Datasheet
=
T
q
x '
BE
V
x
k
K
x
ln
¸
¸
¹
·
¨
¨
©
§
I
2C
I
1C
¸
¸
¹
·
¨
¨
©
§
T =
q x 'V
BE
K
x k x ln
I
F2
I
F1
¹
·
©
§
x
¹
·
©
§
x='
ln
BE
I
I
q
kT
V
K
2F
1
F
F
I
=
I
x
K
t
V
BE
V
©
§
¹
·
S
x
e
«
«
¬
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»
»
¼
º
q
kT
=
t
V
F
I
=
I
x
K
t
V
BE
V
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x
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-1
LM95214
www.ti.com
SNIS146A –MARCH 2007–REVISED MARCH 2013
DIODE NON-IDEALITY
Diode Non-Ideality Factor Effect on Accuracy
When a transistor is connected as a diode, the following relationship holds for variables V
BE
, T and I
F
:
where
•
• q = 1.6×10
−19
Coulombs (the electron charge)
• T = Absolute Temperature in Kelvin
• k = 1.38×10
−23
joules/K (Boltzmann's constant)
• η is the non-ideality factor of the process the diode is manufactured on
• I
S
= Saturation Current and is process dependent
• I
f
= Forward Current through the base-emitter junction
• V
BE
= Base-Emitter Voltage drop (1)
In the active region, the -1 term is negligible and may be eliminated, yielding the following equation
(2)
In Equation 2, η and I
S
are dependant upon the process that was used in the fabrication of the particular diode.
By forcing two currents with a very controlled ratio(I
F2
/ I
F1
) and measuring the resulting voltage difference, it is
possible to eliminate the I
S
term. Solving for the forward voltage difference yields the relationship:
(3)
Solving Equation 3 for temperature yields:
(4)
Equation 4 holds true when a diode connected transistor such as the MMBT3904 is used. When this “diode”
equation is applied to an integrated diode such as a processor transistor with its collector tied to GND as shown
in Figure 21 it will yield a wide non-ideality spread. This wide non-ideality spread is not due to true process
variation but due to the fact that Equation 4 is an approximation.
Texas Instruments invented TruTherm beta cancellation technology that uses the transistor equation, Equation 5,
which is a more accurate representation of the topology of the thermal diode found in some sub-micron FPGAs
or processors.
(5)
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