Surrogate models are a cost-effective replacement for expensive computer simulations in design space exploration. Literature has already demonstrated the feasibility of accurate surrogate models for single radio frequency (RF) and microwave devices. Within the European Marie Curie project O-MOORE-NICE! (Operational Model Order Reduction for Nanoscale IC Electronics) we aim to investigate the feasibility of the surrogate modeling approach for entire RF circuit blocks. This paper presents an overview about the surrogate model type selection problem for low noise amplifier modeling

Croon, Jeroen A

De Tommasi, Luciano

Dhaene, Tom

Gorissen, Dirk

English

QJ Zhang

TH Lee

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Surrogate Modeling of RF Circuit Blocks

Ghent University Academic Bibliography

Surrogate Modeling of RF circuit blocksLuciano De Tommasi1, Dirk Gorissen1, Jeroen Croon2, and Tom Dhaene11 Ghent University - IBBT, Department of Information Technology (INTEC),Gaston Crommenlaan 8 Bus 201, B-9050 Ghent, Belgium,luciano.detommasi@ua.ac.be, {dirk.gorissen,tom.dhaene}@ugent.be.2 NXP-TSMC Research Center, High Tech Campus 37, PostBox WY4-01,NL-5656AE Eindhoven, the Netherlands, jeroen.croon@nxp.com.Surrogate models are a cost-effective replacement for expensive computer sim-ulations in design space exploration. Literature has already demonstrated thefeasibility of accurate surrogate models for single radio frequency (RF) andmicrowave devices. Within the European Marie Curie project O-MOORE-NICE! (Operational Model Order Reduction for Nanoscale IC Electronics) weaim to investigate the feasibility of the surrogate modeling approach for entireRF circuit blocks. This paper presents an overview about the surrogate modeltype selection problem for low noise amplifier modeling.1 IntroductionDesign space exploration of RF circuit blocks involves the solution of con-strained multiobjective optimization problems in order to fulfill the perfor-mance specifications and perform what-if and sensitivity analysis. Optimiza-tion demands a large amount of circuit simulations so making the whole pro-cess very expensive.We aim to develop scalable (parametrized) models of (non-linear) RF cir-cuit blocks. This problem is too hard to be addressed applying model orderreduction techniques. Furthermore, model order reduction is a model-drivenapproach: it needs the mathematical description of the system, which is notavailable when model equations are embedded into the circuit simulator. Onthe other hand, surrogate modeling is a data-driven approach, which doesnot make any analytical assumptions upon the model which has to be re-duced. The simulator is seen as a ‘black box’ which accepts input samplesand provides output samples, see Fig. 1. Basing upon such samples, a cheap-to-evaluate surrogate model is trained. The surrogate has to be able to predictthe outputs given by the simulator when a new input (which has not beenused in the model training) is applied. This means that surrogate modeling isequivalent to construct the surface which fits the samples in Fig. 1 (in fact,surrogate models are also known as response surface models).2 Luciano De Tommasi, Dirk Gorissen, Jeroen Croon, and Tom DhaeneFig. 1. Surrogate modeling approach.Accurate surrogate models for single RF and microwave components havebeen already developed (e.g. using ANNs [1]). In this research activity, weaim to model complete RF circuit blocks. The first considered circuit block isa low noise amplifier (LNA) [2]. Other RF circuit blocks (e.g. mixers, VCOs,etc) can be analyzed following the same approach.The behavior of an LNA is described by means of the admittance and noisefunctions, which are evaluated via accurate transistor-level simulations. Suchfunctions are used to compute the performance figures (gain, input impedance,noise figure and power consumption) used by designers.Each circuit simulation typically requires one to two minutes, which is atoo long time to effectively explore how performance figures of LNA scale withkey circuit-design parameters, such as the dimensions of transistors, passivecomponents, signal properties and bias conditions. Therefore, the transistorlevel model can be usefully replaced with an accurate surrogate model (basedon transistor level simulations) which is much cheaper to evaluate.As first step towards an effective surrogate modeling process, the user ofa modeling software environment has to find out which model type (amongthose ones available [3]) work better with his problem.In this paper we summarize the results of a surrogate model type compar-ison for the LNA modeling problem.2 Software environmentThe surrogate modeling approach developed in this paper, is based on theSUrrogate MOdeling (SUMO) Matlab Toolbox [6]. The modeling flow is shownin Fig. 2. It is based on adaptive modeling and adaptive sampling loops.The surrogate modeling process starts with the evaluation of an initial de-sign (e.g. Latin hypercube, Box-Behnken, etc) which uniformly fills the designspace (the number of samples is specified by the user). Based on this initial setof samples, one or more surrogate models are constructed. Adaptive model-ing implies that a suitable optimization algorithm (e.g. hill climbing, particleswarm, genetic algorithm, DIRECT, etc) is used to tune relevant model hyper-parameters, in order to minimize the error between model and data. Modelerror is evaluated according to one or more measures and functions. After-wards, the models are ranked according to their score, and the best model isselected.Surrogate Modeling of RF circuit blocks 3In order to improve the accuracy, an adaptive sampling algorithm selectsnew samples based on the best performing models and the behavior of thereference function. In this work we applied the gradient-based method [6]because it has shown good performances with the LNA modeling problem.After each sampling iteration, an adaptive modeling iteration includingthe new samples is started, and the whole process repeats itself until one ofthe following three conditions is satisfied: (1) the maximum allowed numberof samples (specified by the user) has been reached, (2) the maximum allowedmodeling time has been exceeded, or (3) the user required accuracy has beenmet.Fig. 2. Surrogate modeling flow.3 Surrogate model type selectionOur feasibility study about surrogate modeling of low noise amplifiers aimsto determine how many design variables can be included in a model and howmany samples (number of simulations) are needed to generate the model.A model is considered sufficiently accurate when its root relative squareerror is lower than 0.05. The maximum number of samples allowed is 1500.Several surrogate model types have been compared (as implemented in theSUMO Toolbox): artificial neural networks, rational functions, radial basisfunctions, least squares support vector machines and kriging [4],[5].In order to reduce the computational cost of such comparison, transistorlevel simulations have been replaced with an analytical model of the LNA3 [4].Although the accuracy of such analytical model is obviously not sufficient toreplace the circuit simulator in the design process, it satisfactorily reproducesthe shape of the simulator outputs.Design parameters (input parameters) are, in order of importance: tran-sistor width W , source inductance Ls, frequency f , transistor length L, gate3Moreover, a cluster of PC has been used to build the surrogates.4 Luciano De Tommasi, Dirk Gorissen, Jeroen Croon, and Tom Dhaenethreshold voltage VGT , gate series inductance Lm. The modeling softwareworks with the following normalized parameters (characterized by the sub-script ‘n’) which lie in the interval [-1,1]: W = 100· 10−6· 10Wn m, Ls =0.5· 10−9· 10Lsn H, f = (11 + 10· fn)· 109 Hz, L = (90 + 30·Ln)· 10−9 m,VGT = 0.275 + 0.2·VGTn V , Lm = 1· 10−9· 10Lmn H. As output parameters,we consider the admittances y11, y12, the input/output noise currents√i2in,√i2out and their correlation ρ. If a (normalized) input parameter is not takeninto account in the modeling, it is clamped to 0, the exception being L whichis clamped to -1.Examples of accurate surrogate models are shown in Figg. 3, 4 and 5.Fig. 3. ANN models of y11 admittance with respect to inputs W and Ls. Left: realpart. Right: imaginary part.Fig. 4. ANN models of noise currents with respect to inputs W and Ls. Left: inputnoise current. Right: output noise current.Surrogate Modeling of RF circuit blocks 5Fig. 5. ANN models of correlation between input and output noise currents withrespect to inputs W and Ls. Left: real part. Right: imaginary part.Table 1 and Figg. 6 and 7 summarize the results4. Models which reach theaccuracy level RRSE < 0.05 are highlighted in bold. It is seen that accuratesurrogate models of LNA can be obtained using at most four input parameters.Best model types are rational functions for admittances and ANNs for noise.As future work, the best model types identified in this study will be usedwith transistor level simulations. In addition, further investigations will beaimed to improve the accuracy of models including five and six input param-eters.Fig. 6. Root relative square error of models of y11 and y12 as function of the numberof design variables. Left: Artificial Neural Networks. Right: best model types otherthan ANN.Acknowledgement. This work was supported by the European Commission throughthe Marie Curie Actions of its Sixth Program under the contract number MTKI-CT-2006-042477. The authors thank Dr. Joost Rommes (NXP semiconductors, Eind-hoven) for several stimulating discussions.4HC stands for ‘hill climbing’ optimization of hyperparameters [6]. GA standsfor ‘Genetic Algorithm’ based optimization [8].6 Luciano De Tommasi, Dirk Gorissen, Jeroen Croon, and Tom DhaeneFig. 7. Root relative square error of noise models as function of the number ofdesign variables. Left: input and output noise currents (Artificial Neural Networks).Right: correlation between input and output currents.Table 1. Best model type and hyperparameter optimization algoritms.N y11 y12 input noise output noise noise correlation2 Rational HC Rational GA ANN GA Rational HC ANN GA, Rational GA3 Rational HC Rational HC ANN GA ANN GA ANN GA, Rational HC4 Rational GA Rational GA ANN GA ANN GA ANN GA5 Rational GA RBF GA ANN GA ANN GA ANN GA6 RBF GA RBF GA ANN GA ANN GA ANN GAReferences1. Zhang, Q.J., Gupta, K.C.: Neural Networks for RF and Microwave Design. ArtechHouse, Boston - London (2000).2. Lee, T.H.: The Design of CMOS Radio-Frequency Integrated Circuits (SecondEdition). Cambridge University Press (2003).3. Hendrickx, W., Gorissen, D., Dhaene, T.: Grid Enabled Sequential Design andAdaptive Metamodeling. In: Proceedings of the 2006 Winter Simulation Confer-ence, WSC 2006, pp. 872–881. December 3–6 (2006).4. Gorissen, D., De Tommasi, L., Croon, J., Dhaene, T.: Automatic Model TypeSelection with Heterogeneous Evolution: An application to RF circuit block mod-eling. In: Proceedings of IEEE World Congress on Computational Intelligence,WCCI 2008, pp. 989-996. Hong Kong, China, June (2008).5. Gorissen, D., De Tommasi, L., Crombecq, K., Dhaene, T.: Sequential Modelingof a Low Noise Amplifier with Neural Networks and Active Learning. Submittedto Neural Computing and Applications, (2008)6. The SUrrogate MOdeling Toolbox Wiki Page. URLhttp://www.sumowiki.intec.ugent.be/.7. Hendrickx, W., Dhaene, T.: Sequential design and rational metamodelling. In:Proceedings of the 2005 Winter Simulation Conference, WSC 2005, pp. 290–298.December 4–7 (2005)8. The Mathworks: Genetic Algorithm and Direct Search Toolbox. URLhttp://www.mathworks.com/products/gads/.Surrogate Modeling of RF circuit blocks 7

Surrogate modeling of RF circuit blocks

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