Analog to Digital Converters - 1

Analog to Digital converters are, in my opinion, one of the most fun peripheral to deal with when working with Microcontrollers.
Why?
Let's face it : most of the measurements you want to do in the real world involve an analog reading, normally a voltage or a resistance returned by some kind of sensor.

Like most of the mcus, the MSP430G2 has an ADC built in (warning : the ADC10 is not included in all the devices of the family, check the datasheet or the specs for the specific device you are dealing with).
I am going to use the MSP430G2553 supplied with the launchpad and that one definitely has an ADC10 onboard.

First of all, it's called ADC10 because it has 10 bits of resolution.
10 Bits is the typical resolution you can find in "cheap"devices, more advanced ones (such as the C2000 or Cortex M3) may have a 12bit adc instead.

What's the difference?
It's about resolution : a 12 bit device, having 2 bits more, achieves a four (2^2) times higher resolution than a 10 bit one.
It's a big difference, however in many (most?) cases it does not really matter.

Let's imagine you are sampling a temperature from a sensor such as the LM35DZ (cheap and common sensor).
This sensor increases it's output by 10mV for each Centigrade, at 0C it will provide 0V (which makes it really simple to use it with mcus).
However this sensor does not provide high accuracy since it's best accuracy is about +/- 0.5C, which can be translated into +/- 5mV.

A 10 bit adc with range between 0 and 3.3V has a resolution of 3.3 / 1024 V/bit =  3mV/bit which is already higher than the accuracy of the sensor itself, therefore a higher adc resolution would be useless.
However this setup would allow us to measure temperatures between 0 and 33C, which it might be ok for some applications, but not enough for others.
The LM35 sensor itself can read temperatures from -55C to 150C (depending of the exact model, check the datasheet) but this would generate voltages from -5.5V up to 15V.
If you apply such ranges to a 3.3V tolerant ADC, you are likely to burn it, so most people normally regard this a as a bad idea.
You can offset and "scale" the signal using a voltage divider (with 3 resistors in case you need to add the offset), but at that point, should you still aim for +/- 0.5C resolution, the 10 bits are not enough anymore.

The example with the LM35 was useful to add some context, but the issue is generic.
Imagine we have a sensor that measures a quantity X and outputs linearly a voltage V(X) = V0+kX.
The constant k is the voltage gain of the sensor, it is a constant if the sensor output is linear.
The range we want to measure is [Xmin,Xmax], which gives us DX = Xmax-Xmin.
Assuming we can exactly map Xmin to the lower reference of the ADC (i.e. 0V) and Xmax to the higher reference (i.e. 3.3V), and we know we want to obtain a specific resolution R, then we can calculate how many bits (minimum) we need to sample the signal.

Say DX = 100X and the needed resolution R is 0.01X, this means that the ADC must have 100X/0.01X = 10.000 "steps".
To get the minimum number of bits you can apply a log2(10.000) or simply compare with the resolution of finite number of bits :
8 bits -> 256
10 bits -> 1.024
12 bits -> 4.096
14 bits -> 16.384
...

in our case we would need a 14 bit ADC, not an easy requirement as very few of the mcu integrated ADCs can get that precision.
At the same time, when sampling with such accuracy, we might have additional issues such as the stability of the reference voltages, the accuracy of the resistors used in an eventual divider, electronic noise etc.
When higher precision and speed must be achieved, the common solution is to use dedicated ADC devices.

If now you feel frustrated because your mcu only supports a 10 bit sampling device, just think this : precision instruments such as Digital Oscilloscopes use 8 bit ADCs (but they are normally extremely fast and equipped with high precision input circuits).
How do they give all that flexibility and precision with 8 bit only?
They allow to set different scales by altering the offset of the signal and the parameters of the input voltage divider.

The other important parameter is the sampling frequency.
Why achieving high frequency and high resolution at the same time can be difficult?
That's related to the way the sampling happens, which I will try to explain in a simple case.
Digital devices only understand two states : on and off, so how do they convert a voltage to an on or off state?
They can compare the voltage with a reference one and say : if the reference is higher, then set to off, else set to on.
Now if the reference voltage V(t) varies starting from V- (lower reference) and linearly climbs to V+ (higher reference) and at the same time we start a timer that counts the number of cpu cycles, at a given point in time, the signal will cross the reference and the comparison will return "on".
At that point the timer count t gives us a measurement of the voltage used in the comparison V(t).
Practically, some more advanced techniques are used, but that's  pretty much the basic concept.
You understand then that the timer speed is affecting the resolution + sampling rate combination.
If we have a 10 bit resolution, the timer must be able to count up to 1024 when V(t) = V+.
Imagine the timer uses the same clock frequency as the CPU being 16MHz -> the maximum sampling rate would be 16/1024 MHz = 15KHz.
As I previously stated, some more advanced techniques (series of approximations etc) are used, allowing the adcs to achieve better performances, but you now probably understand the relation between cpu speed, sampling rate and resolution.

In the next post I am going to experiment with the ADC10 device of the MSP430G2553