are not known, the calibration process can be performed using an auxiliary space-mapping surrogate model. Although the tuning space mapping can be considered to be a specialized case of the standard space-mapping approach, it can offer even better performance because it enables engineers to exploit their experience within the context of efficient space mapping. Our approach is demonstrated using several microwave design optimization problems.      

基于空间映射的RF MEMS 开关建模研究

空间映射的思想是通过构造粗糙模型设计变量与精确模型设计变量之间的映射关系,获得合适的替代模型（校准后的粗糙模型）,从而简化优化过程。本文针对电容耦合式RF MEMS 开关使用初始空间映射算法进行计算和优化,经过迭代,建立了精确空间和粗糙空间的映射关系,最终得到了精确空间优化设计值,利用此映射关系,可将精确空间的优化工作放到粗糙空间进行,从而大大节省时间和电脑资源。计算结果验证了该方法的可行性和高效性。     

EM-based optimization exploiting partial space mapping and exact sensitivities

We present a family of robust techniques for exploiting sensitivities in electromagnetic (EM)-based circuit optimization through space mapping (SM) technology. We utilize derivative information for parameter extractions and mapping updates. We exploit a partial SM (PSM) concept, where a reduced set of parameters is sufficient for parameter extraction optimization. It reflects the idea of tuning and execution time is reduced. Upfront gradients of both EM (fine) model and coarse surrogates can initialize possible mapping approximations. We introduce several effective approaches for updating the mapping during the optimization iterations. Examples include the classical Rosenbrock function, modified to illustrate the approach, a two-section transmission-line 10:1 impedance transformer and a microstrip bandstop filter with open stubs.     

A space-mapping interpolating surrogate algorithm for highly optimized EM-based design of microwave devices

We justify and elaborate in detail on a powerful new optimization algorithm that combines space mapping (SM) with a novel output SM. In a handful of fine-model evaluations, it delivers for the first time the accuracy expected from classical direct optimization using sequential linear programming. Our new method employs a space-mapping-based interpolating surrogate (SMIS) framework that aims at locally matching the surrogate with the fine model. Accuracy and convergence properties are demonstrated using a seven-section capacitively loaded impedance transformer. In comparing our algorithm with major minimax optimization algorithms, the SMIS algorithm yields the same minimax solution within an error of 10/sup -15/ as the Hald-Madsen algorithm. A highly optimized six-section H-plane waveguide filter design emerges after only four HFSS electromagnetic simulations, excluding necessary Jacobian estimations, using our algorithm with sparse frequency sweeps.     

A space-mapping design framework

We present a comprehensive microwave design framework for implementing the original, aggressive, implicit, and response residual space-mapping (SM) approaches through widely available software. General steps and tools for possible SM implementations are elaborated. Our presentation is a reference guide for microwave designers using the SM technique. An instructive "multiple cheese-cutting" example demonstrates the SM approach to engineering design and some possible pitfalls. For the first time, an ADS framework implements the SM steps interactively. A three-section transformer example illustrates the approach, step by step. A six-section H-plane waveguide filter design emerges after four iterations, using the implicit SM and the response-residual space-mapping (RRSM) optimization entirely within the design framework. An RRSM surrogate is developed to match the fine (HFSS) model. We use sparse frequency sweeps and do not require Jacobians of the fine model.     

新型高收敛隐式空间映射算法设计微波滤波器

该文介绍了一种高收敛隐式空间映射算法,改进了隐式空间映射算法中粗糙模型到精细模型之间参数映射。它加入粗糙模型参数选择过程,避免了粗糙模型优化中的假收敛情况,加快精细模型与设计目标的逼近速度。参数选择过程不需要增加精细模型的计算次数,提高了优化效率。该文通过设计一个发卡形滤波器,并与以前的隐式空间映射算法计算结果进行比较,优化得到了比指标性能更优越的结果。同时证明了新算法比旧算法具有更快的逼近速度和更高的优化效率的优点。     

基于空间映射算法的微带滤波器优化设计

考虑到传统电磁优化仿真方法的低效性,在原始空间映射算法的基础上,构造一种有效的输入一输出空间映射算法,并用于优化设计一个微带带通滤波器,其替代模型和精确模型分别采用了基于电路原理的AgilentADS和基于矩量法的全波电磁仿真软件FEKO进行计算分析。仿真结果表明,该算法能够有效增加所设计器件的优化自由度,大大减少计算机优化时间,有效提高了微波器件的设计效率。     

Large-Scale Network Parameter Configuration Using an On-Line Simulation Framework

As the Internet infrastructure grows to support a variety of services, its legacy protocols are being overloaded with new functions such as traffic engineering. Today, operators engineer such capabilities through clever, but manual parameter tuning. In this paper, we propose a back-end support tool for large-scale parameter configuration that is based on efficient parameter state space search techniques and on-line simulation. The framework is useful when the network protocol performance is sensitive to its parameter settings, and its performance can be reasonably modeled in simulation. In particular, our system imports the network topology, relevant protocol models and latest monitored traffic patterns into a simulation that runs on-line in a network operations center (NOC). Each simulation evaluates the network performance for a particular setting of protocol parameters. We propose an efficient large-dimensional parameter state space search technique called “recursive random search (RRS).” Each sample point chosen by RRS results in a single simulation. An important feature of this framework is its flexibility: it allows arbitrary choices in terms of the simulation engines used (e.g., ns-2, SSFnet), network protocols to be simulated (e.g., OSPF, BGP), and in the specification of the optimization objectives. We demonstrate the flexibility and relevance of this framework in three scenarios: joint tuning of the RED buffer management parameters at multiple bottlenecks, traffic engineering using OSPF link weight tuning, and outbound load-balancing of traffic at peering/transit points using BGP LOCAL_PREF parameter.      

Space-mapping optimization of microwave circuits exploitingsurrogate models

A powerful new space-mapping (SM) optimization algorithm is presented in this paper. It draws upon recent developments in both surrogate model-based optimization and modeling of microwave devices, SM optimization is formulated as a general optimization problem of a surrogate model. This model is a convex combination of a mapped coarse model and a linearized fine model. It exploits, in a novel way, a linear frequency-sensitive mapping. During the optimization iterates, the coarse and fine models are simulated at different sets of frequencies. This approach is shown to be especially powerful if a significant response shift exists. The algorithm is illustrated through the design of a capacitively loaded 10:1 impedance transformer and a double-folded stub filter. A high-temperature superconducting filter is also designed using decoupled frequency and SMs     

Combining Global and Local Surrogate Models to Accelerate Evolutionary Optimization

In this paper, we present a novel surrogate-assisted evolutionary optimization framework for solving computationally expensive problems. The proposed framework uses computationally cheap hierarchical surrogate models constructed through online learning to replace the exact computationally expensive objective functions during evolutionary search. At the first level, the framework employs a data-parallel Gaussian process based global surrogate model to filter the evolutionary algorithm (EA) population of promising individuals. Subsequently, these potential individuals undergo a memetic search in the form of Lamarckian learning at the second level. The Lamarckian evolution involves a trust-region enabled gradient-based search strategy that employs radial basis function local surrogate models to accelerate convergence. Numerical results are presented on a series of benchmark test functions and on an aerodynamic shape design problem. The results obtained suggest that the proposed optimization framework converges to good designs on a limited computational budget. Furthermore, it is shown that the new algorithm gives significant savings in computational cost when compared to the traditional evolutionary algorithm and other surrogate assisted optimization frameworks     

交指型MEMS滤波器的优化设计

交指型微机电系统(MEMS)滤波器是采用MEMS工艺制备出的交指型结构滤波器,针对交指型MEMS滤波器电磁优化算法中存在速度慢,占用计算资源大等问题,对交指型MEMS滤波器优化设计方法进行了研究。采用主动空间映射算法,在ADS和HFSS软件中建立滤波器电路结构模型和三维结构电磁模型,并分别将它们用于主动空间映射算法所需的粗糙仿真和精确仿真,仅进行了5次精确仿真就完成了一款Ku波段滤波器的优化设计。结果表明,设计的滤波器中心频率为14 GHz,顶部损耗为1.6 dB,-1 dB带宽为2.2 GHz,满足设计指标要求,同时验证了优化设计方法的可行性。     

A high-efficiency low-voltage class-E PA for IoT applications in sub-1 GHz frequency range

We present and propose a complete and iterative integrated-circuit and electro-magnetic (EM) co-design methodology and procedure for a low-voltage sub-1 GHz class-E PA. The presented class-E PA consists of the on-chip power transistor, the on-chip gate driving circuits, the off-chip tunable LC load network and the off-chip LC ladder low pass filter. The design methodology includes an explicit design equation based circuit components values'' analysis and numerical derivation, output power targeted transistor size and low pass filter design, and power efficiency oriented design optimization. The proposed design procedure includes the power efficiency oriented LC network tuning, the detailed circuit/EM co-simulation plan on integrated circuit level, package level and PCB level to ensure an accurate simulation to measurement match and first pass design success. The proposed PA is targeted to achieve more than 15 dBm output power delivery and 40% power efficiency at 433 MHz frequency band with 1.5 V low voltage supply. The LC load network is designed to be off-chip for the purpose of easy tuning and optimization. The same circuit can be extended to all sub-1 GHz applications with the same tuning and optimization on the load network at different frequencies. The amplifier is implemented in 0.13 μm CMOS technology with a core area occupation of 400 μm by 300 μm. Measurement results showed that it provided power delivery of 16.42 dBm at antenna with efficiency of 40.6%. A harmonics suppression of 44 dBc is achieved, making it suitable for massive deployment of IoT devices.     

Convergent incremental optimization transfer algorithms: application to tomography

No convergent ordered subsets (OS) type image reconstruction algorithms for transmission tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters, and methods based on the incremental expectation-maximization (EM) approach. This paper generalizes the incremental EM approach by introducing a general framework, "incremental optimization transfer." The proposed algorithms accelerate convergence speeds and ensure global convergence without requiring relaxation parameters. The general optimization transfer framework allows the use of a very broad family of surrogate functions, enabling the development of new algorithms. This paper provides the first convergent OS-type algorithm for (nonconcave) penalized-likelihood (PL) transmission image reconstruction by using separable paraboloidal surrogates (SPS) which yield closed-form maximization steps. We found it is very effective to achieve fast convergence rates by starting with an OS algorithm with a large number of subsets and switching to the new "transmission incremental optimization transfer (TRIOT)" algorithm. Results show that TRIOT is faster in increasing the PL objective than nonincremental ordinary SPS and even OS-SPS yet is convergent.     

A generalized space-mapping tableau approach to device modeling

A comprehensive framework to engineering device modeling, which we call generalized space mapping (GSM) is introduced in this paper. GSM permits many different practical implementations. As a result, the accuracy of available empirical models of microwave devices can be significantly enhanced. We present three fundamental illustrations: a basic space-mapping super model (SMSM), frequency-space-mapping super model (FSMSM) and multiple space mapping (MSM). Two variations of MSM are presented: MSM for device responses and MSM for frequency intervals. We also present novel criteria to discriminate between coarse models of the same device. The SMSM, FSMSM, and MSM concepts have been verified on several modeling problems, typically utilizing a few relevant full-wave electromagnetic simulations. This paper presents four examples: a microstrip line, a microstrip right-angle bend, a microstrip step junction, and a microstrip shaped T-junction, yielding remarkable improvement within regions of interest     

Space Mapping With Multiple Coarse Models for Optimization of Microwave Components

The performance of space mapping (SM) optimization algorithms depends primarily on the quality of the underlying coarse model. Models available in the microwave area can be cheap but inaccurate or accurate but too expensive. Here, we consider a multicoarse-model technique that allows us to combine the merits of both types of coarse models to substantially reduce the overall computational cost of optimization in comparison to traditional SM.     

Robust power grid network design considering EM aging effects for multi-segment wires

This paper presents a number of power grid network design and optimization techniques that consider the electromigration (EM) effects for multi-segment interconnect wires. First, we consider a new EM immortality constraint due to EM void saturation volume for multi-segment interconnects. It helps reduce conservativeness in the EM-aware on-chip power grid design. Along with the EM nucleation phase immortality constraint, we show that both EM immortality constraints can be naturally integrated into the existing programming based power grid optimization framework. Second, to mitigate the overly conservativeness of the immortality constrained optimization methods, we further explore three strategies: we first size up failed wires to meet one of the immortality conditions subject to the design rules; second, we consider the EM-induced aging effects on power supply networks for a target lifetime, which allows some short-lived wires to fail and optimizes the remaining wires; third, we propose a large change sensitivity-based optimization scheme to perform localized fixing based on recently proposed coupled EM-IR drop analysis method. Numerical results on a number of IBM-format power grid networks demonstrate that the new method can reduce more power grid area compared to the existing EM immortality constrained optimizations. Moreover, the new method is able to optimize power grids with nucleated wires, which would not be possible with the existing methods. Results also show the sensitivity-based localized power girds fixing can fix EM-induced IR drop violations in a few minutes for synthesized power grid networks from ARM core designs.     

Space-Mapping Optimization With Adaptive Surrogate Model

The proper choice of mapping used in space-mapping optimization algorithms is typically problem dependent. The number of parameters of the space-mapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of space-mapping type may lead to poor performance of the space-mapping optimization algorithm. In this paper, we consider a space-mapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of space-mapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations     

电磁场数值模拟TLM算法及其应用

传输线矩阵（TLM）算法是基于Huygens的波传播模型，与计算机结合起来后，成为一种强有力的三维时域电磁场数值仿真算法，在1971年TLM被首次提出以后，便得到不断的改进，从二维到三维，从扩展型结点到凝缩型结点，从时域TLM到频域TLM，而其应用也从最初的处理电磁场问题发展到对微波电路的模拟，高速IC的设计，以及处理光学，机械学，热学和声学问题，本文详细介绍了二维、三维空间的TLM算法，扩展型结点和几种改进的对称凝缩结点，阐述了TLM在各领域的应用，最后还简单介绍了我们完成的工作。     

Efficient Design Centering of High-Frequency Integrated Continuous-Time Filters

We apply ldquospace-mappingrdquo optimization for design centering high-frequency integrated continuous-time filters. By appropriately choosing the coarse model, a significant simplification of the space mapping technique is possible, since the coarse model design space is almost a translated version of the fine model design space. Graphical intuition is given for the simplified technique. A design example of a fifth-order 71.4-500-MHz constant-C scaled G_m-C Chebyshev ladder filter is presented. Measurement results from fabricated ICs are given.     

基于改进反向传播神经网络代理模型的快速多目标天线设计

针对传统天线设计方法计算代价较大的缺陷,该文构建基于反向传播神经网络(BPNN)的新型天线代理模型。为解决BPNN训练易陷入局部最优的问题,采用粒子群优化(PSO)算法来改善神经网络初始结构参数,进而构建PSO-BPNN天线代理模型,并基于该模型提出多参数天线结构的快速多目标设计方法。设计实例表明,该方法在预测精度以及计算代价等方面优于现有的常用天线设计方法。所提方法对处理复杂高维参数空间天线设计问题具有实用价值。