A mathematical model for AURIGA
It is interesting to obtain an analytical (though simplified) model of the detector, that can give us hints on the sensitivity and performances limits that we can reach with this kind experimental of setup.
We shall therefore go through the entire transduction chain, to understand how the signal is transformed from a mechanical oscillation to an electrical signal.
As the output of the detector is an electrical signal, from a mathematical point of view all mechanical quantities can be interpreted as equivalent electrical components. This can be done in two steps: from the bar to the electromechanical transducer, and then through the amplification stage.
Of course a realistic model have to take into account all the noise sources.
The complete schematics can be solved to obtain the both the signal transfer function and a model for the noise at the output port of the detector.
A simple reasoning shows the existence of an optimum bandwidth for the signal search. A more detailed calculation can be found in the next section.