# ADC Gain Error

## ADC Positive & Negative Gain Error

Analog-to-Digital Converter (ADC) gain error is defined as the deviation of the last step’s midpoint of the actual ADC from the last step’s midpoint of the ideal ADC, compensating for offset error. After compensating for offset errors, applying an input voltage of 0 always results in an output value of 0. However, gain errors cause the actual transfer function slope to deviate from the ideal slope. This gain error can be measured and compensated for by scaling the output values. An example of a 3-bit ADC transfer function with gain errors is shown below:

If the transfer function of the actual ADC occurs above the ideal straight line, then it produces a positive gain error and vice versa. The gain error is calculated as the number of Least Significant Bits (LSBs) from a vertical straight line drawn between the midpoint of the last step of the actual transfer curve and the ideal straight line. In the figure above, the output value saturates before the input voltage reaches its maximum. The vertical arrow shows the midpoint of the last output step.

In the figure below, the output value has only reached six when the input voltage is at its maximum. This results in a negative deviation for the actual transfer function.

## ADC Full Scale Error

ADC Full scale error is the deviation of the last transition (full scale transition) of the actual ADC from the last transition of the perfect ADC, measured in LSB or Volts. Full scale error is due to both gain and offset errors as shown in the figure below. The deviation of the last transitions between the actual and ideal ADC is 1.5 LSB.