Josephson Microphones
Tech Note 6




Application of Measurement Microphones

Measurements of acoustic phenomena are not too difficult to make, but it is often difficult to
determine precisely how accurate the measurement is. Many factors in the environment
degrade the accuracy of the measurement, and careful analysis is required to determine the
effects of these degradations. The human auditory system further complicates the problem,
because many small variations in sound are immediately measurable, but are often inaudible
except where special precautions are taken to restrict the ears' natural adjustment to
differences. Likewise many audible phenomena are difficult to measure with conventional
techniques.

A complete discussion of theoretical acoustics is beyond the scope of this note, but some
basic quantities must be understood before measurements can be meaningfully interpreted.
The related concepts of frequency, speed and wavelength, and of pressure and particle
velocity, must be clear. The physics of the measuring devices are quite simple, and easy to
remove from the measurement one they are understood, but it's easy to be misled by sound
measurements unless the nature of the quantity being measured is well known. Sound is often
the first measurement we normally experience where the dimensions of the waves we're
measuring are significantly large with respect to the other dimensions of the environment. For
example, we can easily conceive of measuring light at a distant spot by using a lens to focus on
a light-sensitive device. Light from nearby objects is absent from the measurement because it
isn't imaged on the sensor. Why can't this be done with sound? The reason is that in order to
be effective, the dimensions of a focusing system (distance to the spot and to the sensor,
diameter, and focal length) must be very large compared with the wavelength of the light. For
an acoustic lens to be as effective in focusing sound as a camera lens is for light, it would need
to be on the order of five miles across. There are arrays of sensors in the ocean, installed for
listening to submarines, that effectively do form a lens tens many miles across, but this is
hardly practical for ordinary acoustic measurement. Although we can safely ignore the wave
nature of light in everyday measurements of it (taking pictures), we can't do the same with
sound.

In the discussion that follows, the conditions are assumed to be constant atmospheric
temperature and pressure at roughly 20 degrees C and 1 bar, zero wind, and the sound
medium being frictionless air. This preface will save a lot of special conditions being attached
to the points being discussed. 

Basics of Sound

Sound is best understood as a rapid variation in air pressure. For otherwise constant
conditions, air pressure is simply the number of air molecules occupying a given volume, in
other words air particle density. A loudspeaker makes sound, for example, by moving its cone
in and out of the box in which it's mounted. The number of air molecules inside the box
doesn't change, and the number of air molecules inside the room doesn't change either. As
the cone moves out, the volume of the room gets smaller, so we say that the pressure rises
because the same number of air molecules are now enclosed in a smaller volume. When the
cone moves back in, the pressure drops because the room is larger than it was before, for an
instant. The magnitude of this pressure change is called the sound pressure. It's a scalar
measurement, which means it has only one dimension: the difference between the maximum
and minimum number of air molecules inside a fixed volume.

As we move away from the sound source, the sound pressure decreases. That's because, in
the case of the loudspeaker mentioned above, the volume change caused by the motion of
the cone is a smaller part of the total volume, the further away we are. In ideal conditions,
we can confirm that sound pressure in a given direction drops off with the square of distance
from the source, which is the same factor by which the total air volume increases as we move
away from the source.

Sound pressure measurement in the case described so far is very simple; measure the change
of air pressure. It becomes more complex in the real world when we have to think about
what happens as the sound wave hits some other object and bounces to the measurement
site. Now we must leave the convenient model of a peak pressure change measurement over
a period, and think about what happens at each instant in time. 

Think about an example where we have 1000 particles of air in a given volume, an imaginary
cubic volume of air. On the positive crest of the sound wave, there may be 1100 particles in
the box, and on the negative crest only 900. We have a peak-to-peak sound pressure of 200
particles. If it's a sinusoidal variation, that is an rms pressure of 71 particles -- the average
particle variation. The frequency of the sound is 1000 Hertz, or 1000 cycles per second. That
means that the number of particles in our measurement box changes from 1000 to 1100,
back to 1000 and then to 900, then back to 1000 particles, 1000 times every second.  

Reflections

Now imagine that the sound continues past our measurement box to a wall, and is reflected
right back. We have the original sound pressure, and now we have the reflected wave too.
Ignoring losses, the peak-to-peak magnitude of this wave is still 200 particles. If the crest of
the reflected wave arrives at the measurement point exactly in time with the crest of the
direct wave, the sound pressure doubles: 400 particles. We say that the reflected wave is in
phase with the direct wave at this point. If the trough of the reflected wave arrives exactly in
time with the crest of the direct wave, the two sounds can cancel completely: +100 from
the direct wave, -100 from the reflected wave, a net pressure change of 0. We say that the
two waves are out of phase.  In normal conditions, only a portion of the wave is reflected,
and the spacing is never such that the direct and reflected are precisely in or out of phase
with each other. The product of a direct wave and a reflected wave added together at a point
in space is some value between zero (perfect cancellation) and the sum of the two waves
(perfect addition).

Wavelength

The wave is moving at 347 meters per second. Since the pressure varies from its resting value
to a crest, to a trough and back to its resting value 1000 times every second, the length of
one of these cycles as the wave moves is 347/1000 meters, or about 1/3 meter. If the wall in
the example above is exactly .347 meters (one wavelenth) away, exactly two complete waves
will fit in the distance from the measurement point to the wall and back again, and the
measured sound pressure will double. We say that the reflected sound path is two
wavelengths long, and the reflected wave is in phase with the direct wave. If the wall is .434
meters away (another quarter of a wavelength distant), the reflected path is two and a half
wavelengths long, and the reflected wave will be out of phase with the direct wave, or 180
degrees apart from it, and the reflected and direct sounds will cancel. Cases of multiple
reflections get more complex, because the reflected waves continue to propagate, even
through areas where the net sound pressure of all the waves is zero.

This issue of sound reflections probably causes the greatest error in the entire sound
measurement process, because the microphone cannot determine the direction from which
the sounds have come. There are applications where total sound pressure in an environment
must be evaluated, so the reflected waves must be considered, but in most measurement tasks
it is desirable to eliminate reflections and measure the sound arriving at the microphone from
the source directly. There are several techniques used to reduce or eliminate the effects of
reflections, see our Tech Note 4, "Speaker Evaluation Without an Anechoic Chamber".

Measurement Setup

It's very easy to make an acoustic measurement: the microphone is simply connected to some
measuring instrument and the sound level read. It's not so easy to know for certain how
accurate this measurement is. The environment and test setup should be evaluated to check all
the assumptions that have been made about what is being measured. If there are reflecting
surfaces, their effect on the measurement must be considered. If there are external sound
sources, their effect must be considered also. Generally it is a good idea to position the
microphone some standard distance, 0.5 or 1 meter, from the sound source, and the
reflections from surrounding surfaces should be reduced so that the loudest reflected sound is
at least 20 dB below the direct sound level. Likewise, the ambient noise level should be at
least 20 dB below the level of the test signal. If these conditions are not possible, special
precautions should be taken to eliminate the effects of reflections and external noise.
Microphone Choice

A microphone should be selected according to the range of sounds being measured. The first
decision is whether the microphone should be a free field or diffuse field, sometimes referred
to as pressure type. The free-field response of a microphone is the ratio of the rms output
voltage to the rms sound pressure existing in the free field at the microphone location, if the
microphone were not there. So-called free-field microphones are made to have a flat response
on-axis -- in an anechoic chamber, the response will be uniform if the sound arrives from the
front of the microphone. The pressure response of a microphone is the ratio of rms output
voltage to rms pressure, uniformly applied over the diaphragm. A so-called pressure-response
or diffuse field microphone has a response that's uniform for sound pressure in a small
enclosed volume like an electrostatic coupler. This response characteristic is also nearly flat
for sounds arriving from random angles of incidence, or from a diffuse sound field.

Nearly all microphones have a frequency response that varies with direction. Measurement
microphones are essentially formed of a cylinder with the diaphragm closing one end. There
are several physical mechanisms that cause high frequencies to be boosted if they arrive from
the front, and more or less attenuated if they arrive from the rear or sides. In anechoic
conditions, one need not be concerned with this problem, but where there are reflections, it
must be considered. 

A diffuse field microphone is used when the whole sound field, consisting of direct and
reflected sounds, or sounds arriving from all directions, is to be measured. The on-axis
frequency response is typically 5 to 7 db higher around 12 kHz than at 1 kHz and below. The
response is nearly flat at 90 and 270 degrees of azimuth, and 5 to 7 dB down at 12 kHz
toward the rear of the microphone. The spherically-integrated frequency response is then
approximately flat. In order to assure that the environment is sampled uniformly, this type of
microphone is often moved about in a circle during the integration period of the
measurement.

As the dimensions of the microphone become smaller, the frequency at which directional
effects become important rises. Half-inch microphones exhibit nearly spherical response up to
6 kHz (typically -3 dB at 180� at 6 kHz), while � inch microphones reach this point at 15
kHz. Nose cones are available for metal diaphragm measurement microphones that extend the
spherical response range by another octave or more.

The noise floor and overload point of the microphone must be considered to determine that
these limits won't compromise the measurement. According to IEC standard 651, the noise
floor of the entire measurement system including the microphone should be at least 5 dB
lower than the sound being measured.

Power Supply
Josephson measurement microphones require either phantom power or individual voltages for
the operation of their circuitry. Phantom power is supplied by several of the currently
available test analyzers, and the standard for individual voltages was set many years ago by the
Br�el & Kjaer 7-pin format. Phantom power consists of a DC voltage supplied through
matched current limiting resistors to both sides of the balanced audio line; the return path for
the DC is through the ground conductor or shield of the cable. The standard is 48 volts, but
equipment is often found with 15 or 24 volt phantom power. The Josephson C550 series of
microphones will operate over the range of phantom power voltages from 15 to 52 V. 
Conventional measurement microphones typically require 200 volts for polarization of the
diaphragm and 85 to 130 volts (120 V is standard) for the amplifier circuitry. 6.3 volts is also
provided, either for the filament of a vacuum tube mic preamplifier, or for a heater resistor
inside the preamp which is used to dispel moisture. Regulation and noise filtering of all voltages
is very important to succesful operation of the equipment. Phantom power supplies must also
use critically matched components to assure a good balance of the power current on the
microphone leads.

Signal Levels

The output level of the microphone is often not high enough to drive the measuring
equipment directly. While the measurement microphone electronics is often called a
"preamplifier," in fact it usually has unity gain, and its main function is that of an impedance
converter. An external gain stage is required to boost the level to the normal operating level
of the measurement equipment. Microphone sensitivity is typically rated in millivolts per Pascal.
1 Pascal is 94 dB SPL, or 94 dB above an rms sound pressure of 0.0002 microbar. From this
figure can be calculated the microphone output at the working sound pressure. If this is well
within the operating range of the instrument used, no external amplifier is needed. It should
be at least 5, and preferably 10 dB above the noise floor of the instrument.

Error Estimation and Reduction

The final outcome of most measurements will be a graph or chart showing amplitude response
versus frequency or time. Not shown on the chart is the set of errors that may be included in
the presented data, and it is important for the researcher or production engineer to have a
clear understanding of the various sources of error so that the accuracy of the chart can be
known. Worst case, the error budget is the sum of the peak-to-peak variations of all the
variable factors in the measurement, and since there is no way to know whether the errors
are correlated for a given measurement or not, it should be assumed that the worst case
conditions exist. Some error sources are:

     Ambient noise
     Reflections from surroundings
     Variation in frequency response versus angle from source
     Variation in frequency response versus angle of incidence
     Error in test signal calibration
     Error in microphone calibration
     Error in measurement equipment response

For the first four error sources, a magnitude estimate can be made simply by observing the
scatter between readings as the ambient noise changes, or as the microphone is moved around
the test area. For ambient noise problems, errors can be often reduced by using longer
integration times or subtraction of noise values from the result. For information on reduction
of errors caused by reflections, see Josephson Tech Note 4, "Speaker Evaluation Without an
Anechoic Chamber".

Test signal and measurement equipment errors can be minimized by using the same test signal
for a known measurement object and again for the object under test. For example, the test
signal can be applied to the microphone preamp input and the system response plotted. Any
subsequent test result, using the acoustic path from the test signal through whatever
transducers are being used, and back to the mic preamp, can then have the test signal and
preamp response subtracted to yield an analysis only of those parts of the signal path that are
different.

Josephson microphone calibration data is accurate to � 0.5 dB or less over the range shown.