Page 449 - Instrumentation Reference Book 3E

432 Electrical measurements

Deflection 0
Pointer
Spring I
Mirror
Counterweight
h

@and
bearing (a) Time
Figure 20.9 Second-order system responses.
(a) Overdamped; (b) critically damped; (c) underdamped.

KW;
G(s) =
S2 + 2Jw,s + w;
The natural frequency of the instrument is given
by w, = J(k/j), and its damping factor E = Dl2
Field-
(flux density J(JW
If 0' > 4 kJ then E > 1 and the system is over-
damped. The response to a step input of current
magnitude I at t = 0 is given by

Suspension band

If D2 = 4 kJ then E = 1 and the system is critically
damped. The response to the step input is given
by
A pointer is attached Suspension band
to the moving coil 8(t) = S . Z[1 - (1 + w,t)e~wn'l

[ b) If D2 < 4 kJ then E < 1 and the system is under-
Figure 20.8 (a) Elernentsof a permanent rnagnet- damped. The response to the step input is given
moving coil instrument; (b) taut band suspension system
by
Damping can be provided by an air damper or
by eddy-current damping from the shorted turn
of the former or from the coil and external circuit. and 4 = c0s-I 5.
For eddy-current damping
These step responses are shown in Figure 20.9.
20.2.1.1 Range extension
where R represents the resistance of the coil cir- The current required to provide full-scale deflec-
cuit and Rf represents the resistance of the coil tion (FSD) in a moving-coil instrument is typic-
making up the former. ally in the range of 10pA to 20mA. D.c. current
The instrument thus has a second-order trans- measurement outside this range is provided by
fer function given by means of resistive shunts, as shown in Figure
Q(s) (klJ) . S 20.10(a). The sensitivity of the shunted ammeter,
=
G(s) = - SA, is given by
Z(S) -t (DIJ) . s + (kIJ)
Comparing this transfer function with the stand-
ard second-order transfer function