AN1149-3A Lumileds Lighting, LLC, AN1149-3A Datasheet - Page 2

• Manufacturer Part Number: AN1149-3A
• Description: Advanced Electrical Design Models
• Manufacturer: Lumileds Lighting, LLC

Diode Equation Forward Voltage Model
Traditionally, the forward current versus forward
voltage characteristics of a p n junction diode
have been expressed mathematically with the
“Diode Equation” below.
Where:
V
I
n = ideality factor, 1 ≤ n ≤ 2
I
T = temperature, °K
k = Boltzmann constant, 1.3805 x e 23 joule/°K
q = electron charge, 1.602 x e 19 coulomb
Note: at room temperature (25 °C), kT/q =
0.02569 V.
The reverse saturation current, I
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
hundred millivolts, the exponential term
predominates and the equation can be re
written as:
F
O
F
= forward current, A
= reverse saturation current, A
= forward voltage, V
F
, greater than a few
O
, varies by
2
The diode equation approximately models the
low current (> 1
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
The values for the diode equation model can be
calculated by using three test currents ( I
and I
of n, IO, and R´S would generate an equation
that intercepts the forward characteristics of at
these points: (I
as shown in Figure 3.1A. The equations for n, I
and R
′
S
= internal series resistance, ohms
F3
′
, such that I
S
are shown below:
F1
, V
µ
A) performance of an LED
F1
F1
), (I
< I
F2
F2
, V
< I
F2
F3
), and (I
). Then, the values
F3
, V
F3
F1
) such
, I
F2
,
O
,