Sensitivity of multiple drivers?

[454Casull]

IMHO, the whole 2.83 V thing is a marketing exercise and hides a lot of the real world realities.... ie it makes your experiment suspect as it lets a number of variables move around skewing the conclusions.

dave

It would definitely be interesting if sensitivity was measured by current (i.e. X dB/1A/m)

 

[Svante]

Dave's result is correct but I think

"By adding the series speaker you are potentially adding 6dB in total..." part is not. Whatever you add in series the total sensitivity should decrease. Here goes the argument:

1) "Then I connect two in paralell, and I get 106 dB@2,83 volts."

This is Ok.

2) "Then I connect anoter pair in series with the two. Then i get back to 8 ohms, but with still 106dB@2,83 volts."

No. You get back to 8 Ohms but not 106dB@2,83 volts. Think as follows: Let P denote the power of one driver,

P = V^2 / R = 2.83^2 / 8 = something

at 2.83 V. (Again we assume "lossy" DC resistance for simplicity but same arguments will apply for more realistic but much complicated AC driven inductive+mechanical load)

Now for the case 2) You will have V/2 at each driver. So, the power of EACH unit will be

P' = (V/2)^2 / R = something / 4

and the total power = 4 x something / 4 = something = P again.

Sensitivity can be defined in terms of power of the sound pressure; so you will get back to 8 ohms, 100dB. Cheers,

Murat

You are calculating the power delivered to the drivers, but what you miss is the effect of acoustic coupling between the drivers, which affects the efficiency. If the 4 (series-parallel connected) drivers are mounted close to each other, they will each deliver half the sound pressure as a single driver (since they receive half the driving voltage), and these pressures add up to 4x 1/2 = twice the pressure of one driver alone or + 6 dB. Since the same power is delivered to the 4 drivers as a single driver, the efficiency and sensitivity has increased by 6 dB.

 

[simon5]

I summed up for you why the theory will collapse Snickers-is :

The theory of 3 dB gain at the same power level when you double the number of drivers will collapse because the drivers too far away will be out of phase with the listener, also because you have friction losses, house wall leaks, enclosure leaks, destruction of cones, surrounds and spiders, explosion of enclosures caused by the high pressure, heating of the air, heating of the voicecoil, losses in the wires, the resistive part of the voice coil impedance, inertia, ...

You can easily see that there's a limit. We don't know where is the limit, could you test it for us with the 0,49$ PartsExpress speakers? It could be funny.

 

[murat]

You are calculating the power delivered to the drivers, but what you miss is the effect of acoustic coupling between the drivers, which affects the efficiency. If the 4 (series-parallel connected) drivers are mounted close to each other, they will each deliver half the sound pressure as a single driver (since they receive half the driving voltage), and these pressures add up to 4x 1/2 = twice the pressure of one driver alone or + 6 dB. Since the same power is delivered to the 4 drivers as a single driver, the efficiency and sensitivity has increased by 6 dB.

The origin of the paradox is the fact that the power associated with a wave (sound, EM, earthquake etc.) is proportional to the square of the amplitude of that wave. A similar paradox is two very close antennas emitting EM wave. If each individual antenna is emmitting power P, at some E&B fileds, two of them will emit 2XE & 2xB which would make 4XP altough both are using P!!!

For speakers the resolution is again the acoustic coupling as you and many others mentioned. For a small number of spekers there is no contradiction since we are just incresing the efficiency - but under the conditions like the the wavelength will be in this range, speaker seperation will be that much depending on the wavelength, you will be listening at this position.... So, I just don't belive that one can get 3 dB increase for two FULL RANGE speakers in series over the whole audible range. In some frequency range, under this and that conditions etc, that's all.

Since the diffraction, acoustic coupling etc will be extreamly difficult to work out for a large number of units the last word will come from the energy conservation arguments (like the limit of the efficiency) since they are undisputable and simple to follow. Cheers,

Murat

 

[Jim Griffin]

Array Speaker Sensitivity Calculations

I do speaker routinely calculate line array sensitivities so you may find my following description the following discussion of interest:

The driver connections in an array determine the overall impedance of the speaker and the resultant sound pressure level of the speaker. Individual drivers can be connected in series and parallel arrangements. For drivers that have sound radiation patterns that overlap other drivers in the array there is a net increase in the overall sound pressure level (SPL) results. For example, two speakers connected in parallel and mounted within a wavelength center-to-center spacing would yield up to a 6 dB increase in SPL—3 dB from the increase in acoustical energy and 3 dB from the reduction in impedance. Conversely, series connection of two speakers maintains the same SPL of an individual driver but doubles the impedance of the pair. In an array various combinations of series and parallel connections can be used to give choices for the overall impedance and SPL values.

The nominal impedance of the array is computed by calculating the series and parallel combination of impedances. That is, the impedance of each series connected branch is added and then the parallel connections combined into the nominal impedance. Both the acoustic response and the resultant nominal impedance of the overall system must be considered.

While ultimately the SPL of the speaker will be measured, in the development process you can compute the system sensitivity (or efficiency) impact of a line array. First, assume that an individual driver in the array has a known SPL value. Next assume that the drivers in the array have overlapping acoustical radiation patterns and are spaced within a wavelength center-to-center from each other. Thus, the acoustical improvement (efficiency gain) at 1 watts, 1 meter distance is given by:

Efficiency Gain = 10*log (Number of Drivers Driven)

while the sensitivity gain or loss at 2.83v, 1 meter is:

Sensitivity Gain/Loss = 10*log (Nominal Driver Impedance/Nominal Array Impedance)

If the nominal array impedance is less than the individual driver impedance, the array sensitivity increases or is a gain. If the array impedance is greater than the individual driver impedance, then the sensitivity decreases or becomes a loss.

Hence, for the overall system

System Efficiency = SPL + Efficiency Gain

System Sensitivity = SPL + Efficiency Gain + Sensitivity Gain/Loss

 

[catapult]

Interesting, Jim, but it still doesn't explain why a system tops out at a certain dB-SPL/electrical-watt, i.e. 100% efficiency.