Electromagnetic Simulation with 3D FEM for Design Automation in 5G Era

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(1.EM Invent,Gdansk 80-172,Poland；2.Faculty of Electronics,Telecommunications,and Informatics,Gdansk University of Technology,Gdansk 80-233,Poland)

Abstract: Electromagnetic simulation and electronic design automation (EDA) play an im⁃portant role in the design of 5G antennas and radio chips.The simulation challenges include electromagnetic effects and long simulation time and this paper focuses on simulation soft⁃ware based on finite-element method (FEM).The state-of-the-art EDA software using novel computational techniques based on FEM can not only accelerate numerical analysis,but al⁃so enable optimization,sensitivity analysis and interactive design tuning based on rigorous electromagnetic model of a device.Several new techniques that help to mitigate the most challenging issues related to FEM based simulation are highlighted.In particular,methods for fast frequency sweep,mesh morphing and surrogate models for efficient optimization and manual design tuning are briefly described,and their efficiency is illustrated on examples involving a 5G multiple-input multiple-output(MIMO)antenna and filter.It is demonstrated that these new computational techniques enable significant reduction of time needed for de⁃sign closure with the acceleration rates as large as tens or even over one hundred.

Keywords: design by optimization; electronic design automation; fast frequency sweep; in⁃teractive design tuning;mesh morphing

1 Introduction

5G technology is going to revolutionize the next decade,allowing wireless connectivity to penetrate the industrial world and society.Huge new markets will open for busi⁃ness,which are expected to play an important role in economy recovery and growth,offering new business opportu⁃nities and changing our lives.Smart cities,factories,autono⁃mous vehicles,intelligent infrastructure,electric grids,mas⁃sive machine-to-machine communications are just a few exam⁃ples of the 5G application scenarios where billions of devices will be connected in radio networks.With 5G infrastructure and technology,companies will provide new mobile services and offer new wireless products with unprecedented capabili⁃ties.To meet the demands for high data throughput,low laten⁃cy,low power consumption,quality of service and safety simul⁃taneously,wireless devices will have to fulfill stringent system and regulatory requirements that can only be satisfied by care⁃fully engineered hardware.Engineers will have to overcome enormous technical challenges and this will not be possible without new generation of electronic design automation (EDA)software that is capable of addressing these challenges with ac⁃curacy and speed not seen before.The core of 5G is wireless connectivity,so EDA software for fast electromagnetic analy⁃sis,which is necessary for accurately simulating 5G antennas and radio chips,will be essential for timely delivery of 5G in⁃novations to market.

2 Simulation Challenges and Solutions

RF circuits cannot be designed easily by using lumped ele⁃ment models.The size of each element and wavelength and electromagnetic effects,such as dispersion,radiation,conduc⁃tor and dielectric loss,and parasitic coupling have to be con⁃sidered.EDA simulates the behavior of a circuit by numerical⁃ly solving Maxwell’s equations and facilitate accurate results with these effects are taken into account.This is not a trivial task and often requires substantial computer resources.To ad⁃dress the challenges related to electromagnetic design,soft⁃ware tools have to use state-of-the-art numerical algo⁃rithms[1–7]that speed up simulations and allow designers to find the solution that meet stringent specifications.

2.1 Frequency Sweeps

To get an idea of challenges associated with computer aided design of RF circuits for the fifth generation (5G) mobile com⁃munications,let us consider an antenna,which is a basic ele⁃ment of any handheld wireless device.To meet the require⁃ments for higher data transfer rate,5G communications sys⁃tems have to use multiple-input multiple-output (MIMO) tech⁃nology.Because a high throughput is essential in 5G,massive MIMO antenna systems are necessary and designed for any handheld devices.On the other hand,different countries have allocated different parts of the spectrum for 5G service.As a result,MIMO antennas for consumer applications have to cov⁃er more than one band.Therefore,numerical simulation of a broadband or multi-band MIMO antenna can be very lengthy.To illustrate this,let us consider modelling of a 4 × 2 broad⁃band antenna for a smartphone proposed in Ref.[8].As shown in Fig.1,the antenna array consists of eight radiating ele⁃ments,each fed by a microstrip line with a tuning stub.The antenna array operates in 3.3 GHz to 6 GHz and provides high isolation between elements.

To analyze the antenna,we will use the finite-element meth⁃od(FEM),which is amongst the most powerful numerical mod⁃elling techniques,for solving partial differential equations of⁃ten used in computational electromagnetics software for highfrequency electromagnetic field simulations(Table 1).

▲Figure 1.Simulation of an 8-element multiple-input multiple-output(MIMO)antenna for a 5G terminal[8].

▼Table 1.Examples of commercial software or modules in software packages for electromagnetic EDA with a computational kernel based on FEM

FEM uses a volumetric mesh where the 3D space is divid⁃ed into small tetrahedral sub-regions (elements).Field in each tetrahedron is represented by a sum of simple (linear,quadratic or cubic) local functions.Field equations are en⁃forced within each element and across all elements.This re⁃sults in a large system of linear equations that is then numeri⁃cally solved at the desired frequency.The number of equa⁃tions is very large (often in the order of millions) so the solu⁃tion is time consuming.Fig.2 shows the results of the simu⁃lation of the antenna using InventSIM EDA software[9]for the frequency band from 2 GHz to 7 GHz.The plot shows select⁃ed scattering parameters,computed characteristics and the results of measurements reported in Ref.[8].It is seen that the agreement is good.

▲Figure 2.Selected scattering parameters(Sij)of multiple-input multi⁃ple-output(MIMO)antenna.

Let us now have a closer look at the simulation runtime.In the basic simulation scenario,called discrete sweep,a cer⁃tain number of frequency points (Nf),uniformly distributed in the band of interest,are selected,and FEM equations are solved at these points.The runtime needed to complete the simulations depends on the number of frequency points,mesh density and the order of local functions for tetrahedra.In the case of our MIMO antenna,we selectedNf=201 and the second order interpolation within each tetrahedron.The runtime for a coarse mesh (118 thousand tetrahedra) was 20 minutes,while for the mesh approximately 3.3 times finer(390 thousand tetrahedra),it was 3 hours and 25 minutes.The runtimes are given for a server with two Intel Xeon Gold 6136 processors and 576 GB RAM installed.This is certain⁃ly not attractive for a designer to wait for almost 3.5 hours to see the results.If the mesh is further refined,by a factor of three,which may sometimes be needed for getting very accu⁃rate results,the number of tetrahedra grows to 1.185 million and the runtime for 201 frequency points increases to over 16 hours.Such long computing time would make FEM simu⁃lations unattractive.This is why all EDA tools presented in Table 1 offer a feature called a fast frequency sweep,which enables much faster broadband response.With the interpolat⁃ing sweep,one of the two most common used sweep ap⁃proaches,the solution is found at a small number of frequen⁃cy points and the response between these points is interpolat⁃ed from them.The points for interpolation are selected auto⁃matically.One disadvantage of this approach is that while the scattering characteristics can be calculated between the sampling frequencies,the electromagnetic field can be com⁃puted only for the nodes.This disadvantage can be avoided in the fast frequency sweeps using model order reduction al⁃gorithms[4–5],[7].In a nutshell,the reduced order model is a mathematical technique that constructs a cheap to evaluate model of a dynamical system by finding a compact set of vec⁃tors that allow to represent the electromagnetic field at any frequency within a limited frequency band.This is possible since the electromagnetic field does not change very rapidly from one frequency point to another,so in fact it can be rep⁃resented as a linear combination of frequency-independent field patterns defined in the entire computational space,called basis vectors.What change with frequency are the am⁃plitudes of basis vectors and these amplitudes can be com⁃puted very fast.The acceleration is impressive; for instance,it took InventSIM 13 minutes to compute the response of the same 4 × 2 MIMO antenna at the 201 frequency points using wideband model order reduction algorithm for the moderately dense mesh consisting of 390 thousand tetrahedra,which is 15 times faster than the original discrete sweep.For the fin⁃est mesh of 1.185 million tetrahedra,the speedup is even larger.For this case the computations are completed in 44 minutes rather than 16 hours (21 times faster).Table 2 pro⁃vides detailed data for the simulations and the runtimes for the interpolating sweep.

It is evident that a good fast frequency sweep technique in an EDA software is crucial for enabling engineers to design and validate the performance of antennas and RF and micro⁃wave components.An optimal design is hard to achieve with⁃out fast frequency sweep.

▼Table 2.Runtime for wideband simulation of a 4×2 MIMO antenna for 5G and three mesh densities

2.2 Optimization

Often the simulation shows that the designed structure does not fulfil the desired specification.The way electromagnetic waves interact with objects,which determines the response of the circuits,depends on their shape.To ensure that the speci⁃fications are met,the geometry of antennas and microwave components in RF chips has to be altered.To achieve good performance,optimization algorithms will be applied.This re⁃quires a number of electromagnetic simulations that are per⁃formed in the optimization loop with design parameters as opti⁃mization variables.In each iteration the geometry is altered(dimensions change) and numerical analysis is then carried out from scratch.Simulations are repeated many times until the response meets the specifications.The number of itera⁃tions depends on the optimization method used and on the quality of the initial design.It is evident that the challenge re⁃lated to long computing time becomes much more severe when it comes to optimization.

A new generation of FEM EDA tools can address the chal⁃lenges not only via fast frequency sweeps,but also by treating iterations as a part of the entire design process in which the geometry gradually evolves rather than as a set of independent simulations for different geometries.In this framework,itera⁃tions are connected via the mesh and the workflow is arranged so that the same mesh is used throughout optimization rather than being generated anew each time a geometry is modified.To enable this,the coordinates of each mesh node change con⁃tinuously as the values of the design variables are modified in an optimization process.This technique is known as mesh de⁃formation or mesh morphing[10–12]and has been found to great⁃ly improve the efficiency of optimization[4].

A four-pole microwave filter is optimized to illustrate the implementation of FEM-based optimization and the signifi⁃cance of a fast frequency sweep using reduced order model and mesh morphing.The geometry of the filter is shown in Fig.3.The goal is to achieve an equiripple response in a cer⁃tain bandwidth,and five geometrical variables could be modi⁃fied to reach this goal.The design variables are the heights of posts in the coupling windows and the heights of the posts in the resonant cavities.Full details related to the geometry and specifications are provided in Ref.[3],where several gradientbased optimization techniques were discussed using FEM and the runtime for simulations was provided.The approaches con⁃sidered in Ref.[3] are the direct EM optimization using se⁃quential nonlinear programming (SNLP),which is one of the optimization techniques available in a commercial tool for electromagnetic design High Frequency Structure Simulator(HFSS),direct EM optimization using MATLAB’s fminimax procedure with the quasi-Newton method for mesh deforma⁃tion,and the new formulation of Newton’s method with con⁃straints (the Lagrangian method)with mesh deformation devel⁃oped speci fi cally for EM optimization.The number of itera⁃tions and runtime used for these three approaches with two starting points are compared in Table 3.Besides,in the last two rows of Table 3,we add the results obtained by InventSIM and its implementation of mesh deformation and fast frequen⁃cy sweep using reduced order modelling,with MATLAB’s fminimax and a built-in optimizer for general Chebyshev fil⁃ters.An important observation that can be made from the data given in the table is that there can be huge differences both in the convergence rate and the total time taken by optimization.As seen from the results,mesh deformation has a significant impact on the convergence rate.The number of iterations is much higher for the HFSS that does not offer mesh morphing,than for any other case presented in the paper,where mesh morphing is employed.For a bad starting point,one EDA soft⁃ware tool results in the time needed for the design closure 100 times shorter than another EDA tool.

▲Figure 3.Structure of the four-pole waveguide filter[3] with five geo⁃metrical variables used for direct EM design optimization.

▼Table 3.Comparison of the number of iterations and runtime of different methods for FEM-based optimization of a four-pole waveguide filter

The optimization of the filter in Ref.[3],even though con⁃sidered as a challenge for direct EM optimization for most EDA tools based on FEM,is still relatively simple in terms of the number of optimizable parameters; the example consid⁃ered above involved just five design variables.In practice,the number of geometry variables that have to be considered by an engineer is much larger.In the next example,we consider an interdigital combine filter with 18 design variables.The geom⁃etry of the filter is shown in Fig.4.The design variables in⁃clude 7 tuning screws,8 lengths between posts,input and out⁃put height,and the height of resonators (common for all).No symmetry was assumed and optimization was performed in In⁃ventSIM with both mesh morphing and fast frequency sweep enabled.For this example,the FEM matrix had 350 thousand rows and columns,and the optimizer needed 18 iterations and less than 56 minutes to converge from the initial design shown by the red curve in Fig.5 to the passband response shown by the blue one in the same figure.

2.3 Interactive Design Tuning

The optimization algorithm is a powerful tool for EDA,but it is time consuming.Moreover,an optimization algorithm it⁃self has no knowledge of the physics governing the operation of a device.It just executes a sequence of steps based on the data provided by a simulator.However,the knowledge-based design is likely to enable an acceptable result much quicker,by which the decisions of what parameters should be adjusted come from the understanding of the operating principle of a circuit or a role of a particular component in shaping the re⁃sponse.A skilled engineer can use his experience to modify certain parameters to improve the performance of the circuit.A very efficient way to do these adjustments is interactive de⁃sign tuning.The idea is to allow an engineer to continuously change one or more design parameters while monitoring the ef⁃fect of the changes.In order to realize interactive design tun⁃ing,the result of any change should be reflected in the re⁃sponse instantaneously.At first glance it seems impossible for EDA of RF circuits; as we showed in the previous sections,the simulations using full-wave FEM take long time and one has to wait for minutes or even hours before the response can be evaluated and displayed.However,this seemingly impossi⁃ble real-time interactive tuning can be achieved if a paramet⁃ric surrogate model is used instead of full-wave simulations to quickly evaluate the response and display the results on the fly each time any design parameter is changed.The surrogate model is constructed from the data computed by the FEM solv⁃er at the initial design point.Obviously,the accuracy of the surrogate model is limited and this model is valid only in the neighborhood of the point in the design space where the FEM model was computed.Nevertheless,this accuracy is often suf⁃ficient,and what is more,once an engineer is satisfied with the response obtained while manually adjusting the design variables,FEM simulations can be run and the surrogate mod⁃el updated.As an example,we show the results of interactive tuning of a dielectric resonator filter proposed in Ref.[13] for use in 2 × 2 Doherty power amplifier for a 5G massive MIMO system application.The geometry of the filter is shown in Fig.6.

Following classical synthesis,the filter was simulated in In⁃ventSIM and then manually tuned by adjusting seven geome⁃try parameters.Regular FEM simulation for this filter using a fast frequency sweep takes about 150 s.If one runs the inter⁃active tuning,the solver needs additional 21 seconds to set up a surrogate model,so manual tuning with on the fly response display for this example needs less than three minutes of pre⁃processing.

▲Figure 4.Inline 7th order interdigital filter operating in 5G band 3.4–3.6 GHz.

▲Figure 5.Initial and final response of optimized interdigital filer.

▲Figure 6.Single-channel of two-pole dielectric resonator (DR) filter for 5G applications[13].

Table 4 gives the values of the design variables before and after manual tuning.During the interactive tuning,the vari⁃ables were modified one by one and the characteristics were updated on the fly using the surrogate model.All design vari⁃ables were altered,most of which were changed by less than 1%–2%but some changed quite significantly (e.g.the tuning screw).Fig.7 shows the initial response computed with FEM(dashed blue curve) while the solid lines shows filter charac⁃teristics for final values of design variables,after interactive tuning.The black curve shows the characteristics predicted by surrogate model prediction while the red curve corresponds to the results recomputed with the full-wave FEM solver.It is evi⁃dent that there is a very good match.

3 Conclusions

Major challenges for electronic design automation tools for 5G solutions have been discussed.Various approaches to ad⁃dress these challenges and speed up the computation time of FEM-based simulation problems have been presented.Fast frequency sweeps,model order reduction,and using mesh morphing in optimization have been shown to give significant reduction of the time needed by EDA software tools to simu⁃late and optimize the performance of antennas and RF passive circuits.The concept of interactive design tuning based on a surrogate model has also been discussed as a good alternative to the optimization process.

▼Table 4.Interactive tuning of dual-channel dielectric resonator fil⁃ter for use in a Doherty power amplifier for 5G massive MIMO sys⁃tem application