Experiments in speaker design for cardioid radiation pattern

[Vineethkumar01]

Recent discussions over in this forum and over at diyaudio reignited my interest in cardioid speakers. So I thought why not create a thread for it, apply little brainstorming and try to build one (the first prototype)..
With recent advances in BEM simulations using ATH software, mabat has presented some very interesting sims on how to make cardioid radiation pattern with woofers with a very simple design. The original discussion is available around here:

Acoustic Horn Design – The Easy Way (Ath4)

Any recommendations? I suggest you move over to augerpro's waveguide thread for dome tweeters https://www.diyaudio.com/community/threads/open-source-waveguides-for-cnc-3d-printing.318190/ and augerpro's dedicated website: https://www.somasonus.net/waveguides

www.diyaudio.com

Recently mabat gave me some ideas for a 5-inch driver-based prototype design. The design is scalable to higher radius drivers.
Let's see if the idea works out or not..
I am reposting mabat's ideas and simulation results here.
Cabinet design for the woofer (red colored portion in below pic is the driver ):

horizontal directivity

Vertical directivity

The kind of final design concept that mabat likes at the moment look like the following:

Cardioid mids+matching horn on top+properly integrated subwoofer for the lowest frequencies

For now let's start with an xps foam prototype box and some measurements
if it works out, we can think about a real build..

 

[Vineethkumar01]

The concept scaled to a cardioid implementation with 15inch woofer, corresponding BEM simulation results and comparison with a monopole 15inch woofer (Again, all these are mabat's simulation results)
Monopole 15 inch woofer in cabinet

Corresponding BEM simulation results for a lot of things, including directivity

15inch woofer in a 'cardioidish' kind of cabinet as described above

Corresponding BEM sim results

Compare the first plot in the above plots (monopole vs cardioid).. Look at the directivity control down to 50 Hz in both cases..
Isn't it fascinating...?

 

[aeroash]

What's the blue coloured marking on top of the box?

 

[Vineethkumar01]

I am posting details of my current system here just for a reference
My current system is DSP active 2/2.5 way system with 2 x Satori WO24P-8s per side and an ST260 KVAR horn attached to a BMS 4550 compression driver
Here is my system playing (Youtube video doesn't do much justice, so this recording is just for fun) before I applied room EQ to the system

Here are its crossover & measurements in a 2-way configuration:

Full measured polars & spin data

Phase response of the system is the grey line in the first graph above
Step response of the system.

Olive preference score (for fun)

Here is the highlight factor of the system (zoomed in horizontal polars from 1kHz to 20kHz)

Nearly constant (slightly rising) directivity index from about 1kHz and up

Speaker response at listening position after room EQ with frequency-dependent windowing and full FIR EQ (measurements before & after room EQ)

Step responses at listening position

I guess I will stop with this for now.. Time to focus on building a cardioid speaker
Ohh.. and by the way the above system is what @aeroash heard at my home when he visited recently

 

[Vineethkumar01]

What's the blue coloured marking on top of the box?

Its the slot through which sound leaks from the back side of the driver to interfere and create nulls to large off axis angles..

 

[rwnano]

really nice speakers vineeth..who built them pl?

 

[Vineethkumar01]

really nice speakers vineeth..who built them pl?

Thanks.
I made the designs for all the speakers. Eight audio built the wooder box for me. The smaller speakers (2way) on the floor were built by Sadik. I made the horns myself using my 3D printer.

 

[Mahi]

I am posting details of my current system here just for a reference
My current system is DSP active 2/2.5 way system with 2 x Satori WO24P-8s per side and an ST260 KVAR horn attached to a BMS 4550 compression driver
Here is my system playing (Youtube video doesn't do much justice, so this recording is just for fun) before I applied room EQ to the system

Here are its crossover & measurements in a 2-way configuration:

Full measured polars & spin data

Phase response of the system is the grey line in the first graph above
Step response of the system.

Olive preference score (for fun)

Here is the highlight factor of the system (zoomed in horizontal polars from 1kHz to 20kHz)

Nearly constant (slightly rising) directivity index from about 1kHz and up

Speaker response at listening position after room EQ with frequency-dependent windowing and full FIR EQ (measurements before & after room EQ)

Step responses at listening position

I guess I will stop with this for now.. Time to focus on building a cardioid speaker
Ohh.. and by the way the above system is what @aeroash heard at my home when he visited recently

Very nice sounding you tube content good sir ' uyierm niyae

 

[Hari Iyer]

I am posting details of my current system here just for a reference
My current system is DSP active 2/2.5 way system with 2 x Satori WO24P-8s per side and an ST260 KVAR horn attached to a BMS 4550 compression driver
Here is my system playing (Youtube video doesn't do much justice, so this recording is just for fun) before I applied room EQ to the system

Here are its crossover & measurements in a 2-way configuration:

Full measured polars & spin data

Phase response of the system is the grey line in the first graph above
Step response of the system.

Olive preference score (for fun)

Here is the highlight factor of the system (zoomed in horizontal polars from 1kHz to 20kHz)

Nearly constant (slightly rising) directivity index from about 1kHz and up

Speaker response at listening position after room EQ with frequency-dependent windowing and full FIR EQ (measurements before & after room EQ)

Step responses at listening position

I guess I will stop with this for now.. Time to focus on building a cardioid speaker
Ohh.. and by the way the above system is what @aeroash heard at my home when he visited recently

Imo, Looking at the step the highs look a bit more delayed by around 100usec. It would be interesting to see the step once again after you move the HF horn ahead by around 3.4cm.

 

[Vineethkumar01]

Imo, Looking at the step the highs look a bit more delayed by around 100usec. It would be interesting to see the step once again after you move the HF horn ahead by around 3.4cm.

I thought it was the lows that were delayed by a minute amount. It could be.
The crossover linearization FIR filter is approximate and not exact, and the delay dialled in was not pinpoint precise.
These will affect the step response by a some amount..
Given that the current state of these speakers is as below (disassembled and in parts), I wont be able to measure any of it anytime soon..

But since VituixCAD sims are very accurate, I can show the effect of a 100ms timing advance applied on the horn branch.
Here is that delay applied in horn branch



Here is the spin data


And here is the new step response:

 

[Hari Iyer]

I am posting details of my current system here just for a reference
My current system is DSP active 2/2.5 way system with 2 x Satori WO24P-8s per side and an ST260 KVAR horn attached to a BMS 4550 compression driver
Here is my system playing (Youtube video doesn't do much justice, so this recording is just for fun) before I applied room EQ to the system

Here are its crossover & measurements in a 2-way configuration:

Full measured polars & spin data

Phase response of the system is the grey line in the first graph above
Step response of the system.

Olive preference score (for fun)

Here is the highlight factor of the system (zoomed in horizontal polars from 1kHz to 20kHz)

Nearly constant (slightly rising) directivity index from about 1kHz and up

Speaker response at listening position after room EQ with frequency-dependent windowing and full FIR EQ (measurements before & after room EQ)

Step responses at listening position

I guess I will stop with this for now.. Time to focus on building a cardioid speaker
Ohh.. and by the way the above system is what @aeroash heard at my home when he visited recently

Imo, Looking at the step the highs look a bit more delayed by around 100usec. It would be interesting to see the step once again after you move the HF horn ahead by around 3.4cm.

I thought it was the lows that were delayed by a minute amount. It could be.
The crossover linearization FIR filter is approximate and not exact, and the delay dialled in was not pinpoint precise.
These will affect the step response by a some amount..
Given that the current state of these speakers is as below (disassembled and in parts), I wont be able to measure any of it anytime soon..

But since VituixCAD sims are very accurate, I can show the effect of a 100ms timing advance applied on the horn branch.
Here is that delay applied in horn branch
View attachment 76700


Here is the spin data
View attachment 76701

And here is the new step response:
View attachment 76702

The simulation was not an issue as seen in post #4, but the measured Response was showing more delay in HF. I had asked for 100usec of delay and not 100msec.

 

[Vineethkumar01]

Imo, Looking at the step the highs look a bit more delayed by around 100usec. It would be interesting to see the step once again after you move the HF horn ahead by around 3.4cm.

The VituixCad simulation I showed above is not just "a simulation". It is showing how the measured polar responses, other derived parameters from them etc change with variations in the signal processing blocks applied to the driver inputs. And once the measured data supplied to the program is accurate one can change relative driver orientations in the x, y and z planes and more and see its effects effects on the response in time and frequency domains very accurately.

If you look at the branch of the crossover connected to the BMS 4550 driver in the above crossover pic, you can see that just before the driver and capacitor, there is a block called A1 which shows a -100us delay applied. The corresponding impact on the step response is showed in the pic right below it. So even if i go and physically measure it again, to a high degree of confidence, the step response will look like the response I have shown

The simulation was not an issue as seen in post #4, but the measured Response was showing more delay in HF. I had asked for 100usec of delay and not 100msec.

It is a typo on my part. If you look at the crossover branch of the tweeter, you can see that I applied 100us and not 100ms advance in time.

 

[Hari Iyer]

I will be more keen to see the measured step response

 

[Vineethkumar01]

Without wasting more time, let's get back to business...

First prototype of the concept using a 5inch SICA coaxial driver being measured:

The slot is undamped. So it is bare driver+cabinet

Full horizontal polar measurements upto 180 degrees:

We have dipole-like directivity (above fancy looking Directivity plot) below 1kHz. But nasty resonances around 1.25kHz. This is not good.
Here is the comparison between BEM simulations and real world results for the 'no damping' case above:

BEM sim results

Real measurements as shown above

Pretty close.. if you ask me..
So we have some confidence now to proceed

 

[Vineethkumar01]

Round-2: Partially damped slot behind the driver

Polar measurement-taking action

Measurement results

We are better now.. we have dipole radiation restricted to less than 500 Hz now and the pesky 1.5kHz resonance reduced.. Confidence inspiring to move forward..

 

[Vineethkumar01]

Round-3: Full damping of slot behind the driver

Measurements

There we have it folks.. Full range cardioid constant directivity.. Pretty exciting if you ask me...
Such a simple concept and build but very nice results..

So That's it. We have achieved the objective of this experiment. That is to achieve full range carioid behaviour in the passband of the woofer. SInce this is a coaxial driver, the tweeter directivity can be blended with the woofer's around 2.5kHz to create a full range cardioidish behaviour.
Here is the tweeter response from round-1 (so Ignore everything below about 600Hz):

But to help the driver I will make it a 3-way and crossover to an omni woofer below 200-300 Hz

 

[Vineethkumar01]

Now its time to focus on a real build and drawing cad diagrams to start with that..

 

[Vineethkumar01]

Here is a version of the full speaker box.
It uses the 5.5 inch sica coax in cardioid radiating mode & a monopole 8.5 inch subwoofer.

 

[diyaudio]

Very interesting. Quite an achievement. Subscribed.

 

[Vineethkumar01]

To put the final nails on the coffin of the closed box..

BEM simulation of closed box cabinet of the above dimensions


Horizontal polars



Cardioid box


Horizontal polars


Here are the actual measurement comparison of the on-axis response of my Sica coax driver in a teardrop-shaped closed box vs cardioid box
ignore the light blue line. Dark blue is teardrop box. Brown is the cardioid box. The wiggles around 600Hz to 1.2kHz are resonances due to the foam box construction and will vanish in a proper build


Summary
Cardioid box not only gives awesome-looking polars and eliminates pesky midrange resonances but it will also yield a gain in response on axis of the order of few dBs, thereby helping with reducing baffle step compared to any similar dimensional sealed/ported box... This is probably due to the constructive interference between the radiation from the leaking port and that from the driver. Hence the need for equalization is less in the midrange up to about 200Hz, below which a monopole woofer takes over.

All in all a win-win situation..