In general, the luminous flux output of LED
emitters varies as a function of the forward
current. Ignoring the effect of heating, the
relationship between luminous flux and forward
current can be modeled with the following
equation:
FV (TJ ) = luminous flux at forward current IF at
junction temperature, TJ
FV (TJ = 25°C) = luminous flux at 25°C, without
heating
k
= thermal coefficient, k @ –0.01
(3.7)
Over the automotive operating temperature
range of –40°C to 85°C, this model matches the
actual data within ± 10%. Figure 3.18 shows
how the modeled data for FV as a function of
temperature compares to the actual data shown
in Figure 3.12. Note that the value selected for k
was chosen to improve the curve fit at elevated
temperatures than at temperatures below 25°C.
Typical values of k for AlInGaP and TS AlGaAs
SuperFlux LED emitters are shown in Table 3.1.
m
FV(IF,TJ = 25°C) @ F V(IF TEST,TJ = 25°C)[IF/IF TEST
]
Where:
FV(IF,TJ = 25°C) = Luminous flux at forward
current, IF, ignoring heating
F (IF TEST,TJ = 25°C) = Luminous flux at test
V
current, IF TEST, ignoring heating
= forward current
IF
I
F TEST = forward current at data sheet test
conditions
m
= linearity factor, 1 £ m £ 2
Thermal resistance is a measurement of the
temperature rise within the LED signal lamp
caused by internal power dissipation as well as
other sources of heat in close proximity to the
LED (i.e. bulbs, resistors, drive transistors, etc).
For a detailed discussion of thermal resistance,
please refer to AB20-4. The units of thermal
resistance are ºC/W. For the same power
dissipation, the LED signal lamp with a higher
thermal resistance would have a larger internal
temperature rise. The basic thermal modeling
equation is shown below:
At forward currents less than 10 mA, m » 1.3 for
AlInGaP LED emitters. At forward currents over
30 mA, the linearity factor, m » 1.0 for AlInGaP
LED emitters. Figure 3.17 shows how the
modeled data for FV versus IF compares to the
actual data shown in Figure 3.10.
For operation at forward currents over 30 mA,
Equation #3.7 can be simplified into a simple
linear equation:
FV(IF, TJ = 25°C) @ FV (IF TEST , TJ = 25°C)[ IF / IF
TJ @ TA + RqJAPD
(3.9)
]
TEST
Where:
The luminous flux varies exponentially with
TJ = internal junction temperature within the LED
emitter, °C
temperature. The simplest model is shown
below:
TA = ambient temperature surrounding the LED
signal lamp, °C
(3.8)
FV(TJ ) @ F V(TJ = 25°C) exp [k(TJ -25°C)]
Where:
RqJA = thermal resistance, junction to ambient,
°C/W
19
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