# Amplifier gain (V) relative to Speaker gain (SPL)

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### Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 1:50 am
Hi all,

I'm interested in hobby electronics. I'm attempting to design a circuit with an amplifier ( Class D Speaker Amplifier) and a speaker attached to it.

I want to adjust the amplifier via the gain (db) to adjust the volume of the speaker in SPL (dB).

How do I convert the gain of the amplifier in terms of voltage into the Speaker volume ( sound pressure level ) in (dB).

For example if I needed a gain of X db in the Speaker what would I set the Voltage gain too. The same? :headbang:

Apologies if i'm asking a really stupid question here.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 4:05 am
It just has to go to 11 :D

Or maybe 42. Never can keep that straight.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 7:27 am
Like voltage, SPL is an absolute value but it needs to be tied to a specific distance from the speaker, nominally 1 metre. So voltage A into speaker B, will produce SPL C at distance D and to complicate things more, at frequency E.

db is normally a measure of differences in voltage or differences in SPL. It's a relative figure for comparison purposes.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 9:20 am
The SPL of a speaker is given by:-
SPL (at 1mtr) =log w.10+s Where w is the power in watts and s is the quoted sensitivity in dBSPL/w/mtr.

Thus, you get the output VOLTAGE from root w.z and divide that by the gain to get your input voltage. Obviously you can shuffle the equations around to get other results.

BUT! The sensitivity quoted by speaker mnfctrs is pretty loose. What is a watt into a complex impedance? Did they use pink noise, white or brown with knobs on? Did they test in a spare bog at the back of the factory or at the NPL?

I am not sure what the purpose of your exercise is but speaker SPL v watts is a very flakey quantity. For example, in the guitar industry two speakers can have identical SPL speccs but one can sound MUCH louder on a music signal because it has a 'shouty' response. The well respected Celestion V30 is one such.

Dave.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 12:20 pm
Tesla_33 wrote:I want to adjust the amplifier via the gain (db) to adjust the volume of the speaker in SPL (dB).

How do I convert the gain of the amplifier in terms of voltage into the Speaker volume ( sound pressure level ) in (dB).

You don't, because the two are not directly related. Other factors are involved and you haven't said what they are! So it's not a stupid question, it's just an incomplete question.

The acoustic output from the speaker, in terms of a Sound Pressure Level (SPL), is dependent on how much electrical power is being fed into it, how sensitive and efficient it is in converting that electrical power into acoustic power, and how far away from the speaker that sound is being measured.

The norm is to measure SPL at 1 metre, so we'll assume that's also the case for you.

The speaker sensitivity or efficiency is normally specified in terms of the SPL generated at 1 metre for for 1 Watt of input power. So it might be 90dB/W/m, say. Without that figure to hand you can't calculate anything, so step one would be to go and find that sensitivity figure for the particular speaker you're using.

And while you're at it, it might be handy to know the nominal impedance of the speaker as well, so that you can calculate the input power provided by the amplifier.

By the way, power amplifiers usually have a fixed, rather than variable gain. The adjustment of output power is normally provided by a variable input attenuator.

So you'll also need to know the amplifier's input signal voltage as well as the 'amplifier gain' and input attenuator setting.

Obviously, the attenuator/amplifier combination could have an overall gain of 30dB, say, but it won't generate any output power to feed to the speakers unless there is an input signal present... and the bigger that input signal the more voltage -- and thus the more power -- the amplifier will deliver to the speaker (up to its clipping level!).

Calculating the square of the amplifier's output voltage, divided by the speaker's impedance, will give the power going into the speaker. Multiply that figure by the speaker's sensitivity and you'll have some idea of the acoustic output level in SPL.

Of course, there are also other factors that can affect the actual SPL in the room, such as the physical design of the speaker cabinet, the position of the speaker within the room, and the specific frequency or frequency range that you're interested in.

For those reasons, a more pragmatic solution might be simply to measure the system's SPL for given input signal levels and amplifier gains, actually in situ, rather than trying to calculate them! ...But it all depends on what you're trying to achieve.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 12:36 pm
Thanks guys. I’m going to clarify how I present my information and then update the thread. Thanks again

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 12:59 pm
tesla_33 wrote:For example if I needed a gain of X db in the Speaker what would I set the Voltage gain too.

Speakers don't have gain. Amplifiers have gain. If you already have a speaker then your design already has constraints. Your design will take into account the power rating of the speaker and you get the SPL you want with a volume knob.

If your speaker is 8 Ohms and 100 Watts that gives an indication of the maximum voltage. As ef37a said it's root (impedance * power) = root (8 * 100) = ~28.28 V

If your input is 1V that gives a maximum gain of 28 which is 20 * log (28) = ~28.94 dB.

If you're designing your own amp it's worth knowing that a gain of 2 isn't exactly +6dB. 20 * log (2) = ~6.02 dB. When doing a design keeping the gain as a number is more useful.

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Sun Aug 23, 2020 5:41 pm
A speaker outdoors up on a pole, or in an anechoic chamber will create a much lower SPL than the same speaker in a corner in a concrete room. If you are trying to 'Calibrate' your listening volumes, a Smartphone app will do the job well. https://www.cdc.gov/niosh/topics/noise/app.html

### Re: Amplifier gain (V) relative to Speaker gain (SPL)

Posted: Mon Aug 24, 2020 8:36 am
Actually, loudspeaker 'systems' can have a gain over a single drive unit.

The line source speaker can be 6 or even 8dB more sensitive than a single chassis. This 'gain' is at the expense of a spherical radiation pattern where for a vertical column the radiation is constrained into a rough cylinder thus not wasting sound into the ceiling and floor. You need a very long column to get any kind of bass though.

Dave.