dB Gain with Series vs. Parallel Wiring

[69stingray]

Hello Everyone. This is a follow-up to a similar post today. I do not want to hi-jack anyone's thread.

OK, ignoring the effects of the amp., if you wire two peakers in parallel, you get +3db gain, correct? What if you wire two speakers in series? 0 db gain? -3 db gain? I know I have read it somewhere but can't find it.

[sr20dem0n]

The 1W sensitivity won't change, but the 2.8V sensitivity will, simply because 2.8V will deliver more power to a lower impedance speaker.

Anyway, it's +3dB for parallel (since impedance is cut in half and voltage remains constant, power is doubled, hence +3dB), and -3dB in series for the same reason.

[69stingray]

Thanks sr20dem0n-

It that case, lets say I have a 3-way system with two woofers, 4 midrange and one tweeter.

The woofers are 8 ohm @ 90 db. If I wire them in parallel, I get 93 dB @ 4 ohms.

The midrange are 87 db @ 4 ohms each. I wire two pair in parallel getting 8 ohm @ 90 db (each). Then wire the two pair in series and get 87 db @ 4 ohm.

Is this correct logic?

[sr20dem0n]

Actually for some reason I was thinking of wiring a dual coil speaker in series vs parallel, still caught up on car audio

Anyway, for your application, there's an easier way (IMO) to go about doing it. Take the spl and impedance of one speaker, if you were delivering 1 watt to the speaker at first, figure out how much power it's now getting after rewiring it (if you added a speaker in series, the original speaker has now had its input power cut by a factor of 4, so it's 6dB quieter). Then when you figure out what has happened to that single speaker, do 20*log(n) where 'n' is the number of speakers to figure out the dB increase you get by having multiple speakers playing at that spl. Then just add that to the efficiency of a single speaker to figure out what the total efficiency is.

So in your case, you have an 8ohm woofer getting 1 watt. If you add another in parallel, the power going to the original is not affected, it's still receiving 1 watt, so it is still playing at 90dB. By adding the second speaker you've doubled the displacement which gives you a 20*log(2)=6dB rise, so the pair of woofers will be playing at 96dB collectively.

The midranges are 87dB each, if you wire them in series/parallel, you've cut the power going to each midrange by a factor of 4, so they're playing at 81dB each. Since you have 4 of them, you have a 20*log(4)=12dB rise, so they'll be playing at 93dB collectively.

[69stingray]

Thanks again sr20dem0n-

This is an excellent explanation......I knew I was missing something and it was the 20*log(x)......

[sr20dem0n]

No problem


Just remember that in the above example you'll need to adjust for power differences. To send 1w to the 8 ohm woofer you would need to send it 2.83 Vrms, and the final efficiency is still based on sending 2.83 Vrms. To send 1w to the 4 ohm midrange you would need to sent it 2 Vrms, and the final efficiency is still based on sending 2 Vrms. To put them on a common playing field you need to normalize the input voltage, which means cutting it down to 2 Vrms for the woofers. This would cut the power going to the woofers in half and lower the woofers' output by 3dB, so it's 93dB for both the woofers and the midranges if they're on a common amp and receiving 1 watt.

[MCPete]

First of all you have to make the assumption which is correct for most solid state amplifiers that output voltage won't vary connecting the speakers in parallel or in series.

For both cases of parallel and series wiring cone area is doubled which doubles SPL or increases it by 3 dB.

For parallel wiring, impedance is reduced by one-half causing wattage consumed by the speaker to double or increase by 3 dB. Therefore for parallel wiring SPL is increased by four times or 6 dB.

For series wiring, impedance is increased by a factor of two and and wattage consumed by the speaker is decreased by one-half or -3 dB. Therefore for series wiring the two effects cancel and SPL is unchanged.

[sr20dem0n]

Originally posted by MCPete
For both cases of parallel and series wiring cone area is doubled which doubles SPL or increases it by 3 dB.

For parallel wiring, impedance is reduced by one-half causing wattage consumed by the speaker to double or increase by 3 dB. Therefore for parallel wiring SPL is increased by four times or 6 dB.

For series wiring, impedance is increased by a factor of two and and wattage consumed by the speaker is decreased by one-half or -3 dB. Therefore for series wiring the two effects cancel and SPL is unchanged.

Not exactly

Doubling displacement increases output by 6dB, not 3dB, for parallel wiring this takes into account the extra power required to push a second speaker to the same level of displacement as the first. When wiring in series, you cut the power going to the speaker by a factor of 4, but you also double displacement, so the -6dB and +6dB cancel.

Another thing is it depends on if you're talking about voltage sensitivity or power sensitivity. For a 1 watt input, wiring in either series or parallel will increase 1 watt efficiency by 3dB (each speaker gets 1/2 watt, so that's -3dB, and you have 2 speakers which doubles the displacement, so that's +6dB, regardless of how they're wired). For voltage sensitivity, wiring in parallel will increase efficiency by 6dB and wiring in series will leave efficiency unchanged.

[454Casull]

I don't see what displacement has to do with sensitivity. Do you mean surface area?

[sr20dem0n]

surface area * excursion = displacement

surface area is only one part of spl, it also depends on how far the cone is moving, which is proportional to the voltage applied. If you go from one speaker getting 1 watt to 2 speakers getting 1 watt total, the power being delivered to the original speaker has been cut in half, or in other words the voltage has dropped to 70% of the initial, which means the excursion has dropped to 70% of the initial, which means the displacement has dropped to 70% of the initial. Since you have 2 speakers receiving this amount of power each, you end up with 140% of the initial displacement, which is +3dB. Or if you go from one speaker getting 1 watt to 2 speakers getting 1 watt each, the displacement of the original speaker remains the same, so by adding the second you end up with 200% of the initial displacement, which is +6dB.