Baffle Diffraction Step Loss In My MiniOnkens ~ Dealing With It 30Apr24

Speakers and drivers are normally modeled in 2pi space; this means they are expected to be projecting forward in a hemisphere. I model this way. When measuring and listening to the NestMT MiniOnkens (currently deployed as surrounds) in free space, I see and hear a significant rising sound pressure level (SPL) with frequency. The measurement is a smidge flatter when the speakers are directly against the wall (SPL graph not shown). Speaker designers want a flat response over frequencies and humans even prefer a declining SPL with frequency (that's why I always look for a system matching my personal "house curve"). What is going on here? It is called baffle diffraction step (BDS) loss.

What Is Baffle Diffraction Step (BDS) Loss?... The acoustical load that the front baffle of a speaker presents is different for low frequencies than high frequencies. Speakers tend to project mid-high frequencies directly forward in a 2 pi hemisphere while lower frequencies project in a full sphere (4 pi). This difference results in a ~6dB loss in presented sound pressure level at the lower frequencies. The step for this occurs at the frequency whose wavelength is about 8X the width of the baffle. In multi-driver speakers this is often handled in the crossover circuit by attenuating the tweeter.

Reviewing The DRC miniOnkens... My MiniOnken's baffle is beveled (which helps with diffusion and ameliorates ripples in SPL) and presents about a 4.15" width. To find the frequency of the expected baffle diffraction step one takes 1/8 the speed of sound and divides by the width of the baffle: (1/8 * 13560 in/sec)/4.15in = 1099Hz. Does the expectation match the observed measurement? Yes ~ exactly!

Dealing With Baffle Diffraction Step (BDS) Loss... One can of course "do nothing." Purely acoustically one can place speakers with this attribute directly against a wall, which will likely improve low freq SPL by bringing the much larger/wider baffle load into play which will make the low frequencies present more forward in a hemisphere. Depending on the situation: sometimes you can, sometimes you can't. Little else can be done to the cabinet/speaker itself acoustically. However, one can build a simple passive circuit which will reduce the high frequencies by the 6dB and make the overall SPL flatter. The implication is though, that doing so will reduce the efficiency of the speakers (less so if the correction is at line level); either is something I rue as I tend to seek high efficiency drivers/speakers and drive them with lower power amplifiers. A guy's gotta try though. Dr John Murphy showed an accepted approach for building a passive circuit for Loudspeaker Diffraction Loss and Compensation... I won't delve into his math or derivations further, but I get modeling acoustics and electronics like this, but jump to accepted correction circuits.

Correcting BDS Loss In The DRC MiniOnkens... I will not typically have access to adding a simple RC circuit to the line level so will need to use an RL circuit directly on the speaker level signals (grrr... loss, just to heat). This is just what crossovers and the like, which are internal to many speakers, do, so it's an accepted correction scheme. I'll do calculations here based on the full 6dB attenuation of the high end (even though in my room the attenuation might be less due to the wall). The 6dB assumption is right on for free space speaker placement.

R2 is the speaker system resistance (the FE108E∑ is 6.8Ω and the MiniOnken system is nominally 7Ω, say) and we'll make R1=R2=R. Murphy derived the equation for inductance given the width (W in meters) of the baffle and nominal system resistance R: L1 = W * R / 1.021 = 0.1054 * 7 / 1.021 = .723mH = 723µH. This correction assumes 3dB down at the step frequency and 6dB at the high end. Well, this is a fairly expensive and large inductor, and equally rare resistor... bummer. I imagine I will ultimately make a box with adjustable components to allow me to investigate passive circuit correction on a variety of speakers but here are the right components for a 6dB passive circuit for the MiniOnkens.

BDS Correction Experiments Using A Digital XOver... Whoa, here's an idea. I have a miniDSP 2x4HD and can experiment with various high freq BDS correction attenuation levels as well as step freq settings and compare results! I can even measure in free space and in the "closer to the wall" listening position. This won't be a permanent install of the 2x4HD as I don't like the processing delay introduced by it. It will however give me an solid indication of what attenuation and knee I should be targeting in any correction circuit. Glad I haven't sold the 2x4HD. I built a simple 6dB high freq attenuation in the 2x4HD with the knee at 1.1KHz as my original measurements above suggested. 

Voila, using my measurement mic and REW I swept the speakers corrected and uncorrected/bypassed and can see the appropriateness of a BDS correction for the MiniOnkens, as doing so has the speakers right on my desired house curve. Somewhat surprising to me is that measuring the MiniOnkens against the wall did NOT substantially change the rising SPL phenomenon.

These experiments have shown me that the passive circuit described above, and even the values calculated for the resistor and inductor, would have the desired effect to correct the MiniOnken's BDS behaviors.

Measuring The Corrected MiniOnkens & Implications Of Compensating For BDS Loss... Uh, you will have to wait for an update to this entry where I disclose the final results of this work... it is just system design and experiments thus far. I'd like to see what effect the circuit would have on efficiency.

08Jul24 UPDATE ~ Implemented & Measured MiniOnken BDS Correction Circuits... I finally purchased a 727µH inductor (very close) and 7Ω/1w resistor (again, close) to implement the BDS correction circuit I modeled and "approved" earlier with DSP. Recall I measured a 6dB rise above 1100Hz and my circuit design for speaker level signalling was intended to attenuate above 1100Hz (the mid-highs and highs) by 6dB. Practically, how did I do it and how did it work? Well, here are the parts, the circuit, the circuit in action, the measurement strapping and the results. It worked exactly as designed & intended and is installed in the NestMT height/presence speakers, "in production."

It's cool when an observation followed by scientific assessment and measurement leads to an engineering fix. Though, I am creating heat and reducing efficiency to get the declining SPL.