EECS 100 Basic CNN Cell Experiments EE 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 dxij xij akl y kl bkl u kl z ij dt kl Sij kl Sij where yij f xij xij 1 xij 1 2 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 1 EECS 100 Basic CNN Cell Experiments yij f xij 1 1 xij 0 1 Elimit 1 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 0 0 1 1 1 A and B stand for feed back and feed forward coefficients respectively a 0 5 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 2 EECS 100 Basic CNN Cell Experiments 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 dv v C x x x ix dt Rx and the cell output is v y f v x 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 R R7 R4 R v 2 under the condition that 4 6 In this case the output you that i x R3 R7 R3 R5 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 R8 R9 R10 R11 Esat Elimit where usually Elimit 1V R8 R11 3 EECS 100 Basic CNN Cell Experiments Figure 5 Op amp realization of the Basic CNN Cell 4 EECS 100 Basic CNN Cell Experiments 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 470 and 100 respectively Does the current depend on the load resistor strongly Explain possible reasons of this behavior b Set the output of the function generator to a 1kHz sine wave with Vpp amplitude 2V and apply it as the input voltage of the VCCS Let Rx again be 1k Measure and display both the input and the output voltages Vu and Vx What is the phase between these two
View Full Document
Unlocking...