I may add a thing or two 
. In Europe we do not have such discount subwoofer brands as there are in the US. When these subs are sold here the cost 50% more.
The factory to customer thing doesn't work in Europe. Nubert and Teufel are no discount deal but pretty pricy.
A DIYS sub made from components costing 500€ can play in the high end league without a problem if you know what to pick. What you do not get is automated room correction directly from the sub. This is of limited value anyway, as it only sees the sub. A better way is to adjust the sub manually (by DSP) for the room and let a good room correction (Maranz = Audessey) then match it to the other speakers.
If you are not into home theater, a sub tuned to 30-35Hz is fine for music in 99% of all cases. Two 10" are fine for that in 55 square meter. If want to go deeper for HT, 20-25 Hz tuning will need two 12" in your room. With the sub housed in a 40cm cube and external amp, you will end up with a net volume of about 45-50 liter, closed and filled with some damping material. This is on the small side for 12" and quite large for 10".
Plate amps are overpriced for the little they offer. PA amps are less than half the price if you compare objectively. One thing about PA amps and pro DSP, you hardly loose any money when you decide to sell them. Just have a look at eBay. In Europe Thomann will sell you it's "t.amp" line, which has become a standard over the years. They are HIFI quality soundwise and far better suited for sub work because of their reserves no HIFI amp even 2 times the price can match. You don't find plate amps but only PA stuff in any serious home cinema installation for a reason. Maybe have a look at the wheight to get an idea what power supply works inside, if these are build conventional.
If you look for 12" sub chassis, I would choose a Dayton or the Eminece LAB12. Mind that Dayton is much more expensive in Europe! So the recommendations from the US may not fit your bill.
If you don't mind a bit unconventional, there is a very good Alpine 12" of German design for under 100€: https://www.ebay.de/itm/274392231518
The chassis is solid steel and it's performance is great. A "secret tipp" for multi chassis sub installation and maybe the best low cost 12" sub around. Perfect for 40-50 litre. Don't drive it with an 80 Watt plate amp!
With 10" also have a look at the Reckhorn chassis, which have the best value for money IMO. At 90€ each, use 2 per cube and you are a happy camper. Another good sub chassis is the REDCATT SW10.4 PC at 125€. Both are exceptional value usually found in the 200€ class.
Please keep an eye on the nominal impedance if you want to use more than one chassis. A PA amp will drive two chassis in any case, a single mono plate amp will not like less than 4 Ohm.
I prefer a pair of chassis with a linear excursion of about 12mm over a single one with 24mm, independent of price. The larger cone area sounds relaxter than huge excursions of extreme chassis which are more suited for space saving in car audio, even as the moved air volume is identical.
With subwoofer chassis cone area x excursion are what counts. The TSP data tell you which cabinet they need. WinISD is a free and precise tool to calculate closed and vented constructions. It is very usefull for comparing a number of chassis.
You can basically trade volume for amp power. If you lift the response by 3dB you need twice the power. A strong argument for vented constructions.
. In Europe we do not have such discount subwoofer brands as there are in the US. When these subs are sold here the cost 50% more.The factory to customer thing doesn't work in Europe. Nubert and Teufel are no discount deal but pretty pricy.
A DIYS sub made from components costing 500€ can play in the high end league without a problem if you know what to pick. What you do not get is automated room correction directly from the sub. This is of limited value anyway, as it only sees the sub. A better way is to adjust the sub manually (by DSP) for the room and let a good room correction (Maranz = Audessey) then match it to the other speakers.
If you are not into home theater, a sub tuned to 30-35Hz is fine for music in 99% of all cases. Two 10" are fine for that in 55 square meter. If want to go deeper for HT, 20-25 Hz tuning will need two 12" in your room. With the sub housed in a 40cm cube and external amp, you will end up with a net volume of about 45-50 liter, closed and filled with some damping material. This is on the small side for 12" and quite large for 10".
Plate amps are overpriced for the little they offer. PA amps are less than half the price if you compare objectively. One thing about PA amps and pro DSP, you hardly loose any money when you decide to sell them. Just have a look at eBay. In Europe Thomann will sell you it's "t.amp" line, which has become a standard over the years. They are HIFI quality soundwise and far better suited for sub work because of their reserves no HIFI amp even 2 times the price can match. You don't find plate amps but only PA stuff in any serious home cinema installation for a reason. Maybe have a look at the wheight to get an idea what power supply works inside, if these are build conventional.
If you look for 12" sub chassis, I would choose a Dayton or the Eminece LAB12. Mind that Dayton is much more expensive in Europe! So the recommendations from the US may not fit your bill.
If you don't mind a bit unconventional, there is a very good Alpine 12" of German design for under 100€: https://www.ebay.de/itm/274392231518
The chassis is solid steel and it's performance is great. A "secret tipp" for multi chassis sub installation and maybe the best low cost 12" sub around. Perfect for 40-50 litre. Don't drive it with an 80 Watt plate amp!
With 10" also have a look at the Reckhorn chassis, which have the best value for money IMO. At 90€ each, use 2 per cube and you are a happy camper. Another good sub chassis is the REDCATT SW10.4 PC at 125€. Both are exceptional value usually found in the 200€ class.
Please keep an eye on the nominal impedance if you want to use more than one chassis. A PA amp will drive two chassis in any case, a single mono plate amp will not like less than 4 Ohm.
I prefer a pair of chassis with a linear excursion of about 12mm over a single one with 24mm, independent of price. The larger cone area sounds relaxter than huge excursions of extreme chassis which are more suited for space saving in car audio, even as the moved air volume is identical.
With subwoofer chassis cone area x excursion are what counts. The TSP data tell you which cabinet they need. WinISD is a free and precise tool to calculate closed and vented constructions. It is very usefull for comparing a number of chassis.
You can basically trade volume for amp power. If you lift the response by 3dB you need twice the power. A strong argument for vented constructions.
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