How to calibrate the nRF51 ADC to correct offset and gain error

Question

According to the nRF51822 PS v3.1, table 51, offset error for the internal ADC is up to 2% and the gain error can be up to 2%. Is it possible to correct this error to obtain better accuracy for the ADC?

Stefan Birnir Sverrisson · Accepted Answer

The offset and gain error is different from IC to IC and may therefore be calibrated for each IC to obtain acceptable accuracy. On nRF51 third revision IC's the offset and gain error has been measured and written into non-volatile memory for 10-bit ADC resolution, see update on this thread from 10.4.2015. To otherwise generally correct the offset and gain error, perform the following steps: 
 
 Configure the ADC to use 1.2VBG reference voltage and to sample from an analog input pin, use e.g. this code . 
 Connect a voltage source to the configured input pin that provides a steady 0.1V. Read the ADC output (actual ADC output at 0.1V) 
 Set the voltage source to 1.1V and read the ADC output (actual ADC output at 1.1V) 
 
 The transfer function is: 
 
 Update 10.4.2015 
An easier way to apply ADC calibration for third revision nRF51 is to read the gain error and offset error numbers available in memory address 0x10000024. This information is not available for first or second nRF51 revision ICs. For third revision nRF51 devices, the offset and gain error values have been measured for each nRF51 chip after production and have been written to memory address 0x10000024. The register at this memory address is listed below and the gain error and offset error values are valid for 10-bit sampling only. For 8-bit and 9-bit sampling, there are no values available: 
 
 The ADC offset and gain error are read with the following command: 
 nrfjprog --memrd 0x10000024 --n 4
 
 
 
 If e.g. the perceived value is
"0x10000024: FFFF0102" then
GAIN_ERROR=1 and OFFSET_ERROR=2. 
 
 
 The offset and gain values are two's
complement numbers. This means that
if e.g. the observed value is
0xFFFF03FF, then GAIN_ERROR=3 and
OFFSET_ERROR=-1 
 
 
 Similarly, if the observed value is
0xFFFFFEFC, then GAIN_ERROR=-2 and
OFFSET_ERROR=-3 
 
 
 The calibrated value y is obtained for 10-bit ADC sample x with: 
 y = x * (1024+GAIN_ERROR) / 1024 + OFFSET_ERROR - 0.5
 
 where 0.5 LSB is subtracted to compensate for ADC quantization error. 
 Update 27.10.2015 
 To obtain the offset error and gain error at runtime the FICR value can be read with: 
 static uint32_t ficr_value_32;
	static int8_t offset_error;
	static int8_t gain_error;

	ficr_value_32 = *(uint32_t*)0x10000024;
	offset_error = ficr_value_32;
	gain_error = ficr_value_32 >> 8;

XavierYin · Answer

The above sample code doesn't look good to me. I suspect it falls to the 3rd case below. C99 6.3.1.3 Signed and unsigned integers

When a value with integer type is converted to another integer type other than _Bool , if the value can be represented by the new type, it is unchanged.

Otherwise, if the new type is unsigned, the value is converted by repeatedly adding or subtracting one more than the maximum value that can be represented in the new type until the value is in the range of the new type. 49)

Otherwise, the new type is signed and the value cannot be represented in it; either the result is implementation-defined or an implementation-defined signal is raised.

A proposed alternative: 
 int8_t offset_error = *(int8_t*)0x10000024; int8_t gain_error = *(int8_t*)0x10000025;

How to calibrate the nRF51 ADC to correct offset and gain error

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