Lately, I decided to give the STM32F0 discovery board [3] a try. The ADC 
seemed to be extremely noisy and I decided to investigate the problem.

I'd like to present my results here, just in case someone else 
experiences the same problems.

Test setup:
  * STM32F0 discovery board
  * ADC clock from internal 14MHz oscillator
  * Analog input 10 (GPIOC0, configured as analog I/O, of course): I use 
1.5 ADC clock cycles sampling time with this input
  * Internal voltage reference: I use the advised 239.5 ADC clock cycles 
sampling time here.
  * FTDI USB<->RS232 converter
  * STM32F0 running at 48MHz PLL source, clocked from internal 8MHz RC 
oscillator.
  * STM32F0 connected to FTDI via USART1, 19200 baud (highest setting 
that works reliably with the internal RC oscillator)

I measured the internal voltage reference and an external voltage 
applied to GPIOC0. For the voltage reference, I transmitted the raw ADC 
values to the PC, for the external voltage I transmitted the calculated 
millivolt-value.

Every value was converted to decimal (for easy debugging) and output to 
the serial port. This should result in about 400 readings per second (I 
didn't verify this, because that's not very important here).

The external voltage is generated by a 22k potentiometer connected to 
VDD and GND. The cable from the potentiometer to the I/O-Pin is about 
40cm long.

As a side note: The DC resistance of the potentiometer is far higher 
than the suggested value which may have caused an unneglectable loading 
of the potentiometer voltage divider and thus cause a voltage deviation 
from the unloaded value. I'm aware of this but in this series of 
measurements I was not interested in such effects (which may even grow 
with the sample rate (higher sample rate -> more S&H cycles per second 
-> more input current)). I take the ADC input voltage (which, for 
absolute accuracy checks I measured directly at the ADC input) as given 
and I am only interested in how to get low noise and a stable rading for 
stationary signals.

At least 40e3 values were acquired for each dataset.


First test
----------
Potentiometer connected to GPIOC0. In the middle of the cable, 
approximately 20cm from the PC0 pin header of the discovery board, I 
connected a 100nF ceramic capacitor from PC0 to ground. The purpose is 
to lower the dynamic impedance of the potentiometer. This reduces the 
noise introduced by the ADC sample and hold considerably. Otherwise the 
impedance of the potentiometer would be far too high.
The result was a disaster. You can see a plot of the acquired values in 
PC0.pdf, dataset (a). The plot shows a time-series of the first 5e3 
datapoints in the left subplot and a histogram of all datapoints in the 
right one. Yes, the input voltage was only about 200mV in this case but 
the noise wasn't better with higher values. The measured voltage 
scattered roughly 100mV in total, a completely unacceptable result.

Second test
-----------
This time I selected the internal voltage reference as input. This 
should rule out any problems caused by long external cables and bad 
external setup. The result is plotted in vref.pdf, dataset (a).
At least the individual ADC counts are visible in the time series plot, 
but the scatter is horrible, again. The center part of the histogram 
looks somewhat "gaussian" but not the tails left and right. Something's 
obviously wrong here.

As it turns out, ST didn't respect their own power supply decoupling 
requirements. The STM32F0 discovery board doesn't seem to have any 
capacitors on the VSSA and VDDA analog supply pins, whereas the 
datasheet tells us 1uF || 10nF is required [2].
I put a piece of PCB onto the top of the MCU with double sided adhesive 
tape and soldered the decoupling capacitors onto it (see setup.jpg).

Third test
----------
I repeated the second test, now with the decoupling capacitors in place.
The result can be seen in vref.pdf, dataset (b). The result looks much 
better, the tails in the histogram have gone, the scatter is smaller.

This was a first step, but the results of the external voltage didn't 
improve. I decided to move the 100nF cap very close to the I/O pin and 
therefore placed it on top of the MCU, too (see setup.jpg).

Fourth test
-----------
Repetition of the first test. Result in PC0.pdf, dataset (b). Almost all 
of the scatter is gone. Don't worry about the different average value. 
I've touched the potentiometer between the tests. Please notice that the 
highest bar of the histogram goes up far higher but I set a limit of 0.3 
on the y-axis.

Summary, possible explanations and lessons learned
--------------------------------------------------
Apart from the proper supply decoupling, it is extremely important to 
drive the ADC input with a very low impedance. This seems obvious -- the 
datasheet ([2], Electrical characteristics, Table of R_AIN,max for f_ADC 
= 14MHz) lists a required maximum impedance of 400 Ohms for the fastest 
sampling time -- but you have to keep in mind, that the impedance must 
be provided directly at the MCU pin. The 20cm wire to the capacitor in 
the first test completely messed the results up.
For slowly varying inputs (like a potentiometer) it may be sufficient to 
connect a capacitor directly to the analog input like I did. (Please 
note that I didn't try out the minimum size of this cap, but the 100nF 
seem reasonable as you can see by this eyeball-calculation: The S&H 
capacitance is about Cint = 8pF, according to the documentation [2]. The 
ADC has 12bits, thus we have 4096 values. If we allow a voltage change 
of the external capacitor Cext of one step size during the sampling 
process and assume that all current is drawn solely from Cext, we arrive 
at the conclusion that Cext > Cint*4096 = approx. 33nF. Add some safety 
margin and you arrive at 100nF for a standard value.)
If you want to digitize a fast changing signal, you'll probably need a 
very fast buffer close to the ADC input; The fastest sampling time is 
only 110ns(!) and the buffer should keep the ADC input voltage stable 
during this time.

References
----------
[1]: RM0091: Reference Manual, STM32F05xxx/06xxx advanced ARM-based 
32-bit MCUs 
(http://www.st.com/web/en/resource/technical/document/reference_manual/DM00031936.pdf)
[2] STM32F051x4 STM32F051x6 STM32F051x8: Data sheet 
(http://www.st.com/web/en/resource/technical/document/datasheet/DM00039193.pdf)
[3] UM1525: User Manual, STM32F0DISCOVERY, Discovery kit for STM32 F0 
microcontrollers
 (http://www.st.com/st-web-ui/static/active/en/resource/technical/document/user_manual/DM00050135.pdf)