Straightforward Approach To Setting An Optimized Audio System Gain Structure

June 15, 2012, by Brian Elwell

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).*

Now that the amplifier size has been determined, the next thing to look at is processing level inputs and outputs.

Most sound consoles can comfortably handle an output level between +18 dBu and +24 dBu.

This, in turn, will feed the processing equipment. Analog processors can usually handle +18 dBu input and output signals. This is the first place in line where attenuation or a pad may be required.

If you are using a console that can output +24 dBu, you will want 6 dB of attenuation at the input of the audio processor. This can usually be achieved by the input attenuators on the signal processor.

The outputs of the signal processors require a bit more discussion. Many DSP devices have either output switch settings or output jumper settings that can select between 0, +6 dB, or +12 dB, so the obvious questions are “Why are there different options?” and “When do you use them?”

To answer this, we must first continue our discussion about amplifiers.

AMPLIFIER INPUT LEVELS

Many manufacturers have input selection settings than can choose between 0.775V, 1.4V, X20 (or 26 dB), or X40 (or 32 dB). For the purpose of discussion, the table below indicates the input level that 200-, 400-, and 800-watt amplifiers will accept before the amp clips.

The 0.775V and the 1.4V input level settings indicate that all amplifiers will clip at the same input level. For the X20 (26dB) or the X40 (32dB) selection settings, the size of the amplifier and the load on the amplifier will determine the level at which the amp will clip. It is very important to be able to understand the clip levels and gains of the amplifiers in both dB and in voltage.

**For 0.775V or 1.4V input sensitivity**

(Equation 5a) Gain (volts) = sqrt [Max power rating * load (ohms)] / input sensitivity

(Equation 5b) (dB) = 20 log[Gain (voltage)]

(Equation 5c) Clip Level (volts) = input sensitivity (0.775V or 1.4V)

(Equation 5d) Clip Level (dB) = 20 log [clip level (volts)]

**For X20 (26 dB) or X40 (32 dB) gain**

(Equation 6a) Clip level (volts) = sqrt [Max power rating * load (ohms)] / gain (20 or 40)

(Equation 6b) Clip level (dB) = 20 log[Clip level (volts) / 0.775V]

(Equation 6c) Gain (volts) = gain (20 or 40)

(Equation 6d) Gain (dB) = 20 log[gain(volts)]

**Amplifier Input Clip Levels**

———————-200 Watts————————400 Watts————————800 Watts

X20 (26 dB)———-8.2 dB———————————11.2 dB—————————-14.2 dB

X40 (32 dB)———-2.2 dB———————————5.2 dB——————————-8.2 dB

0.75V——————0 dB————————————-0 dB——————————-0 dB

1.4V——————-+5 dB———————————-+5 dB——————————+5 dB

Now that we have thrown all of these numbers out there for you to ponder over, we now need to know when we would want to use these different input settings.

The primary factor in determining which settings to use is determined by the designer’s requirement for the system’s noise floor.

If noise floor is not absolutely critical (NC-25 or higher spaces), then the amplifiers can safely be set on 0.775 (or preferably 1.4V if available).

Because the actual gain of the amplifiers is quite high (~X40 for a 100 watt amp to ~X130 for a 2500 watt amp), the noise floor will be higher. The clear advantage, however, is that you do not need to calculate the attenuation needed for every channel of every amplifier.

If noise levels are a critical concern, then constant gain settings should be used, but you will need to calculate the attenuation for each amp channel.

To conclude our discussion on signal processing and the output level switches on DSP devices, if you are using an amplifier that has its input sensitivity set on 0.775V, then the output of the DSP should be set at 0 dB. This will provide 18 dB of attenuation between the console and the amplifiers.

If the input sensitivity of the amps are set at 1.4V, then the output of the DSP should be set at 6 dB. If you are using constant gain, then each output needs to be addressed on an individual basis.

One final note on gain structure worth mentioning is to always have a good sense for what is occurring with the system equalization. Let’s assume that there is a large +10 dB boost in the EQ at 8K.

During system tuning it may make the speakers sound very well and provide extended high end frequency response, but 8K signals will clip the amplifiers 10 dB sooner than the rest of the system.

Similar problems may arise from very large EQ cuts, but if at all possible, for gain structure purposes, it is better to cut than to boost, and it will always be best to keep your cuts and boosts to an absolute minimum.

**Brian Elwell** is senior consultant with Acoustic Dimensions and has contributed to system designs at major stadiums, houses of worship, theme parks and many other venues.

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