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# How to comput the SPL for a given output word?

Hi

I use the ADMP441 and I want to know how to compute the SPL value for a given digital output word. I know, that 120 dB SPL is mapped to the FS value of the ADC. Is the EIN value also mapped to the the value of the noise floor so that 33 dB SPL (EIN) is equivalent to the -87 dBFS word? Is the relationship between the SPL and the ADC word linear in this range? The data sheet and the application notes I read, couldn't answer this questions.

Thank you very much for any kind of help

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• To get the instantaneous level of a digital signal in terms of the acoustic sound pressure level, you have to know the sensitivity of the microphone that was used to capture the sound. The text below is taken from an upcoming data sheet. I hope that this does a good job to describe how to measure the amplitude of a digital microphone signal. In your case, with 24-bit data, a value of -8338608 would represent negative full-scale, or -1.0 D.

The sensitivity of a PDM output microphone is specified in units of dBFS (decibels relative to a full-scale digital output). A 0 dBFS sine wave is defined as a signal whose peak just touches the full-scale code of the digital word. This measurement convention means that signals with a different crest factor may have an rms level higher than 0 dBFS. For example, a full-scale square wave has an rms level of 3 dBFS.

1 kHz, 0 dBFS Sine Wave

The definition of a 0 dBFS signal must be understood when measuring the sensitivity of a digital microphone. An acoustic input signal of a 1 kHz sine wave at 94 dB SPL applied to the ADMP521 results in an output signal with a −26 dBFS level. This means that the output digital word peaks at −26 dB below the digital full-scale level. A common misunderstanding is that the output has an rms level of −29 dBFS; however, this is not the case because of the definition of a 0 dBFS sine wave.

There is no commonly accepted unit of measurement to express the instantaneous level of a digital signal output from the microphone, as opposed to the rms level of the signal. Some measurement systems express the instantaneous level of an individual sample in units of D, where 1.0 D is digital full scale. In this case, a −26 dBFS sine wave has peaks at 0.05 D.

For more information about digital microphone sensitivity, see the AN-1112 Application Note, Microphone Specifications Explained.

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• To get the instantaneous level of a digital signal in terms of the acoustic sound pressure level, you have to know the sensitivity of the microphone that was used to capture the sound. The text below is taken from an upcoming data sheet. I hope that this does a good job to describe how to measure the amplitude of a digital microphone signal. In your case, with 24-bit data, a value of -8338608 would represent negative full-scale, or -1.0 D.

The sensitivity of a PDM output microphone is specified in units of dBFS (decibels relative to a full-scale digital output). A 0 dBFS sine wave is defined as a signal whose peak just touches the full-scale code of the digital word. This measurement convention means that signals with a different crest factor may have an rms level higher than 0 dBFS. For example, a full-scale square wave has an rms level of 3 dBFS.

1 kHz, 0 dBFS Sine Wave

The definition of a 0 dBFS signal must be understood when measuring the sensitivity of a digital microphone. An acoustic input signal of a 1 kHz sine wave at 94 dB SPL applied to the ADMP521 results in an output signal with a −26 dBFS level. This means that the output digital word peaks at −26 dB below the digital full-scale level. A common misunderstanding is that the output has an rms level of −29 dBFS; however, this is not the case because of the definition of a 0 dBFS sine wave.

There is no commonly accepted unit of measurement to express the instantaneous level of a digital signal output from the microphone, as opposed to the rms level of the signal. Some measurement systems express the instantaneous level of an individual sample in units of D, where 1.0 D is digital full scale. In this case, a −26 dBFS sine wave has peaks at 0.05 D.

For more information about digital microphone sensitivity, see the AN-1112 Application Note, Microphone Specifications Explained.

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