Check my math please

[farmy87]

Okay, I am planning to build a couple speakers, and have been scouring the internet for information on powering them, etc, and thank I have a pretty good idea of how this works, but just want some verification. This is regarding wiring identical drivers together. The numbers on the amp/drivers below are all hypothetical:

Driver: 90DB @ 1W/1M/1Khz 8 Ohm
Amplifier: 200W @ 4 Ohm (28.28V)

-----------------------------------------------------------------

1 Driver (Impedence = 8 Ohm):
Amplifier power output = V^2 / R
= (28.28^2) / 8
= 100 Watt

Max DB = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(100))
= 110DB

-----------------------------------------------------------------

2 Drivers in Series (Impedence = 16 Ohm):
Amplifier power output = V^2 / R
= (28.28^2) / 16
= 50 Watt (25 watt/driver)

Max DB for 1 driver = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(25))
= 104DB

Max DB for 2 driver = Max DB of 1 driver + 3DB
= 107DB
------------------------------------------------------------------

2 Drivers in Parallel (Impedence = 4Ohm):
Amplifier power output = 200W (100W/driver)

Max DB for 1 driver = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(100))
= 110DB

Max DB for 2 driver = Max DB of 1 driver + 3 DB
= 113DB

-------------------------------------------------------------------

Assuming all my figure are correct, I have a couple questions:
1.) I have seen some amp that list like 50W @ 8 Ohm, but only 75W @ 4 Ohm. I don't understand this, shouldn't it be double at 4Ohm vs 8Ohm?
2.) I left the theorotical 3DB couping gain out of the double driver calculations - does anyone have any information on how to get this as close to 3DB as possible? Specifically, what box size would I use for the drivers, comparted to the size of 1 driver?

THanks in advance, hopefully I'm not too far off on any of this.

 

[bandphan]

dumb question, but do you use software to model the speakers or are you attempting to go old school spread sheet? What is the project your attempting? Is this your first build?

 

[farmy87]

First build, not using any software, just collecting alot of information before I get started, any suggestion for free software that can help? I'm just trying to build a couple 2-ways & trying to decide what I want to do for the mid/woofer.

But I am really just trying to make sure my understanding of how this all goes together is correct at the moment & then I will apply it to my own situation

 

[bandphan]

A good book to start with is Vance Dickason's The Loudspeaker Design Cookbook or Speaker Building 201 by Ray Alden. As for software, HT Audio has some good products but not free.

 

[highfigh]

Okay, I am planning to build a couple speakers, and have been scouring the internet for information on powering them, etc, and thank I have a pretty good idea of how this works, but just want some verification. This is regarding wiring identical drivers together. The numbers on the amp/drivers below are all hypothetical:

Driver: 90DB @ 1W/1M/1Khz 8 Ohm
Amplifier: 200W @ 4 Ohm (28.28V)

-----------------------------------------------------------------

1 Driver (Impedence = 8 Ohm):
Amplifier power output = V^2 / R
= (28.28^2) / 8
= 100 Watt

Max DB = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(100))
= 110DB

-----------------------------------------------------------------

2 Drivers in Series (Impedence = 16 Ohm):
Amplifier power output = V^2 / R
= (28.28^2) / 16
= 50 Watt (25 watt/driver)

Max DB for 1 driver = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(25))
= 104DB

Max DB for 2 driver = Max DB of 1 driver + 3DB
= 107DB
------------------------------------------------------------------

2 Drivers in Parallel (Impedence = 4Ohm):
Amplifier power output = 200W (100W/driver)

Max DB for 1 driver = SPL + 3DB Each time power is doubled
= 90 + 3*(log2(100))
= 110DB

Max DB for 2 driver = Max DB of 1 driver + 3 DB
= 113DB

-------------------------------------------------------------------

Assuming all my figure are correct, I have a couple questions:
1.) I have seen some amp that list like 50W @ 8 Ohm, but only 75W @ 4 Ohm. I don't understand this, shouldn't it be double at 4Ohm vs 8Ohm?
2.) I left the theoretical 3DB couping gain out of the double driver calculations - does anyone have any information on how to get this as close to 3DB as possible? Specifically, what box size would I use for the drivers, comparted to the size of 1 driver?

THanks in advance, hopefully I'm not too far off on any of this.

When speakers are wired in series, the impedance is added, regardless of the number for each. Also, in series, you don't add 3dB- the net output is the same as one driver. The power is halved when using a 2.83VAC reference signal if the impedance doubles but because of the increase in cone area and acoustic output, the 3dB loss from halving the power is canceled.

As far as the 50/75W issue- if the power supply and output devices were capable of power doubling with halving the impedance, you would see 100W at 4 Ohms. This costs a lot more to build than something that does 75W @ 4 Ohms. It's a theoretical result and harder to accomplish in real life.

If you use 1 driver in a box, you'll have one result but if you add a driver without adding to the box volume, the Fb tuning frequency will rise considerably. You would need to double the box volume to get the same response.

 

[farmy87]

At the same power output from the amp, I see how 2 drivers in series would be teh same vs 1 driver. But wouldn't you lose 3DB with the amp maxed - since the amp can only put out half the power due to the impeadence doubling?

 

[highfigh]

At the same power output from the amp, I see how 2 drivers in series would be teh same vs 1 driver. But wouldn't you lose 3DB with the amp maxed - since the amp can only put out half the power due to the impeadence doubling?

It doesn't have to be maxed- the SPL will be the same with two drivers as with one because of the increased impedance at any power level. If you were to connect one driver to the right channel and another to the left channel, you would see a 6dB increase- 3dB because of the increased acoustic output and 3dB because of the power delivered to the second speaker. The effect is that the added acoustic output makes up for the increased impedance, for a zero net gain/loss.