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Audio Measurements Workshop
Fons Adriaensen
Casa della Musica, Parma
Linux Audio Conference 2014
ZKM Karlsruhe, Germany
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Overview
• Techniques and tools to measure
* Soundcards
* Analog hardware
* DSP software
• Theory
* Levels, decibels, noise, calibration,. . .
• Tools
* jaaa, jnoisemeter, jsignal,. . .
• Practice
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Philosofical issues
• Why measure things ?
* Verify your design and programming.
* Have you been ripped off ?
* To know limits and create a level of confidence.
* Curiosity.
• Always expect the unexpected. It happens. If your measurements are exactly as you imagined they would be, then
* Congratulations !
* It’s time to verify things and ask some questions.
• Audio measurements often involve a mix of electrical and
acoustic units as well as purely numerical values, and conversions between them. This can be very confusing unless
you have a solid grip on the basics.
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Theory
• Signals
* Levels, power, impedance, balancing, . . .
* Measurement methods.
• Decibels.
* Reference levels, . . .
• Acoustic units and levels.
• Noise.
* Distribution, spectrum, density.
* Measurement methods and standards.
* Thermal noise.
* Equivalent input noise.
• Understanding audio specs.
* Microphones.
• Calibration.
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Analog signals
• Measured in Volts (V).
* Rough levels: mics: 1 mV, consumer: 100 mV, pro: 1 V.
* Current: i = u/Z (A).
* Power: P = i ∗ u = u2/Z = i2 ∗ Z (W).
• Analog audio connections are almost always voltage driven.
* Input impedance is much higher than output impedance.
* Allows splitting the signal without level changes.
* Exception: long analog lines (rarely used today).
• For numerical signals (no physical units), ’power’ means the square
of amplitude.
• The ’gain’ of AD and DA converters requires some care to define
without ambiguity as one side uses physical units and the other not.
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Balancing
• Balanced connections:
* Inputs take difference of two signals, cancels interference.
* Different kinds of outputs and inputs are not always compatible.
• Outputs
* Impedance balanced – very common.
* Antiphase outputs – different variations.
* Differential – rare.
* Floating – requires transformer.
• Inputs:
* Differential with unbalanced impedance – very common.
* Differential with balanced impedance.
* Floating — requires transformer.
* Common mode rejection of input defines performance.
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Balanced outputs
+G
impedance balanced
differential
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-1
-G
antiphase outputs
antiphase outputs
+x
+x
+x
+x
transformer balanced
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Balanced inputs : CMRR
• A ’perfect’ differential input ignores the common signal.
• Real-life balanced inputs are not perfect.
• The Common Mode Rejection Ratio indicates
by how much the common signal is attenuated.
• CMRR is usually a function of frequency.
• Typical figures:
* Cheap: 20. . . 25 dB
* Reasonable: 40 dB
* Transformer balanced: 80. . . 90 dB
• Common mode signals can be the source of large errors.
• Common mode input or output impedances are usually
not the same as the differential impedance.
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Balanced inputs: CMRR
+A/2
A
??
Gd * A
Gc * A
-A/2
CMRR = Common Mode Rejection Ratio = Gd / abs (Gc)
R1
R2
M
R2
R1
Unbalanced signal with balanced attenuator.
If M is not connected to ground the common mode signal is not attenuated.
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Audio level meters
• Defined by filter, detector, ballistics.
• Filter: flat, lowpass, A, C, ITU 468,. . .
• Detector: what is measured.
* Peak or pseudo peak value.
* Average of absolute value.
* RMS.
• Ballistics: response to level variations.
* Rise and fallback times.
* Burst response, can be different from rise time.
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RMS meters
• RMS = Root Mean Square =
* The square root of the average value of the
square of the signal.
* The average power expressed as an amplitude.
• The RMS value is independent of the relative phases
of the different frequencies in a signal.
• ’Mean’ or ’average’ means some form of lowpass filter:
* Rectangular window.
* First or second order IIR, which is an exponential
window.
• AC voltages are always shown as an RMS value, even if
the meter is not an RMS one. In that case the measured
value is correct only when the signal is a sine wave (e.g.
almost all multimeters, VU, . . . )
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Decibels
• Logarithmic unit used to indicate ratios.
• 1 dB = 0.1 Bell. One Bell is a ratio of 10 to 1.
• Always a ratio of powers or something proportional
to power.
10 * log10 (ratio of powers)
20 * log10 (ratio of amplitudes)
• Absolute measurements require a reference value.
• Memo trick: the 1/3 octave band frequencies: 1, 1.25,
1.6, 2, 2.5, 3.16, 4, 5, 6.3, 8, 10. Each step is 1 dB for
powers or 2 dB for amplitudes.
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Decibels – reference levels
ζ
• 0 dBm = a power of 1 mW. A standard impedance is assumed.
* Audio: usually 600 ohm
* RF: 50 or 75 ohm.
• 0 dBu = 0.7746 Volt, the voltage corresponding to 1 mW in 600
ohm. Quite often ’dBm’ is used when ’dBu’ is meant.
• 0 dBV = 1 Volt. Simple and easy. 0 dBV = +2.22 dBu.
• 0 dB FS = the amplitude of a maximum level sine wave in a digital
system.
If this is RMS, and the range is ±1, then the actual RMS
amplitude of a sine wave at 0 dB FS is not 1 but sqrt (0.5) =
0.7071.
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Acoustic levels
• Sound Pressure Level (SPL) is measured in Pascal (Pa).
• 0 dB SPL = an RMS sound pressure of 2 * 10−5 Pascal.
* This is the threshold of human hearing at 1 kHz.
* A sound pressure of 1 Pa is +94 dB SPL.
• For electrical signals we have i = u/R and P = u ∗ i = u2/R.
• For acoustic signals we have v = p/Z and I = p ∗ v = p2/Z.
* p = sound pressure (Pa)
* v = particle velocity (m / s)
* Z = acoustic impedance (N s / m3)
* I = acoustic intensity (W / m2)
• The acoustic impedance of air at 20 degrees Celsius is 413.3 N s / m3.
• Note: electrical current and power are scalars, but particale velocity
and intensity are vectors – they have a direction.
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Acoustic levels – example 1
ζ
We have a sound source with an acoustic power of 1 Watt.
What is the SPL at a distance of 3 meters ?
• The power is spread over the surface of a sphere with radius 3 m.
• This surface is 4 ∗ π ∗ R2 or 113.1 m2.
• So the intensity I is 1 W / 113.1 m2, or 8.842e-3 W / m2.
√
2
• Now I = p /Z, or p = I ∗ Z.
• Hence the pressure is sqrt (8.842e-3 * 413.3) = 1.91 Pa.
• 1.91 Pa = 20 * log10 (1.91) + 94 = 99.6 dB SPL.
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Acoustic levels – example 2
ζ
We have an SPL of 1 Pa (+94 dB) and a microphone with
a membrane of 5 cm2 (1 inch diameter). How much acoustic
power does the mic receive ?
• I = p2/Z = 1 / 413.3 W / m2.
• P = I ∗ S (S = surface area) so
• Power = 5e-4 / 413.3 = 1.21e-6 Watt
• This should be compared to thermal noise power (later).
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Noise
• A random or pseudo random signal.
• Probabilty distribution
– Rectangular, Gaussian,. . .
– We normally don’t hear differences in distribution.
– A sum of many independent random values will have a
Gaussian distribution.
– Filtered noise tends to have a Gaussian distribution.
• Density spectrum
– Noise density N0 = power per Hz.
– At any particular frequency there is zero power.
– White noise: constant density. P = B ∗ N0
– Pink noise: density proportional to 1/F .
– White and pink noise must be limited in bandwidth,
or they would have either infinite power or zero density.
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Measuring noise
• Requires either a true RMS meter, or one that is very tightly specified.
• Meter ballistics must be slow to have a stable value.
• Usually weighted using a standard frequency response.
• If no other filter is used the bandwidth must be defined.
• A number without specified measurement method is meaningless.
• Standard methods
* 20 kHz equivalent bandwidth + RMS
* IEC-A filter + RMS
dB(A)
* IEC-C filter + RMS
dB(C).
* ITU468 filter and pseudo-peak meter
dB(20kHz)
dB(ITU468)
• dB(A) is typically 1.9 dB lower than 20 kHz equivalent BW.
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Standard noise weighting filters
20
ITU-468
10
0
IEC-C
10
20
30
40
IEC-A
50
60
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ITU468
• The ’best’ method for measuring mics and mic preamps.
• Originally developed to measure noise on long analog audio lines.
• Filter emphasizes the most critical frequency region.
• Pseudo-peak meter having
* a very slow response, as required for noise,
* but very sensitive to short bursts and impulsive noise
e.g. from a switching power supply or digital electronics.
• Typical measured values are around 9 dB higher than A-weighted.
• Used mostly in Europe, Americans use dB(A) because it looks better.
• The ’Dolby variant’ uses lower gain and an average meter, but it is not
and official standard.
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ITU468 step and burst response
0
-10
-20
-30
-40
-50
-60
0.001
0.01
0.1
1
Step response and
burst response of the ITU468 meter.
Burst response specification.
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Thermal noise
• Aka Johnson or Nyquist noise. Generated by thermal motion of
electric charge carriers in all conductors.
• Essentially white (up to very high frequencies).
• Power density is proportional to absolute temperature.
• Power P = 4kBT
– k = Boltzmann’s constant, 1.381 * 10−23 Joule / Kelvin
– B = Bandwidth in Hz
– T = Temperature in Kelvin.
• At room temperature and a BW of 20 kHz this means
* Power P = 3.24 * 10−16 Watt
√
* RMS voltage vn = 18 nV * R
* For R = 150 ohm vn is 220 nV = -133.1 dBV = -130.9 dBu
• Other noise sources are present in real-life electronics,
but mostly at low frequencies (below 100 Hz).
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EIN: Equivalent input noise
ζ
• All components of an electronic circuit generate thermal noise.
• It is always possible to model an amplifier or an AD converter as
a ’perfect’ noiseless one with a single noise source at the input.
• EIN = noise measured at the output / gain.
• The noise generated near the input will contribute most, as it is
amplified.
• For a well-designed amplifier, EIN will be independent of gain as
long as the gain is high.
• Other low level signals may be present (e.g. 50 or 60 Hz and
harmonics).
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EIN of microphone preamps
ζ
• The EIN of mic preamps is usually measured with at maximum
gain with a source impedance of 150 ohm.
• Some preamps can be a dB or so less noisy when measured with
a lower impedance source or short-circuit.
• The EIN can be compared to the self-noise of the mic to find
out which generates most noise.
• Some example values:
note: 150 ohm generates -135 dBV(A)
Preamp
EIN dBV(A)
RME Micstasy
-131.2
Aphex 1788A
-129.0
Sony SPR-V110
-133.5
Behringer PRO8
-132.9
Edirol UA5
-122.2
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EIN vs full scale input level
-105
-110
-115
-120
-125
-130
-135
-45
-40
-35
-30
-25
1788A
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-20
-15
-10
-5
0
PRO8
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EIN vs gain: why
En
En
R1
R2
R1
R2
A
Gain = 1 + R1 / R2
B
En = thermal noise due to R1 k R2
+ amplifier input noise voltage
+ amplifier input noise current × R1 k R2
• Except at low gains, R2 R1 and R1kR2 ' R2.
• A: For lower gain R2 increases and En increases.
• B: R2 is fixed and En is almost constant.
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Audio specs and unspecs
ζ
• Very few manufacturers of ’prosumer’ HW provide specs that have any
real meaning, or that can be compared to others. This is of course
entirely intentional.
• Example: M-Audio ’octane technology’ mic inputs. All you are supposed
to know about those is: signal/noise ratio = 97 dB.
• Specs that don’t define measurement conditions are completely useless.
• Even levels are ambiguous. In pro audio +4 dBu is the ’work level’, peak
level is at least 15 dB higher. Yet cards that can be switched between
a peak output of -10 dBu and +4 dBu are presented as supporting pro
signal levels.
• Most equipment reviews that can be found on the web don’t verify or even
mention any technical specs. They are at best useless, if not completely
bogus (the author got a free sample).
• If specs are not completely unambiguous, the only sane reaction is to
mistrust them, and spend your money on something else.
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Microphone specs
• When recording low-level signal (acoustic instruments, voice, natural sounds, . . . ) the combination of microphone and preamp will
determine performance.
• The important values are sensitivity and self-noise.
• Sensitivity is usually specified as the output for 1 Pa (+94 dB) SPL.
• Self noise is the acoustic level corresponding to the noise generated
by the microphone, usually dB(A) or dB(ITU468).
• Comparing specs for dynamic and condensor mics may require some
calculations.
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Dynamic mics
• Sensitivity and impedance are specified. Self noise is thermal
noise corresponding to impedance. Given sensitiviy, this can be
converted to SPL.
• Example: Beyer M160: 1.0 mV/Pa, 200 ohm.
1.0 mV = -60 dBV.
Thermal noise is 18 nV *
√
200 = 254 nV = -131.9 dBV.
Self noise is -131.9 + 94 + 60 dB = 22.1 dB = 20.2 dB(A).
• Example: Shure SM58: 1.85 mV/Pa, 300 ohm.
1.85 mV = -54.7 dBV
Thermal noise is 18 nV *
√
300 = 312 nV = -130.1 dBV.
Self noise is -130.1 + 94 + 54.7 dB = 18.6 dB = 16.7 dB(A).
• To use the full dynamic range a preamp with an EIN better than
-130 dBV is required.
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Condensor mics
• Sensitivity and self noise and/or S/N ratio are specified. S/N ratio
is relative to 1 Pa, so self noise + S/N ratio = +94 dB. Given
sensitivity, either can be converted to noise voltage.
• Example: Neumann KM184: 15 mV/Pa, self noise 13 dB(A).
15 mV = -36.5 dBV.
Noise voltage = 13 - 36.5 - 94 dBV(A) = -117.5 dBV(A).
• Example: Neumann TLM103: 23 mV/Pa, self noise 7 dB(A).
23 mV = -32.8 dBV.
Noise voltage = 7 - 32.8 - 94 dBV(A) = -119.8 dBV(A).
• A preamp with an EIN of around -122 dBV(A) or better will allow
the full dynamic range of these mics to be used.
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Q&A
Questions and answers, hands-on practice.
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