Straightforward Approach To Setting An Optimized Audio System Gain Structure

Over the years I’ve seen many haphazard approaches in establishing gain structure through a sound reinforcement system.

Often rough adjustments can be made to make the problem less apparent, because gain is easily and cheaply available in today’s industry.

Years ago, when a 100-watt power amplifier was used to power the main loudspeaker system, gain structure was a critical issue. Today, with the advent of amplifiers that can output levels of 1,000 watts or more per channel, proper gain structure can be easily overlooked as a critical element in the performance of a system.

Powerful amplifiers, however, are not an excuse for an individual to lack a firm understanding of proper gain structure. Many of today’s signal processors and amplifiers have jumpers, switches, or knobs that, if adjusted properly, will maximize the systems signal to noise ratio while also ensuring the system will safely operate at the levels that are required.

First we’ll determine how much gain is required throughout the system, from the console to the listener. Then, once overall gain requirements are known, we can discuss the approach to setting the system’s gain structure.

How much gain is enough?

A good designer will always have an established sound pressure level (SPL) criteria for each system in which he/she is working on. Without this pre-determined resultant SPL, you may often find yourself over or under specifying the total gain required in a system.

So, let’s establish a criteria for the purpose of discussion. We will assume that we are designing a sound system for a church that has a contemporary music program. During the music portion of the program, it is anticipated that peak levels in the room need to reach nominal levels of 95 dB SPL, with peaks of 101 dB. It is also the intent to provide 10 dB of headroom. Our design criteria is now determined, and we can begin our discussion of gain structure.

The first thing to determine in the system is the amount of loss due to distance. For the purpose of our example, let’s assume that the furthest distance a listener will be from the speaker is 80 feet. Because sound radiates spherically, the attenuation is proportional to the square of the distance from the source, and thus there is a 6 dB reduction for each doubling of distance.

Assuming that the sensitivity of the loudspeaker is given in reference to 1 meter, this can be represented mathematically by the equation:

(Equation 1) SPLdist-loss = 20 log (distance in feet / 3.3)

The 3.3 factor is used to convert feet to meters. Using this equation, we determine there will be a total loss of 28 dB as a result of distance. We can now calculate the maximum output level of the loudspeaker that we will require in order to achieve our design criteria.

We have already determined that we need a maximum SPL level of 111dB at the listener position (101 dB peaks with 10 dB of headroom). At the loudspeaker we will need a maximum SPL level of 139 dB (111 dB at the listener position + 28 dB of loss due to distance.)

The selection of the loudspeaker is the next step in the process. Any loudspeaker that is specified will have a sensitivity and a maximum power rating. The sensitivity is normally given in dB SPL at 1 meter when a 1-watt signal is applied to the input of the loudspeaker, and is usually given in AES watts.

This AES measurement is a clearly defined standard in which a band of pink noise from 125Hz to 8Khz, with +6 dB peaks, is applied to the input of the loudspeaker for a period of two hours. Any loudspeaker that has its power rating in AES watts can very easily handle short-term peaks of +6 dB above the AES rating.

The maximum output level at 1 meter away from a loudspeaker will be derived from the formula:

(Equation 2) SPLmax-AES = sensitivity + 10 log (AES power rating)

(Equation 3) SPLmax = sensitivity + 10 log (AES power rating) + 6

Any loudspeaker we select must have an SPLmax of at least 139 dB. We will take one particular manufacturer’s loudspeaker that has a sensitivity of 112 dB at 1 watt/1 meter. The high frequency component can handle 200 watts, AES. Using the equation above, we find that the SPLmax equals 141 dB. This loudspeaker will have the ability of achieving our design criteria.

To complete the design, we must choose the correct amplifier size for the application. Amplifier power ratings are given in watts, but unlike loudspeaker AES power ratings, amplifier power ratings are the upper limits and do not include any crest factors.

For the purpose of discussion, let’s assume that we have a 3-way loudspeaker system (loudspeakers with high, mid and low sub-sections), with the following AES power ratings and sensitivity ratings:

**Loudspeaker Sensitivity & Power Ratings**

Loudspeaker—————————Highs———————Mids————————-Lows

Sensitivity———————————112————————-109————————101

AES power rating————————200————————-400———————-1000

Peak SPL———————————141————————-141————————137

(Using Equation 3)

The high and mid sub-sections of a single loudspeaker can handle the minimum SPL requirements of 139 dB at 1 meter. However, the low frequency sub-section will require two loudspeakers.

And then, by doubling the number of loudspeakers, we will obtain a +6 dB gain, which results in a low frequency peak SPL of 143 dB. We can now go directly to our amplifier selection. In order to calculate the amount of power required, we need to use the following equation:

(Equation 4a) PWR(dB) = SPL Criteria peak - sensitivity + SPLdist-loss

(Equation 4b) PWR (watts) = 10 PWR(dB)/10

The peak SPL criteria was established earlier at 111 dB SPL (96 dB nominal + 6 dB peaks + 10 dB headroom). The loss due to distance is 28 dB. By plugging these numbers into equations 4a and 4b (above), we obtain the following results:

**Amplifier Power Requirements**

Loudspeaker—————————Highs——————-Mids————————Lows*

Calculated Minimum Power———27 dB——————30 dB———————-32 dB

Power in watts**——————-500 watts—————1000 watts—————1585 watts

** One loudspeaker will be required to provide an SPL criteria peak of 105dB SPL since two loudspeakers will give us our required SPL criteria peak of 111 dB SPL.
** This is peak power, not AES. The AES power handling would -6 dB lower than this (divide by 4).*

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