My caller last week was in a real bind. He was trying to pick an op amp for a new design and, as always, it seemed he was trying to serve two masters. The application demanded a low noise amplifier and at the same time a low quiescent current device. It seemed that each time he picked for one parameter he was over budget on the other.
After some consolation discussion I proceeded to explain that his demands could, in fact, establish mutually exclusive specifications. If we look at a single transistor, as in the front-end of an op amp we start with the shot (Schottky) noise cause by the collector current. This is given by:
At the emitter side of the transistor the current, working in conjunction with the thermal voltage is developing the emitter resistor:,
at 25C. Therefore, the noise current through Re develops a noise voltage that is:
Following through on the algebra:
Here it is seen that the voltage noise goes down as one over the square root of the collector current. In order to get lower noise the collector current must go way up.
As an example, assume a collector current of 1.25mA. The resulting noise voltage is 0.42nV/sq-rt Hz. Notice that all of the calculations here are noise density values and therefore have the root-Hz unit modifier.
This is half of the input stage of an operational amplifier. The other half of the differential pair would contribute the same magnitude noise but uncorrelated. As these are independent noise sources they collect as the root-sum-square. The total of the two devices would be 1.414 times the noise from one.
If we turn this relationship around the input stage current necessary to get to a noise density of 1nV/sq-rt Hz is 432uA per transistor, or 862uA for the input stage. A good estimate is that half of an op amp quiescent current is through the input transistors and half is used for the rest of the device. Therefore, under ideal conditions the total device quiescent current for a 1nV/sq-rt Hz op amp will be over 1.7mA.
For FET input stages the situation is worse because the Vt term is replaced with 1/gm. As gm is lower in a FET the voltage noise for a given device current is higher.
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