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“We Need More Power, Captain!” But Just How Much Amplifier Power Is Needed?
There are two goals: Power the loudspeakers so they play as loudly as possible without burning out; achieve a certain loudness in a certain venue. Here's an exhaustive overview covering both topics and much more.
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Determining which power amplifier is appropriate for a specific application is not as easy as one may think. To fully understand what needs to be considered, three specific case studies will be outlined:

• A client wants to play folk music in a coffee shop. How much amplifier power do they need?

• A rock group will be playing in a 2,000-seat concert hall. How many watts will you need to provide?

• A jazz-fusion group bought some PA loudspeakers. They want to play the loudspeakers as loud as they can get without blowing them up. Which amplifier should you recommend?

Questions such as these arise in any sound system design. To help you specify an optimum amount of amplifier power for a system, I’ll explain the relevant audio concepts here.

There are two goals:
1) Power the loudspeakers so they play as loudly as possible without burning out. In other words, determine the optimum powering for the chosen loudspeakers.
2) Achieve a certain loudness in a certain venue.

We’ll cover both topics.

Signal Levels
First let’s review the concept of average levels and peak levels.

As shown in Figure 1 (below), a musical signal changes in level (voltage) continuously as it plays. Imagine a musical passage with a low-level synth pad, but with high-level drum hits. The average level or volume of the passage is low, but the transient peak levels are high.

Peak levels may be up to 24 dB above average levels depending on the type of signal. Percussive sounds have much higher peaks than continuous sounds do (synth pads, organ, flute) – even if the two signals have similar average levels.

The peak-to-average ratio of the signal is called the crest factor or peak factor. In other words, crest factor is the difference in dB between the peak levels and the average level of the signal. Percussive sounds have a high crest factor.

Flutes, organs and violins have a low crest factor. The crest factor of speech is about 12 dB. Highly compressed rock music has a crest factor of about 6 dB: the peaks are about 6 dB higher than the average level.

See Figure 2 (below). It is a graph of signal level versus time when the amp is fed a typical musical signal. The average level corresponds to the signal’s loudness. The peak level is 6 to 24 dB above the average level, depending on the type of signal. In other words, the signal crest factor is 6 to 24 dB.

The bottom of Figure 2 shows an example of amplifier power output versus time when the amp is fed a musical signal. The amplifier is rated at 800 W continuous power. That’s the maximum power it can produce at rated distortion.

However, in this example the amplifier is putting out 50W on the average, so that occasional peaks of 12 dB don’t exceed the amp’s 800 W capability. Also, there is a little headroom so that the peaks don’t clip.

Headroom

In Figure 2, headroom is the difference in dB between the signal peak levels and the amplifier’s clipping level. Normally you want to allow at least 3 dB of headroom so that signal peaks don’t accidentally clip.

Peakroom
This term, coined by Syn-Aud-Con instructor Pat Brown, is crest factor plus headroom. Peakroom indicates how many decibels that peaks can be above the average level without clipping.


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