Thiel CS2 2 loudspeaker First-Order Filters

Sidebar 1: First-Order Filters: Panacea or Pain?

As mentioned, the Thiel CS 2 2's crossover features first-order, 6dB/octave slopes. Many audiophiles state, without specifying why, that first-order slopes are "the best." A first-order crossover is unique in that it offers the minimum phase error through the crossover region between the two drive-units, hence the best time-domain behavior (least ringing and overshoot). The drive-units also work in phase outside of the crossover region in a time-coherent manner; ie, they are both in phase and in time-step with the input signal. More complicated crossover filters, such as the popular fourth-order Linkwitz-Riley, allow the drive-units to be in phase in the crossover region, but at the expense of the overall time coherency: the drive-units may have the same acoustic polarity, but only because one has had its phase rotated through 360°; it therefore lags the input signal by that amount of phase shift.

The downside of first-order crossover filters is that they offer the lowest out-of-band rejection of any. An octave above or below the nominal crossover frequency, the driver's output has only been halved (reduced by 6dB), compared with a fourth-order filter's reduction in output to just 1/16 (reduced by 24dB). Any drive-unit problems that are nominally out of its passband—a tweeter's fundamental resonance, a woofer's cone breakup modes—will therefore still affect the sound quality of a speaker using a first-order crossover. The drive-units must therefore be much better behaved overall than normal.

Second, what matters is the ultimate acoustic slope of the crossover filter after being transduced by the drive-unit. Merely driving a woofer through a series inductor will not in itself result in a first-order rollout if the driver itself inherently rolls out with a 6dB/octave slope above the crossover region, which is often the case. The ultimate slope in this case will be 12dB/octave, and the design will no longer be time-coherent. In a speaker using a true first-order crossover, the drive-units must therefore maintain their flat response well beyond their nominal passband. In addition, the drive-units' impedance must not vary too much with frequency from its nominal value, as this, too, will, affect the ultimate slope.

Third, because of the shallow rollout slopes and the fact that the drivers are, of necessity, vertically separated in space, a speaker using first-order slopes will have an overall frequency response critically dependent on listening axis, due to the very broad overlap between adjacent drivers. The distance from the listener's ear to each of the drivers must be equal for their outputs to add up in a time-coherent and flat-amplitude manner; if not, there will be nulls in the amplitude response at the frequencies where the difference in distance equals one half-wavelength.

Another way of looking at this is that two drive-units used one above the other on a flat baffle, crossed over with first-order filters and connected with the same electrical polarity, will have a listening axis downtilted from the horizontal (by about 15° for a typical two-way design). Reversing the electrical polarity of the tweeter will tilt the main response lobe up by the same amount, implying that the speaker would then sound and measure okay on a shorter-than-normal stand. The time-coherent nature of the first-order crossover would, however, be compromised.

A designer intending to use first-order slopes must therefore choose the listening axis, then carefully slope or step the speaker's front baffle (or place the tweeter below the woofer) so that the outputs of the drivers do indeed sum correctly in both time and frequency domains on that axis.

I hope it is obvious that deciding to design a speaker with a first-order crossover is not the simple business that many audiophiles feel it to be of just using a single series element in the feed to each drive-unit. Nevertheless, in the hands of a talented, careful designer—Jim Thiel, Richard Vandersteen, and Robin Marshall of Epos are probably the leading practitioners—such a speaker can be arranged to have flat frequency response and time-coherent performance.—John Atkinson

Thiel Audio Products
1026 Nandino Boulevard
Lexington, KY 40511
(606) 254-9427