An approach for maintaining the directional pattern of high-poweredsubwoofers and loudspeakers By David Gunness

The ability to achieve low-frequency directional control — passively — has suchobvious appeal that one might wonder why manufacturers haven’t been doingit all along. Well, it isn’t for want of trying, and in a sense, some already have.

For example, the classic open-back guitar cabinet is actually a passive figure-8 pattern loudspeaker. And in 1970, Bobby Beavers of Altec Lansingfiled for a patent covering a passive cardioid loudspeaker. While the patentincluded all of the necessary design equations, no commercial product wasever produced under the patent. Presumably there were unresolved challenges in implementing a product.

Various other passive cardioid patents have been awarded over the years,including in 1971 (Iding, for Philips Corp.), 1997 (Mizogushi, for Sony Corp.),and most recently in 2010 (John Meyer, et al.). What all of these attemptshave in common is that they could only be implemented on a small scalewhich is to say, at not-very-low frequencies and not-very-high sound pressurelevels.

Our approach, which is patent pending, addresses the problem of maintainingthe directional pattern even when the total air flow is extreme, as it is in highpowered subwoofers. The technology was first introduced in the FL283 passivesubcardioid line array, followed by the FLS115 companion subwoofer and theCS118 stand-alone passive subcardioid sub. Most recently, the lineup has beenfurther expanded to include the CS121, a 21-inch passive subcardioid sub.

Inner Workings

So, how does one produce a cardioid radiation pattern using only one source?To understand, let’s look at how a cardioid subwoofer is produced using twosources: a forward facing cone loudspeaker varies from “nearly omnidirectional” at very low frequencies to “slightly directional” at the upper end of thefrequency range typically covered by subwoofers.

To produce a cardioid pattern, add a second cone loudspeaker facing backward; EQ it to match the magnitude response of the forward facing cone ata point on the back axis of the loudspeaker (essentially a low-pass filter);add signal delay to the rear-facing loudspeaker until the phase response alsomatches at that point; and finally, invert the polarity of the rear-facing loudspeaker. The two sources will sharply cancel on the back axis, producing astandard cardioid pattern.

Next, progressively reduce the delay to produce a supercardioid (with a lobeon the back axis and a null at 109.5 degrees off axis) or a hypercardioid (withthe null at 126.9 degrees off axis). Then increase the delay to produce a subcardioid, which has no sharp nulls but provides significant attenuation overthe entire back hemisphere.

In short, the sound coming from the back of the box has to be inverted, lowpass filtered, and delayed, relative to the sound coming from the front of thebox. With a single source, the polarity inversion is easy because the soundradiating from the back of a cone is opposite in polarity from the sound radiating from the front of the cone.

The low-pass filter and requisite delay can be achieved by way of a carefully balanced arrangement of acoustical elements. This is in fact the same way that a cardioid microphone works, except of course in reverse and on a much larger scale.

Several Advantages

Aside from the obvious advantage of requiring only one DSP channel and oneamplifier channel, there are numerous other advantages to passive cardioidloudspeakers: higher efficiency, lower cost, cleaner sound in the back, andmore control over the shape of the polar response.

Let’s start with higher efficiency and lower cost. The maximum output of apassive cardioid is similar to the maximum output of an active cardioid usingtwo of the same drivers, but it accomplishes it with half as many drivers,half as much amplifier power, and a simpler enclosure. As a result, passivecardioids are more efficient and much less expensive than active cardioids.Essentially, the rear radiation of the cone is used productively over a broaderfrequency range, providing everything that the second driver in an active cardioid provides.

In an active cardioid, the two drivers receive different signals from theirrespective amplifiers; plus, no two drivers are exactly the same. As a result,distortion products produced by the front and rear drivers are not exactly thesame, so the distortion doesn’t entirely cancel in the back.

And, since the fundamental is much lower in the back, the distortion is significantly more audible than it would be for a non-cardioid loudspeaker. Thetechnical term for this is “grunge;” active cardioids tend to sound grungy inthe back at high levels.

In a passive cardioid, both the front radiation and the back radiation areproduced by the same cone. Any distortion originating at the driver is present in both the front and back radiation, so the distortion cancels in the backhemisphere just like the fundamental does. One of the surprising attributesof passive cardioids is that the sound behind the loudspeaker is cleaner thanthat of an active cardioid.

There are many variables in the implementation of a passive cardioid with whichto adjust its performance. The rear radiation of a Fulcrum passive cardioid emanatesfrom ports instead of an identical driver, and there is significant flexibility as to howthose ports are implemented. The number of ports can be varied; their location canbe adjusted; and their surface area, length, and even expansion can be adjusted.

And, to produce the desired shape of low-pass filter, there must be resistance in the ports — yet another variable. All of these variables affect theshape of the polar plots, so by carefully balancing all of them it is possible toachieve more consistent polar plots than is possible with an active cardioid.

Why Subcardioid?

There are several advantages to the subcardioid pattern. Of the four standard“cardioid” shapes, the subcardioid is the most efficient at low frequencies. Thesharp nulls in the polar response of the other three shapes come with an efficiency penalty and they only affect a limited region of the sphere. By targetingconsistent attenuation across the back hemisphere instead of trying to achievea deep null somewhere, higher sensitivity can be maintained at low frequencies.

Above the cutoff frequency of the acoustical low-pass filter, the rear radiation ceases and the loudspeaker transitions from a subcardioid pattern to thenatural directionality of a forward facing cone. The polar pattern of a forwardfacing cone in an enclosure is quite similar to a subcardioid pattern. Becauseof this and all of the variables that can be adjusted to subtly change the shapeof a passive cardioid’s polar response, a more consistent spectrum can beachieved over the entire sphere.

The bottom line is that this technology is applicable in a wide variety ofsound reinforcement applications. As a result, it will be implemented in anexpanding range of our products from this point forward.

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DAVID GUNNESS is vice president of research and development as well as leadproduct designer at Fulcrum Acoustic (fulcrum-acoustic.com), and he holds severalpatents for loudspeaker design.