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Artificial Neural Networks for RF and Microwave Design: From Theory to Practice Qi-Jun Zhang + Kuldip C. Gupta* and Vijay K. Devabhaktuni + +Department of Electronics, Carleton University, Ottawa, ON, Canada *Department of ECE, University of Colorado, Boulder, CO, USA

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Introduction and overview Neural network structures Neural network model development process RF/Microwave component modeling using neural networks High-frequency circuit optimization using neural network models Conclusions Outline

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Accurate RF/Microwave design is crucial for the current upsurge in VLSI, telecommunication and wireless technologies Design at microwave frequencies is significantly different from low-frequency and digital designs Substantial development in RF/microwave CAD techniques have been made during the last decade Further advances in CAD are needed to address new design challenges, e.g., 3D-EM optimization, CPW and multi- layered circuits, IC antenna modules, etc Fast and accurate models are key to efficient CAD Neural network based modeling and design could significantly impact high-frequency CAD Introduction

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A Quick Illustration Example: Neural Network Model for Delay Estimation in a High-Speed Interconnect Network

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High-Speed VLSI Interconnect Network Driver 1 Driver 2 Receiver 1 Driver 3 Receiver 2 Receiver 3 Receiver 4

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Circuit Representation of the Interconnect Network C1R1R2C2 C4R4 C3R3 L1L2 L3 L4 1 2 3 4 Source Vp, Tr Rs

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A PCB contains large number of interconnect networks, each with different interconnect lengths, terminations, and topology, leading to need of massive analysis of interconnect networks During PCB design/optimization, the interconnect networks need to be adjusted in terms of interconnect lengths, receiver-pin load characteristics, etc, leading to need of repetitive analysis of interconnect networks This necessitates fast and accurate interconnect network models and neural network model is a good candidate Need for a Neural Network Model

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Neural Network Model for Delay Analysis L 1 L 2 L 3 L 4 R 1 R 2 R 3 R 4 C 1 C 2 C 3 C 4 R s Vp T r e1 e2 e3 …... 1 2 3 4

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Simulation Time for 20,000 Interconnect Configurations Method CPU Circuit Simulator (NILT) 34.43 hours AWE 9.56 hours Neural Network Approach 6.67 minutes

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Neural networks have the ability to model multi-dimensional nonlinear relationships Neural models are simple and the model computation is fast Neural networks can learn and generalize from available data thus making model development possible even when component formulae are unavailable Neural network approach is generic, i.e., the same modeling technique can be re-used for passive/active devices/circuits It is easier to update neural models whenever device or component technology changes Important Features of Neural Networks

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Neural models are efficient alternatives to closed-form expressions, equivalent circuit models and look-up tables Neural network models can be developed from measured or simulated data Neural models can also be used to update or improve the accuracy of already existing models Neural network models have been developed for active devices, passive components and interconnect networks These models have been used in circuit simulators for circuit- level simulation, design and optimization Neural Networks for RF/Microwave Applications: Overview

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Neural Network Structures

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A neural network contains neurons (processing elements) connections (links between neurons) A neural network structure defines how information is processed inside a neuron how the neurons are connected Examples of neural network structures multi-layer perceptrons (MLP) radial basis function (RBF) networks wavelet networks recurrent neural networks knowledge based neural networks MLP is the basic and most frequently used structure Neural Network Structures

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MLP Structure (Output) Layer L (Hidden) Layer L-1 12 NLNL N L-1 321........... (Hidden) Layer 2 (Input) Layer 1 321 N2N2 N1N1 312 x1x1 x2x2 x3x3.. xnxn y1y1 y2y2 ymym

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Information Processing In a Neuron (.) ….

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Input layer neurons simply relay the external inputs to the neural network Hidden layer neurons have smooth switch-type activation functions Output layer neurons can have simple linear activation functions Neuron Activation Functions

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Sigmoid ( )=1/(1 +e - ) Activation Functions for Hidden Neurons Arc-tangent ( )=(2/ )arctan( ) Hyperbolic-tangent ( )=(e + -e - )/(e + +e - )

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MLP Structure (Output) Layer L (Hidden) Layer L-1 12 NLNL N L-1 321........... (Hidden) Layer 2 (Input) Layer 1 321 N2N2 N1N1 312 x1x1 x2x2 x3x3.. xnxn y1y1 y2y2 ymym x z (1) z (l -1) z (2) z (L) y

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Z1Z1 Z2Z2 Z3Z3 Z4Z4 y 1 y 2 x 1 x 2 x 3 W jk W ki Outputs y j = W jk Z k k 3 Layer MLP: Feedforward Computation Inputs Z k = tanh( W ki x i ) Hidden Neuron Values i

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How can ANN represent an arbitrary nonlinear input-output relationship? Universal Approximation Theorem (Cybenko, 1989, Hornik, StinchCombe and White, 1989) In plain words: Given enough hidden layer neurons, a 3-layer MLP neural network can approximate an arbitrary continuous multidimensional function to any desired accuracy

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The number of hidden neurons depends upon the degree of non-linearity, and dimension of the original problem Highly nonlinear problems and high dimensional problems need more neurons while smoother problems and small dimensional problems need fewer neurons To determine number of hidden neurons experience empirical criteria adaptive schemes software tool internal estimation How many hidden neurons are needed?

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Development of Neural Network Models

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Notation y = y(x, w): ANN model x: inputs of given modeling problem or ANN y: outputs of given modeling problem or ANN w: weight parameters in ANN d : data of y from simulation or measurement

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Define Model Input-Output and Generate Data Define model input-output (x, y), for example, x: physical/geometrical parameters of the component y: S-parameters of the component Generate (x, y) samples (x k, d k ), k = 1, 2, …, P, such that the data set sufficiently represent the behavior of the given x-y problem Types of Data Generator: simulation and measurement

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Uniform grid distribution Non-uniform grid distribution Design of Experiments (DOE) methodology central-composite design 2 n factorial design Star distribution Random distribution Where Data Should be Sampled x1 x3 x2

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Input / Output Scaling The orders of magnitude of various x and d values in microwave applications can be very different from one another. Scaling of training data is desirable for efficient neural network training The data can be scaled such that various x (or d ) have similar order of magnitude

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Training, Validation and Test Data Sets The overall data should be divided into 3 sets, training, validation and test. Notation: T r -Index set of training data V-Index set of validation data T e -Index set of test data In RF/microwave cases where overall data is limited, validation and test (or training and validation) data can be shared.

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Error Definitions Training error: Validation and test errors E V and E Te can be similarly defined. Training Objective: Adjust w to minimize E V, but the update of w is carried out using the information and At end of training, the quality of the neural model can be tested using test error E Te

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Sample-by-sample (or online) training: ANN weights are updated every time a training sample is presented to the network, i.e., weight update is based on training error from that sample Batch-mode (or offline) training: ANN weights are updated after each epoch, i.e., weight update is based on training error from all the samples in training data set An epoch is defined as a stage of ANN training that involves presentation of all the samples in the training data set to the neural network once for the purpose of learning Types of Training

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Neural Network Training The error between training data and neural network outputs is feedback to the neural network to guide the internal weight update of the network Neural Network W y Training Data d Training Error -

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Typical Training Process Step 1: w = initial guess, set epoch = 0 Step 2: If ( E V (epoch) max_epoch) then STOP Step 3: Compute (or and ) using all samples in training data set (i.e., batch-mode training) Step 4: Use optimization algorithm to find and update the weights Step 5: Set epoch = epoch + 1 and GO TO Step 2

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Gradient-based Training Algorithms where h is the direction of the update of w is the step size Gradient-based methods use information of and to determine update direction h Step size is determined in one of the following ways: Small value either fixed or adaptive during training Line minimization to find best value of Examples of algorithms: backpropagation, conjugate gradient, and quasi-Newton

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Example: Backpropagation (BP) Training (Rumelhart, Hinton, Williams 1986) In the gradient algorithm, Let the update direction h be the negative gradient direction, then: or where is called learning rate is called momentum factor

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Desired accuracy achieved? Yes Flow-chart Showing Neural Network Training, Neural Model Testing, and Use of Training, Validation and Test Data Sets in ANN Modeling Evaluate validation error Perform feedforward computation for all samples in validation set Assign random initial values for all the weight parameters Select a neural network structure, e.g., MLP STOP Training Evaluate test error as an independent quality measure for ANN model reliability Perform feedforward computation for all samples in test set START Perform feedforward computation for all samples in training set Compute derivatives of training error w.r.t. ANN weights Update neural network weight parameters using a gradient-based algorithm (e.g., BP, quasi-Newton) Evaluate training error Evaluate validation error Perform feedforward computation for all samples in validation set Assign random initial values for all the weight parameters Select a neural network structure, e.g., MLP Evaluate test error as an independent quality measure for ANN model reliability Perform feedforward computation for all samples in test set STOP Training Perform feedforward computation for all samples in training set Compute derivatives of training error w.r.t. ANN weights Update neural network weight parameters using a gradient-based algorithm (e.g., backpropagation) Evaluate training error START No Yes Desired accuracy achieved? Evaluate validation error Perform feedforward computation for all samples in validation set Desired accuracy achieved?

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Example: EM-ANN Models for CPW Circuit Design and Optimization

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Example: CPW Symmetric T-junction Range of input parameters of CPW T-junction model Input Parameter Minimum Value Maximum Value Frequency 1 GHz 50 GHz Win 20 m 120 m Gin 20 m 60 m Wout 20 m 120 m Gout 20 m 60 m Substrate: H=25 mil r =12.9 tan = 0.0005 Strip: t metal = 3 m W a = 40 m CPW T-junction Geometry Strip G out W out WaWa W in G in

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Error Comparison Between EM-ANN Model and EM Simulations for the CPW Symmetric T-Junction |S 11 | S 11 |S 13 | S 13 |S 23 | S 23 |S 33 | S 33 Training Data Average Error Std. Deviation 0.00150 0.00128 0.754 0.696 0.00071 0.00058 0.176 0.172 0.00084 0.00097 0.246 0.237 0.00106 0.00109 0.633 0.546 Test Data Average Error Std. Deviation 0.00345 0.00337 0.782 0.674 0.00088 0.00085 0.141 0.125 0.00126 0.00105 0.177 0.129 0.00083 0.00068 0.838 0.717

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Example: ANN Based Design of a CPW Folded Double-Stub Filter

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CPW Transmission line CPW Bend CPW Short-circuit CPW Open-circuit CPW Step-in-width CPW Symmetric T-junction List of EM-ANN Models Trained from Detailed Electromagnetic (EM) Data

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CPW Folded Double-Stub Filter Designed Using EM-ANN Models of Circuit Components ANN Based Optimization: Goal: Resonant at 26 GHz Optimize l stub and l mid Required 7 overall circuit simulations CPU-Time: 3 minutes Simulation of the optimized filter circuit using EM-ANN models: 30 seconds 100 frequency points Full-wave EM simulation of the optimized filter circuit: 14 hours 17 frequency points CPW folded double-stub filter geometry

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Comparison of Optimized Circuit Responses From EM- ANN Based Simulations and Full-Wave EM Simulations

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Example: FET Modeling Using Neural Networks

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Source L W a NdNd Drain Gate Neural Model for MESFET Modeling …. I d q g q d q s L W a N d V gs V ds

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V d (V) FET I-V curves: Neural model vs FET test data V g = 0V -1V -2V -3V -4V -5V I d ( mA )

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FET S-parameters: Neural model vs FET test data Frequency (GHz) S 21 S 11 S 22 S 12 S -parameters (dB)

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SIMULATOR Harmonic Balance Equation Solver Linear subnet Nonlinear subnet YV I, Q V V Incorporating Large-Signal FET Neural Network Model into HB Circuit Simulator I, Q y V x Neural Model

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Example: Yield Optimization of a 3-Stage MMIC Amplifier Using Neural Network Models

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Three-Stage X-Band Amplifier Circuit With 3 FETs Represented By ANN Models V d1 V d3 V d2 V g1 V g3 V g2 Input Output

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Distributions for Statistical Variables

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3-Stage Amplifier: Before and After ANN Based Yield Optimization 500 Monte Carlo Simulations are Shown

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ANNs can be trained to learn RF/Microwave data and the resulting ANN model is fast and can accurately represent the corresponding input-output relationship ANN development is a computer-based training process as opposed to human-based trial-and-error process in developing empirical/equivalent circuit models Neural network modeling approach is generic, i.e., the same ANN method can be used to model passive or active components, for devices or circuits Neural models can be used in place of CPU-intensive detailed models to enhance high-level CAD operations such as circuit simulation and yield optimization Neural network based modeling and design promises to address ever increasing demand for efficient CAD Conclusions

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Advanced methods of combining neural networks with RF/Microwave knowledge for efficient modeling Towards full automation of model generation process using neural networks featuring online data generation and ANN training Modeling nonlinear dynamic behaviors of devices and circuits employing neural network techniques 3D-EM modeling of passive components using ANNs Combining neural networks with other advanced CAD concepts such as the space mapping (SM) technique Application of artificial neural networks for RF and microwave measurements Knowledge Aided Design (KAD) of microwave circuits exploiting neural networks Emerging Trends

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A HyperLink to NeuroModeler NeuroModeler is a software for developing neural network models for passive and active components/circuits for high-frequency circuit design. Here is a Web demonstration version with which you can train a MLP neural model, test it with test data, and see the neural model reproducing the input-output relationship it learnt.

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Basic Steps of Running NeuroModeler The demonstration version is self-explanatory, where the basic steps are: Press the New Neural Model button to define the neural model structure and number of input, output and hidden neurons Press the Train Neural Model button to train the neural model Press the Test Neural Model button to test the quality of the model Press the Display Model Input-Output button to see the input-output relationship reproduced by the neural model

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Start NeuroModeler Make sure your computer is connected to the Internet. Now you can click NeuroModeler here to start the Web demonstration version of the program.

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