DeVries & Lampton Speaker: Crossover & Large Enclosures
Dear Sir:
The comments by deVries and Lampton ("Build an ES Tweeter/Cone Woofer System," AUDIO, Aug., 1974) on crossover design re quire comment, since their proposed crossover design is demonstrably non-optimal.
The authors correctly point out the conflict between "constant voltage sum" crossover, where the "total woofer voltage plus tweeter voltage is constant with respect to frequency," and the "constant power sum," where the sum of the radiated powers from the woofer and tweeter is constant with frequency. What the authors apparently don't realize is that this conflict can be resolved by several circuits which meet both criteria simultaneously. Unfortunately, the second-order Butterworth configuration specified by the authors meets only the constant power requirement.
However, if slightly lower "Q" filters are used, then we can meet the constant voltage requirement (al though the sum of the voltages is phase-shifted with respect to the in put). Unfortunately, the constant power requirement is now violated.
But all is not lost. As Ashley and Henne (J. Robert Ashley and Lawrence M. Henne, "Operational Amplifier Implementation of Ideal Electronic Crossover Networks," J. Audio Eng. Soc., Vol. 19, No. 1.. p. 7) have ob served, the third-order Butterworth configuration seems to offer the best of all possible worlds: it is constant-power; it is constant voltage (al though there is a frequency-dependent phase shift in the voltage sum with respect to the input); it offers maximally-flat magnitude characteristics (thus minimizing strain on the individual drivers), and it offers very sharp cutoff characteristics, which minimizes the need to make woofer and tweeter responses well-behaved beyond the crossover frequency. For these reasons, the third-octave Butterworth is arguably the single optimal crossover network design.
It can be mentioned in passing that a pair of first-order (6 dB/oct passive RC filters) can also meet the criteria.
Unfortunately, this circuit has insufficiently sharp cutoff to be of interest in most cases. In fact, any odd-order Butterworth pair will meet the criteria.
I have included a practical circuit (Fig. 1) to realize the third-order low- and-high-pass Butterworth filters. The unity-gain feedback circuit used by the authors to realize the lowpass filter is not optimal because its characteristics have higher sensitivity to resistor and capacitor tolerances and drift than does the "multiple feed back" circuit of the type illustrated.
Unfortunately, a practical high-pass version of the multiple feedback circuit does not exist, so the high-pass filter is best realized with a unity-gain feedback circuit of the type that the authors specified. The specified opamp, the RC4558, is a Raytheon de vice.
Fig. 1-Orban crossover for Lampton/deVries speaker system.
Fig. 2-Relationships of cutoff frequency and volume for three woofers.
-Robert Orban Menlo Park, Calif.
The author's reply:
In view of the gratifying response to the loudspeaker design articles by myself and L.M. Chase (AUDIO, Vol. 57, #12, p. 40, December, 1973) and G.J. deVries (AUDIO, Vol. 58, #8, p. 28, August, 1974), we would like to expand upon some of the technical matters raised by readers.
We have received a number of helpful comments from readers, such as Mr. Orban and Prof. Ashley, concerning our suggested use of second-order Butterworth high- and low-pass filters as loudspeaker crossover circuits. The comments are generally that third-order filters offer a number of advantages with regard to their transient response and on-axis frequency response.
Accordingly, we bread-boarded such a circuit-specifically, the one given by J.R. Ashley and A.L. Kaminsky (J. of the Audio Eng. Soc., Vol. 19, No. 6, p. 494, June, 1971)--and find through listening tests that there is in deed an improvement in the clarity of the reproduced sound. We therefore recommend the use of the third-order filters in crossover applications, and invite the comments of other experimenters who have the opportunity to try them.
Also we would like to emphasize that there are infinitely many possible tuning and damping combinations for bass reflex loudspeaker en closures. Most of these combinations do not perform very well: They exhibit poor frequency response curves and do not get the best possible performance from a loudspeaker in terms of distortion. The quantitative foundations for predictable designs were established by the pioneering works by Novak and by Thiele, who identified a variety of practical combinations of tuning and damping ratios which give precisely characterizable performance curves.
Fig. 3-Relationships of efficiency and volume for three woofers.
Fig. 4-Relationships of duct-to-cone-mass ratio and volume for three woofers.
Fig. 5-Relationships of required speaker Q and volume for three woofers.
Three key parameters principally govern this performance: (1) the stiffness ratio S which is the ratio of the enclosure air spring stiffness to the stiffness of the suspension of the loudspeaker cone; (2) the mass ratio M which is the ratio of the vent air mass to the speaker cone mass, and (3) the speaker's Q factor, which is the ratio of its reactance to its motional resistance. Once the speaker is chosen, the stiffness ratio is fixed by the box volume. For values of S greater than 1.414, a good choice of response curve shape would be any of the quasi-Butterworth or "double-point" alignments. In larger enclosures where S is less than 1.414 a good choice would be the appropriate sym metrically bounded ripple tuning. For the value of S equal to 1.414, it is possible to achieve a maximally flat or Butterworth response, provided again that M and Q are properly set.
In Fig. 6, these various possibilities are illustrated in the form of the values of M and Q necessary when a given value of S has been chosen. To the left, the bounded ripple alignments are shown; to the right, the quasi-Butterworth alignments; and in the center, marked by small circles, the maximally flat tuning and damping ratios. The curve marked G is an interesting measure of performance:
It is the ratio of the complete system's low-end 3dB cutoff frequency to the woofer's free air resonant frequency. When G is less than one, the system goes deeper than the FAR. To achieve this requires a big box.
Some readers have inquired as to how to design reflex enclosures for multiple drivers. As long as the drivers are alike, a straightforward procedure is to use for design purposes a fake speaker having the total effective cone piston area, cone mass, and cone stiffness of the members of the collection. The FAR and Q are essentially unaffected.
Many readers have requested that Figs. 2, 3, 7, and 9 of the Chase article be extended to much larger values of volume stiffness products. I have done this in the accompanying Figs. 2, 3, 4, and 5. These have all been de rived from Fig. 6 for loudspeakers having effective piston areas of .032 square meters (typical for ten-in. frame diameter loudspeakers), 0.050 square meters (12-in.), and .085 square meters (15-in.). Because of variations in actual piston areas among various manufacturers and models, the frame diameter is only a rough guide to the effective piston area. Using Figure 6, these curves can be generated for any size speaker.
Fig. 6--S, ratio of enclosure air stiffness to cone suspension stiffness.
On each of the curves, a small circle indicates the location of the maximally flat tuning; the portion of the curve lying to the left of this point will give a quasi-Butterworth characteristic, and to the right a bounded ripple design results.
-Michael Lampton Jan deVries Lee M. Chase; Berkeley, Calif.
Pardons, Amnesty, & Lennon
Dear Sir:
In this time of pardons and amnesty and in the light of our national self re-evaluation, isn't it also time we consider the deportation of John Len non an injustice-not only to him, but to us and to America.
-Bernie Mitchell; President, U.S. Pioneer Electronics; Moonachie, N.J.
Gee whiz, Bernie, I always thought what made America great was its ability to be a melting pot, to be able to handle--within its tolerant borders-just about anyone and any thing, to have room enough for nearly any point of view. I'm enough of a believer in the fundamental paradox of life to think that a person can have both dangerous and worthwhile qualities, but I see little or none of the former in Lennon. And if he does have them, they are quite outweighed by the latter. -Ed.
Organ Servicing
Dear Sir:
I have enjoyed your magazine's fine articles since I stumbled on it in the Engineering Library Stacks at the University of Illinois during my freshman year. I am wont to find each issue both thorough and readable. How ever, your November issue's article on organ servicing seemed dangerously over-simplified.
I am a professional organ-repair specialist. I am not just trying to keep jobs for myself, as many items in Mr. Turino's article seem quite useful and simple enough for the average owner.
However, I would like to offer a few warnings, using the Lowery organs as examples, since they are excellent instruments and rather typical of most electronic organs.
In regard to annual vacuuming, I have seen a heart-sinking number of organs with damaged contact springs and busses, broken leads, and disconnected wires as a result of well-in tended but slightly careless vacuuming. And I have never known any amount of dust or cobwebs to interfere with proper operation of an organ. (Mice are another story.) The modern Lowerys contain a number of coils, easily accessible and very attractive for VOM testing. The first and only time I tried one, I destroyed it. Also present on many boards are regular and large-scale integrated circuits, along with MOS FETs, some of which can be damaged by static charges on the fingertips, and are impossible to really test without a 'scope or an advanced logic probe.
Contact cleaning I recommend heartily, it being a messy and boring job for me. Watch out for tube organs though, as keying voltage is 430 volts on some models. Also, it takes me between an hour and an hour-and-a-half to clean contacts on some Lowerys, most of which is spent gaining access to the contacts themselves.
And remember that I know how to take them apart too. Few service manuals have opening instructions, and I must confess I felt horrible scratches on a few organs before I got my methods perfected.
If I may question one last point, regarding the ease of dealing with ninety percent of organ problems: On evaluating my records on my last 100 Lowery organ calls, which included a large percentage of tube organs up to 20 years old, only 12 had contact trouble and I changed only five tubes.
-David R. Shaddock; Meyers Music Streator, Ill.
Dear sir,
Allow me to add my plaudits for Richard Heyser's new speaker analysis program. I have read with interest his articles in the JAES, and I am especially interested in his findings with regard to phase linearity. Phase response has become a subject in tensely probed by psycho-acousticians (a spinoff of quadraphonic research), and I am sure that many other readers would appreciate some articles by Mr. Heyser on the physical aspects of non- and minimum-phase response networks. Not only transducers, but purely electronic links in the high fidelity chain should be studied in this light.
-Tom Tollefsen; Olympic Valley, CA
(Source: Audio magazine.)
Also see: Dear Editor (Aug. 1975)
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