A DC accuracy specification is a way of stating the worst-case deviation of a measurement device from an ideal linear response. It includes both offset error and gain error.

In the graph opposite, the black staircase represents the ideal ADC transfer function, with the line of best fit shown as a black dashed line. The red staircase and dashed line represent the measured response of a fictional 3-bit ADC (analog-to-digital converter). This example is a much less accurate version of the ADC that you would find in a real oscilloscope.

To express the difference between the black and red lines, we begin by calculating the linear equation for each line in the form *y = mx + c*. The gradient of the black line is (7 ADC counts / 1 volt) and the offset is 0 as the line passes through the origin. The equation is therefore:

*y*_{IDEAL} = 7*x* + 0

The gradient of the red line is (7 ADC counts / (7.5 / 7 volts)) and its offset is –7 / 7.5 volts. Its equation is therefore:

*y*_{ADC} = (2 x 7^{2} / 15)* x* – (14 / 15) ≈ 6.533*x* – 0.933

Now we have enough information to calculate the gain and offset errors. Offset error is the difference between the measured offset (–0.933 V) and the ideal offset (0 V):

OE ≈ (– 0.933 V) – 0 V ≈ –0.933 V

Gain error is the percentage difference between the measured slope (6.533 counts/V) and the ideal slope (7 counts/V) :

GE ≈ (6.533 V – 7 V) / 7 V ≈ 6.67% of full scale

Each batch of oscilloscopes that we make has a range of different gain and offset errors, but we guarantee that the errors will fall within a specified range. After testing a number of oscilloscopes like the one above, we might find that the majority of them have offset errors between –1 V and +1 V, and gain errors between –10% and +10%. We would then publish the following specification:

DC accuracy: ±1 V ± 10% of full scale

Offset error specifications for Pico oscilloscopes, where specified, range from ±200 µV to ±500 µV. Gain error specifications range from ±0.25% (for 16-bit oscilloscopes) to ±3% (for 8-bit oscilloscopes) of full scale. Some models do not have separate gain and offset error specifications, but instead have a single percentage figure that includes both gain and offset error.