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Berkeley ELENG 100 - Basic CNN Cell Experiments - Theory

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EECS-100 Basic CNN Cell Experiments 1EE-100 Lab: Basic CNN Cell Experiments - Theory 1. Objective In this laboratory measurement you will learn some basics of cellular neural networks (CNN), a possible op amp realization of the basic CNN cell, and some potential cellular neural network applications. 2. Introduction: Cellular Neural Network – CNN A Cellular Neural Network is any spatial arrangement of locally-coupled cells, where each cell is a dynamical system evolving according to some prescribed dynamical laws. Therefore, a CNN is defined by two mathematical constructs: • the dynamics of the cell • the coupling law relating one or more relevant variables of each cell to all neighbor cells within a prescribed sphere of influence. A standard two-dimensional CNN architecture consist of an MxN rectangular array of cells (Ci,j) where every cell is connected locally to its neighbors only as shown in Figure 1. Figure 1 A CNN cell Cij with a 3x3 sphere of influence Each cell is a dynamical system which has an input, an output, and a state variables evolving according to the following dynamical laws: where 211)(,−−+==+⋅+⋅+−=∑∑∈∈ijijijijijSklklklSklklklijijxxxfyzubyaxdtdxijij is depicted in Figure 2. • where u, x, y, stand for input, state, and output variables of a cell, respectively; • f(x) is the cell output function; • aij and bij are feed-back and feed-forward weighting coefficients, respectively, describing the coupling law among cells; • zij is the cell bias term (or offset level).EECS-100 Basic CNN Cell Experiments 2 ijx()ij ijyfx=111−1−0limitE Figure 2 Output function of the standard CNN cell 5. Cellular Neural Network Applications CNN has found numerous applications. Many artificial, physical, chemical, as well as living (biological) systems can be very conveniently modeled via CNN (chaos, self organization, dissipative structures, etc.). This paradigm allows not only the modeling but also the engineering of complex systems. For instance, as a high speed analog array signal processor, CNN can process two-dimensional images solve many time consuming image processing problems in real time. Some of these applications include high-speed target recognition and tracking, real-time visual inspection of manufacturing processes, intelligent vision capable of recognizing context sensitive and moving scenes. As an example, let us consider a relatively simple image processing task, i.e. edge detection. The following CNN program (coefficient weights) called a CNN template extracts edges from a gray-scale image and produces a binary output (black and white) image containing only the object boundaries, as shown in Figure 3. 0 0 0 -1 -1 -1 A = 0 2 0 B = -1 8 -1 z = -0.5 0 0 0 -1 -1 -1 A and B stand for feed-back and feed-forward coefficients, respectively. a) b) Figure 3 a) Input gray-scale image, b) Binary output image containing edges of objects n the left You can get a CNN template and algorithm simulator running on Windows from the following link: http://lab.analogic.sztaki.hu/Candy/ - CANDY CNN Simulator.EECS-100 Basic CNN Cell Experiments 3 4. Op Amp Realization of the Basic CNN Cell The circuit shown in Figure 4 is a simplified CNN cell circuit of cellular neural networks. It consists of the basic circuit elements, namely, a linear capacitor Cx, a linear resistor Rx, a linear voltage-controlled current source, and an output sub-circuit with the piecewise-linear output function - f(xij). Figure 4 Simplified CNN cell circuit The dynamics of the CNN cell core is the following. and the cell output is )(,xyxxxxxvfviRvdtdvC=+−=⋅ One possible op amp implementation of the above circuit is shown in Figure 5. The voltage-controlled current source is realized by op amp A1. It can be shown (good exercise for you) that 2734vRRRix⋅⋅−= under the condition that 57634RRRRR+= . In this case, the output current (ix) of the VCCS is independent of the value of the load resistor (Rx), i.e. it works as an ideal VCCS. The piecewise-linear output function is realized by op amp A2 with the constraint that 8 9 10 11limit811/satRR R REERR++==, where usually limit1EV=.EECS-100 Basic CNN Cell Experiments 4 Figure 5 Op amp realization of the Basic CNN CellEECS-100 Basic CNN Cell Experiments 5 EE-100 Lab: Basic CNN Cell Experiments – Experiment Guide You will be provided a special box designed for this laboratory measurement (Figure 8). Exp1 – Measurement of the CNN cell core and the nonlinear output function Set N1, …, N4 switches to their UP position (inverter is ON). Set N5, …, N8 switches to their LEFT position (VCCS output is not connected to the core cell). Set N9 switch to its RIGHT position (no Initial state). Set VDD=12V and VSS= -12V. a) Set the voltage level of the Initial state around zero. Switch N9 to the Initial state (LEFT position) and measure both Vx and Vy. Determine the levels of Esat and Elimit as well. A LED should be red if the Vx is above +Elimit and green if it is below –Elimit. Checking the nonlinear output function b) Set N9 switch again to its RIGHT position (no Initial state). Set the output of the function generator to a 200mVpp, 1kHz sine wave with 0 DC offset and connect it to the CNN cell (label Vx).Using the scope, observe the waveform of the input signal (Vx) and the output of the limiter (Vy). Enlarge the voltage level up to 2V. Draw both input and output signals and determine the saturation level. Hint: to determine the saturation level more exactly you can change to a more appropriate waveform (e.g. a triangle waveform). Switch to XY mode and determine the transfer characteristic. c) Now, set the scope to display the transfer characteristic (X/Y mode). Set the voltage scale to 500mV/div. Draw the transfer characteristic and determine the slope of the linear region and the saturation levels as well. Exp2 – Measurement of the voltage-controlled current source (VCCS) Connect the output of the first current generator to the core of the CNN cell (N5 is set to RIGHT). Do not connect the cell capacitor (Cx) yet. The load resistor will only be Rx. a) Using the 6V output of the power supply set the input voltage of the first VCCS to 1V, 2V, and 3V respectively (N1 should be UP). Measure the output current (ix) and determine the current amplification (g). Repeat the measurement using different CNN cell resistance (let Rx be 470Ω and 100Ω,


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