Due to the low impedance at the base, high transconductance, and output resistance compared to MOS devices, the BJT is characterized as current-controlled current source useful to compute nonlinear functions by their logarithm dependence between base-emitter voltage
[V.sub.BE], collector current [I.sub.C], and temperature, which recently has led to its integration into the CMOS-based architectures [5-8].
where "[mathematical expression not reproducible]" is base-emitter voltage
for [Q.sub.2] ([approximately equal to] 0.7 V), "[V.sub.t]" is the electron thermal voltage ([approximately equal to] 0.026 V), "[V.sub.OS]" is the input offset voltage for operational amplifier, "n" is the ratio between number of [Q.sub.2] and number of [Q.sub.1].
By exploiting the temperature-dependent base-emitter voltage
[V.sub.BE] of the parasitic substrate bipolar transistors (PNPs) available in standard CMOS technology, the temperature information is extracted.
Most electronic engineers know that a transistor's base-emitter voltage
([V.sub.BE]) has a temperature coefficient (TC) of about -2 mV/[degrees]C.
This technique helps to stabilize the base-emitter voltage
of the biasing circuit, ensuring insensitivity towards an abrupt change of the supply voltage.
Hence, the base-emitter voltage
corresponding to 10 ns pulse with 0dB power level is taken as a reference.
The last output transistor will not saturate because its collector-emitter voltage is now equal to the sum of its own base-emitter voltage
and the collector-emitter voltage of the previous transistors.
If the TF characteristic of a bipolar device was given in terms of the dependence of collector current on base-emitter voltage
, [i.sub.C][[v.sub.BE]], it would be approximately exponential.
Their proportional to absolute temperature (PTAT) variation is apparent due to the negative factor the base-emitter voltage
[V.sub.BE2] is multiplied by.
The principle of the analog and digital output temperature sensor is that the forward base-emitter voltage
[U.sub.BE] of a transistor is temperature and current dependent according to the following equation 
Some ICs from SMSC use an external 2N3904 transistor as a sensor, measuring the base-emitter voltage
to obtain a temperature.