Waveguie and Cardioid on a Slim Baffle

[ds21]

Hey boris, any more test/progress... your first design looks like the Amphion Krypton 3, as far as your flow resistive pattern, was wondering what the theory is behind it, I was first just interested in getting cardioid in the bass but now thinking of going to the midrange also. I just made a little testbox with a single mid and poked some holes in it just to see what is what, first started with holes of .25" one inch appart, didn't really get good results (all testing done by ear, I have a measurement setup but it's very easy to tell if something is headed in the right direction or not) anyway had to to up to .5 holes and 80% stuffed to really get anything working, will begin measurements today.

[boris81]

Originally Posted by ds21

Hey boris, any more test/progress... your first design looks like the Amphion Krypton 3, as far as your flow resistive pattern, was wondering what the theory is behind it, I was first just interested in getting cardioid in the bass but now thinking of going to the midrange also. I just made a little testbox with a single mid and poked some holes in it just to see what is what, first started with holes of .25" one inch appart, didn't really get good results (all testing done by ear, I have a measurement setup but it's very easy to tell if something is headed in the right direction or not) anyway had to to up to .5 holes and 80% stuffed to really get anything working, will begin measurements today.

I don't have a solid grasp on the theory myself. One major point is that cardioid resulting from vents on the sides of the cabinet is not the same as cardioid from a U-frame.
NaO U-frame
In this study of the U-Frame design, John Kreslosvky finds that the back wave develops a resonance above the dipole peak. Alternatively, side vents designs have the advantage of a consistent polar response at the expense of sensitivity.

Often I see mentioned that the total area of the vent holes exceeds the area of the woofer. I don't know how that affects the response but 80% of Sd on each side (x2) seems to be common. I don't know the effect of the hole pattern either, I copied it from the Amphion Krypton 3 and Kimmo Saunisto's designs.


I'm excited to see your measurements. I will hopefully have something soon myself. I am going for an open structure with driver mufflers instead of a leaky box. I got the drivers and I cut the front baffle and now I'm thinking of how to execute the driver magnet mounting. Ideally I would like to use bamboo plywood but I wasn't able to find any in my area. The most attractive alternative at my local Home Depot was this wooden composite board. It is intended for making steps and it is very heavy.

----
"Some Krypton 3 comments from people who know what they are talking about: "Amphion at $ 19.9.K is a bargain""

[boris81]

The basic concept behind Open Baffle is that there are 2 waves going out in space, one from the front and another from the rear of the driver. They are at equal power but opposite polarity so they will act to cancel each other out. The cancellation is not complete but partial and depends on the wavelength and the distance a wave must travel around the baffle from the driver center at the front to the back. A naked driver with no baffle represents the classic dipole model - no cancellations occur at high frequencies when the wavelength is shorter than the driver cone; as soon as the wavelength grows enough for the driver to begin radiating in >2pi space, the front and rear wave "meet" and we begin to encounter cancellations. The amount of cancellation is proportional to the amount of energy that is able to "wrap around" the baffle and generally follows a -6dB/octave slope. (comb filter nulls will develop in higher frequencies on an open circular baffle but their effect can be minimized with a rectangular baffle)

In a U-Frame configuration the wings of the baffle delay at what wavelength the rear wave can "wrap around" effectively shifting the geometry of the dipole cancellation towards the back. Since the rear radiation is contained in 2pi space for lower in frequency than the front an irregularity in the FR will form at the rear.

On a flat open baffle when the rear wave is partially absorbed the dipole cancellation will be shifted to the rear and form a cardioid-type response as well. But in this case it will be the result of different power at the front and rear contrary to the case of different distances(phase) as it is with a U-Frame cardioid. The rear absorption method will have the advantage of more consistent power response over a U-Frame at the expense of sensitivity.

[njoak]

I am not entirely done with the theory myself, but at a glance I can not see why you would assign different physical reasons to the effect in the U-frame and open baffle cases?

In the case of side ports at least, I tend to think delay rather than power damping.

Edit: And in that case you will get a net result by the superposition of the sub-patterns caused by each port; so equations valid for the case of a rear port (which I compare the u-frame case) can not be used as are.

[boris81]

Originally Posted by njoak

I am not entirely done with the theory myself, but at a glance I can not see why you would assign different physical reasons to the effect in the U-frame and open baffle cases?

In the case of side ports at least, I tend to think delay rather than power damping.

Edit: And in that case you will get a net result by the superposition of the sub-patterns caused by each port; so equations valid for the case of a rear port (which I compare the u-frame case) can not be used as are.

Because in a classic dipole the front and rear wave (at the center axis) will have the exact same Frequency Response and the Phase of both will generally track together with a 180deg difference for the frequency range of the driver.

A U-Frame will keep a stable cardioid response only below the dipole peak where the FR and phase will track together. The rear wave will of course be attenuated compared to the front one but the traces should track together analogous to the phase. Above the dipole peak the front and rear phase will seize to track together and resonances will develop in the rear wave response.

I don't exclude the possibility to be wrong about this. But I prefer to approach the theory of a box with leaky side panels as a dipole with an attenuated rear wave rather than a U-Frame with an offset rear opening. I expect the FR and phase to track together even above the dipole peak, especially for supercardioid.


U-Frame theory
NaO U-frame
DIY-dipole-1

Measurements from builders of cardioid leaky boxes
2-way: Waveguide + Cardioid-like
Cardioid bass
Adventures in cardioid

[njoak]

I don't exclude the possibility that you are right about this, but I was under the distinct understanding that there would be the equivalent of a dipole peak in a side port system as well. And that you would not be able to obtain a cardioid response above this threshold.

In the u-frame case one discusses the acoustic separation of the two out-of-phase monopoles, and must delay the rear source according to this separation. In the side port case, a similar separation exists due to the baffle and position of the ports down the side of the cabinet. A similar delay is then necessary?

Having said this, I admit to having no intuition for the result of two non-delayed sources of differing intensity. So I'm not sure.

Edit: By the way, I always interpreted the bettered result seen without baffle in the "adventures in cardioid"-thread as related to what we are discussing here.

[njoak]

A quote from Holmes (this is all he writes about side ports,
unfortunatelly):

1.3 Position of Resistor Vent--Rear versus Both Sides

The effect of dividing up the resistive vent area-
into a pair of symmetrically placed side vents, for
instance--can be analyzed by treating the system as a
set of subsystems, each with its own volume velocity
and axial direction. Each subpattern can then be derived
independently.

Overlaying these subpatterns, with their axes intersecting
at front center, will now yield the net pattern, always with
a beta value lower than those of the subpatterns.

[njoak]

A quick, late, thought:

Is it at all possible to attenuate/damp without causing a delay?

[boris81]

Originally Posted by njoak

In the u-frame case one discusses the acoustic separation of the two out-of-phase monopoles, and must delay the rear source according to this separation. In the side port case, a similar separation exists due to the baffle and position of the ports down the side of the cabinet. A similar delay is then necessary?

The way I understand the mathematical abstraction is that there is NO delay in the dipole model between the two out-of-phase sources. There is a delay in the U-Frame model and it is there to represent that the 2 out-of-phase sources begin to radiate in >2pi space at different wavelengths.

I don't think that there would be a delay in the cardioid model of a leaky box with side vents. I'm under the impression that the front and rear wave will continue tracking together in phase at 180degrees apart. There might be some delay caused by the low-pass function of the box but I assume that it will be minimal and not relevant.

[njoak]

Originally Posted by boris81

The way I understand the mathematical abstraction is that there is NO delay in the dipole model between the two out-of-phase sources. There is a delay in the U-Frame model and it is there to represent that the 2 out-of-phase sources begin to radiate in >2pi space at different wavelengths.

I don't think that there would be a delay in the cardioid model of a leaky box with side vents. I'm under the impression that the front and rear wave will continue tracking together in phase at 180degrees apart. There might be some delay caused by the low-pass function of the box but I assume that it will be minimal and not relevant.

What I see in those figures is exactly what I am trying to argue: If you have no delay, you get a dipole. Add delay, get cardioid. In my mind it is all about how the radiation sources (the point where the waves exit the box, if we put it that way) interfere. To have two monopole sources sum to a cardioid pattern, they must be phase-inverted, and the rear one delayed by T=D/c, where D is the separation. A different delay gives a different pattern (0 gives dipole, D/(2c), roughly, gives supercardioid).

Edit: By the way, the relation between the separation and the caridoid-izable wavelengths is seen in the right figure as well. You need to keep the separation such that you are in the roughly linear region in the response plot.