(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
)
V
F max
=
VDIODE
(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 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´
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.
In most situations, the worst case 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
)
Advanced Thermal Modeling Equations
Note that, Equations #3.3 in AB20 3 or #3.6 in
AB20 3 can be combined with Equation #3.9 in
AB20 3 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.
T
J MAX
≅
T
A
+
R
θ
JA
I
F MAX
V
F MAX
≅
T
A
+
R
θ
JA
I
F MAX
(V
O HH
+ R
S HH
I
F MAX
)
Or written as a standard quadratic equation:
Equations #3.7 in AB20 3, #3.8 in AB20 3, and
R
θ
JA
R
S HH
I
F MAX
+ R
θ
JA
V
O HH
I
F MAX
+ T
A
– T
J MAX
≅
0
2
Figure 3.4A shows Equation #3.6A graphed as a
function of
T
A
and
R
θ
JA
for an HPWA xH00 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.
#3.9 in AB20 3 can be combined together in
different ways to model the luminous flux (or
luminous intensity) of LED emitters due to the
effects of internal self heating (i.e.
R
θ
JA
P
D
) and
ambient temperature. Equation #3.7A models
the expected reduction in luminous flux due to
internal self heating compared to the
Thus, the positive root solution of
I
F MAX
is equal
to:
4
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