The
quality of bass you get from OB speakers is fantastic. But it’s hard to get
quantity of bass without ladles of bass boost gravy from DSP.
DSP is great if you’re building an active system, but what about passive crossovers?
I discovered a way to add 4-7dB boost in a ½ octave bass band, plus the ability to use any woofer you desire as long as it has a Qts > 0.5. This opens up many new choices in drivers for Dipoles.
You do this with an unusual passive high pass filter. I sure I’m not the first person in history to do this, but I’ve never seen this explained or modeled anywhere else.
Ideally passive OB woofers have Qts ranging from 0.7 to 2 or even 3. But very few woofers have high Qts, since high Q woofers aren’t very useful in closed or ported box designs. Many of the ones that do have Qts >1.0 are lower quality budget drivers. Most don't have good Xmax. So this is a new way to pull off a solid Dipole using a high quality woofer with Q of less than 1.
It is not terribly obvious to the average speaker builder that, across a limited range of frequencies, it is possible to get
more voltage out of a passive crossover network than you put in. But you can do it with high-Q filters.
Above: 8-ohm tweeter with a 2nd order high pass filter; filter Q = 2. The red curve shows the input voltage to the tweeter, which is +6dB at 2KHz, followed by a 12dB/octave rolloff below that point. Simulated in
VituixCad.
The price you pay for this is lower impedance. The circuit draws additional current from the amplifier and dissipates it in the tweeter. An 8-ohm tweeter with the filter in place has an impedance curve that looks like this:
You see that the impedance dips down to 2 ohms. So if the tweeter had 90dB sensitivity for 2.83 volts at 2KHz, after the filter it produces 96dB at 2KHz.
Oftentimes, when multi-way speakers have extreme dips in impedance, it’s because the designer has taken advantage of this. This feature is extremely useful and quite fun to play with.
Now that I’ve established this, I’d like to show you how to use this to boost bass 4-7dB in a Dipole / Open Baffle system.
The concept is very simple: Add a 2nd order high pass filter with a corner frequency somewhere between 20Hz-60Hz,
tailored to the exact details of your design. I call this the “Marshall Bass Boost” circuit. In practice it's not so simple and it takes simulations or measurements to pull off.
A popular Open Baffle woofer is the Eminence Alpha 15A, which has Thiele-Small parameters as follows:
Fs 41Hz
Qts 1.26
Vas 260 liters
SPL 95dB
The Q of 1.26 means its natural response at 41Hz in an infinite baffle is +2dB. (A Q of 0.7 would be -3dB; a Q of 0.3 would be -10.5dB.) In the Open Baffle system described further down in this post, the enclosure starts dropping off at about 60Hz at 6dB per octave. That means at 40Hz it’s down 5-7dB. The bass, while adequate, is thin compared to sealed or reflex enclosures.
We fix this by adding a high-Q 45Hz high pass filter… with the added benefit of a steep infrasonic filter that shields the woofer from signals below 40Hz.
Below are my impedance measurements of the Eminence Alpha 15A:
At the 41Hz resonance, impedance peaks at 25 ohms. We are going to use this peak to our advantage, because when we add a high pass filter, the complex driver impedance will interact with the filter in interesting and useful ways. So now we’re going to model it using VituixCad and design a filter that gives us exactly what we want.
With experimentation I find that a 20mH inductor and 450uF capacitor gives a +6dB boost at 48Hz, with a steep cutoff below 40Hz.
This +6dB boost will blend very nicely with the natural rolloff of the Open Baffle enclosure at about 60Hz. But we have to watch the impedance very carefully:
Above: Impedance of Eminence Alpha 15A with 20mH + 450uF high pass filter. Instead of peaking at 25 ohms, we get an impedance dip of 3 ohms. The additional current drawn from the amplifier gets dissipated in the woofer which gets us +6dB bass boost. Note the rising impedance below 40Hz because the filter blocks super low frequencies.
Because the Bass Boost circuit creates an impedance dip, we need to use 8 ohm woofers or 4 ohm woofers in series (unless your amp is comfortable with 2 ohm loads).
Not just theory. This really does work.
Below is an actual measurement of the circuit I described above: 20mH inductor and 450uF capacitor.
Above: Eminence Alpha 15A;
Blue trace = input signal from amplifier,
Purple trace = voltage at speaker terminals after the filter. Filter delivers 2X the voltage at 45Hz. Note the steep reduction of infrasonic signals. -10dB at 30Hz, -17dB at 20Hz. Prevents woofer damage and reduces distortion.
Audible Differences
The 6dB boost transforms this system from having somewhat lean “Open Baffle Bass” to plump, rich bass like you get with the luxury of DSP. The infrasonic filter also greatly limits cone excursion at low frequencies, so these deliver full impact down to 40Hz.
They are able to play a good deal louder than without the filter in place, even though the circuit is pushing the woofer harder in the 40-60Hz range.
The benefits are that not only do you get substantial bass in the 40-50Hz region, the infrasonic protection reduces overall excursion and thus distortion drops as well.
Big Inductors & Capacitors + Cost Considerations
This demands much larger caps and coils than are often sold by speaker parts vendors. Also the inductors have to have sufficiently low DC Resistance.
US Coil (
www.UScoils.us) sells large ferrite core inductors of many varieties, in small and large quantities. The circuit above calls for a 20mH inductor with DCR of <0.8 ohms. US Coil’s USLC56-16-20000 costs $27.65 and has a DCR of 0.7 ohm. A 450uF capacitor made with 2 x 100uF and 1 x 250uF in parallel costs $11.30 from the same site. Total cost per channel, approximately $40.
$40 might sound like a lot... but compared to what? How much does it cost to build a large reflex or acoustic suspension cabinet? How much does it cost in both money and extra amplifiers to add DSP? How many otherwise great woofers with too low a Q for Open Baffle will you now be able use successfully?
I’m a huge fan of DSP, and
I've designed many DSP based OB systems and
discussed them here on this forum, but it’s not always the most realistic choice. The ability to get +6dB bass boost for only $40 per channel is attractive.
Example 2: GRS K33-4 15” woofer from Parts Express
This driver has parameters:
Fs 32Hz
Qts 0.52
Vas 274 liters
SPL 96dB
Impedance 4 ohms
Since the K33-4 has 4-ohm impedance, I’m going to wire two in series, driven by a Bass Boost circuit.
Now, using the filter functions in VituixCad, I am going to simulate 1) the roll off of the driver (Q=0.52, Fs 32) (“2nd order filter” above) and 2) the roll off of the Open Baffle (“1st order filter”) with a simple 6dB per octave slope starting at 50Hz:
Based on the woofer’s natural response, combined with the Open Baffle 6dB/octave rolloff starting at 50Hz, we achieve flat response down to 40Hz with a 3-ohm minimum impedance.
Practical Guidelines for the Marshall Bass Boost Circuit
- Woofer should have 8 ohm or higher impedance, or 4 ohm drivers wired in series
- Woofers should have a Q of at least 0.5. Otherwise you’re fighting against the natural downward tapering response of the woofer.
- Inductors should have DC resistance below 1 ohm. Capacitors should have Equivalent Series Resistance (ESR) below 0.5 ohm.
- The resonance of the woofer should be lower than your target cutoff frequency.
- The tuned frequency of the filter should be above the woofer’s resonance.
- The cutoff point of the Open Baffle (a function of its size and depth) should be similar to, and no more than ½ octave above, the filter’s tuning frequency.
- Watch the impedance with caution because it’s easy to generate dangerously low impedances of 1-2 ohms if you’re not careful. An 8-ohm driver with a Bass Boost filter will typically reach down to 3 ohms minimum, when designed properly.
You can use the
Loudspeaker Database to search for, say,
woofers between 14-16" diameter with Q > 0.5 and SPL > 93dB and Xmax >3.5mm. When I searched today I got 19 results. All of them are decent candidates for the Bass Boost circuit.
In a separate article I give details on a 2-way 100% passive system with a Bass Boost circuit. Eminence Alpha 15A woofer, SB Acoustics Satori TW29R tweeter with Visaton WG148R waveguide. 5 on-axis measurements in the room, distance 1-2 meters, averaged together from both left and right speakers:
Here are photos with on- and off-axis response curves:
Above: 1/6th octave measurements in real room. No attempt to gate reflections. Curves are 0, 15, 30, 45, 60, 75 and 90 degrees off axis. Curves show Constant Directivity with strong in-room response down to 40Hz. Impedance 4 ohms.
An Open Baffle with no box is much less heavy. If you're using expensive hardwood, it's a lot less expensive than a box. These were made with slabs of Live Edge walnut. These compete
very well with reflex designs in terms of SPL, bandwidth, and output. And especially
size and
weight! The money you invest in those big inductors and capacitors will pay off 10X in shipping cost alone by saving you the weight and expense of a large box.
The Bass Boost allows you to trade off a larger woofer w/ more expensive crossover components against a much smaller, lighter, less expensive cabinet. Using smarts instead of brute force. These speakers weigh 35 pounds (16kg) each.
Below: Nearfield measurements of woofer and tweeter. The boost at 50Hz compensates for Open Baffle cancellation which is not visible nearfield:
The Marshall Bass Boost circuit enables this system to yield full, plump bass down to 40Hz, 93dB SPL 2.83V/1M. It comes pretty close to Constant Directivity response across the entire spectrum, and excellent blend with the tweeter with a 1250Hz crossover. The crossover is 100% passive, no DSP. All the advantages of Open Baffle with a LF punch more typical of a Bass Reflex “rock and roll” speaker.
Above: Impedance of
15” 2-way system with Bass Boost circuit. Impedance curve is completely different from a conventional speaker. Note the 4.5 ohm minimum at 42Hz, where the woofer enjoys a 5.5dB bass boost.
Handy Dandy 2nd Order Filter Formulas
For a 2nd order high- or low-pass filter with an inductor and capacitor, the resonant frequency is:
F = 1 / (2π√(LC))
Q = Z√(C/L)
Where F is frequency of the filter, L is inductance, C is capacitance, and Z is the impedance of the speaker.
So you can calculate L and C based on frequency (F) and Q:
L = Z / 2πFQ
C = Q / 2πFZ
At the resonant frequency, a filter’s boost or cut in dB = 20LogQ, so if the Q is greater than 1, then you get a boost near the tuning frequency of the filter. Most standard crossover tables are based on a filter Q of 0.5 (-6dB at the crossover point) or 0.7 (-3dB at the crossover point). But again, you can have Q’s above 1.
P.S.: You can also use this circuit in an acoustic suspension woofer with a Qb of, say, 0.5, which is an entirely different topic of modeling and exploration. The virtue in that situation would be optimizing the system for high mid-band efficiency with a large magnet and high BL, while gaining the extra LF protection of the high pass filter. Think of it as a 6th order closed box alignment with some very interesting tradeoffs that can be put to use by a resourceful designer.
Special thanks to
@nc535 for helping me with the VituixCad simulations.
