Calculating=20
the total error of a system can be tricky, especially when the =
specifications=20
units vary widely. When calculating the total error, all specifications =
must be=20
converted into a common unit before combining. This blog will show you =
how to=20
convert between units of volt, percentage and parts per million (ppm) to =
ensure=20
proper calculation of total system error.
Most errors=20
in a linear device=E2=80=99s datasheet are referred to the input =
(RTI). Referring=20
errors to the input has three main benefits: It separates each =
error=E2=80=99s=20
contribution to the total error at the output, eliminates the need to =
know the=20
gain of the device, and simplifies the calculations to refer the total =
error to=20
the output. To convert input referred specifications between units of =
volts,=20
percentage, parts per million, and refer the total error to the output =
use the=20
following equations.
To=20
convert from volts to percentage:
Where,=20
=
; =
=20
Error(V) =3D The error in units of volts.
=
; =
=20
Error(%) =3D The error as a percentage of the full-scale =
range.
=
; =
=20
FSRInput =3D The full-scale range of the =
input.
To=20
convert from percentage to ppm:
Where,
=
; =
=20
Error(ppm) =3D The error in parts per million of the full-scale=20
range.
To=20
refer all errors to the output in units of volts:
Where,
=
; =
=20
Total Output Error(V) =3D Total error referred to the output in =
units of=20
volts.
=
; =
=20
FSROuput =3D The full-scale range of the =
output.
To=20
show an example of how to use the above equations, we will use the =
circuit shown=20
in Figure 1 and calculate the combined error in ppm due to a couple=20
specifications of the INA826. The circuit has an input signal of 20mVpp, =
and RG is=20
set for the INA826 to have a gain of 100V/V.
The first=20
error we will look at is input offset voltage. Figure 2 shows the input =
offset=20
voltage specification for the INA826.
Since this=20
specification is in units of volts, use Equations 1 and 2 to convert =
this to=20
ppm. To solve Equation 1 we need to know the full-scale range of the =
input. The=20
FSR of Figure 1 is the total voltage range at the input of the INA826. In this case, it is 20mVpp. Now that we =
have all the=20
needed information, let=E2=80=99s plug in the numbers.
Now lets=20
look at gain error. Figure 3 shows the gain error specification for the =
INA826.
The gain=20
error specification is given as a percentage. Therefore, we only need to =
use=20
equation 2 to convert to ppm.
Now that=20
both sources of error are in units of ppm, we can combine them by =
calculating=20
the RSS, or root-sum-square, value as shown in Equation 7.
This is the=20
total error due to the gain error and offset voltage referred to the =
input.=20
However, most people want to see how much error they can expect to =
measure at=20
the output. To refer the error to the output, use Equation 3. Equation 3 =
uses=20
the variable FSROutput, which is the full-scale range =
of the=20
output. In the example shown in Figure 1, the FSR of the output is 2Vpp. =
This is=20
calculated by multiplying the input signal (20mVpp) and the gain =
(100V/V). The=20
total voltage error at the output is calculated in Equation =
8.
Although=20
these are not all the errors of the INA826, a similar analysis can be done to include=20
them.
Now that=20
you know how to convert specifications between units of volts, =
percentage, and=20
parts per million, you can now calculate the total error of your system. =
If you=20
would like another example of how to calculate total system error, check =
out=20
Appendix B in TI Design TIPD156.