Static and Dynamic Response of a Design of Differential ... - aerade

R2 is the acoustic equivalefit of the diaphragmmechsnical resistance
L2 is the acoustic equivalent of the diaphragm mass
C2 in the acoustic equivalent of the diaphragm compliance
V is the input voltage equivalent in Che aoou&ic system to the
differential pressure.
For convenience consider the generalised circuit of fig.lO(c) in
which the impedeme in each branch oA * f'ig.lO(b) is denoted by Z tith an
t
approFiate subscript (Z is the operator R + L $ + h
ZI=IutL~++ d1 ’
+
o “Idt\ ,.
i
The eouivalent impedance of the whole circuit, G, is
ZE =
(z, + z )(z*z, + z*z t 22,z )
zqz2 + z2z3 c 2",Z3 t 2;
The Input current, I, = dL and the current in Z2,
%
vz
i = z,z2 t z2z3 t 22,z3
i 0
dt such that
The pre-;sure registered by the pick-up is, by analogy, the voltage,
v, across C2 in fig.lO(b), and this is given by
v = 1
c2 J
ETm take the Laplace transforms of 14 and 15, and to avoid confusion with
the symbol for pressure denote the Laplace trsnsfrm symbol by S instead
of the more usual p, so that
Then
? =
i
0
00
i dt
i emSt dt etc.
VT3 + g(s)
? = -- -- --
z1z2 + z2z3 t 2z,z3 (16)
where g(S) is a function of the initial conditions only.
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