ANN for fast and accurate design of spiral inductors

Transcription

1 NCC 2009, January 16-18, IIT Guwahati 54 ANN for fast and accurate design of spiral ductors Rakhesh Sgh Kshetrimayum, Member, IEEE, S. S. Karthikeyan and M. Vamsi Krishna Radio Systems Laboratory, Department of Electronics and Communication Engeerg, Indian Institute of Technology, Guwahati, India, Abstract --- Artificial Neural Network (ANN) has been employed for calculation of ductance and quality factor for spiral ductor. The number of turns (N), the width of the metal trace (W), the turn spacg (S), ner radius ( D ) and the frequency of operation (f) are taken as put parameters for the ANN model. It has been observed that as the number of trag samples creases, the testg error decreases. The error testg also decreases with the crease the number of neurons the hidden layer of the three layer multi-layer perceptron (MLP) network. The computational efficiency for this approach is very high comparison to electromagnetic (EM) techniques, which takes more time. Usually it takes less than a fraction of a second for trag and testg the 81 samples usg ANN whereas the EM simulator takes few hours to generate a sgle data and few days to obta 81 samples, which is a huge ga terms of computational efficiency. The accuracy of this approach is also very close to the EM simulation technique with 1%-3% errors for Neuromodeler. A MATLAB based ANN has been developed for design of RF/microwave devices. This code gives a root mean square error (RMSE) for the same design of spiral ductor approximately 1%. I. INTRODUCTION The rapid development of commercial markets for wireless communication products over the past decade had led to an explosion of terest improved circuit design methods the radio frequency (RF) and microwave areas. Electromagnetic (EM) simulation techniques for high frequency structures developed over the past decade have helped to brg the computer-aided design (CAD) for hybrid RF or microwave circuits to its current state of the art. But modelg still remas a major bottleneck for CAD of certa classes of RF/microwave circuits like coplanar waveguide (CPW) circuits, multi-layered circuits, tegrated circuits (ICs), etc. Another factor RF and microwave design is the creasg need for optimization based design automation. There will be a trade-off between computation speed and accuracy this approach. The recent development to overcome these issues is the use of artificial neural network (ANN) to the RF and microwave CAD problems. ANNs, are formation processg systems with their design spired by the studies of the ability of the human bra to learn from observations and to generalize by abstraction [1]. Trag ANN configurations usg the data obtaed from the EM simulations develops an ANN model for each of these components. Such ANN models have been shown to reta the accuracy obtaable from EM simulators and at the same time exhibit the efficiency terms of computation. ANN is also suited for modelg active devices and for circuit optimization and statistical design. Neural-network modelg is an unconventional and modern approach for RF and microwave device designs [2]. Neural networks can be traed to learn the behavior of passive/active components/circuits [3]. A traed neural network can be used for high-level design, providg fast and accurate answers to the task it has learned [4]. Neural networks are attractive alternatives to conventional methods such as numerical modelg methods, which could be computationally expensive, or analytical methods that could be difficult to obta for new devices, or empirical modelg solutions whose range and accuracy may be limited. No prior knowledge about the put/output mappg is required for ANN model development. Unknown relationships are ferred from the data provided for trag. ANN can generalize, i.e., they can respond correctly to the new data that has not been used for the model development. ANN has the ability to model highly nonlear as well as lear put/output mappgs. ANN provides a general methodology for the development of accurate and computationally efficient electromagnetic traed ANN models for use CAD of RF/microwave circuits, anteas and systems. In today s portable wireless communications market, there is a demand for low cost, low power dissipation, high frequency IC buildg blocks that corporate spiral ductors on the silicon substrate. The availability of spiral ductor models that meet the demands of the emergg wireless communication designs is a crucial element of a successful design flow. In the early 1990s, models were built usg a discrete model library where a number of spiral ductors were fabricated and the measured data tabulated lookup tables. This provided the end user with a model database that offered a limited number of spiral topologies and an even more limited parameter sets. This approach, even though it offered very good accuracy at the selected pots, greatly limited design options. It was nonpredictive and if the process was changed, the entire effort of manually buildg the model needed to be performed all over aga. In conventional modelg techniques, numerical approaches such as solvg algebraic and differential equations are computationally expensive to obta accurate results. With empirical models cludg analytical expressions and equivalent circuits, the parasitic and couplg effects, especially high frequency doma, are often missed [5]. Yet for

2 NCC 2009, January 16-18, IIT Guwahati 55 artificial neural network approach, once traed, the weights and biases will be fixed. The relationship between model output and put becomes a closed-form expression, which makes the computation time of the modeled parameters negligible [6]. Also owg to its accuracy RF modelg [5], the artificial neural network-based approach is drawg tense attention the above applications. In this paper, neural network based software known as Neuromodeler [7], developed Prof. Q. J. Zhang s group at the Carleton Unievrsity, Canada is traed to model the ductance and quality factor of spiral ductor, which is a passive device. The number of turns (N), the width of the metal trace (W), the turn spacg (S), ner radius ( D ) and the frequency of operation (f) are taken as put parameters for the ANN model. Data generation for the spiral ductor is performed a Fite Element Method based EM simulator. The ductance and quality factor are calculated from the Y- parameter values obtaed from the EM simulator. A three layer Multi-layer Perceptron (MLP) is used for modelg of this device. We have also developed an MATLAB based ANN for designg RF/microwave devices. Both Neuromodeler as well as MATLAB based ANN for designg RF/Microwave devices give fast and accurate modelg of RF/Microwave devices. Usually it takes a fraction of a second for rug these programs for RF/microwave modelg whereas the EM simulator takes hours and sometimes days to generate those results. II. ANN MODELS FOR RF/MICROWAVE DESIGN A. Neural network structures A typical neural-network structure has at least two physical components, namely, the processg elements and the tercoections between them [1]. The processg elements are called neurons and the coections between the neurons are known as lks or synapses. Every lk has a correspondg weight parameter associated with it. Each neuron receives stimulus from other neurons coected to it, processes the formation, and produces an output. Neurons that receive stimuli from outside the network are called put neurons, while neurons whose outputs are used externally are called output neurons. Neurons that receive stimuli from other neurons and whose outputs are stimuli for other neurons the network are known as hidden neurons. Different neural-network structures can be constructed by usg different types of neurons and by coectg them differently. B. Generic notation Let n and m represent the number of put and output neurons of a neural network. Let x be an n-vector contag the external puts to the neural network, y be an m-vector contag the outputs from the output neurons, and w be a vector contag all the weight parameters representg various tercoections the neural network. The defition of w, and the maer which y is computed from x and w, determe the structure of the neural network. C. Neural network modelg approach The neural network can represent the behavior of any microwave device only after learng the origal x y relationship through a process called trag. Samples of (x- y) data, called the trag data, should first be generated from origal device EM simulators or from the device measurements. Trag is done to determe neural network weights w such that the neural model output best matches the trag data. A traed neural network model can then be used durg microwave design providg answers to the task it has learned. The origal EM based microwave device modelg problem cab be expressed as y=f(x) where f is the detailed EM based put output relationship [2]. The neural network model for same device is defed as y= f (x, w). The neural-network approach can be compared with conventional approaches for a better understandg. The first type is the detailed modelg approach such as EMbased models for passive components and physics-based models for active components. The overall model, ideally, is defed by a well-established theory and no experimental data is needed for model determation. However, such detailed models are usually computationally expensive. The second type is an approximate modelg approach, which uses either empirical or equivalent-circuit-based models for passive and active components. The evaluation of approximate models is much faster than that of the detailed models. However, the models are limited terms of accuracy and put parameter range over which they can be accurate. The neural-network approach is a new type of modelg approach where the model can be developed by learng from accurate data of the RF/microwave component. After trag, the neural network becomes a fast and accurate model representg the origal component behaviors. D. MLP Neural Network In the MLP neural network, the neurons are grouped to layers [1]. The first and the last layers are called put and output layers, respectively, and the remag layers are called hidden layers. For example, an MLP neural network with an put layer, one hidden layer, and an output layer, is referred to as three-layer MLP (or MLP3). In the MLP network, each neuron processes the stimuli (puts) received from other neurons. The process is done through a function called the activation function the neuron, and the processed formation becomes the output of the neuron. The universal approximation theorem states that there always exists a three-layer MLP neural network that can approximate any arbitrary nonlear contuous multidimensional function to any desired accuracy. This forms a theoretical basis for employg neural networks to approximate RF/microwave behaviors, which can be functions of physical/geometrical/bias parameters. MLP neural networks are distributed models, i.e., no sgle neuron can produce the overall x y relationship. For a given x, some neurons are switched on, some are off, and others are transition. It is this combation of neuron

3 NCC 2009, January 16-18, IIT Guwahati 56 switchg states that enables the MLP to represent a given nonlear put output mappg. Durg trag process, the MLP s weight parameters are adjusted and, at the end of trag, they encode the component formation from the correspondg x y trag data. E. Network size and layers For the neural network to be an accurate model of the problem to be learned, a suitable number of hidden neurons are needed. The number of hidden neurons depends upon the degree of non-learity of f and the dimensionality of x and y (i.e., values of n and m). Highly nonlear components need more neurons and smoother items need fewer neurons [3]-[4]. However, the universal approximation theorem does not specify as to what should be the size of the MLP network. The precise number of hidden neurons required for a given modelg task remas an open question. So, either by experience or a trial-and-error process is used to judge the number of hidden neurons. The appropriate number of neurons can also be determed through adaptive processes, which add/delete neurons durg trag. The number of layers the MLP can reflect the degree of hierarchical formation the origal modelg problem. In general, the MLPs with one or two hidden layers (i.e., three- or four-layer MLPs) are commonly used for RF/microwave applications. are the number of turns (N), the width of the metal trace (W), the turn spacg (S) and ner radius ( D ) Fig. 1.Top view of spiral ductor showg its dimensions III. MATLAB BASED ANN FOR RF/MICROWAVE DESIGN Steps volved the development of MLP ANN model can be summarized as below: 1. Selectg and analyzg data for trag and testg the model 2. Scalg of both trag and test data 3. Selection of the number of hidden neurons 4. Creation of feed-forward neural network 5. Selection of trag algorithm 6. Submission of trag samples for computg feed forward response 7. Computg the trag error and validation check of model 8. Trag stops when trag and validation errors are nearly equal 9. Testg of the neural model for calculatg root mean square error (RMSE) 10. The number of neurons the hidden layer are then changed and the entire process is repeated 11. The MLP ANN exhibitg the lowest RMSE is selected as fal model. A MATLAB based ANN has been developed followg the above steps modelg of RF/microwave devices. IV. SPIRAL INDUCTOR RESULTS The top view of a square spiral ductor fabricated a sample CMOS process is shown the Fig. 1. The geometry parameters of the spiral ductor Fig. 2 A widely used circuit model of the spiral ductor A general circuit model of spiral ductors is depicted Fig. 2. We will not discuss detail the circuit model of spiral ductor this paper (refer to [8]-[9] for a detailed explanation on spiral ductor circuit model). Instead we will directly generate data (put and output) of spiral ductor usg EM simulator and use that data to tra and test ANNs usg Neuromodeler as well as MATLAB based ANN for RF/microwave device design. A. Data generation for ANN model of a Spiral Inductor Square spiral ductor [10], the put parameters of the spiral ductor are the number of turns (N), the width of the metal trace (W), the turn spacg (S), ner radius ( D ) and the frequency of operation (f). The output parameters of the ANN model are ductance (L) and quality factor (Q). Data generation for the spiral ductor is performed a Fite Element Method based EM simulator. The ductance and quality factor are calculated from the Y- parameter values obtaed from the EM simulator. The equations used for the calculation of ductance and quality factor [11] are 1 L = (1) 2π f Im( Y )

4 NCC 2009, January 16-18, IIT Guwahati 57 Q Im( Y ) = (2) Re( Y ) The square spiral ductor is developed on a silicon dioxide layer below which silicon substrate is present. The put port is excited usg a lumped port. All of the spiral ductor structure is enclosed an air box and the simulation is done Driven-termal mode to fd the Y-parameters. Three spiral ductors with range 1.5 turn to 5.5 turn with step size 2 is simulated driven termal mode with ner radius varyg from 30 µm to 90 µm with step size of 30 µm, width of the spiral varyg from 10µm to 30µm with step size of 10 µm, spacg varyg from 1 µm to 5 µm with step size of 2 µm. It can be seen from Table 1, the ranges of put parameters are very different from one another. Hence all the put and output data are transformed to [-1, 1] by means of two-sided logarithmic scalg. and computational efficiency of the neural approach, extraction results for 16 test spirals are presented the Fig. 5, 6 and 7. The RMS error between the EM simulated data and neural model output for the 16 spirals is below 5% from the desired. In comparison to the EM simulator, which takes few hours to generate a sgle spiral data, ANN based approach takes fraction of a second to generate output once the network is traed, which is a huge ga terms of computational efficiency. Trag error: No. of epochs: 200; No. of samples: 2600; Trag method: Back Propagation MLP; Trag error: The testg error for 640 samples is Fig. 3 A three layer MLP network with 5 put neurons, 3 output neurons and 20 hidden neurons Fig. 4 Graph of trag error versus epochs Table 1: Trag and Test data Parameter M Max Step Ier Radius(µm) Width(µm) Spacg(µm) Number of Turns Frequency(GHz) B. NeuroModeler Results By usg full-factorial method for sample distribution, we have 81 spirals for the modelg. Out of the 81 spirals, 75 spirals are used for trag the neural network structure and 16 spirals are used for testg purpose. A three layer MLP network with 5 put neurons, 3 output neurons and 20 hidden neurons (refer to Fig. 2) is constructed usg the NeuroModeler [7] software to directly map the spiral ductor geometry characteristics to the ductor characteristics. Note that the output parameters are L, Q 11 and Q 21. The put parameters are N, W, S, D and f. The MLP neural model is then traed usg the back- propagation algorithm until low root mean square (RMS) trag and testg errors of and respectively are achieved. To demonstrate the accuracy Fig. 5 Graph showg the accuracy between neural model output versus test data for Q 11 C. MATLAB based ANN results The same MLP network is constructed usg the MATLAB software and then traed usg the Backpropagation algorithm gave the RMS trag error of The trag of the three layered ANN is stopped after 68 epochs and converged to the error of 10 2 for the validation. The RMS error between the EM simulated data and neural model output for the 16 spirals is between 1 to 3% from the desired. The graph

5 NCC 2009, January 16-18, IIT Guwahati 58 of trag and validation error versus number of epochs is depicted Fig. 8. The mean square error (MSE) for testg 640 samples is Fig. 6 Graph showg the accuracy between neural model output versus test data for Q 21 Fig. 7 Graph showg the accuracy between neural model output versus test data for self ductance (L) of neurons the hidden layer. The computational efficiency for this approach is very high when compared to EM technique, which takes more amount of time. Usually it takes less than a second for trag and testg the 81 samples usg ANN. In comparison to the EM simulator, which takes few hours to generate a sgle data and few days to generate 81 samples, ANN based approach takes less a second to generate 81 results, which is a huge ga terms of computational efficiency. The accuracy of this approach is also very close to the EM simulation technique with 1%-3% errors for the Neuromodeler and approximately 1% MSE for the MATLAB based ANN developed for RF/microwave design, which is quite accurate. In future, we will try to explore other RF/microwave device design usg ANN. REFERENCES [1] S. Hayk, Neural Networks: A comprehensive Foundation, Prentice Hall of India, July 1998 [2] Q. J. Zhang and K. C. Gupta, Neural Networks for RF and Microwave Design, Artech House, July 2000 [3] Q. J. Zhang, K. C. Gupta, and V. K Devabhaktuni, Artificial Neural Networks for RF and Microwave Design, IEEE Trans. Microw. Theory Tech., pp , Apr [4] X. Dg, V. K. Devabhaktuni, B. Chattaraj, M. C. E. Yagoub, M. Deo, J. Xu, and Q.-J. Zhang, Neural-Network Approaches to Electromagnetic-Based Modelg of Passive Components and their Applications to High-Frequency and High-Speed Nonlear Circuit Optimization, IEEE Trans. Microw. Theory Tech., pp , Jan [5] Q. Zhang, K. C. Gupta, and V.K. Devabhaktuni, "Artificial neural networks for RF and microwave design - from theory to practice," IEEE Trans. Microwave Theory Tech., vol. 51, no. 4, [6] G. L. Creech et al., "Artificial neural networks for fast and accurate EM-CAD of microwave circuits," IEEE Trans. Microwave Theory Tech., vol. 45, pp , May [7] Neuromodeler 1.5, Carleton University, Canada [8] N. M. Nguyen and R.G. Meyer, Si IC-compatible ductors and LC passive filters, IEEE J. Solid-State Circuits, vol. 25, no. 4, pp , Aug [9] C. P. Yue, C. Ryu, J. Lau, T. H. Lee and S. S. Wong, A physical model for planar spiral ductors on silicon, Techn. Dig. IEDM, pp , [10] S. Tamura, and M. Tateishi, Capabilities of a Four-Layered Feedforward Neural Network: Four Layer Versus Three, IEEE Trans. Neural Networks, Vol. 8, 1997, pp [11] K. Okada, H. Hosho and H. Onodera, Modelg and optimization of on-chip spiral ductor S-parameter doma, 2004 Int. Symp. Circuits and Systems, vol. 5, pp , May Fig. 8 Graph of trag, testg and validation error versus number of epochs for the proposed neural model V. CONCLUSION ANN has been employed for fast and accurate determation of the ductance and quality factor of spiral ductors. It has been observed that as the number of trag samples creases, the testg error decreases, the error also decreases with the crease the number