Introduction to Acoustics

1026 Part H Engineering Acoustics
Part H 24.3
24.3 Reciprocity Pressure Calibration
24.3.1 Introduction
High precision in acoustical measurements is needed
even though the human ear cannot discern a change
in sound level much smaller than 1 dB. For example,
to certify aircraft for regulations, it is necessary to obtain
measurements with a known uncertainty, usually
0.1–0.2 dB (Unless otherwise stated, the uncertainties
referred to in this chapter, may be taken as better than
two standard deviations. However, in most cases, the
quoted statements on uncertainty are unclear in the
source documents. Further complications are introduced
when the original data are converted to decibels. For
a more rigorous treatment of uncertainties, one should
consult [24.31]). It is reasonable to assume that laboratory
standard microphones (working standards) should
be approximately an order of magnitude better than this,
say with an uncertainty ranging from 0.01 to better
than 0.1 dB. For research and development purposes, including
the study of microphones and monitoring their
stability, the primary calibration of condenser microphones
should have an uncertainty no larger than several
thousandths of a decibel.
One of the most accurate techniques to calibrate
a primary standard condenser microphone is the absolute
method of reciprocity pressure calibration (sometimes
called the coupler method), which currently has a best
uncertainty of less than 0.01 dB at 250 Hz, under
a fully controlled environment under reference conditions
[24.20]. If the calibration were to be performed
on a laboratory bench without any control on the environment,
such as barometric pressure, temperature
and humidity, the estimated uncertainty of the coupler
method is approximately 0.05 dB at lower and middle
frequencies.
The theory of absolute pressure calibration methods
for condenser microphones and some of the relatively
modern implementations have been described
in [24.1–29].
24.3.2 Theoretical Considerations
The reciprocity method measures the product of the sensitivities
of each pair of a set of three microphones in
terms of related electrical and mechanical quantities,
from which the absolute sensitivity of each microphone
can be deduced.
The acoustic impedance ZAB, of a cavity with
a pair of microphones A and B, as shown in Fig. 24.5
is
ZAB = γ Ps[iω(V + VeA + VeB)] −1 , (24.10)
where γ is the ratio of specific heats of the gas in the
coupler, Ps is the barometric pressure, ω equals 2π f ,
where f is the frequency of the driving sinusoidal signal,
and V, VeA and VeB are the equivalent volumes of
the cavity and of microphone A and microphone B, respectively.
Equivalent volumes, as the name implies, are
volumetric measures that represent the physical volumes
of the cavity and of the coupled microphones modified
by thermal and finite impedance factors.
The relationship between the alternating pressure p
inside the cavity and the volume velocity u is
p = uZAB = uγ Ps(iωVAB) −1 , (24.11)
where the equivalent volume of the cavity with microphones
A and B is
VAB = (V + VeA + VeB) . (24.12)
The reciprocity theorem states that, in a passive linear
reversible (reciprocal) transducer, the ratio of the
volume velocity u in the cavity to the input current I
when used as a sound source is equal to the ratio of the
open-circuit voltage eA across the electrical terminals
to the sound pressure p acting on the diaphragm when
used as a receiver. The theorem enables one to write the
From
oscillator
Zx
I
VeA
VeB
(A) (B)
VAB
Fig. 24.5 Calibrating condenser microphones by the reciprocity
method (after Wong, [24.29], Chap. 4)
eA
eB