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I was reading up on bandgap references. I noticed that a CTAT voltage can be simply produced by taking the Vbe voltage of a BJT.

However, when generating the PTAT voltage, most books seem to mention that you need two bipolar transistors operating at unequal current densities, then the difference between their base-emitter voltages is PTAT.

My question is, if we have an easy way of generating a CTAT, why do we need a PTAT? Can we simply not just generate another CTAT and invert it by plugging it into the inverting input of an differential amplifier? Why isn't that good enough?

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The voltage from a single device not only varies with temperature but also with the current through it, the specific processing of the device itself as well as non-idealities such as terminal resistances. Using two identical devices at different currents (or current densities) cancels all of those items to give a voltage virtually independent of real-world non-idealities.

Many temperature measuring devices actually use just a single device and sequence it at two different currents at a few hundred Hz, then subtract the two resulting voltages to give the voltage proportional to absolute temperature (PTAT).

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