Page 131 - Mechanical Engineers' Handbook (Volume 2)

120 Measurements

i E o (2)
m
Z AB Z L
and the voltage E L across Z L is
EZ
E iZ oL
L
m L
Z AB Z L
or
E E o (3)
L
1 Z /Z L
AB
Equations (2)–(7) are frequency-domain equations.
In a measurement situation E would be the voltage indicated by the voltmeter, Z would
L
L
be the input impedance of the voltmeter, and Z AB would be the output impedance of the
linear network. The true output voltage, E , has been reduced by the voltmeter, but it can
o
be computed from the voltmeter reading if Z AB and Z are known. From Eq. (3) it is seen
L
that the effect of the voltmeter on the reading is minimized by making Z as large as possible.
L
If the generalized input and output impedances Z and Z are defined for nonelectrical
gi
go
systems as well as electrical systems, Eq (3) can be generalized to
q
q im iu (4)
1 Z /Z gi
go
where q is the measured value of the effort variable and q is the undisturbed value of the
iu
im
effort variable. The output impedance Z go is not always defined or easy to determine; con-
sequently Z should be large. If it is large enough, knowing Z go is unimportant.
gi
If q is a flow variable rather than an effort variable (current is a flow variable, voltage
i1
an effort variable), it is better to define an input admittance
q
Y i1 (5)
gi
q i2
rather than the generalized input impedance
effort variable
Z
gi
flow variable
The power drain of the instrument is
q 2
P qq i2 (6)
i1 i2
Y gi
Hence, to minimize power drain, Y must be large. For an electrical circuit
gi
I I u (7)
m
1 Y /Y i
o
where I measured current
m
I actual current
u
Y output admittance of circuit
o
Y input admittance of meter
i
When the power drain is zero and the deflection is zero, as in structures in equilibrium, for
example when deflection is to be measured, the concepts of impedance and admittance are