Accurate modeling of SiGe HBT using artificial neural networks: Performance Comparison of the MLP and RBF Networks

Transcription

1 Accurate modeling of SiGe HBT using artificial neural networks: Performance Comparison of the MLP and RBF etworks Malek Amiri Abdeboochali Department of Electrical Engineering Razi University Kermanshah, Iran Mohammad M. Karkhanechi Department of Electrical Engineering Razi University Kermanshah, Iran Abstract In this paper, we compare different architectures of Multi-Layer Perception (MLP) and radial basis function (RBF) neural networks for modeling of silicon-germanium (SiGe) heterounction bipolar transistors (HBTs). Model has been trained and tested with different sets of input/output data. Accuracy of the model is examined for all the DC and S parameters in a wide range of bias and frequencies. First, different architectures of the MLP and RBF are created to determine the best topology and training algorithm in term of accuracy. Then, the performance of best configuration of the MLP and RBF is compared. umerous simulation results in the paper demonstrate that the RBF provides much better performance than MLP neural networks when it comes to this type of modeling. Keywords- SiGe HBT; eural networks; modeling. I. ITRODUCTIO Heterounction Bipolar Transistors (HBTs) have become very useful devices for different applications at the microwave and millimeter-wave frequencies. HBT technology is considered as very appropriate for RF front-end circuits in next-generation wireless communications [1]. In recent years, the SiGe hetero-unction bipolar devices (HBTs) have obtained great importance due to their good noise and high frequency (HF) performance. Due to remarkable capabilities of artificial neural networks (As) such as generalization, parallel processing, nonlinear system modeling, adaptation and function approximating, As have been extensively studied and applied in a wide array of contexts [2]-[3]-[4]. The most important feature of neural models is their ability to generalize, i.e. The correct answer even for input values not used during the A training process provides. In that way, the developed models can be used for a reliable prediction over a wide range of input parameters. eural networks have been applied in microwave nonlinear device modeling and noise modeling of SiGe HBT s [5]-[6]. In this paper we study different architectures of MLP and RBF neural networks to find the network which is the best for modeling SiGe HBT DC and S parameters. The overall model architecture is composed of 9 artificial neural network (A), among which one take care of the DC fitting and the rest are for modeling the RF behavior. The inputs for the DC output (collector current) are dc collector-emitter voltage (V ce ), dc base current (I b ) and those corresponding to the RF outputs (real and imaginary part of S parameters) are the frequencies in addition to the dc collector-emitter voltage and dc base current. A simplified overview of the proposed A model is shown in Fig. 1. The rest of the paper is organized as follows: The following section gives a brief insight of the multilayer perceptron neural network. In Section III, a brief description of the radial basis function neural network is given. The DC and RF modeling using A and the corresponding results, and discussions are followed in the next section. II. THE MLP The schematic diagram of an MLP illustrated in Fig. 2. In the conventional structure of an MLP, a neuron receives its Figure 1. A simplified overview of the proposed A model for DC and S parameters modeling of SiGe HBT.

2 radial activation function (a nonlinear transfer function) and each output unit implements a weighted sum of hidden units outputs. The structure of the RBF network is shown in Fig. 3. The output of ith neuron in the output layer of the RBF network is determined as follows: M y ( x) w x c ; i 1 m i i,..., 1 Figure 2. The MLP structure. input either from other neurons or from external inputs (input vector). A weighted sum of these inputs constitutes the argument of a nonlinear activation function. The resulting value of the activation function is the neural output. In this structure, the weights correspond to the synapses in a biological neuron, while the activation function is associated with the intracellular current conduction mechanism in the soma. An artificial neuron is an oversimplified but useful approximation of the biological neuron. This simple model ignores many of the characteristics of its biological counterpart, e.g. it does not take into account the time delays that affect the dynamics of the system [7]. In Fig. 2, the output Y of the MLP is a vector with n components determined in the terms of m components of an input vector X and l components of the hidden layer. The mathematical representation may be expressed as: l m yi vi g w k xk bw bvi i 1,..., n 1 k1 Where (.) is the basis function which is described using x c, c is the center vector for hidden neuron and w i is the weight between the node of the hidden layer and the node i of the output layer, m is the number of nodes in the output layer. The norm is typically taken to be the Euclidean distance and the basis function is taken to be Gaussian: c 2 x c x exp 2 2 Where is the width parameter of the th hidden unit in the hidden layer [7]. In an RBF network there are three types of parameters that need to be chosen to adapt the network for a particular task: the center vectors c, the output weights w i, and the RBF width parameters. In this way, the training process is usually divided into two steps: First, the center and width parameters of the hidden layer are determined using only the input data set and by utilizing unsupervised training algorithm such as K-means [9], decision trees [10] and self-organizing feature maps [11]. Second, the output weights (connecting the hidden layer with the output layer) are determined using both input and output data and by Singular Value Decomposition (SVD) or Least Mean Squared (LMS) algorithms [12]. Both steps are relatively fast when compared to back-propagation training algorithm. The number of basis functions controls the Where v i and w k are synaptic weights, x k is k th element of the input vector, g(.) is an activation function and b is the bias which has the effect of increasing or decreasing the net input of the activation function depending on whether it is positive or negative, respectively. It has been shown that the MLP with a tanh nonlinearity or other monotonic nonlinearities is a universal approximator to any arbitrary input-output mappings provided that some reasonable conditions on the nonlinear mapping are satisfied [8]. III. THE RBF Radial basis function neural networks are special classes of the feed-forward neural network models. RBF network is a three-layer network, where each hidden unit implements a Figure 3. The RBF architcture.

3 complexity and the generalization ability of the RBF network. RBF networks with too few basis functions can not fit the training data adequately due to limited flexibility. I. SIMULATIO RESULTS AD DISCUSSIO In order to train an A model, the most common approach is to divide the data samples collected from experiments into two groups, the training and validation data sets. The training group is used to train the A model by adusting the weight matrices of the network model. The validation group is used to ensure that the A has properly learned the relationship between inputs and outputs and has been able to generalize the results. This data set should include samples which are not included in the training data set. This method is suitable when there are enough data samples to train the neural network. In this section, the DC and S parameters modeling of SiGe HBT will be presented. The DC modeling is done in the wide range of Vce (0 to 5 V), Ib (25 to 125μA) and RF modeling is done in the frequency range (0.1 to 40 GHz), Vce (2 and 6 V) and Ib (10μA). The DC and S parameters values used for the training data are taken from advanced design system (ADS) software. For the SiGe HBT, Vertical Bipolar Inter Company (VBIC) model into ADS simulation is used [13]. Each of the DC network and eight RF networks are trained using 380 and 302 samples of simulated data, respectively. Different sets of 125 and 100 input/output simulated samples were used as test data for validating the DC and RF behavior, respectively. The test and training data samples should be different and are selected randomly from the original database (ADS). We used MATLAB to train the A model. To decide the best network in the accuracy test we used the mean relative error (MRE%) and the average error (AE%) to compare the accuracy of these networks. for testing data set, where the relative error for variable X is given by: RE% x (sim) (pred) 100 x x (sim) where sim and pred stand for ADS simulation (the actual values) and the predicted values, respectively. Also, the Mean Relative Error is given by: TABLE I. DC/RF Prediction THE MEA RELATIVE ERROR AD AVERAGE ERROR FOR MLP MODEL WITH TEST DATA Several proposed multilayer perceptron (MLP) network configuration with different number of neurons in two hidden layer were trained using the training set. The number of neurons for each hidden layer were in the range of On the basis of two above-mentioned criteria, the MLP model with structure (i.e., two neurons in the input layer, eleven neurons in the first hidden layer, nine neurons in the second hidden layer and one neuron in the output layer) for DC modeling and, the MLP model with structure for RF modeling were selected as the best model. Gaussian basis functions with constant smoothing parameters were used for the RBF. After several trial-anderror simulations and to improve generalization, we selected σ=0.2 for RBF network. It is noted that training processes in RBF use optimized number of hidden neurons that in turn allow for efficient approximation of the mapping function between the input and output spaces. In this technique, neurons are added to the network until the sum-squared error falls beneath an error goal or a maximum number of neurons have been reached. Based on the accuracy test results that are shown in table I and table II it is clear that RBF network has better accuracy to model SiGe HBT DC and S parameters. The accuracy for RBF network is also shown graphically in Figs. 4-8, where the DC and S parameters, obtained by the ADS simulation and A model (RBFn) for bias points outside of training set i.e., test set are presented. TABLE II. Test error DC/RF Test error MRE% AE% Prediction MRE% AE% Re(S 11) Im(S 11) Re(S 12) Im(S 12) Re(S 21) Im(S 21) Re(S 22) Im(S 22) I c THE MEA RELATIVE ERROR AD AVERAGE ERROR FOR RBF MODEL WITH TEST DATA 1 x(sim) x(pred) MRE% 100 x i 1 (sim) DC/RF Prediction Test error DC/RF Test error MRE% AE% Prediction MRE% AE% Re(S 11) Im(S 11) where is the number of points. The average error for variable X is given by: 1 AE% 100 x ( sim) x(pred) i1 Re(S 12) Im(S 12) Re(S 21) Im(S 21) Re(S 22) Im(S 22) I c The results proved that RBF networks have a good performance for noise modeling of SiGe HBT s.

4 Figure 4. Current voltage characteristics curve (I c-v ce) for SiGe HBT using ADS (line) and A (scattered). Figure 7. Plot of ADS simulation and A model of S 11 and S 21 for V ce=6v Figure 5. Plot of ADS simulation and A model of S 11 and S 21 for V ce=2v Figure 8. Plot of ADS simulation and A model of S 12 and S 22 for V ce=6v REFERECES [1] Z. Marinković, A. Stosić, V. Markovic, and O. Pronic, As in Bias- Dependent Modeling of S-parameters of Microwave FETs and HBTs, Microwave Review, pp , June [2] M. Amiri, H. Davandeh, A. Sadeghian, and S. Chartier, Feedback associative memory based on a new hybrid model of generalized regression and self-feedback neural networks, eural etworks, 23(7), pp , [3] M. Amiri, M. B. Menha, and M. J. Yazdanpanah, A eural-etwork- Based Controller for a Single-Link Flexible Manipulator: Comparison of FF and DR Controllers, IJC, IEEE, pp , Hong Kong, [4] M. Amiri, A.Sadeghian, and S. Chartier, One-shot training algorithm for self feedback neural networks, Annual Conference of the orth American Fuzzy Information Processing Society - AFIPS, no , Toronto, Canada, Figure 6. Plot of ADS simulation and A model of S 12 and S 22 for V ce=2v

5 [5] X. Li, J. Gao, and G. Boeck, Microwave nonlinear device modeling by using an artificial neural network, Semicond. Sci. Technol, vol. 21, pp , [6] A. Stosić, Z. Marinković, and V. Marković, eural etwork for oise Modeling of SiGe HBT S, Journal of Automatic Control, University of Belgrade, vol. 16, pp , [7] M. Amiri, M. Rafienia, and A. Sadeghian, Estimation of betamethasone release profiles from an in situ forming system based on the biodegradable polymer using artificial neural networks, IFMBE Proceedings, pp , Germany, [8] T. Chen, and H. Chen, Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical system, IEEE Trans, eural etworks 6, pp , [9] J. Moody, and C. Darken, Fast Learning etworks of Locally-Tuned Processing Units, eural Computation, pp , [10] M. Kubat, Decision Trees Can Initialize Radial-Basis Function etworks, IEEE Transactions, eural etworks, pp , [11] J. Robert, and L.C.J. Hewlett, Radial Basis Function etworks 2, ew Advances in Design, [12] Yu. Bing, and He. Xingshi, Training Radial Basis Function etworks with Differential Evolution, Proceedings of World Academi of Science, Engineering and Technology, 11, ISS, pp , [13] A. Chakravorty, R. Garg, and C. K. Maiti, Comparison of state-of-theart bipolar compact models for SiGe-HBTs, Applied Surface Science, vol. 224, pp , 2004.