AN1149-3A [LUMILEDS]

Advanced Electrical Design Models; 先进的电气设计模型


型号：	AN1149-3A
厂家：	LUMILEDS LIGHTING COMPANY
描述：	Advanced Electrical Design Models 先进的电气设计模型
文件：	总7页 (文件大小：187K)
中文：	中文翻译
下载：	下载PDF数据表文档文件

application brief AB20ꢀ3A

replaces AN1149ꢀ3A

Advanced Electrical

Design Models

Table of Contents

Diode Equation Forward Voltage Model

Derivation of Diode Model

Calculation of Diode Model Parameters

“Worstꢀcase” Diode Models

Advanced Thermal Modeling Equations

Maximum Forward Current Vs. Ambient Temperature

ThermallyꢀStabilized Luminous Flux

Diode Equation Forward Voltage Model

Traditionally, the forward current versus forward

voltage characteristics of a pꢀn junction diode

have been expressed mathematically with the

“Diode Equation” below.

The diode equation approximately models the

low current (> 1 µA) 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:

V_F= forward voltage, V

Where:

I_F= forward current, A

R′_S= internal series resistance, ohms

n = ideality factor, 1 ≤ n ≤ 2

I_O= reverse saturation current, A

T = temperature, °K

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 R´S 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′_Sare shown below:

k = Boltzmann constant, 1.3805 x eꢀ23 joule/°K

q = electron charge, 1.602 x eꢀ19 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 reꢀ

written as:

Figure 3.1A. Diode Equation Forward Voltage Model

for LED Emitter (Semi-Log Scale).

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.

Figure 3.2A shows how the diode equation

model compares to the forward current versus

forward voltage curve shown in AB20ꢀ3,

Figure 3.8.

Since there is little correlation between the

forward voltages at each test condition, there

are eight possible worstꢀcase 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}) ⇒

Figure 3.2A. Diode Equation Forward Voltage Model

for HPWA-xHOO LED Emitter Shown in Figure 3.8

(Semi-Log Scale).

(n _LLL, I_{O LLL}, R′_S

)

LLL

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 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

)

(I_F1, V_{F1 nom}), (I_F2, V_{F2 nom}), (I_F3, V_{F3 nom}) ⇒

LHL

(n _nom, I_{O nom}, R′_S

)

nom

(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

(I_F1, V_{F1 max}), (I_F2, V_F2min), (I_F3, V_{F3 max}) ⇒

(n _HLH, I_{O HLH}, R′_S

V_{F max}= VDIODE (I_F, n _HHH, I_{O HHH}, R′_S

= VDIODE (I_F, n _MAX, I_{O MAX}, R′_S

)

HHH

)

HLH

MAX

(I_F1, V_{F1 max}), (I_F2, V_{F2 max}), (I_F3, V_F3min) ⇒

(n _HHL, I_{O HHL}, R′_S

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 voltage 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´_Sterm) is that I_Fas

a function of V_Fcan only be solved through an

iterative process. In addition, the reverse

)

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 worstꢀcase range of

forward current and forward voltage can be

estimated with only two permutations of the

diode equation model:

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.

V_{F min}= VDIODE (I_F, n _LLL, I_{O LLL}, R′_S

= VDIODE (I_F, n _MIN, I_{O MIN}, R′_S

)

LLL

)

MIN

Advanced Thermal Modeling Equations

Note that, Equations #3.3 in AB20ꢀ3 or #3.6 in

AB20ꢀ3 can be combined with Equation #3.9 in

AB20ꢀ3 to derive the maximum DC forward

current, I_{F MAX}, versus ambient temperature, T_A,

and thermal resistance, Rθ_JA, shown in Figure 4

of the SuperFlux LED Data Sheet.

Figure 3.4A shows Equation #3.6A graphed as a

function of T_Aand Rθ_JAfor an HPWAꢀxH00 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, “HPWAꢀ

XX00 Maximum DC Forward Current vs. Ambient

Temperature” graph, in the SuperFlux LED Data

Sheet.

T_{J MAX}≅ T_A+ R θ_JAI_{F MAX}V_F

MAX

≅ T_A+ R θ_JAI_{F MAX}(V_{O HH}+ R_{S HH F}

)

MAX

Or written as a standard quadratic equation:

Equations #3.7 in AB20ꢀ3, #3.8 in AB20ꢀ3, and

#3.9 in AB20ꢀ3 can be combined together in

different ways to model the luminous flux (or

luminous intensity) of LED emitters due to the

effects of internal selfꢀheating (i.e. Rθ_JAP_D) and

ambient temperature. Equation #3.7A models

the expected reduction in luminous flux due to

internal selfꢀheating compared to the

Rθ_JAR_{S HH}I_F²+ Rθ_JAV_{O HH}I_{F MAX}+ T_A– T_{J MAX}≅ 0

MAX

Thus, the positive root solution of I_{F MAX}is equal

to:

instantaneous luminous flux (i.e. at initial turnꢀ

on) when the LED emitter is driven at a constant

forward current at a constant ambient

flux over temperature compared to the thermally

stabilized luminous flux at test conditions of I_F

TEST

V_{F TEST}, and Rθ_{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.

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 Rθ_{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

Figure 3.4A. Maximum DC Forward Current versus

Ambient Temperature for HPWA-xxOO LED Emitter

with Different System Thermal Resistances.

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 AB20ꢀ3

and #3.8 in AB20ꢀ3 that can be used to calculate

the maximum forward current as a function of

ambient temperature and thermal resistance.

Note that this equation 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

AB20ꢀ3, #3.8 in AB20ꢀ3, and #3.9 in AB20ꢀ3 in

order to model various thermal effects on the

light output of the emitter. Note that Equation

#3.10A models Figure 3 (Normalized Luminous

Flux versus Forward Current) on the SuperFlux

LED Data Sheet.

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_Fand Rθ_JAfor an HPWAꢀxH00 LED

emitter with a nominal forward voltage (i.e., V_F=

2.25 V at 70 mA). Values of Rθ_{JA TEST}= 200

°C/W, m = 1.0, k = –0.0106, 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/HPWTꢀxx00 Relative

Luminous Flux vs. Forward Current” graph, in

the SuperFlux LED Data Sheet.

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