Characterising low frequency noise?

[alanambrose]

Well I have not tested the BJTs myself so you might be right ... but I'm working on the theory that Analog selected them in AN159 so they are most likely not horrible parts and also THAT corp provide two spice models for the THAT300 array - 'rf' and 'noise' models and I'm using the noise model here. Of course, that's only a 'balance of probabilities' argument, 'the proof will be in the pudding' as they say (I wonder why they say that?)

Regarding your earlier points - I tried modifying the operating point for the BJTs and it looks reasonably optimal for noise purposes - it might be possible to reduce the current by a factor of two or so without a great penalty - I'm still investigating. Also unless the protection resistor is brought down to about 50 ohms it hurts the noise performance a lot. Lastly, adjusting R30/R31/R32/C25 by a factor of 10 doesn't impact the noise much, so you're right, that's a good change.

This all assumes the spice models are reasonably accurate...

Alan

p.s. https://en.wiktionary.org/wiki/the_proof_of_the_pudding_is_in_the_eating 'you will see it when you fry the eggs'!

[Kleinstein]

Changing the current of the BJTs does influence the noise. Good BJTs are close to the ideal behavior:  With a higher current the voltage noise goes down with the square root and the current noise goes up about the same way. So the ration of voltage to current noise, which gives the source impedance for the best noise figure, depends on the current. The other way around the optimum current depends on the source impedance - higher current for a low impedance source and less current for a high impedance source.

The input capacitor (not the resistor to GND) limits the source impedance a low frequencies - this is why the 10-100 mHz range might want a lower current. A 1.5 to 15 K input impedance is not that low and thus should have a low current (more like 100 µA instead of 1.5 mA).
Form National Semiconductor LB52 the optimum current is at  26 mV*sqrt(hfe)/Z_source. This is without 1/f noise. As 1/f noise if often higher in the current, this should shift to even lower currents at low frequencies.

Good quality BJTs can have a 1/f cross over in the 1 Hz range, but especially at the highest level the performance can be different from sample to sample. I am just a little skeptical in expecting leading etch performance for a part that does not even have 1/f noise specs in the data-sheet.  The measurements will show how good the transistors really are.

Looking at the Datasheet of the LM194 transistor pair might give a good idea of what to expect from good BJTs. So performance might be acceptable at much lower currents (e.g.  < 100 µA).

[alanambrose]

Ah, many thanks for your clear description of optimum operating points, voltage and current noise vs. source impedance.

>>>  I am just a little skeptical in expecting leading etch performance for a part that does not even have 1/f noise specs in the data-sheet.

Yes I understand and it seems odd that THAT corp is seemingly too lazy to document and test the noise specs of something they market for 'low noise front ends'.

I had guessed that, for AN159, that Linear must have measured the noise of a number of a BJTs and selected the best for their application. Presumably, not more that a day or so of work for a junior engineer if you have the right equipment sitting on the bench. If that was the case, I was simply piggy-backing on their work.

However, I noticed a couple of days ago (reading AoE on a flight ) that tables 8.1a and 8.1b have H&H's own BJT noise measurements. For multiple parts (table 8.1b), the THAT300 is shown as 0.9nV/sqrt(Hz) at 1mA i.e. well towards the good end of the table. So, Linear might have duplicated H&H's work or they might have simply read the numbers in the AoE table.

Alan

[Kleinstein]

Something like 0.9 nV/Sqrt(Hz) at 1 mA is about what many BJTs get if they are not to small. The big question is, where is the 1/f corner. Here the simulation looks to good to be true, likely they just omitted the 1/f noise as it is not that relevant for audio applications. Also 1/f noise can change quite a lot between wafers - so not all parts are the same in this respect. Not specifying 1/f noise also makes testing easier, as low frequency noise tests are time consuming and thus expensive.
 
AN159 even shows 1/f noise - here the corner is at about 100 Hz, which is much more realistic.

So that amplifier circuit is good for the 10 Hz - 100 kHz range, but not really below 10 Hz.

For the low frequency end, the input capacitor is rather high impedance (e.g. 1-10 K range) so an BJT based amplifier should be more using a lower working current, more like 100 µA. Also high gain transistors have an advantage. So maybe even a relatively high gain BC548C could be a better choice. If you really want to go BJT, I would consider something like a  MBT6429DW1 or similar, maybe a few of them in parallel. So a high gain transistor, so one can use higher collector current.