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Discrepancy in my dB SPL calculations

Merida

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I posted on a couple of other forums. i haven't had much luck. I realize this post is very specific & complex. But i can't figure out on my own what my mistake is. Hoping someone here will be able to help me out. Using this post as a reference, I tried an experiment.

I connected a Extech sound level calibrator to a Type 4189 microphone. The output sensitivity of the microphone is

50 mV/Pa, -26 dB ± 1.5 dB re 1 V/Pa

This microphone is connected to a Type 2671 preamp. Using a BNC 50 ohm cable the preamp is connected to a signal conditioning amplifier through a 50 Ohm BNC-BNC cable.

The output from the amplified is connected to a standard oscilloscope.
The calibrator generates a consistent 1 kHz, 94dB SPL sound. The calibrator was recently calibrated, so the output is assumed to be the standard.
The gain at the signal conditioning amplifier is 100mV/unit.

The Vpp measured at the oscilloscope was 16.2 Vpp. Converting that to Vrms,
Vrms = 16.2/2.828 = 5.72843

Calculating for dBrms = 20*log10(5.72843/0.05012) = 41.1605
Since the gain at the signal conditioner is 100 mV/unit. the dB value is -20 dB.
For dB SPL = 41.1606+94-26-20 = 89.1605.
Would I be wrong in expecting this to have amounted to 94 dB SPL instead? If so, why the discrepancy ? what am I missing?
 

solderdude

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Lets look at it the other way around... so assuming the calibration is correct, the mic and preamp is fine and the conditioner is 100mV/V (10x gain = 20dB).

94dB SPL = 1Pa (reason for the calibrator to be 94dB SPL)
Mic is specified at 50mV/Pa +/- 1.5dB so can be between 42mV/pA and 59mV/Pa
Lets assume it outputs 50mVrms
Goes into the 2671 and looses 0.3dB (-3.5%) = 48mVrms
Goes into 20dB amp (10x gain) = 480mVrms*2*Sgrt2 = 1.36Vpp is what can be expected.
But as the mic is +/-1.5dB the extremes could be between 1.14Vpp and 1.62Vpp

Your output seems to be off by 21.5dB (+/- 1.5dB) or by 20dB to 23dB.

Maybe the scope was set for 10x probe but a 1x probe was used ?
Maybe the conditioner was set to 10mV/unit ?
 

SIY

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This is running IEPE mode at 4mA. The gain is 100mV/unit, not 100mV/V, so maybe that's the discrepancy for @solderdude ?
 

solderdude

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Don't know... the 2671 is specified for 4mA to 20mA and in all cases should provide 50mVrms at 1Pa ?
The conditioner uses 4mA which is in the range of the 2671 so assume works as expected.
The OP states the gain is 20dB and reckon he checked this ?

The 1.62Vpp could have made sense if he measured 16.2Vpp with the scope on a 10x probe setting while connected with a BNC cord directly.

But indeed the conditioner does not have V as unit so any of the settings (A, V1, D1, V2 or D2) may well account for the differences as well.
In this case the gain may not have been 20dB (as stated/assumed) but could be ... well ... different.
 

AnalogSteph

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This stuff's all Greek to me, but it would appear that the signal conditioner has two distinct settings related to gain - there is variable input sensitivity as well as various output sensitivity range settings. They really couldn't have made the specs any more cryptic if they tried to. Also, leave in acceleration (A) mode.
 

SIY

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Yeah, I think you have to do a cal step in the signal conditioner to set what the "unit" is. Or make life easy for yourself since you know the voltage level for 94 dB SPL and use that as a reference.
 
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Merida

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I'm certain the conditioner amplifies by 100, because of this test that I did earlier to this experiment.

I connected a function generator to the Signal conditioner. the output from the signal conditioner is connected to the oscilloscope.

IMG_2938.jpg



The input is set at 10 mV.

IMG_2940.jpg



The signal conditioner is set to 100 mV/unit



IMG_2939.jpg


The output on the scope is 1.02 Vpp.



Input = 10mV
Amplification = 100mV = 20*log10(0.1) = 20 dB
Output = 1.02 Vpp

So the amplification works as i expected it to. For the sake of linearity, i also tried 20 mVpp to get a 2.0x Vpp at the output.
 
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Merida

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Based on the above setup, i replaced the function generator with the Extech signal generator for the experiment that I did. Every other setting remained the same.

But I do see that I'm off by a factor of 10 in my experiment. i am trying to account for this factor.
 

solderdude

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Use a T splitter on the output of the 2671 and connect the conditioner (which is intended for accelerometers) and connect the scope to it as well.
You should measure 192mVpp.
 
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Merida

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Before i try this. just another thought.

based on the Func Gen --> Sig cond --> Osc setup.

10 mV at func gen = 100 mV/unit at Sig Cond = 1.02V at Osc

There is an amplification factor of 100.

Now, with my actual experiment,

input . 50 mVrms
Same amplification factor of 100 .
Output at Osc is 16.2 Vpp or 5.7 Vrms

The amplification factor is evident with a discrepancy of 0.7 V. Do you think this discrepancy can be attributed to the connections ?

However my dB SPL calculation still isn't correct, which is another story.
 
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Merida

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I couldn't locate a T splitter, so I tried connecting the 2671 directly to the scope. There is no visible output signal on the Scope. The signal is visible only if I connect through the Sig Conditioner.
 

solderdude

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The 2671 is getting its power from the conditioner so there will be no signal without it or an external PS.
That's why the splitter.

You seem to have determined the gain is 40dB instead of 20dB and seems to explain the the lost 20dB.
 
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Merida

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yes. From a electrical point of view, it all adds up. But I need some clarity while calculating dB SPL. Hoping someone will be able to clarify.

Input is 94 dB SPL reference to 1 pa. Because of the microphone sensitivity

50 mV/Pa, -26 dB ± 1.5 dB re 1 V/Pa

we will assume a Vrms value of 0.05012 V RMS/ Pa .

As per the experiment I did earlier, the amplification factor at the signal conditioner is 40 dB.

The o/p at the oscilloscope is 16.2 Vpp. which is 5.7276 Vrms.

Calculating for dB,

20*log10(5.7276/0.05012) , I get = 41.1592 dB

Calculating for 1 Pa, the dB SPL value becomes = 41.1592+94 = 135.1592 dB SPL

Accounting for the amplification factor of 100, which is 40 dB = 135.1592 - 40 = 95.1592 dB SPL

This is a dB SPL number that I could accept as the output. However according to this post, I need to further subtract -26 (the microphone sensitivity) from my final output, which makes the calculation wrong. The question then is

a. Why should the microphone sensitivity further be subtracted from the final output since my calculations were all done in Vrms with respect to 1pa as the reference already?

b. Or if I am mistaken with the logic, could someone point out the flaw in my math please?

Thank you.
 

solderdude

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You measure 5.73V
Gain is (most likely) 40dB = 100x
So the input in the amp is 57.3mV
Then the 2671 lowers by 0.3dB so in reality the mic outputs 3.5% more so 59.3mV

The mic is specified at 50mV/Pa +/- 1.5dB (+/- 19%) so can be between 42mV/pA and 59mV/Pa
The actual sensitivity is an unknown unless you have a calibration report telling exactly what it is.
The -26dB is in the spec sheet to indicate the 50mV/Pa which is -26dB opposite the 1V/Pa and is why it is there.

But of course there is also the calibrator and its coupling to the mic.
If that is off slightly then that may give small errors as well.

3 unknowns being actual sensitivity of the mic, calibration of the reference (which most likely is accurate as it has recently been calibrated ?)
and the gain of the conditioner may not be exactly 40dB. Can it be off a few % ?

because of this calculating it the other way around says little as there are uncertainties.


The mic is -26dB opposite 1V, the 2671 = -0.3dB the gain is 40dB so added it is +13.7dB opposite 1V which = 4.84V, which is 0.5dB off from the measured value.
This is well within the specified +/- 1.5dB.

Working from the result to mic sensitivity (which you appear to be determining) the calc is as follows.
To use dB's you need a reference which is set to 1V in this case as we are looking for a voltage.

The measured value = 5.73V = +15.16dB
subtract gain (40dB) = -24.8dB
add 0.3dB (2671) as the pre-amp attenuates so -24.5dB
When referenced to 1V the -24.5dB = 59.6 mV (not exactly the same as 59.3mV due to rounding errors when using dB's and voltages with just 1 decimal.
 
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Merida

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You measure 5.73V
Gain is (most likely) 40dB = 100x
So the input in the amp is 57.3mV
Then the 2671 lowers by 0.3dB so in reality the mic outputs 3.5% more so 59.3mV

The mic is specified at 50mV/Pa +/- 1.5dB so can be between 42mV/pA and 59mV/Pa
The actual sensitivity is an unknown unless you have a calibration report telling exactly what it is.
The -26dB is in the spec sheet to indicate the 50mV/Pa which is -26dB opposite the 1V/Pa and is why it is there.

But of course there is also the calibrator and its coupling to the mic.
If that is off slightly then that may give small errors as well.

3 unknowns being actual sensitivity of the mic, calibration of the reference (which most likely is accurate as it has recently been calibrated ?)
and the gain of the conditioner may not be exactly 40dB. Can it be off a few % ?

because of this calculating it the other way around says little as there are uncertainties.


The mic is -26dB opposite 1V, the 2671 = -0.3dB the gain is 40dB so added it is +13.7dB opposite 1V which = 4.84V, which is 0.5dB off from the measured value.
This is well within the specified +/- 1.5dB.

Working from the result to mic sensitivity (which you appear to be determining) the calc is as follows.
To use dB's you need a reference which is set to 1V in this case as we are looking for a voltage.

The measured value = 5.73V = +15.16dB
subtract gain (40dB) = -24.8dB
add 0.3dB (2671) as the pre-amp attenuates so -24.5dB
When referenced to 1V the -24.5dB = 59.6 mV (not exactly the same as 59.3mV due to rounding errors when using dB's and voltages with just 1 decimal.


Thank you for that. That explanation justifies what I obtained as an output.
 
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