How to build end-fire arrays, a variation on gradient arrays
In our last article we covered the basics of gradient arrays, now we’ll build on that knowledge to look at end-fire arrays.
Here, in Fig 1, we see two sources separated from their acoustic centers by a distance D and a delay has been applied to the forward cabinet, this delay is equal to the propagation of sound over distance D. The arrow shows the direction of propagation. The idea is as the wave-front arrives at the front source, there is addition. In the opposite direction the delayed signal causes cancellation.
Fig. 1: Source Configuration
If we set the distance D to be equal to say 1.0 meter (40in) grill-to-grill, then the delay time will equal 2.9 ms and we will obtain directivity patterns as shown in Fig 2a, 2b, and 2c.
Fig. 2: End-Fire Polars (a 31Hz, b 86Hz c 125Hz)
The one meter spacing clearly shows the null point at 86Hz which equals the ¼ wavelength
(1.0m =344hz /4 = 86Hz) changing this spacing/delay time will allow us to control the directivity of this array.
Adding more elements to the array gives us greater control, the next example is a standard end-fire array (See fig 3), using 4 elements.
Fig. 3: Standard End-Fire Configuration (Mauricio Ramirez)
This configuration is usually setup as in Fig. 4a either in single elements or vertical stacks Fig. 4b
Fig. 4: Array Setup
In the first example we are going to space them 1 meter separation (40in) grill–to-grill and the delays will be 0ms, 2.9ms, 5.8ms and 8.7ms from the back (0) to the front (8.7) and the responses are shown in Fig 5a, 5b, and 5c.
We’ll call this the Standard-End-fire array, notice it’s about an average of 90 degrees spread but goes long distances.
Fig 5: Standard End-Fire Spaced 1m at (a) 31Hz, (b) 63Hz, and (c) 125Hz
The next configuration varies the spacing between elements using “borrowed” antenna theory and logarithmic spacing of 0.85m, 1.0m and 1.4m and delay times of 0ms, 2.4ms, 5.3ms and 9.4ms. (See Fig. 6). We’ll call this Log-Spaced End-Fire Array.
Fig 6: Log-Spaced End-Fire Configuration (Mitchell Hart)
Changing to this spacing and delay times broadens the front coverage pattern (See fig 7a, 7b, and 7c)
Now notice that the coverage opens up to about 110 degrees but the wave front has flattened and we’ve lost a little “throw.”
Fig 7: Log-Spaced End-Fire Polars (a) 31Hz, (b) 63Hz, (c) 125Hz
The final variation is shown in Fig 8, here we have kept the same spacing but varied the delays using logarithmic spacing of the intervals, the new delay times are now 0, 1.8ms, 4.0ms, and 7.1ms, we’ll call this Log-Log-Spaced End-fire Array*.
Fig 8: Log-Log End-Fire Array Configuration. (Mitchell Hart)
Fig 9a, 9b, and 9c shows the polars and we can see a broadening of the pattern again at the expense of throw distance, but we’re out to about 125 degrees now.
Fig 9: Log-Log-Spaced End-Fire Polars (a) 31Hz, (b) 63Hz, (c) 125Hz
Next time we’ll discuss broadside arc-delayed arrays
Assuming Omni-directional sources and anechoic conditions –YMMV – always verify coverage with measurements to avoid Mister Murphy’s first law of “unintended consequences.”
*If you make them – you get to name them!
About Martyn “Ferritt” Rowe
Industry veteran and OSA’s Director of Engineering Services Martyn “Ferrit” Rowe brings nearly three decades of real-world experience in live event technical services. Ferrit most recently came from Martin-Audio as the technical training manager for MLA, and uses his vast knowledge and expertise of the multi-cellular technology to support client projects as well as support and train engineers and technicians.
Ferrit began his career running cables on a Thin Lizzy “Live and Dangerous Tour,” and then taking on the roles of running monitors, front of house, and system technician for some of the most popular acts in music, such Judas Priest, Ozzy Osborne, Black Sabbath, The Police, KISS, The Who, Elton John, Poison, Bon Jovi and Van Halen.
Ferrit’s training career began in 2000 when the first of the line array’s from V-DOSC emerged and became an instructor on the line array theory and continued that path with various systems over the years before joining the Martin-Audio MLA division, and then bringing his knowledge and expertise to OSA International, Inc.