An ideal programmable gain amplifier (PGA) amplifies an input voltage by a precise programmed
gain value, *G*. If the PGA is ideal, the voltage measured at the output can be
divided by *G* to determine the input voltage. However, many PGA implementations
have two imperfections that must be considered in an application. First, there is an
input offset voltage that is effectively added to the input signal before amplification.
Second, the actual gain may be slightly different from the programmed value due to
analog component tolerances, etc.

Figure 1. PGA with Gain and Offset
Equations

The figure above depicts a high-level representation of a PGA with gain and offset
equations included. For an input signal *x*, an offset value of *C* is added,
and then the sum *(x+C)* is multiplied by the gain value *G* to obtain the
output signal *y*. The fundamental idea behind gain and offset calibration is to
input two different values, *x _{a}* and

As a realistic example, consider a PGA that has been programmed to have a nominal gain of
16. First, a voltage of 60 mV is input, and the output voltage is measured as 986 mV, so
*x _{a}* is 60 mV, and