Simple P-N junctions, as found in bipolar transistors, exhibit a very useful property that can be used to measure absolute temperature. When biased at two different currents, the difference in voltage across the P-N junction is linearly related to absolute temperature, with little dependence on semiconductor process variations.

The basic diode equation is:

*n* = Diode ideality factor (process dependent)

*k* = Boltzmann’s constant

*T* = Temperature (Kelvin)

*q* = Electron charge

*Ic* = Diode current

*Is* = Reverse saturation current (process dependent)

Note: An astute reader may notice that a “+ 1” term was neglected in the above equation. This is a valid, simplifying assumption as long as *Ic* >> *Is*, which it is for most practical applications.

When measured at two currents, the difference in voltage (delta VBE) is related to the ratio of the currents:

Since *k* and *q* are constants, the delta VBE is linearly related to absolute temperature. As long as *n* is constant, the measurement is very repeatable to the accuracy of the current ratios.

## Effect of Diode Ideality Factor

The diode ideality factor (*n*) is a process dependent factor and scales the gain between the current ratio and the delta VBE voltage. However, it is relatively constant, much more so than *Is*. Because of this, the delta VBE effect can make a very accurate temperature measurement. Many bipolar transistors such as the common 3904 have an ideality factor of around 1.004. Transistors with other ideality factors can be used, and simply result in a different gain factor.

## Cancellation of Resistive Effects

Resistance in series with the diode sense element can cause temperature errors. Various proprietary techniques have been developed to cancel these effects. One such solution can be found here.