Transfer function calculation: v_M/u_G
Question
By using the previous theoretical elements, give the transfer function's expression
of the vibrator.
Draw the module of this transfer function, relative to frequency.
In the scope of this exercise, we consider that the frequency range is that where the electrical impedance
of the inductance of the coil is negligible relative to the DC resistance R_e of the coil.
We consider that the source impedance
is negligible relative to the DC resistance,
, of the coil.
After taking into account the hypothesis, the equivalent circuit of the vibrator in the mechanical domain becomes
With
By applying Kirchhoff's voltage law to the circuit, the following expression can be obtained:
or
The representation of this frequency response is therefore the following:
The vibrator has a resonant behavior: for a given input voltage, the velocity of the mobile part is maximal at resonance.
.
