Member Since: January 3, 2011

Country: United States

• The original equation wasn’t necessarily incorrect, but the interpretation of the values need to follow the equation that is used. The 10-bit ADC contains 1024 different values each representing a range of voltages not one singular analog voltage. This is due to the fact that most common ADCs operate using comparators. With this in mind, the equation is V_analog = (V_ref / 2n)V_digital; where V_analog is not a singular voltage! For example, if the reading 1023 is received by your favorite microcontroller (on a 3.3V system) it should not be interpreted as (3.3/1024)1023 = 3.2967V but as an analog voltage in the range represented by the digital value 1023 and 1024 or 3.2967V and 3.3V. Furthermore, the same reading of digital zero should not be interpreted as 0 analog volts; rather an analog voltage existing between 0 volts and 3.222mV. If you choose to use the equation V_analog = (V_ref / (2n-1))*V_digital the result should be interpreted as an analog voltage in the range between V_digital and V_digital-1. However, the interpretation of V_digital=0 falls apart as the value should NOT be interpreted as ranging between 0V and -3.22mV! This is why the first equation given herein is a more correct equation. I believe it should be changed back above. All of this may be rather silly though given that many of these ADCs we are discussing here have a error equal to ~1 LSB or 3.22mV in the above example.

• The capacity of a battery is trickier than given here. While, at the given measurement, the capacity is Amps*hours it can supply said current, the relationship is not linear. In other words, the 2Ah battery cannot supply 1uA for 228 years! The same is true for 12 amps, the battery will not last 10 minutes, but something less. Furthermore, above, the rating claims to be given for over one hour, but that is not always the case. Commonly a capacity rating will come along with a C factor, for example a 40Ah C20 means that the capacity is 40Ah when tested over 10 hours (4 amps). These intricacies have to do with a non-linear relationship in the chemistry of the battery along with the internal, series, resistance of the battery as mentioned by Mr. Chris20.

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