Speaker and Amplifier HEADROOM Calculations

In calculating required amplifier channel wattage, there are two places where 'headroom' is involved. What is each headroom value intended for?
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The CTS-D exam guide suggests adding 20dB of headroom when calculating 70V speaker tap wattages.
It also suggests multiplying an amp channel's required wattage by 120% to add headroom when calculating required amplifier channel wattages.

When we add 20dB of headroom when calculating tap wattages from distance-to-listener and speaker sensitivity, we are told that it accounts for the difference between RMS values and peak values... and thus to use 20dB for program music, 10dB for speech, and as much as 40dB for live performance.

However, when we proceed to use the aforementioned calculated tap wattages summed together in our amplifier calculations, we are told to multiply the result by 1.2 for additional headroom.  This should NOT be required for rms-to-peak level dynamism as that has already been accounted for in the tap settings. 

Is this extra 20% then to assure that the customer has a bit of room to crank up the volume beyond the assumed 'target' volume?   Or is this something else?

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Great question!  The short answer is to make up for the losses in the transformers.

Many years ago, I was doing the calculations for distributed loudspeaker systems and then doing physical measurements to see the accuracy of the methods.  It turned out the measurements were not very close to the calculations.  The measure impedance at the amplifier was always less than the calculated amount.  It turns out the part missing was the transformer specifications.  Looking at loudspeaker specifications, many times there is no mention of the transformer.  Every transformer has loss.

I'm a bit concerned about your comment about 1.2x multiplier as the math sheet that is given at the CTS-D test offers a 1.5x multiplier.  I will have to review the Study Guide and see if we need to these into alignment.

I multiplier of 1.2 is really subtracting about 0.8dB and a multiplier of 1.5 is subtracting about 1.8dB from the output.  Or, put the other way, the amplifier needs an additional 0.8 or 1.8dB gain to make up for the transformer loss.  Based on my measurements, I would opt for the larger number.  Remember, a 3dB change is doubling the wattage of the amplifier.  

In practice, under sizing an amplifier can cause real problems.  An under sized amplifier will clip and distort the audio signal.  If clipping continues over an extended period, the loudspeakers can overheat and damage the coils.  The amplifier will be drawing as much current as it can, overheating the amplifier circuits which can cause premature failure.  The audio quality coming from the system will not sound very good.

I hope that helps answer your question.

awesome. Thanks, @Paul Streffon, CTS-D, CTS-I! And thanks for bringing this question to the group, @Christopher Eloranta!

Go to the profile of Christopher Eloranta
7 months ago

Excellent answer to my question.  Thanks very much!

Also, I had forgotten that this is actually not a question of required wattage, but of amplifier output impedance.  70v systems don't "get quieter under higher loads," they "drive lower and lower impedances with higher tap setting totals."  The headroom calculation makes a lot more sense when you realize you need to drive a speaker leg that represents a load over 2ohms (or whatever.)