# Basic loudspeaker theory question

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#### Andrej

Hi !

I have a simple question!

Let say we have a perfect 2 waz crossover at frequency f. As far as I know the crossover is designed in such a way that it's response is down 3 dB for each of the two drivers.
From info on Linkwitzlab site I have read that if you combine two drivers with equal phase their combined output goes up 6 dB.
That would give us a 3 dB bump at crossover frequency.
Am I rugh or am I wrong ?

I would also apreciate if someone could point me to the sources on the web where this stuff (acoustics and loudspeakers) is explained in detail and correctly.

Thanks

#### Nelson Pass

Paid Member
All this depends not only only on the slopes and "Q"
of the filters, but on the phase and amplitude responses
of the drivers, which are not likely to be ideal.

You will have to be prepared to experiment with different
crossover settings to get what you want, and you should
not assume that idealized values will do the trick.

#### Andrej

My first dum question and look who replies.

Well to make things clear, I am not talking (well typing...) about anything practical here. I would just like to have some things sorted out for my own peace of mind.
So back to my hypothetical crossover.
It's just that Xovers are usualy refered to as being -3dB @ Xover frequency. And if all things are considered perfect, the sum of acoustical outputs of both loudspeaker drivers should yield a 3dB bump. A logic of a simple man would suggest that both drivers should be 6dB down at Xover frequency.

I know that in real world the phase difference between tweeter and mid are, let say 100 degrees, so that should account for 3 dB loss and response could look straight.

Why do 2 drivers put 6dB more acoustical output ? Because the output is proportional to the square of radiating area, if all other things like voltage and current stay the same.

To make long story short.. What I need is loudspeaker theory for dummies.

#### secateurs

good question

I have wondered a similar thing. If you weren't using a crossover for some reason, would the frequency responses at certain frequencies simply add together if the two drivers were in phase? In the real world, is there any way you can measure or calculate how out of phase they are? If so, would you then add them using vectors?

#### AndrewJ

Andrej A simple question unfortunately demands a complicated answer!
You have to consider the order of the filter and hence its phase response. You are correct in saying that two drivers in phase add together to produce a 6dB increase. Therefore two filters should be 6dB down at the xover frequency, BUT only if they are in-phase at the xover frequency. 1st order and 3rd order networks sum to a flat response when only 3dB down, because their relative phase response (90deg difference) causes the drivers to fight each other and partially cancel to offset the 3dB down level. However this has repercussions off axis where at a certain angle the response is now in phase and a peak is produced. Even order networks (2nd and forth) when correctly configured sum in phase and therefore are arranged to be 6db down. Off axis they produce only a dip, and this is audibly preferrable to a peak.
Now I am referring here to the overall acoustic response combination of driver plus network, ie if the drivers are perfect and flat from d.c to light !! then the comments apply purely to the network. In the real world as Nelson points out, the drivers are imperfect, and the role of the network is to both equalise and roll-off the response. It is the combination response I am talking about here, the so called "Target Function" response, a term coined by Laurie Fincham at KEF.
Secateurs, You are correct. You need to consider the vector summation of the two responses. When you measure drivers and xovers, you need to measure both the amplitude and phase response to get a complete picture of the behaviour. These days this is routinely possible with measuring systems such as mlssa and Clio, but was very difficult in the old days.

#### bostarob

well said (far better than I could have)

A good reading is Vance Dickason's Loudspeaker Design Cookbook. I have got a copy and it looks as it had been out in the rain or something. In depth crossover discussions answer your questions, except for series xover.
-andy

#### AudioFreak

under theoretically ideal circumstances, -3dB @ crossover point will yeild a 3dB hump in the nearfield frequency response. For nearfield listening, you theoretically need to be -6dB @ the crossover to have a flat response aka Linkwitz Riley 4th order.

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