Error calculation in a measurement chain

[MathError]

[Mentor Note -- thread moved to the schoolwork forums from the technical forums]

Summary:: I would like to understand how to calculate the error of a measurement provided by a measuring chain

Hello to everyone, I'm going to explain the problem I would like to understand better. Thank you for the help.
I have to measure the pressure using a system of measurement with a piezoresistive pressure transducer and an amplifier. From the data sheet I know these characteristics:
Transducer:
Pressure Range=0-100 (bar)
Linearity(+-%FSO)=0.2%
Amplifier (measuring chain):
Voltage Range=0-10(V)
Linearity(+-%FSO)=0.2%

These data should be enough, I guess. I really don't know what is the right method to solve the problem. According the data, I think the transducer should provide the value of pressure with an error which is constant and equal to 0.2%FSO, so I would say:
p=(p_m+-0.2)bar
The amplifier's output should be proportional to the pressure value, so that:
p=0(bar)--->V=0(V)
p=100(bar)--->V=10(V)
V=0.1*p (V)
Also in this case the error on the voltage should be 0.2%FSO,so that +-0.02(V).
However I really don't understand how I have to combine the error of the transducer and the ampliefier in order to obtain a characteristic with one only band of error.
I hope you can help me. Thank you so much

 

[berkeman]

Is this for schoolwork? Or is it a real-world problem from your work?

These data should be enough, I guess.

I'm not so sure about that. Is "linearity" the only specification that is given on the datasheet? Not anything about absolute accuracy, temperature coefficients, aging effects, etc.? And what is the output voltage of the transducer and the gain of the amplifier? Or does the transducer output 0-10V and the amplifier is just a buffer? What is the output impedance of the transducer, and the input impedance of the amplifier? Is the amplifer an opamp and the gain is set by external resistors?

 

[MathError]

Yes it's actually just an exercise based on real instruments. I have the complete datasheet but I don't know if I can share it. There are a lot of other informations but I don't know if they are useful. In particular:
Transducer:
Excitation=1(mA)
Output signal(FSO@1mA)=100(mV) (nominal)

The datasheet doesn't provide other information you requested

 

[berkeman]

I have to measure the pressure using a system of measurement with a piezoresistive pressure transducer and an amplifier.

Transducer:
Excitation=1(mA)
Output signal(FSO@1mA)=100(mV) (nominal)

How can a pressure transducer have a current as an input? And if the output of the transducer is 100mV (nominal? what does that mean?), and you want the output of the amplifier to be 10V, how is the amp going to accomplish that? With a resistor ratio? (If so, use 0.1% tolerance resistors or commit to using a 10-turn potentiometer in a well designed opamp circuit to get better accuracy...

If the question is to calculate the overall accuracy of the system, then you will need to identify all of the sources of error that I posted earlier (and maybe others), and use them to figure out the overall precision and accuracy of the system.

 

[MathError]

Hi, thse are the datasheets of the transducer (which is a piezoresistive pressure transducer) and amplifier.
I hope they can help to understand a bit more the problem.
I can try to explain one solution I found but I can't understand very well.
According this solution, we have the characteristcs of the system transducer+amplifier, which is a straight line passing in:
A=(0,0) and B=(p_max,V_max)=(100,10)
The band of error will be given by:
eps=(eps_T^2+esp_A^2)^0.5
where:
esp_T=error of the transducer=0.2%
esp_A=error of the amplifier=0.2%
so that we obtain the results of the following pic

Transducer (first pic)

Amplifier (second pic)

 

[haruspex]

The output is effectively the product of two functions, the conversion from pressure to voltage followed by linear amplification.
The resulting expected error is therefore given by the f=AB case in https://en.m.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulae.
Since the two errors are presumed independent, $\sigma_{AB}=0$.

 

[MathError]

The output is effectively the product of two functions, the conversion from pressure to voltage followed by linear amplification.
The resulting expected error is therefore given by the f=AB case in https://en.m.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulae.
Since the two errors are presumed independent, $\sigma_{AB}=0$.

Thank you so much this is a good starting point. I know how to calculate de standard deviation of a quantity f(a, b). Can you explain me why the system amplifier+transducer can be described as a function f=A*B?

 

[haruspex]

Thank you so much this is a good starting point. I know how to calculate de standard deviation of a quantity f(a, b). Can you explain me why the system amplifier+transducer can be described as a function f=A*B?

An amplifier, in principle, multiplies its input by a constant to produce an output. If A is the output of the transducer and B is the multiplier then the final output is AB.