LED Display Driver Design: Linear Regression Analysis and Circuit Design, Lab Reports of Electrical and Electronics Engineering

Download LED Display Driver Design: Linear Regression Analysis and Circuit Design and more Lab Reports Electrical and Electronics Engineering in PDF only on Docsity! 1 PSEUDO-LABORATORY REPORT 2260 DESIGN OF AN LED DISPLAY DRIVER A. Introduction This report describes the results of experiments on the current-versus-voltage characteristics of an LED. This report also describes the design of a simple circuit to drive the LED. The handout reproduced in Appendix A gives the detailed procedure and motivation for the project. In brief, this report contains results for the following tasks: 1) Use of linear regression to find parameters for a Shockley law model of an LED, 2) Use of nonlinear optimization algorithm to find parameters for a Shockley law model of an LED, and 3) Calculation of a suitable resistor value to be used in series with an LED. B. Linear Regression Model for LED As described in Section C of Appendix A, an LED's voltage and current were measured with a simple experimental setup consisting of a 12 Volt power supply across a potentiometer in series with an LED. By adjusting the potentiometer, the voltage across and current through the LED were varied. Table I lists results measured with a digital current/voltage meter in the laboratory. TABLE I LED MEASUREMENTS voltage (V) current (mA) 1.30 0.6 1.35 2.2 1.40 13.6 1.41 21.1 We can use the data in Table I to fit a Shockley's law model describing the relationship between current and voltage for diodes: € i = Is e v /VT −1( ) (1) where i ≡ current through diode in Amps v ≡ voltage across diode in Volts Is ≡ reverse saturation current in Amps VT ≡ thermal voltage = kT /q in Volts ≈ 26 mV at room temperature k ≡ Boltzmann constant = 1.38·10–23 J/˚K T ≡ temperature ˚K (293 ˚K = 68˚F, 300˚K = 80.6˚F) q ≡ electronic charge = 1.602·10–19 C 2 Because we wish to use linear regression as our first method of modeling the diode, we reduce Equation (1) to a linear approximation. Our first step is to ignore the –1 term in (1). i = Ise v / VT (2) Our second step is to take the natural log of both sides of (2): ln i( ) = ln Is( ) + v VT (3) We observe that (3) has a linear form ln i( ) = a0 + a1v (4) where a0 ≡ ln(Is) a1 ≡ 1/VT The Matlab™ script "lin_reg_diode.m" in Appendix B finds the values of a0 and a1 that give the best fit, (in the least-squares sense), of the data in Table I to the line described by (4). Note that lin_reg_diode.m employs the Matlab™ backslash, \, operator to compute the optimal linear regression (or least-squares) fit. Fig. 1 shows the fit obtained. Table II lists the values of a0 and a1, as well as the values of Is and VT obtained from a0 and a1 by the following equations: Is = e a0 (5) VT =1 a1 (6) 1.3 1.32 1.34 1.36 1.38 1.4 1.42 0 0.005 0.01 0.015 0.02 0.025 Fig. 1. Linear regression fit (solid line) to LED data (circles) in i-v format. Horizontal axis =voltage (V); vertical axis = current (A). TABLE II LED LINEAR REGRESSION PARAMETERS parameter value a0 0.6 a1 2.2 Is 2.52e-22 (A) VT 357 (˚K)