LTM8080 datasheet(20/32 Pages) AD

20 / 32 page

LTM4703

Rev. 0

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Temperature Monitoring

Measuring the absolute temperature of a diode is possi-

ble due to the relationship between current, voltage, and

temperature described by the classic diode Equation 8.

ID =IS •e

η• VT

⎛

⎝⎜

⎞

⎠⎟

VD = η• VT •In

(8)

where ID is the diode current, VD is the diode voltage, η is

the ideal factor (typically close to 1.0), and IS (saturation

current) is a process-dependent parameter. VT can be bro-

ken out by Equation 9.

VT =

k • T

(9)

where T is the diode junction temperature in Kelvin, q

is the electron charge, and k is Boltzmann’s constant.

VT is approximately 26mV at room temperature (298K)

and scales linearly with Kelvin temperature. It is this lin-

ear temperature relationship that makes diodes suitable

temperature sensors. The IS term in Equation 9 is the

extrapolated current through a diode junction when the

diode has zero volts across the terminals. The IS term

varies from process to process, varies with temperature,

and by definition must always be less than ID. Combining

all of the constants into one term (Equation 10).

KD =

η•k

(10)

where KD = 8.26–5, and knowing In (ID/IS) is always pos-

itive because ID is always greater than IS, leaves us with

Equation 11.

VD =

•KD •In

(KELVIN)

(11)

where VD appears to increase with temperature. It is

common knowledge that a silicon diode biased with a

current source has an approximate –2mV/°C temperature

relationship (Figure 6), which is at odds with the equa-

tion. The IS term increases with temperature, reducing

the absolute value and yielding an approximate –2mV/°C

composite diode voltage slope.

TEMPERATURE (°C)

–50 –25

0.3

0.5

0.8

0.4

0.7

0.6

100

4703 F06

125

Figure 6. Diode Voltage VD vs Temperature

To obtain a linear voltage proportional to temperature

we cancel the IS variable in the natural logarithm term

to remove the IS dependency from Equation 10. This is

accomplished by measuring the diode voltage at two cur-

rents I1, and I2, where I1 = 10 • I2) and subtracting, we

get Equation 12.

VD = T(KELVIN)

(KELVIN)

•KD •ln

(12)

Combining like terms, then simplifying the natural log

terms yields Equation 13.

VD =T(KELVIN)•KD•IN(10)

(13)

and redefining the constant given by Equation 14.

K'D = KD •ln(10) =

198µV

(14)

yields Equation 15.

VD = K'D • T(KELVIN)

(15)

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