Talking About Microphones

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Talking About Microphones

The decibel is widely misunderstood. Its definition came from acoustic studies in the early 1900s and has been widely adopted by many disciplines, most notably electronics. In the very beginning was the Bel (named in honor of Alexander Graham Bell). The Bel was first defined in terms of acoustic power, but it can be generalized as the logarithm of the ratio of two quantities with the same units.

Since logarithms are extraordinary compressors, the magnitude of the Bel was deemed inconvenient for typical acoustic calculations, so it was subdivided into 10 (deci) parts and abbreviated dB.

In acoustic research, the power level of sound was defined as 10 log₁₀ of measured sound power divided by reference sound power. Because it is more convenient to measure sound pressure than sound power, the pressure level of sound was defined as 10 log₁₀ of measured sound pressure squared divided by reference sound pressure squared. Since log₁₀ (N)² = 2 log₁₀ N, the sound pressure level (in dB) can be rewritten as 20 log₁₀ of measured sound pressure divided by reference sound pressure.

This would seem to be an unfortunate definition, because now everyone has to remember whether to use 10 times the log₁₀ or 20 times the log₁₀ when calculating common dB values. For acoustic and electrical power, use 10; for acoustic pressure and electrical voltage, use 20.

Sensitivity

Fortunately, stating the sensitivity of microphones in V/Pa (volts/pascal) is gaining popularity. Since the output of any type of microphone is linear with pressure, the units of V/Pa fall out naturally. As an indication of the confusion still prevalent in defining microphone sensitivity, the Endevco model 2510 piezoelectric microphone has several numbers and units listed for sensitivity (the electrical output from piezoelectric microphones is commonly expressed in picocoulombs [pC], rather than volts).

Although sensitivity units of V/Pa (or pC/µbar in the case of piezoelectric microphones) are commonly used now, the older units are still in use, and microphone sensitivity can be expressed in dB using a calculation that simply references the output of the microphone to a theoretical microphone which can pump out 1 V rms for 1 Pa of rms pressure. Since no one (to our knowledge) has yet marketed a microphone with such a high output, microphone sensitivities in dB are negative (e.g., -60 dB re 1V/Pa).

Conversions

The following conversions can be viewed by downloading the full PDF version of this document:

(Let S1 be the known value, S2 be the unknown value of sensitivity)

• To convert from S₁ dB (re 1V/Pa) into S₂ V/Pa
• To convert from S₁ dB (re 1V/Pa) into S₂ mV/psi
• To convert from linear sensitivity S₁ into S₂ dB (re 1V/Pa), excepting piezoelectric microphones
• To convert from linear sensitivity S₁ into S₂ dB (re 1pC/µbar) for piezoelectric microphones

Dynamic Range/Resolution

Resolution (or threshold) defines the lower limit of the dynamic range. Electrical noise in the transducer and signal conditioning is the primary limiter. The lower limit of dynamic range for a microphone may also result from the acceleration ("g") sensitivity. Similarly, an upper limit for the dynamic range is based on the maximum pressure where the output is still reasonably linear.

For 10g sinusoidal vibration, the output would be 114 dB SPL (a factor of 10 equates to 20 dB). These large equivalent dB SPL values indicate that vibration sensitivity, rather than electrical noise level, may often be the limiting factor at the low end of the range. Since the sensitivity of a microphone diaphragm to vibration goes as the cosine of the angle to the axis of vibration, mounting the unit with the diaphragm at 90° to the vibration input dramatically reduces or eliminates the error.

Calibration

For units with DC response, such as silicon based microphones, it is possible to perform a static calibration using a precision dead weight tester and directly measure V/Pa and then convert the V/Pa into logarithmic units if required. Since the sensitivity calculations are made in ratios, dc instead of ac (rms) measurements may be substituted in the equations without having to convert from rms to dc levels. Similarly, we may substitute other instantaneous voltages and pressure values, e.g., mV pk at 1 psi pk for measuring acoustic shock.

For units with only AC response, such as piezoelectric or condenser microphones, various methods have been devised for generating a precise acoustic wave, e.g. piston phone, or a step function pressure may be generated using a quick dump valve and a dead weight tester.

Click here for a complete version of this technical paper with additional information plus detailed equations, calculations and conversions.


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