1 application brief ab203a replaces an 1149 3 a advanced electrical design models table of contents diode equation forward voltage model 2 derivation of diode model 2 calculation of diode model parameters 2 worstcase diode models 3 advanced thermal modeling equations 4 maximum forward current vs. ambient temperature 4 thermallystabilized luminous flux 4
2 diode equation forward voltage model traditionally, the forward current versus forward voltage characteristics of a pn junction diode have been expressed mathematically with the diode equation below. where: v f = forward voltage, v i f = forward current, a n = ideality factor, 1 n 2 i o = reverse satura tion current, a t = temperature, k k = boltzmann constant, 1.3805 x e23 joule/ k q = electron charge, 1.602 x e19 coulomb note: at room temperature (25 c), kt/q = 0.02569 v. the reverse saturation current, i o , varies by several orders of magnitude over the automotive temperature range so this effect must be included to properly model the forward characteristics of the led lamp over temperature. for forward voltage, v f , greater than a few hundred millivolts, the exponential term predominates and the equation can be re written as: the diode equation approximately models the low current (> 1 a ) performance of an led emitter. however, at forward currents above a few ma, the ohmic losses must be included to accurately model the forward voltage. thus, the diode equation becomes: where: r s = internal series resistance, ohms the values for the diode equation model can be calculated by using three test currents ( i f1 , i f2 , and i f3 , such that i f1 < i f2 < i f3 ). then, the values of n, io, and rs would generate an equation that intercepts the forward characteristics of at these points: ( i f1 , v f1 ), ( i f2 , v f2 ), and ( i f3 , v f3 ) such as shown in figure 3.1a. the equations for n , i o , and r s are shown below:
3 figure 3.1a. diode equation forward voltage model for led emitter (semi-log scale). figure 3.2a shows how the diode equation model compares to the forward current versus forward voltage curve shown in ab203, figure 3.8. figure 3.2a. diode equation forward voltage model for hpwa-xhoo led emitter shown in figure 3.8 (semi-log scale). using the values of the nominal forward voltage at the three test currents in equations #3.3a, #3.4a, and #3.5a would generate the typical diode equation forward voltage model. (i f1 , v f1 nom ), (i f2 , v f2 nom ), (i f3 , v f3 nom ) ? (n nom , i o nom , r s nom ) figure 3.3a. worst-case diode equation forward voltage models for led emitters. note graph shows forward voltage variations for led emitters from a single forward voltage category, tested at i f = 70 ma. since there is little correlation between the forward voltages at each test condition, there are eight possible worstcase permutations of forward voltage at the three test currents. as shown in figure 3.3a, these eight combinations of forward voltage can be used with equations #3.3a, #3.4a, and #3.5a to generate eight different diode equation forward voltage models ( n , i o , and r s ): (i f1 , v f1 min ), (i f2 , v f2 min ), (i f3 , v f3 min ) ? (n lll , i o lll , r s lll ) (i f1 , v f1 min ), (i f2 , v f2 min ), (i f3 , v f3 max ) ? (n llh , i o llh , r s llh ) (i f1 , v f1 min ), (i f2 , v f2 max ), (i f3 , v f3 min ) ? (n lhl , i o lhl , r s lhl ) (i f1 , v f1 min ), (i f2 , v f2 max ), (i f3 , v f3 max ) ? (n lhh , i o lhh , r s lhh ) (i f1 , v f1 max ), (i f2 , v f2 min ), (i f3 , v f3 min ) ? (n hll , i o hll , r s hll )
4 (i f1 , v f1 max ), (i f2 , v f2 min), (i f3 , v f3 max ) ? (n hlh , i o hlh , r s hlh ) (i f1 , v f1 max ), (i f2 , v f2 max ), (i f3 , v f3 min) ? (n hhl , i o hhl , r s hhl ) (i f1 , v f1 max ), (i f2 , v f2 max ), (i f3 , v f3 max ) ? (n hhh , i o hhh , r s hhh ) in most situations, the worstcase range of forward current and forward voltage can be estimated with only two permutations of the diode equation model: v f min = vdiode ( i f , n lll , i o lll , r s lll ) = vdiode ( i f , n min , i o min , r s min ) v f max = vdiod e (i f , n hhh , i o hhh , r s hhh ) = vdiode (i f , n max , i o max , r s max ) for analyzing the operation of an electronic circuit, it is convenient to be able to write the electrical forward characteristics of a component both in terms of forward vo ltage as a function of forward current as well as forward current as a function of forward voltage. the difficulty in using the diode equation (with the r s term) is that i f as a function of v f can only be solved through an iterative process. in addition, the reverse saturation current, i o , varies by several orders of magnitude over the automotive temperature range so this effect must be included to properly model the forward characteristics of the led emitter over temperature. advanced thermal modeling equations note that, equations #3.3 in ab203 or #3.6 in ab203 can be combined wi th equation #3.9 in ab203 to derive the maximum dc forward current, i f max , versus ambient temperature, t a , and thermal resistance, r ja , shown in figure 4 of the superflux led data sheet. t j max ? t a + r ja i f max v f max ? t a + r ja i f max (v o hh + r s hh i f max ) or written as a standa rd quadratic equation: r ja r s hh i f max 2 + r ja v o hh i f max + t a C t j max ? 0 thus, the positive root solution of i f max is equal to: figure 3.4a shows equation #3.6a graphed as a function of t a and r ja for an hpwaxh00 led emitter with a maximum expected forward voltage (i.e. v f = 2.67 v at 70 ma ). values of t j max = 125 c, v o hh = 1.83 v , and r s hh = 12 ohms were used for figure 3.4a. note that figure 3.4a is the same as figure 4a, hpwa xx00 maximum dc forward current vs. ambient temperature graph, in the superflux led data sheet. equations #3.7 in ab203, #3.8 in ab203, and #3.9 in ab203 can be combined together in different ways to model the luminous flux (or luminous intensity) of led emitters due to the effects of internal selfheating (i.e. r ja p d ) and ambient temperature. equation #3.7a models the expected reduction in luminous flux due to internal selfheatin g compared to the
5 instantaneous luminous flux (i.e. at initial turn on) when the led emitter is driven at a constant forward current at a constant ambient temperature. equation #3.8a models the thermally stabilized luminous flux at any forward current compared to the instantaneous luminous flux prior to heating at a specified forward current and a constant ambient temperature. equation #3.9a models the thermally stabilized luminous flux at any forward current compared to the thermally stabilized luminous flux at test conditions of i f test , v f test , and r ja test at a constant ambient temperature. a good example of an application for equation #3.9a is the normalized luminous flux versus forward current graph shown in figure 3 of the superflux led data sheet. finally, equation #3.10a models the thermally stabilized luminous flux over temperature compared to the thermally stabilized luminous flux at test conditions of i f test , v f test , and r ja test , at 25 c. note for equations #3.8a, #3.9a, and #3.10a, that for forward currents over 30 ma, m 1.0 . figure 3.4a. maximum dc forward current versus ambient temperature for hpwa-xxoo led emitter with different system thermal resistances.
6 figure 3.5a. thermally stabilized luminous flux versus dc forward current for hpwx-xhoo led emitter with different system thermal resistances. figure 3.5a shows equation #3.9a graphed as a function of i f and r ja for an hpwaxh00 led emitter with a nominal forward voltage (i.e., v f = 2.25 v at 70 ma ). values of r ja test = 200 c/w , m = 1.0 , k = C0.0106, v o nom = 1.802 v, and r s nom = 6.4 ohms were used for figure 3.5a. note that figure 3.5a is the same as figure 3, hpwa/hpwtxx00 relative luminous flux vs. forward current graph, in the superflux led data sheet. this section discussed the key concepts of modeling the electrical, optical, and thermal performance of led signal lights. equation #3.6a is a combination of equations #3.3 in ab203 and #3.8 in ab203 that ca n be used to calculate the maximum forward current as a function of ambient temperature and thermal resistance. note that this equati on models figure 4 (maximum dc forward current versus ambient temperature) on the superflux led data sheet. equations #3.7a, #3.8a, #3.9a, and #3.10a show different combinations of equations #3.7 in ab203, #3.8 in ab203, and #3.9 in ab203 in order to model various thermal effects on the light output of the emitte r. note that equation #3.10a models figure 3 (normalized luminous flux versus forward curr ent) on the superflux led data sheet.
7 company information lumileds is a worldclass supplier of li ght emitting diodes (leds) producing billions of leds annually. lumileds is a fully integrated supplier, producing core led material in all three base colors (red, green, blue) and white. lumileds has r&d deve lopment centers in san jose, california and best, the netherland s. production capabilities in san jose, california and malaysia. lumileds is pioneering the highflux led technology and bridging the gap between solid state led technology an d the lighting worl d. lumileds is absolutely dedicated to br inging the best and brig htest led technology to enable new applications and markets in the lighting world. lumileds www.luxeon.com www.lumileds.com for technical assistance or the location of your nearest lumileds sales office, call: worldwide: +1 408-435-6044 north america: +1 408 435 6044 europe: +31 499 339 439 a sia: +65 6248 4759 fax: 408 435 6855 email us at info@lumileds.com lumileds lighting, llc 370 west trimble road san jose, ca 95131 ? 2002 lumileds lighting. all rights reserved. lumileds lighting is a joint venture between agilent technologies and philips lighting. luxeon is a trademark of lumileds lighting, llc. pr oduct specifications are subject to change without notice. publication no. ab203a (nov 2002)
|
