The smallest Chip with 12-16 bit ADC @ 10 measurement points/millisec

MSP430F2003 and 2013 comes in 4mm by 4mm QFN and have 16bit SAR

TI does have WCSP (Chip scale) 2x2mm, but soldering something that small is only for factories.
And probably needs a pre-order of 1K

Running everything on 1.2V Ultra low power: MSP430L092
and the battery would be smaller.(maybe one time use coin Silver Oxide)
Or maybe a SuperCap charged up to a 1.85 Voltage
Like PAS311SR-VA6R (0.03gram)
if you have room for resistor+1.8v zener charging it to 2.6V may get longer power span.

Good thing is that L092 the have 2K RAM instead of Flash, so for a temporary data logger it uses less power.

Bad things, 14tssop and 8bit A/D

Tough it needs to boot up from external spi-flash or compiler, you don't have to include that part with the bee back-pack.

Benjamin Paffhausen said:

The data would be eighter send or saved.

How much data per experiment? - Sending data wirelessly having given power/weight seems unrealistic.

For a Micro Controller you can have a look at: http://www.ti.com/lsds/ti/microcontrollers_16-bit_32-bit/msp/products.page select for minimal 2 ADC and there are multiple choices.

For an amplifier: http://www.ti.com/lsds/ti/amplifiers-linear/single-supply-products.page#p1811=9;161 for example the INA321.

And for Wireless: http://www.ti.com/lsds/ti/wireless_connectivity/products.page some include ADC.

Benjamin Paffhausen said:

As a battery I got the MS412FE-FL26E, it is very heavy with 70mg when the total weight the bee could lift is ~100mg. The battery only has 1 mAh. The KL03 would use that up in 6 minutes,

The battery is rated for 10 micro Amp discharge rate not 10mA.

Peter

PS You are looking for a stereo microphone recorder ( 2 x 10 ksps )

The smallest amount of data would be binary with one point per millisec for 5 - 10 minutes.
I would do so by recording the neuronal activity with a PC until I have activity. Usually a spike jumps out tree times the baseline noise, That threshold would be taught the microprocessor, and it would then when the pc is disconnected write a 1 for every jump through the threshold, and a 0 for the rest. That should not be to big of a file. It can be stored on the bee and read later.

Peter wrote:
PS You are looking for a stereo microphone recorder ( 2 x 10 ksps )
Is there anything so small and so amplified that I can record with a resolution of 1 µVolt?
Are there batteries that weight below or around 50µg that would be suited for the job? Isn't there a method of sending power via induction? The bee could flight in a closed faraday room of one cubic meter.

(I am a biology PhD with some experience in smd soldering under magnification, Arduino raspberry and MatLab. And in case this idea is not completely off, I would get an engineer or a programmer to help me)

Benjamin Paffhausen said:

The smallest amount of data would be binary with one point per millisec for 5 - 10 minutes.

How many bits per data point?

1 bit, there is eighter a 1 or a 0. (Or do I understand this wrong?)

or in case of writing the analog values,

I dont know, a tenth of the noise so 0,5 µVolt in a ragne of 100 or 500 µVolt. If the amplifier could spread this range over a scale of 1024 analog values, 10 bit would be fine. 

Benjamin Paffhausen said:

I dont know, a tenth of the noise so 0,5 µVolt in a ragne of 100 or 500 µVolt. If the amplifier could spread this range over a scale of 1024 analog values, 10 bit would be fine. 

10 bits, 1000 sps for 10..15 minutes. Right? I don't think the technology is there yet - to transfer such amount of data wirelessly or store on memory chip in case of 1mAh / 10 microAmp battery

I'm not optimistic on this project.

Both the size and weight constraints present serious challenge.

There is one interesting and somewhat related commercial product: the pill camera used for capsule endoscopy.

Google "pillcam teardown" for details

Peter