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Diminishing Returns: When “A Little More” Isn’t Enough For A System
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Intuition is one of the most valuable tools of the sound system designer. But sometimes intuition can lead us astray. Humans tend to think in terms of linear relationships rather than proportional relationships.

But most significant changes in an audio system are related to the proportional change rather than linear change.

For example, a 2-to-l power ratio produces a 3 dB increase in level, regardless of the initial power. A 1 watt to 2 watt increase produces the same proportional change as a 500 watt to 1000 watt increase – not exactly intuitive. This is why audio relationships are normally plotted on logarithmic scales.

Also interesting is the fact that it usually requires a 2-to-l change to make a significant difference when human perception is considered.

Most have heard the riddle of the “doubling penny.” A ruler offered a man the choice between a $1 million lump sum payment or a single penny that would be doubled each day for one month. The wise man took the penny realizing that the 2-to-1 growth rate would make him far wealthier than a mere one million dollars.

In fact, there would quickly come a time where it would be no longer possible to double the sum with each successive day, because the man would already possess all of the wealth of the kingdom!

Audio system designers must understand when they have reached the point of diminishing returns – the point when it is no longer practical (or possible) to double the parameter being considered. Let’s look at a few examples.

AMPLIFIER POWER

One electrical watt makes a handy reference quantity when considering what size amplifier to buy. This relatively small amount of power can only be practically doubled about 10 times before one reaches the point of diminishing returns.

In other words, the first few 3 dB level increases are quite economical. Then it becomes increasingly more difficult and expensive to get the next 3 dB. This makes amplifier peakroom pretty expensive, since it must be added after the power required to produce the perceived loudness is determined.

Each 3 dB reduction in available peakroom reduces the amplifier size by one-half. Peak limiters are an important part of the signal chain!

System designers must have other ways of achieving the desired level. And these other methods will also reach a point of diminishing return. One of these ways is increased loudspeaker directivity.


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