rminology by division into two types. The spectral acoustic crossover has equal levels at i^t'j augment ^e termrange, the summation of drivers covering different frequency ranges fed by a frequency a particular fr^^uc^c^. n ^ ^ -rhe spatial acoustic crossover has equal levels at a location in the space. It is (spectral) divi ^Qurces covering a common frequency range fed by a spatial divider (separate speakers and ^summation single language is used for the analogous features of both types and the related solutions processing channelsj t\ Jjore easily understood. ■ zones are common to both types. A primary goal is to place the acoustic crossover in the coupling flie '""""^Q^iary goal comes into play when coupling can no longer be maintained: Reach the isolation zone ^^vkJ6 asT'ossible Filters accomplish this for spectral crossovers, whereas directional control, splay angle and ae thp snatial crossover. In both cases we strive to minimize the combing and transition zones, sparing manage uic »f HA2 Summation zone progressions Summation zones follow several standard crossover progressions (Fig. 4.22). Let's add A + B and follow them. ■ 1-step (coupling (AB)): Speakers with little or no directional control are in extremely close proximity, eg. subwoofer arrays. ■ 2-step (coupling (AB) to cancellation (AB)): coupling on the front side, cancellation in the rear. This is used in cardioid arrays. ■ 3-step (isolation (A) to coupling (AB) to isolation (B)): Very achievable in a spectral crossover, but much harder in full-range spatial crossovers. As frequency rises we can expect to see more areas fall into the combing and transition zones, with the realistic goal being minimization, not elimination. ■ 5-step (isolation (A) to transition (AB) to coupling (AB) to transition (BA) to isolation (B)): Practically achievable in closely coupled arrays if the coverage angle provides enough isolation to prevent combing. ■ 7-step (isolation (A) to transition (AB) to combing (AB) to coupling (AB) to combing (BA) to transition (BA) to isolation (B)): the full progression. This results when isolation is unachievable before combing begins. In the HF this is often the only practical option. Success can be viewed in terms of the share of the progression spent in the combing zone. A progression with more combing zone than coupling and/or isolation zone would rate poorly. 145 Spectral Acoustical crossover progressions Spatial Coupling Zone Phwe c*»Mov»r I fMM i OOMov»r Isolation Coupling Isolation Zone Zone Zone Isolation I' Transition Coupling Transition Isolation Zone Zone Zone Zone Zone Subwoofer arrays (no isolation zone) Coupled arrays (LF and MF ranges) Coupled arrays (LF and MF ranges) Uncoupled arrays (LF) Coupled arrays (MF and HF ranges) Uncoupled arrays (all ranges) spectral and spatial 146 equal to, PARTI Sound systems 4.3.3 Crossover classifications 4.3.3.1 CLA55 We first classify crossover by the three possible level outcomes to the summation: The crossover range is greater than or less than the isolated ranges of the individual elements (Hg. 4.23). Crossover class • Unity: Level through crossover matches the isolated levels (A + B = 0 dB @XAB). • Overlapped: Level through crossover is higher than the isolated levels (A + B > 0 dB @XAB). • Capped: Level through crossover is lower than the isolated levels (A + B < 0 dB @XAB). 4.3.3.2 SLOPE Crossover slopes are rated by filter order: first order, second order, etc. The slope steepens as order increases For spectral crossovers this refers to filters, whereas for spatial crossovers the separation is related to speaker coverage pattern (tighter coverage being higher order). 4.3.3.3 SYMMETRY We classify crossover symmetry by two possible outcomes: symmetric or asymmetric. Spectral crossovers can have asymmetric filter slopes or filter topologies. Spatial crossovers can be asymmetric by speaker model, splay angles, level and more. 4.3.4 Spectral dividers and spectral crossovers Let's get practical about the types of spectral crossovers we're likely to find in a modern speaker system. We are either marrying two drivers that already live together in the same box, or arranging one for speakers that are just now meeting. DRIVER (A AND B) PHYSICAL CONFIGURATION • Fixed combination: fixed ratio of A and B drivers, known positions, same box. ■ Variable combination: variable ratio of A and B drivers, unknown positions, separate boxes. With fixed combinations we encounter varying levels of manufacturer support. CHAPTER4 Summation Crossover classes Overlap: A + B > 0 dB @ XAB Unity: A + B = 0 dB @ XAB Gap: A + B < 0 dB @ XAB B Crossover slope First-order (6 dB) B Second-order (12 dB) B Third-order(18dB) A\/B Asymmetric slope and level Asymmetric slope B Asymmetric level B Asymmetric slope and level B FIGURE 4.23 Spectral crossover classes, slope and asymmetry Spectral acoustic crossover: Combined acoustic response I Amplitude Spectral crossover region (CouDliacLionel LF only (Isolation zone')'" HF only (Isolation Coupling zone: substantial addition above the component levels in crossover area. Isolation zone: Minimal change. PeaKea amplitude response arojnd crossover due to overlap. This can be equalized. Watched nrase responses at ! crossover combine to create a single ■ seamless response. The spectral crossover point is not easily detected. I ■ Phase responses above and below spectral crossover are isolated and retain their original character. Amplitude Spectral acoustic crossover: Component electronic responses ^ My (Isolation lonel Acoustic crossover Electronic crossover '900 Hz) MfiPOHz) I HF only (Isolation The electronic "crossover" point is , | found 2/3rd octave above the spectral acoustic crossover shown previously. This frequency range has 10 dB of , isolation in the acoustic response due to asymmetry between the drivers. I I I Pfiase ossover«ampie show no individual and combined acoustical and electrical responses Slope responses and levels are asymmetric to compensate for the driver asymmetry. The unmatched electronic phase responses at 900 Hz create the I matched phase responses seen in the previous acoustic measurement. Matched phase responses at the electronic "crossover" area will not ■ ensure an acoustic match.The acoustic| response is the combination of mechanical, acoustical and electronic | responses. 147 PART I Sound systems ELECTRONIC CONFIGURATION OF A AND B CHANNELS FOR FIXED COMBINATIONS • Fixed: Settings are not user settable. • Programmed: Factory presets are loaded into the crossover (hopefully correctly). ■ Suggested: Factory settings are programmed by user into the processor (6 dB more hope required). ■ Figure it out yourself: cowboy time! Spectral crossover analysis of fixed driver combinations can be simply a verification process when factorv-set programmed or suggested settings are used. When no guidance is given we need to evaluate the individual elements and make choices (Fig. 4.24). We also encounter several levels of manufacturer support with variable combinations, but there are many unknowns, leaving us with more need to customize. We will use a typical example, the combination of subs and full-range boxes with a manufacturer-suggested setting of 100 Hz (Fig. 4.25). SPECTRAL CROSSOVER CONSIDERATIONS FOR VARIABLE DRIVER COMBINATIONS ■ Relative quantity affects crossover frequency (e.g. might be two subs with one top or vice versa). The former raises the crossover and the latter lowers it. Level can be adjusted to match at 100 Hz. • Driver efficiency affects crossover frequency (e.g. sub might be less (or more) efficient at 100 1 Iz). The formei lowers the crossover and the latter raises it. level can be adjusted. ■ Driver location affects time offset between drivers (e.g. sub might be closer (or farther)). Delay can be set to phase align the crossover. ■ Driver response differences affect phase offset at crossover. Phase align the crossover with delay. ■ Driver ranges affect the overlap at crossover, (e.g. sub and full range share 60 1 Iz to 120 Hz). EQ can reduce the summation peak in the overlap area or LPF and HPF filters can reduce the overlap to create unity gain at crossover. U3 41 UNITY SPECTRAL CROSSOVER (LF*HF) . The standard unity crossover brings LF and HF sections together a, -6 dB 0- phase offset (Fig^^f™" variety of filter slope and topology combinations that can achieve this. The most straightforward (and pop , topology is the Linkwitz-Riley (L-R). The straightforward feature is that the cutoff f^*^^* point (most other filters use the -3 dB point). If the crossover frequency has already been selected the pro six steps. Quantity effects on crossover frequency ■ *~ A. M \ .XOVR = 100, 140 170,200 Hz V J y M K i f-c 1 \ j | r Full range sr. >eaker i / 1, 2, 3, 4 subwoofers w f \ ( 5 dB/div 32 Hz 125 Hz 500 Hz 2 kHz 8 kHz FIGURE 4.35 Quantity effects on crossover frequency (subwoofers vs. mains) CHAPTER 4 Summation Linkwitz-Riley 24 dB/octave @ 100 Hz LF + HF = Unity XOVr _ 6 dB/div | - 25 Hz 40 Hz 63 Hz 100 Hz 160 Hz Phase \ - -- ' 'I " 1.. y ~60'/div 1 ' ^ 25 Hz 40 Hz 63 Hz 100 Hz 160 Hz FIGURE 4.26 Overlap and unity spectral crossover examples Creating a unity gain crossover ujith L-R filters (LF + HF) • Determine a reference level: 0 dB. • Set both the LF and l IF channel cutoffs to die target frequency (e.g. 1 kHz). • Drive each speaker and observe die acousdc response of each individual channel. • Adjust the relative levels until they match at the crossover target (turn down the louder one). • Adjust the relative phase until they match at the crossover target (delay the earlier one). • Drive both channels together. The summed response should match the nominal level and be +6 dB above the individual responses at crossover. Ihe above holds true regardless of the L-R filter order precisely because the cutoff frequency is die -6 dB point in all cases. Ihe choice of filter order here changes the amplitude response around the crossover frequency but not the frequency itself. If the order is changed (or made asymmetric) the phase offset may need adjustment and die behavior around crossover observed to see which gives the smoothest summation. Other filter topologies (standard LPF HPF Bessel, Butterworth, Chebyshev, etc.) require extra work because they use -3 dB as the cutoff specification. An LPF specified at 100 Hz has the same -3 dB point for a first-order slope as an eighth-order one, but a vastly different -6 dB point. To achieve -6 dB at 100 Hz we will need to set the LPF somewhere below 100 1 Iz, the exact location for which will vary (closer to 100 Hz as filter order rises). The HPF has (MPn"* S'tUaI'0n in reverse- Electronic settings that would appear to create a gap, such as 80 Hz (LPF) and 125 Hz Hm C3n aaua">' create a unity crossover. As filter order rises, the gap between the electronic settings shrinks but i ,„ 7 rea^nes zcra When asymmetric topologies and/or filter orders are used we must be mindful of where each lands * the-6 dB milestone. bating a unitu n ■ ■ Determi. crossover uiith other filter topologies (LF ♦ HF) lSet*™',e a reference level: OdB. lne,°' *e LF and HF cutoffs to an octave beyond the target frequency (e.g. 2 kHz for the low and 500 Hz for ■ Drive eact 'S 'eaves the rrossovcr area free of filter effects for reference. * Adjust th 1 S*?eal- «hlation zone and minimizing combing. discussio " spea'-6 dB, 0 °) + B (>-6 dB, 0 °) at XAB and sums to >0 dB (+6 dB max). Summation XAB and lessens off center (Fig. 4.33). The summed coverage pattern is re-evaluated using gain is '1'^ie^^ center reference. The combination is wider, narrower or the same as individual elements, depending ssover as ta„e (majority overlap narrows, majority isolation widens). Highly overlapped systems might 0Verl"PhCf isolation zone (level offset doesn't reach 10 dB). crossover as on over . never reach the isolatio Creating an overlap spatial crossover tuith A and B speakers Determine a nominal reference standard: 0 dB. " Alternate soloing A and B to find the equal-level location (matched at >-6 dB from the reference level). This is " crossover location XAB (e.g. if the A and B levels are -2 dB then the summation will be +4 dB). . Adjust the relative phase until they match at XAB (delay the earlier one). Drive both channels together. Summed response should exceed the individual levels by +6 dB. ■ If some frequencies are overlapped and others are not, then equalization can be applied to the overlapped ranges (same procedure as overlapped spectral crossovers). 4.3.5.6 GAPPED SPATIAL CROSSOVER (A»B) The gap crossover adds A (<-6 dB, 0°) + B (<-6 dB, 0°) at XAB and sums to <0 dB (Fig. 4.33 again). Summation gain is greatest at crossover and lessens off center (whereas individual levels get stronger). The gapped zone is defined as the area where levels are below the 0 dB reference. Gaps of 6 dB or more are equivalent to off-axis response. Cap crossovers are used to avoid areas such as balcony fronts. 4.3.5.7 ISOLATION BY ANGLE We've looked at bringing speakers together. Now we'll evaluate getting them apart. The first way is angular isolation, othenvise known as splay. This method is implemented in the point source array by aiming the speakers apart in front. A symmetric pair will have a centered crossover, which may be overlapped, unity or gapped. The road to isolation (level offset >= 10 dB) begins at crossover and heads toward the outer edge of the coverage. We reach it first in a gap splay, second in a unity splay and last (if at all) in an overlap splay. The coupled point source has a clearly definable isolation zone: A given frequency has a cenain angle at which isolation occurs, an angle that holds FIGURE 4.35 The unity spatial crossover 11 crossovers over distance. For example, if isolation at 8 kHz begins at 20 ° away from crossover, it will (a) hold the same level isolation over distance and (b) be more isolated at angles further away from crossover. 4.3.5.8 ISOLATION BY DISPLACEMENT The next avenue toward isolation is separation/displacement. Move speakers far apart and they must cover a lot of ground before they can connect. This is an uncoupled array configuration, and therefore will morph through different summation zones over distance. A simple example: Two speakers are placed 10 m apart. If we walk a straight line from the front of A (at 1 m) to the front of B (at 1 m) we will move from isolation (A) to a gap (XAB) to isolation (B). The same path at 20 m in front of the speakers will be constant overlap (and combing). At some distance between we can walk a line and go from isolation (A) to unity (XAB) to isolation (B). In front of the unity line is too close (pre-coverage), and past it is too far (post-coverage). Our goal will be to close the gap at the right place, and conduct damage control on the overlap. Wide spacing of narrow elements would maintain isolation the longest, and close spacing of wide elements the least. 4.3.5.9 ISOLATION BY LEVEL We can shift the summation zone balance by leaving speakers in position and turning one down. The crossover location will move toward the lesser speaker (B). Think of the level reduction as the B speaker yielding territory to A, an asymmetric-level distribution. On the A side we'll see isolation arrive sooner (because B will more quickly fall 10 dB behind), whereas the inverse is true for the B side. 4.3.5.10 ISOLATION BY COMMITTEE All the isolation mechanisms just listed can be brought together to create the desired shaping. We can move them apart, splay them apart and turn one down. The transition to isolation comes quickly for the dominant speaker. For the smaller one, welcome to life as a fill speaker. 4.3.5.11 CROSSOVER DETECTABILITY Hiding spatial dividers is challenging because tire crossover frequency range extends to the upper limits, it's virtually impossible to transition through crossover without some HF combing. Spatial crossovers can have substantial physical displacement, which makes the combing zone volatile. Transitions between high order systems with steep angular slopes may be easily detectable but only in a very small portion of the space, whereas low-order systems will be less detectable, yet spread over a wider space. A classic tradeoff. The most salient contrast to spectral crossovers is that spatial crossovers are detectable only in specific locations. Detectable spectral dividers may be obvious over large areas. Spatial crossovers can be placed on aisles, balcony fronts and other places that render their deficiencies academic. Not so the spectral divider. The spatial divider gives itself away by shifts in angular position. Our ears can pick up localisation clues, vvhlch]|e become easier to spot as angular offset rises. Other clues could be mismatched responses in the crossover art most obvious is when one speaker has I IF range extension well above the other. This must be carefully managni when combining small-format fill speakers with extended VI IF with large-format main systems. The mixer w hear the VHF in the frontfills but the first row surely will. Another clue comes in the form of the relative distance. Close speakers have superior direct-to-reverberant raU^ distant ones. The level of close delay speakers must be minimized so they don't stand out above the dista speaker. 4.3.6 The spectral/spatial crossover Most of the two-way loudspeakers in the world have displaced drivers: I IF next to LF or centered b"W^"sS0Ver woofers. The spectral crossover is also a spatial crossover. LF and HF have a crossover frequency and a cr^ ^ location (Fig. 4.34). The exception is the coaxial design, where the HF driver is centered inside the li which case the displacement is in the depth plane rather than horizontal or vertical). Phase alignment made on the horn axis changes over distance Phase alignment made on the equidistant axis holds over distance FIGURE US'* Spectral/spatial crossover This adds a second dimension to the quest for combing-free crossover performance. The goal is to stay in the coupling zone until we are out of the angular coverage, i.e. spectral coupling until spatial isolation. We return to the isosceles triangle (our representative of the spatial coupling zone and target for phase alignment). We can view the drivers as a spatial crossover and align the spectral level and phase by the unity spatial crossover procedure outlined previously (4.3.5.4). Spatial stability is evaluated by measuring off center of the crossover (above and below or side to side). Observe the crossover frequency range and see if the response holds out long enough to reach the spatial coverage edge. This is best done at a distance long enough to represent real-world applications. This allows the time offsets to settle into the range where the speaker will actually be used. Measuring too dose can make a perfectly functional spectral/ spatial crossover appear troubled. Wl SPEAKER ARRAYS Let s apply our study of summation and the acoustic crossover to the practical construction of speaker arrays. Add two speakers and the sum will depend on their level and phase offsets. Add ten speakers and they will behave exactly as the summation of the summations. The individual element coverage patterns, their displacement, relative Jges and levels drive tire spatial distribution. If we successfully merge the systems at the spatial crossovers, the rest coverage area will become predictable and manageable. All of these factors can be independently controlled in the design and optimization process. Speaker array types 'rademarked°ntradt W°U'd 'ead US 10 believe there are hundreds of different speaker array types, with various have gone the way of th^d" ^ ""^ ^ ^ a"d a" 0theI confiBurations 'hen move W c,lassli> arrays into two families of three types. First we separate coupled from uncoupled and n to angular orientation. A"ayType s^^Une source £U*dP°in. source SSEdestination II- plea "ne source C0uP^ point destination Configuration Speakers together in parallel Speakers together with outward splay angles Speakers together with inward splay angles Speakers separated in parallel Speakers separated with outward splay angles Speakers separated with inward splay angles PARTI Sound systems CHAPTER >t Summation How do we separate coupled from uncoupled? It's harder than you think. The 600:1 ratio of wavelengths these arrays transmit makes the gray become grayer. The easiest way to clarify is by function. Coupled array functions Power gain Radial coverage expansion Radial coverage reduction Uncoupled array functions Radial coverage expansion Lateral coverage expansion Forward coverage expansion Power gain requires coupling zone summation, as does radial coverage narrowing. Radial and lateral coverage expansions require isolation zone summation. The transition zone is the preferred bridge between coupling and isolation whereas the combing zone is to be avoided as much as possible. Let's return now to the coupled/uncoupled question. As an example we have a straight line of eight subwoofers spaced 1 m apart. On top of each is a small full-range frontfill. We have both a coupled and uncoupled array. The quantity of eight subwoofers adds power gain and narrows coverage. The quantity of eight fromfills creates a lateral coverage expansion. If we need more LF power we add subs. If we need more frontfill coverage we add fromfills. If we need more frontfill power we get a bigger frontfill. Coupled vs. uncoupled. Any speaker array can create a coupling zone along the coverage centerline (the isosceles triangle). Closely spaced arrays can maintain the coupling for a substantial portion of the spectrum and the room. Adding space between the elements lessens coupling in both. We can rescale our arrays, but not the size of 500 Hz. We conclude the obvious: Coupled arrays have superior coupling zone behavior. Duh! Once we run out of coupling capability we seek isolation, which we can get by angle, spacing or level. Angle is the most effective and long lasting. Isolation by displacement is effective, but as advertisers love to say "for a limited time only!" Level tapering, on its own, is the most limited, and should be considered more as an addendum to isolation than a primary means. We can use them together to great effect. Which arrays can isolate? The point source is the master of angular isolation. The line source has none. The point destination can provide angular isolation after its beams have passed through the center. This gives it limited applicability. The uncoupled arrays are the winners for displacement isolation. Any array can taper level, but this is not much help without a head start from angle or displacement. Let's look at the scorecard (Fig. 4.35). One array configuration provides extensive coupling and long-range isolation: the coupled point source. It's no coincidence that this is the main array used in most sound reinforcem systems. The coupled point destination can also provide both but runs into mechanical challenges such as spea e blocking other speakers from crossing through to the opposite side. The coupled line source has no effective isolation mechanism. The result is a concentrated beam focused at infinity. Array summation properties Array type Isolation method Summation zones Range Angle j Distance Level LF MF HF Coupled line source No No Coupling Coupling Coupling Unlimited Coupled pt. source Yes No Yes Coupling Isolation Unlimited Coupled pt. destination No Yes Coupling Isolation Unlimited Uncoupled line source No Yes Yes Combing Isolation BSSüS Uncoupled pt. source Yes Yes Yes Isolation Isolation Uncoupled pt. destination No Yes Yes Combing Combing Isolation Short FIGURE 4.35 Array summation properties Speaker array types Line source (0°) All units oriented in parallel No point ot virtual origin or destination Uncoupled Point source (>0°) All units splayed outward to make virtual point source behind the speakers Point destination (d oives rL„ 'S US£ the rest oftnis chapter. This series brings together the summation icons presented earlier 8 them context with the spatial crossover locations. ^J^COUPLED LINE SOURCE sir"pler array toXTcrh^ a"°W Unlimited element quantity at the most limited angle quantity: one. There's no ^"d sour™ :.SC" e' No an8le details, only element coverage pattern, quantity and displacement. The virtus couPled lin sourre is elon ~H ""B'C UCLdlls' only element coverage pattern, quantity and displacement. The virtual rgated, stretched over the array length rather than a single point. The consistent feature of the --f"=u unc source j , alla.v ■cngui wuiti man a single poun. i ne consistent reature ot tne totl1 most a»ra„-S 1 31 overlaP dass behavior comprises virtually the entirety of the system's response. This is crm„r- . ."""active and mntt nm!-----____-T.1________.... .1 . ..... cost of minin most ominous feature. The overlap gives it the maximum power addition, but at the "mum uniformity. order S0Urce' It's a train wrecks 4 ,?' where we see the results of a Pair of fust-order speakers arrayed as a coupled line he only position to enjoy a ripple-free frequency response is the exact centerline: the Summation ^"regression factors lor the coupled line source array, first-order speakers and extremely CHAPTER 4 Summation the result of excessive overlap and displacement. The summation zone progressions move from spatial cr0SS0V^ rj nt jhe combing zone dominates in the 10 kHz range, both near and far all the way to the center *^o^)ing zcme dominates the IF range due to close proximity. e ? h'rd order elements is seen in Hg. 4.38. The individual high-frequency coverage is so narrow that the gap A pair °f1 ir °an^e Seen in the near field. litis quickly gives way to overlap coverage where three beams can be coverage z°"^ anj (wo sjje lobes). Notice the lack of uniformity over frequency, with extremely narrow HF wide LF response (just like the solo element). Summata zone progression factors for the coupled line source array, third-order speakers Quantity vi vbe we just need more boxes. An additional third-order element is added in Fig. 4.39, extending the gap ossover range into two sections. It does little to address the discrepancy between the HF, MF and LF shapes. The com lexity of the triangulation geometry increases with the addition of the third element. There are now multiple triangles stacked together, which increases the overlap with distance, narrowing the coverage angle. We digress for a moment to address the coupled line source's fundamental property: the pyramid-shaped series of coupling zone summations. The pyramid effect comes from the cascading summations (Fig. 4.40). The phase contours of the three elements converge initially into two zones of addition (and one of cancellation). As we move farther away the three phase responses converge to form a single beam, the pyramid peak. Once the pyramid assembly is complete, the coupled array will assume the characteristics of a single speaker: a definable ONAX, a loss rate of 6 dB per doubling and a consistent coverage angle over distance. These milestones aren't found until the anay has fully coupled (the pyramid top), which will make it challenging to place mics for optimization. An eight-way line source pyramid is shown in Fig. 4.41. The foundation begins with tire isolated elements (the gapped crossover) and then continues with seven twoway overlapping crossovers until it eventually converges into a single eight-way overlapped coupling zone summation. The distance to the first pyramid step (the two-way ^mrnation MeP'09ressioi factors for the coupled line source array, change of quantity PARTI Sound systems Summation Coupled line source array: The parallel pyramid 1 kHz, AX spacing, 1 kHz, 3 x third-order speaker 1 x 3-way overlapping crossover 2 x 2-way overlapping crossovers 3 x singles~| Pyramid zones Phase contours add/subtract Pyramid zones & phase Level contours FIGURE 4.40 Parallel pyramid for three elements Coupled line source array: The 8-way parallel pyramid Note: Image »s st-.-;:"--^_ I 1 x 8-way crossover Pyramid zones Level contours (1st 5 zones) Pyramid zones Level contours Pyramid zones & level (Top 3 zones) & level FIGURE 4.4l Parallel pyramid for eight elements ontrolled by the same factors discussed earlier: element coverage angle and displacement. The crossover) is co^ sufCessive step is the same, so the total height is found by multiplying the step height by one less distance to ^ ^ ^ eight-element pyramid height = distance to first crossover « 7). As elements become than the e e ^ ^ displacement increases, the step height multiplier extends. Because directionality is variable more directio^ ^ pyramid step height will vary over frequency, which when multiplied can create vast differences £S3ape over frequency. ■ ■ wide speakers yields less width. Combining narrow speakers yields more narrowing. The more the Combining ^ e|ement starts with wide LF and narrow HF, the array response will end up the same way (relatively PalT 120°). Let's start with two elements spaced 1 ms apart. Start with F = 33 Hz (T = 30 ms). The phase offset is 1 /30 A (12°). We win. Next: F = 333 Hz (7 = 3 ms).The phase offset is 1/3 (120°). It's a tie. Things don't look good for 3333 Hz do they? We can't beat the phase offset, which maxes out at 1200°. How about level? Bear in mind that our maximum phase offset (1200°) is along the non-coupling line, which is 90° off axis from crossover. If our speaker has less than 180° of coverage it won't make it to the 90° finish line with enough level to win. The critical location is the radial angle that corresponds to 120° phase offset. The answer for 3333 Hz is ±10° as shown back on Fig. 4.21. A displacement of 3 X creates 120° phase offset at the radial 10° mark (relative to center between the elements). Raise the frequenq' an octave and we have only ±5 ° to work with. The same thing happens if we double the displacement. We've established a sliding scale. For a given displacement we can neutralize the combing zone damage by proportional reduction of the coverage pattern. We maintain our position if we halve the coverage as we double the frequency. It should be obvious that the advantage in combing suppression is balanced by a senous side effect: radically different coverage over frequency. But this is the fate of the coupled line source if it Plays with wavelengths too hot to handle. If we keep it on the down low, in the heart of the coupling zone, we can leave coverage out of the equation. But if we keep wide coverage all the way to the top end in a coupled line source we will pay the price. = 0.33 x T) where T is the displacement in ms. ' = 110 Hz. Coupled line source conclusions • Coupling frequency limit is set by element displacement (FLIM = ■ Wibl mS d'Splacement (about 1 m), FLIM = (0.33 x 0.003). P" display C°m','n^ effects can be reduced if the coverage pattern narrows as phase offset rises (due to acement). The maximum comb-free coverage angle = 60°/X displacement. Example: Two sources 4 X apart ' InisanmaXlmUmc0vera8ean8leon5° (60°/4). y type works for subwoofers but has severe limitations above that range. SOurce, but the6 ^ COnc'us'on mat eliminates first- and second-order speakers from contention in the coupled line (560° wide) can1'1SS1Ve commng we saw in Figure 4.37 should help to alleviate any doubts. First-order elements to 3 \ Thats q j., exceed 1 /. displacement. Second-order speakers range down to 20° wide, which corresponds speakers. This |eav ms at ' ^ k] lz (as long as these six words). These elements must be very closely spaced small Pattern as frc es us w'm Proportional beamwidth third-order speakers with their ever-narrowing coverage c°verage over fr ^'lere are no rooms that get narrower as frequency rises so this will not provide uniform couPling (povver en0)'' ' 'le '''ird-order proportional beamwidth element does have two things going for it: lots of Sam) and the highest tolerance to overlap. We'll soon put it to use by adding some splay. PARTI Sound systems 4.4.2.8 COUPLED POINT SOURCE The coupled point source approaches arrays from an entirely different angle (one that's not 0°). Adding spla, to the equation enables an isolation mechanism that opens up many possibilities for variable array shapes \v mix speaker orders, splay angles and levels for shaping. The coupled point source has one feature no other ^ type can duplicate: maintaining a unity class crossover over extended distance. It's not automatic, and is variab? over frequency, but no other array can duplicate this for even a single frequency. The coupled point source is the steady long-distance runner. If the coverage angle remains constant over frequency, so will the unity class rrossove That's what we call uniformity of coverage. The gap, unity and overlap areas are all angularly defined and maintain their character over distance. Let's begin with a first-order pair (90°) at unity splay (Fig. 4.42). The summation zone progression originates at XOVR (coupling zone) and reaches isolation after a brief stay in the combing zone. The progression maintains its angular qualities over distance. Isolation zone behavior is visible in the HF response. The displacement is small enough to limit the MF disturbance to a single -9 dB null before breaking into isolation. The small displacement keeps the I.F range entirely in the coupling zone Note the overall resemblance of the HH MF and LF shapes, indicative of a similar frequency response across the 180° coverage arc. Next is a second-order (40°) pair at unity splay (Fig. 4.43). The zone progression is more angularly compressed than the first-order pair. Isolation arrives more quickly due to the steeper spatial filter slope of the second-order speaker. The 40° splay angle results in 0% overlap (unity) @10 kHz, creating a combined shape of 80°. Coverage is highly overlapped at 1 kl Iz (100° elements at 40° splay), creating more combing and a much wider combined coverage angle of around 140 °. The LF response is simi lar to the first-order scenario. Next is a third-order proportional beamwidth element with an I ir unity splay of 8° (Hg. 4.44). A notable feature of this highly directional element is the visible gap in the near-field HF response. Farther away the crossover has reached unity which will hold out for an extended range. Recall that the third-order system has the highest LF/MF/HF coverage angle differential, which reduces the unity splay range to a small minority of die spectrum. The overlap percentage exceeds Zone Progression " Crossover Line Summation zones: Coupled point source array Speaker order effect: First-order speakers @ 90° 1/24th octave 2 x first-order @ 90" 12 X 12 meters Zone key Oms I J FIGURE W.Ue Summation zone progression factors for the coupled point source array, first-order CHAPTER4 Summation ... Zone Progression Crossover Line Summation zones: Coupled point source Speaker order effect: Second-order speakers @ 40" 1/24th octave 2 x second-order @ 40' 12 x 12 meters Transition, isolation Off axis. Xover FIGURE 4.43 Summation zone progression factors lor the coupled point source array, second-order 167 ^•""izone 'tactorsforthe coupled point source array, third-i 3'ds- PARTI Sound systems 168 «■ Zone Progression Crossover Line Summation zones: Coupled point source Overlap effects: 0%. 50% & 75% overlap (first-order) 1/24th octave 2 X first-order 12 x 12 meters FIGURE 4.1*5 Summation zone progression factors for the coupled point source array, overlap effects 90% @ 1 kl Iz, resulting in a null depth greater than 20 dB. The presence of midrange combing does not eliminate this array from consideration. We will see, later, that an increased quantity of elements will have strong effects in highly-overlapped arrays. For now we return to the ratio of LF/MF/HF coverage, where we find that the two-element array has decreased the disparity over frequency. The combined coverage shape widens the 1 If (dominant zone is isolation) and narrows the I.F (dominant zone is coupling). The combined ratio can be represented by this approximation: Vi If/ MF/2 x HE As we will see in Chapter 9, this will be the guiding principle in third-order speaker applications. We now focus on the percentage overlap effects in the HF range of a first-order speaker (Fig. 4.45). The isolated (0% overlap) version from Fig. 4.42 is included for reference. The other panels show the response with 50% (45° splay) and 75% overlap (22° splay). The trend is obvious: The overlap percentage is equal to the proportion of the coverage that is in the combing zone, with the remainder being in the isolation zone. Overlap PercenIa^fi] must be carefully controlled whenever displacement is large relative to wavelength. Overlap is most effective w coupling is maintained via small displacements and angular control. Summation zone progression It's possible to make the run from coupling to isolation without combing, but we shouldn't admit defeat the full seven-step summation zone progression. We can minimize the combing near crossover but can j_a^/g eliminate it. The isolation zone is largest with a unity splay crossover. As speaker order rises, the spatta ^ steepens, increasing the percentage of coverage in the desired zones (coupling and isolation). It s a race angular isolation provides level offset relief when we get in phase offset trouble. We can use any speaker or choosing to divide the pizza into large or small slices. 4.14.2.3 COUPLED POINT DESTINATION We don't need to spend much time on the coupled point destination array Its acoustical behavior is angu similar to the point source, but with a forward focal point. The location where the speakers cross (the^^nd* destination) becomes the substitute point source. It's the same principle as a concave mirror. The chie CHAPTER 4 Summation . destination are mechanical and practical. There isn't a vortex disturbance in front of the speakers the coupled pom se|£Cte[j on|y unc]er duress, like an I-beam is blocking the hom of a point source as some mig ^ ^ ^ welding torch or invert things and make it a point destination that can reach the audience. For the coupled point destination array tonally equivalent to the coupled point source (splay angle, frequency, etc.). " Risk of reflecting off neighboring elements rises with quantity and overall splay. " ble to array beyond 90 ° because elements are aimed through other elements. " torn driver placement at the cabinet rear creates unfavorable geometry. Point destination arrays usually have " higher displacement than their comparably angled point source counterpart. Preferable only when physical logistics win over the point source counterpart. 4.4.3 Uncoupled arrays We now add the second isolation mechanism: spacing the speakers apart, i.e. uncoupling. We pay a price in power gain but add shaping capabilities not present in the coupled arrays: lateral and forward extension. Uncoupled arrays n st be evaluated in progressive stages over distance, lhe elements begin as clear soloists and then make duos, trios and entire choruses. As we'll see, sweet harmony often ends at the trio and gets worse from there. RANGE PROGRESSIONS FOR AN EXTENDED SERIES OF UNCOUPLED ELEMENTS ■ Pre-coverage: isolation (A) to gap (XAB) to isolation (B) and onward. ■ Unity line: isolation (A) to unity (XAB) to isolation (B) and onward. ■ Limit line: isolation (A) to overlap (AB) to overlap (ABC) to overlap (BCD) and onward. ■ Post-coverage: overlap (AB) to overlap (ABC) to overlap (ABCD) and onward. The pre-coverage range is used for fill speakers in singular areas. The unity line maintains consistent coverage by the principle of the unity class crossover. The limit line indicates where multiple paths with differing time offsets give the combing zone the majority. The most uniform coverage area lies between the unity and limit lines. In practice IN design uncoupled systems to transition coverage to others at the limit line. Beyond the limit line are the tall weeds of the combing zone. I he locations for these milestones are influenced by element coverage (speaker order), spacing and splay. Narrow speakers push the start points deeper, as does wider spacing and outward splay. Wide speakers, closer spacing and inward splay hasten the progression. Fhe range progressions show a clear favoritism for speaker order. Hide's advantage to having all frequencies Progress through the zones together. We don't want the LF and MF ranges to be in post-coverage combing when the frequence '1'ts tne univf "ne- The ideal uncoupled array element would have a flat beamwidth over the entire *l can 'an8e- This is unrealistic but we can dream, eh? In practical terms, we seek the longest beamwidth plateau element^' 'S 'S stall^ar^ operating procedure for first-order speakers. They are, by far, the favored uncoupled narrow t ^ sma" formats. Second-order speakers have a greater challenge. A long beamwidth plateau at a barrier to travTh"/08 3 'lorn' ^Ve m'gnt see these as festival frontfills that have several meters of open security starter hen travel before hitting the audience. Don't expect to see them at Wicked. ihird-order speakers are a non- ^•3-1 UNCOUPLED I WavekngrJiPdoes'ne S°UrCe ^eTS fxom its coupled cousin in scale only. That's not a small detail, however, because triable performa' SCa'e ^ couP'in8 of tne parallel pyramid will be restricted to the LF range. Expect highly couPling as fr= anCe a',Hve that. An uncoupled array has a continuum of behavior, with tendencies toward S as frequency falk a„,i _____\, L. r _ _ ... Web, I LINE SOURCE uency falls ancj isolation and combing as frequency rises. le&nwitht --v-i vj| e coupled point'S ^raSt'ca"^ different over depth, a standard feature of all uncoupled arrays. This contrasts n°rizontal themes h°t ^"a ^lrst"ora-cr elements with 3 m spacing (Fig. 4.46). Notice that the response has repeating wrth the source array, which held its angular shape over distance. The gap zone is visible in the 169 PARTI Sound systems CHAPTER I* Summation Zone Progression * Crossover Line Summation zones: Uncoupled line source Distance effects: First-order speakers @ 3 m spacing 1/24th octave 5 x first-order @ oe 12 x 12 meters Zone key 0.1 ms j---^Jj 1.0 ms ^ • —j 10 ms [ ^-j Off axis, Xover FIGURE 4.46 Summation zone progression factors lor the uncoupled line source array, first-order speaker near-field HF response. The first summation zone progression is the unity class crossover line, which alternates between isolation at ONAX and coupling at XOVR, with transitions into combing between. Positions along this line enjoy the highest uniformity and immunity from ripple. We lose die isolation zone as we move deeper into the shared coverage of two or more (or more again) speakers. The multiple paths created a cascade of combing zone summations. Recall the multiple levels of the parallel pyramid. They are back, but in this case they decimate the response with combing rather than concentrate it with coupling. The weave becomes increasingly dense as we go deeper, with peaks and dips that vary with frequency and location. Maximum uniformity over the width is found in the range between the unity crossover line and the limit line (the depth where three elements converge). Combing becomes increasingly dominant beyond the limit line, which means we need another system to takeover the coverage. The relationship between the unity line and limit line is simple for the line source (assuming ma'c elements and spacing): The limit line is double the distance of the unity line. If we close the gap in 2 m (unity i then we want to end the party at 4 m (the limit line). Let's turn to the I.F response where we can see the para e pyramid, evidence that our spacing is close enough to maintain coupled line source behavior in this range. Let's change to a second-order element, which extends the distance to the unity line and enlarges the gap area. for the I IF range (Fig. 4.47). The MF response (and the MF unity line) is the same as previously, which "^"^j1^ transitions are now progressing at different depths. The MF range is already overlapped before the F1F has c'°.s[entover gap. The easiest way to keep the unity line consistent over frequency is to build it with elements that are con frequency (i.e. a flat beamwidth over a wide range). 'I his carries through for all of the uncoupled array con gu 1 1TÍ2 4.48)- Round three features a horn-loaded second-order system with increased 1 IF and MF directional contro I This extends the crossover progressions in both the HF and MF regions at nearly the same rate. The uni ^ coverage area (between the unity and limit lines) starts later and has greater depth extension than the rs system even though the displacement is the same. First-order elements with an extended beamwidth plateau are well suited for uncoupled line source app ^j^-ord" Second-order systems can also work well provided their directional control extends below the HF range, elements are unsuitable because of their inconsistent shape. . Zone Progress""1 . Crossover Line Summation Zones: Uncoupled line source Distance effects: Second-order speakers @ 3 m spacing 1 /24th octave 5 x second-order @ 0° 12 x 12 meters Zone key I TwHz |""t Coupling """I FIGURE 4.47 Summation zone progression factors for tie ixoupled line source array, second-order speaker -i^Xover pt0gressionfactors for the uncoupled line source array, second-order horn-loaded speaker ■ CHAPTER 4 Summation 172 4.4.3.2 UNCOUPLED POINT SOURCE The uncoupled point source utilizes both isolation mechanisms: angle and displacement. It doesn't share the foremost feature of its coupled counterpart. It can't maintain a unity class crossover over infinite distance Think about it. LInity splay in a coupled point source makes the edges touch, forever. Pull them apart and there's a e forever. A 3 m displacement and a unity splay angle means they'll never meet (always 3 m apart). It's one way to handle a center aisle! If we want unity somewhere we'll need some angular overlap to compensate for the source displacement. Once the gap is closed, this array will have a greater working depth dian a comparably spaced uncoupled line source, because it takes longer for the third element to reach die first (the angles are twice as far apart). The design process includes strategic placement and splay to achieve the desired unity and limit line positions (covered in section 11.5). We begin again with first-order speakers and resume our 3 m spacing. In the first scenario (Fig. 4.49) we splay the elements with 75% overlap, which extends the gaps and the unity line depth beyond that of the line source. The central area is the most affected because it becomes triple-covered by the middle of the panel. Another notable effect here is the correspondence of the I.F response shape to that of the MF and HI shapes over distance. The three ranges have similar overall contours at die unity line (a combination of displacement and angular isolation). The IF response narrows beyond that as it resumes its coupled pyramid behavior. The second scenario opens the splay angle to 50% overlap (Fig. 4.50). A large isolation zone dominates the HF response panel. The outer elements will never meet because they are angularly isolated and 6 m displaced. 4.4.3.3 UNCOUPLED POINT DESTINATION The isolation roads are angle and displacement. The uncoupled point destination turns the angle inward, giving us "reverse isolation." Our countermeasure is displacement. The uncoupled point destination is the most spatially variable array type and yet a necessary tool for us. Variability rises as we turn the angles inward, reducing our usable coverage range. Zone Progression Crossover Line Summation zones: Uncoupled point source Distance effects: 75% source overlap (22"). first-order 1/24th octave, 3 x first-order @22" 12x12 meters FIGURE 4.49 Summation zone progression lactors for the uncoupled point source array, first-order, 75 /»overlap Zona Progression Crossover Line Summation zones: Uncoupled point source array Distance effects: 50% source overlap (45°), first-order 1/24th octave, 3 x first-order @ 45° 12 x 12 meters FIGURE 4.50 Summation zone progression factors lor the uncoupled point source array, 50% overlap A symmetric uncoupled point destination has its most uniform response in the isolated pre-coverage area, where speakers arc more soloists than array elements. Infill speakers are like diis. Each covers its side and we hold our nose at center. I >"n i you just love that the critics always sit there? Another symmetric version is left and right mains (if fumed inward and run mono). The most well-loved symmetric form is the monitor sidefill. Will it make you feel better, or worse, to know this configuration has the statistically highest possible spatial variance? There is a worst-case scenario and this is it. Ihc most common asymmetric version is the main + delay speaker combination. The coverage patterns overlap so t e isolation mechanism turns out to be asymmetric level (the delays drop off quickly due to their short doubling ance). They meet at crossover but can continue to be dose in level only for a limited range. Other asymmetric rsions include various arrays of arrays (e.g. joining the mains to the frontfills in the third row). pattem" * f'rSt_order Pair facing 45° inward (Fig. 4.51). The unity crossover (XOVR) is found where the couplin^ofimerSea destmaUon)' Dut th's must be a different kind of unity. The other arrays have coupled *e have* ° °'TAX edges together to build a unity crossover to match the isolated ONAX locations. In this array this breed'of™1'''''11^ ZOne at ,rie on"axis center line and the isolation zone seems to have disappeared. What is distance ben ""'^ crossover referenced to? Unity compared to where? The unity location (ONAX) is found half the een 'he speakers anH yovd wk.,7 \u-------— - =-------- - J Mnesummat as it gets for js i v......«^vx... 1»..».. uy uic iwcai speaker, so inis will DC as gc "able and the XOx" rcs'10r's<' Some familiar behaviors are present: The isolated area (ONAX) is the most (combing) but doe 3rea E 'eaSt' Movement between XOVR and ONAX changes the distances between the sources not necessarily give us isolation by angle (we may still be in the coverage of both speakers). '"■"mation^^'^^nce points on our map, we can begin to analyze the spatial qualities of this array. The ^"ters around ON>AX^I'eSSmu'''P'e mrect'°ns outward from the crossover point. Our area of principal concern standard sum •' ^ C3n ^lnd an8u'ar'y related off-axis points from here that will define the coverage edges. and ^'ond XOVR3"0" pro£ression ""Ids when traveling between ONAX and XOVR, albeit highly combed. The 18 wild country dominated by combing. —ween the sn«i cumpaieu io wnerer ine unity location (ONAX) is found half th ( dB 6 dB we lose I,™u X°VR" WHy? W" retUm l° inVCTSe SqUare law: Double the distanre and '"on The miri " , mld_Point (ONAX) and the crossover (XOVR) will be returned to us in couplim ition should be dominated in level by the local speaker, so this will be as good PARTI Sound systems •■• Zone Progression •••• Crossover Line Summation zones: Uncoupled point destination Angle effects: 45° between sources 1/24th octave, 2 x first-order @ 45° 12 x 12 meters Zone key Oms j j Coupling 0.1 ms| yd 1.0 ms Transition, isolation Off axis, Xover FIGURE 4.51 Summation zone progression factors for the uncoupled point destination array, 45° angle effects We can increase the inward splay angle to 90° (Fig. 4.52). As we approach one speaker we are moving perpendicular to the other. Our reference points are the same: mid-point (isolated) and crossover (coupling). The angular change has a muted effect between our two reference points but has a very pronounced effect on the surrounding areas. As the angle rises, the rate of response change in the peripheral areas increases proportionally-Additionally the proportion of areas with redundant and highly displaced MF and HF coverage rises, creating wore case scenario combing. Combing becomes even more widespread with a 135° inward angle (Fig. 4.53) and finally we reach the most inward angle of all: 180°. This array has the dubious distinction of having the most rapid movement into the combing zone and the least prospect of escape. If we are within the coverage of one element, we are within the coverage of the other. It's guaranteed. The rate of change is the highest because a movement toward one ele de facto a movement away from the other. We move on to the asymmetric version of this array. A common application is the delay speaker com|5'"eC^'e' the mains (Figure 4.54). The speakers are displaced, yet have the same angular orientation, so "on axis is ^ line for both. The delayed speaker is turned down in level, which gives us a range for unity combination. ONAX reference is forward of the delay, and depends on exactly where we want it to be for the aPP''catl°!^£jje c set the level so that the patrons in the delay area (XOVR) have matched combined level to those in the mi^ ^ the hall (isolated mains coverage). Time offsets begin to accrue and combing zone interaction takes its ^ move away from XOVR. Level asymmetry limits the range of combing zone interaction as we depart the cro area because the main speaker retains level dominance over most areas, due to its longer doubling ^'St3^y combing is inevitable in any case, but, like its symmetric counterpart, rate of change is highly influence ^ angular relationship between the sources. Fig. 4.54 shows the relationship of angle to rate of change for The proportion of combing zone interaction rises as angle increases.