((NOTE: My usage of the term “PA system” in this section of the site is solely in reference to installed low-power multi-room/whole-building intercom/paging systems, as often used in school buildings and retail facilities. This equipment has little to do with the type of high-power single-area, often mobile, “PA system” used by musicians and entertainment venues. That’s a topic for another day and another section of the site.))
“distributed” intercom/public-address systems
The popular manufacturer, Bogen, published an informational document, Loudspeaker Installation Methods and Connection Techniques, that very effectively describes the basic design principles behind these systems. I highly recommend that you read it. Right now. Seriously; go read it and then come back. (Note: please tell me if Bogen no longer offers this document so I can upload it.)
Done? Okay, now I will add a few points that I have figured out along the way:
The line-matching transformers are the worst sounding components of the system, from a high-fidelity music program standpoint. This distortion is caused by the limited bandwidth of the transformers themselves, or failure to pass high and low frequency content. (The above document hints at this, but I’ll say it straight.) Physically larger transformers (especially when compared to similarly rated models) have wider bandwidth—and, therefore, will sound better (at a given output level).
Why do I still use a 25v line rather than 70v? Because you can use more common 70v transformers on a 25v line, but not the other way around. Therefore, the 25v line standard is better suited to smaller hobby/home systems, in my opinion.
A 70v transformer will draw about one-eighth of its marked power when connected to a 25v line. More technically, there exists a 9dB offset relationship between the two system types—the rated power is halved three times for a given impedance (going from 70v to 25v lines), in other words. For example, I use Atlas HT-82 (25v rated) and HT-87 (70v rated) transformers on a 25v line. An HT-82 gives 8-, 4-, 2-, and 1-watt taps, and an HT-87 gives 1-, 1/2-, 1/4-, and 1/8-watt taps, in this case.
a quick calculation for a distributed PA system (for beginners)
Rule #1: Doubling the power of a signal increases the Sound Pressure Level (SPL) of a speaker by 3dB (three decibels), and halving the power reduces the SPL by 3dB. Therefore, transformer taps are usually provided in 3dB steps. Also, increasing the power ten times produces a 10dB higher SPL, and vice-versa.
Rule #2: Doubling the distance of a listener from a speaker reduces the SPL he experiences by 6dB, and halving the distance increases the experienced SPL by 6dB. Also, increasing the distance ten times decreases the experienced SPL by 20dB, and vice-versa.
Let’s say we have a PA head with various program sources, monitored by a VU meter, containing a high-quality amplifier (Dukane 1A3000-series or equivalent). The background music program peaks at –15dB-VU, the timed chime signal peaks at –10dB-VU, and pages peak at 0dB-VU, on average.
The amplifier is adjusted with a sine wave tone to deliver 8.84 volts RMS at 0dB-VU into a 25v line, thereby giving 9dB of headroom. Note the following chart:
volts RMS signal level volts RMS
25 0dB 70.7
17.68* –3dB 50*
12.5 –6dB 35.35
8.84* –9dB 25*
6.25 –12dB 17.675
4.42* –15dB 12.5*
3.125 –18dB 8.8375
2.21* –21dB 6.25*
There exists a small quiet room (with no reflections or other real-world acoustic oddities!) in which we will place a speaker in a wall-mount cabinet. A listener in this room, approximately six feet directly in front of the speaker, desires to hear the music program at “about the level of normal conversation”—let’s say 65dB SPL.
The speaker will be an Atlas-Soundolier C10AT82 set. The C10A driver is rated at 94dB at 1-watt/meter, the HT-82 transformer is rated for an insertion loss of 0.6dB, and our long wire run introduces some loss; so let’s say the set has a sensitivity of 93dB at 1w/m. In other words, when our program source reaches 0dB-VU, with the transformer tapped at 1-watt, we should be able to measure an SPL of 84dB at a point one meter in front of the speaker.
With our music program at –15dB-VU, the transformer taps can allow the speaker to deliver the following SPLs at two meters: 72dB, 69dB, 66dB, and 63dB. Therefore (as 6ft and 2m are functionally equivalent), we will use the 2-watt tap to deliver the desired sound level of the music program. This same listener will experience pages at an average peak SPL of 81dB.
There exists a rural residence with an outdoor horn loudspeaker mounted on the side of an antenna tower overlooking the garden area. It is desired for the chime to be recognized over noisy small engines in the garden about 30 feet in front of the speaker, but for the highest signal level to not exceed a negligible level at the property line about 400 feet away.
The speaker is an Atlas-Soundolier WT-15T, a “full range” two-way coaxial horn, rated to deliver 117dB at 4 feet with 15 watts of signal through its internal 70v transformer. On a 25v line, the maximum tap would be about 2 watts, and the maximum SPL would be about 108dB at 4 feet.
Using our derated 25v system above, the loudest tap would deliver a page/chime/music at about 81dB/71dB/66dB to the garden and 59dB/49dB/44dB to the property line.
Unfortunately, nothing other than a yelled page is likely to be heard over even the nicest tractor in the garden; but, fortunately, music at this level is unlikely to even be detected by neighbors who are at least twice as far away as the property line. Of course, the actual measured value at the property line would be much lower than stated, as the speaker is aimed down at the garden.
NOTE: The above calculations were made very quickly to demonstrate the kind of “controlled fun” one can have with this type of equipment. I don’t think I invented any new laws of physics here, but I might have—error-check me, please! And, the phrase “but it’s only 60dB (see, look at the meter)” will not keep your neighbors from hating you. Please be advised: tap responsibly.
This section of the site is currently in the planning phase; please check back later. For now, enjoy a view of my PA system head console from a few years ago: