Speaker – Amp – Match

The articles that I have found on power amplifier sizing keep speaking of this “Rule-of-Thumb” and I find differences of opinions on this “Rule-of-Thumb”. By conducting my own study and research, I think I can elaborate on this some to make more since and explain why each of these rules were selected.

I found the three “Rule-of-Thumb” to recommend:

  • 80 to 125% RMS
    • First, there is no RMS in speakers. This value is referred to as continuous for speaker per AES organization.
  • 100 to 150% of RMS
    • If the specification show a difference between the Continuous (RMS) and Peak in only 3dB (2x RMS) then a maximum of 150% of the RMS should be used.
  • 150 to 250% continuous.
    • In case of the specification show 250 Continuous (RMS), 500 Program and 1000 Peak then we are looking at using 200% of the Continuous.

The goal here is to get as much as you can of your speaker with protection of the speaker as a priority. These above rules-of- thumb are worthless.



Power Amplifier Notes

Speaker to Amplifier Matching

The best comment that I have run across has been from Martin Sound, that stated that ideally the amplifier should deliver full peak power without the risk of clipping. This is meaning that a speaker that is rated at 1000 watts peak should be provided with an amplifier with 1000 watts peak power. Now the question is, how do I interpret these values from the ratings within the specifications.

First, the speaker specifications states a rating of 250 watts that is tested under EIA or AES specification. This results in a continuous rating using pink noise. Since this value is a continuous signal of all frequencies define for this driver, the real world rating is the maximum power handling rating, that is also referred to as program or music power, will be equal to two times this continuous rating. Another two times this value will be the peak rating of the speaker. The result will be:

250 watts continuous;
Continuous x 2 = 500 watts program;
Continuous x 4 = 1000 watts peak

For the amplifier, you will need to look closely at the footnotes of the specifications. Typically the rating is defined as the maximum average or continuous output in watts at a given THD level at 1 kHz. Now one instance I found the rating to be maximum output power. In this case, this is peak power. One customer was complaining because the specifications stated 1600 watts but he was only measuring 1131 watts. This person did not interpret the specifications correctly because 1600 times 0.707 will equal 1131 watts. In this case 1600 watts peak (maximum) will be 1131 watts continuous or RMS. The result will be:

707 watts continuous or RMS;
Continuous x 1.414 = 1000 watts peak;
Maximum (peak) x 0.707 = continuous watts

In this case above, a 1000 watts peak speaker should require a 707 watt continuous amplifier.

Maybe to simplify this, you could say that:

250 watt continuous speaker times 2.8
would require a 700 watt amplifier.

500 watt program power speaker times
1.4 would require a 700 watt amplifier.

This is the optimum requirement but this will usually play havoc on your budget. To compromise and fit your budget better, the minimum amplifier requirement for the matching of a speaker would be:

500 watt program power speaker
would require a 500 watt amplifier.


The initial requirement provides for the amplifier peak power to be equal to the speaker peak power with no Peak limiter would be required. This results in the amplifier RMS power above the speaker thermal limit and an RMS limiter would be required with a -1.5 dB threshold to provide thermal protection.

The optimum solution in turn provides for the RMS amplifier to be equal to the thermal limit which is the program power of the speaker. This allows for the peak power of the amplifier to be 1.5 dB below the speaker peak power and might require a Peak limiter. If a Peak limiter is not used, it would be recommended to closely monitor the Clip indicator on the amplifier.

While conducting a test and set all pieces of equipment thresholds in my chain to 0UV using pink noise. I used this pink noise and I adjusted the amplifier gain to the point where I was not getting the CLIP LED. This result was about 75% of the gain adjustment on the amplifier. Now I only get the CLIP LED occasionally during the loudest passages. This has covered for 95% of my peak issues.

The optimum solution would be the best choice which would reduce the cost of the amplifier but still no limiter would be require eliminating any extra cost for your system.

Sound System Engineering – Common Parameter for Reference

The most useful parameter for comparison of a sound system would be the Max dB value. This calculates the variables that include the amount of power recommended (speaker program power) and the speaker or cabinet sensitivity to provide a common parameter that can be used for comparison from system to system.

The Max dB calculation defines the dB value or ratio of rated amplifier power applied to the reference of one watt at one meter. This power is added to the speaker sensitivity or dB SPL level at reference value.

The speaker sensitivity is the amount of SPL measured in dB produced when applying one watt of power or 2.83 volts at eight ohms and measured at one meter from the speaker.

The power calculation above provides the increase of dB for that given wattage. The result provides for the Max dB SPL at rated power at one meter.

Power Ratio Calculation
Max dB SPL = 10 * Log10(Amplifier Wattage/Reference of 1W)+Speaker Sensitivity at 1W

  • Amplifier Power             600W    600W    500W    1000W
  • Speaker Sensitivity        98 dB   95 dB     98 dB   98 dB
  • Max dB SPL                  126dB   123dB    125dB    128dB  

Note: A change in Speaker Sensitivity has an effect of 1 to 1.
Note: The doubling of wattage is required to provide an increase of only 3 dB.

Now that this value has been defined, using the inverse square law, the dB level may be determined for a given distance. With the doubling of distance, a loss of – 6dB shall be realized for point source system where only a -3 dB loss shall be realized for a line array system.

  • Distance in Meters         1          2          4          8          16         32 
  • Distance in Feet            3.2      6.4    12.8   25.6     51.2     102.4
  • dB Loss w/ref 98dB       98       92        86      80        74         68 

Use of dBu on limiter threshold settings.

I was looking at some plate amplifiers with the DSP option. Looking at their DSP software, the threshold setting for their Noise Gate, Compressor and Limiter were all in dBu and I went berserk. In my research and study for these type applications over the past 10 years, I do not remember any of these Threshold settings being in dBu. I had lengthy argument over this with this vendor and was about to tell him where he could stick it. So I backed up to rethink the situation.

First of all, we are working with the voltage relationship to the speaker and the amplifier. This is calculated by square root function of the wattage divided by the impedance. SQRT(watts*ohms)

Speaker Program Power of 800 watts at 8 Ohm load = 80 volts
Amplifier of 1000 watts at 8 Ohms load = 89 volts

With dB calculations you are using the 20 * Log function with the ratio between the speaker voltage and the amplifier voltage output to define your speaker protection. 20*Log(Speaker Voltage/Amplifier Voltage). The result of this would be -0.97 dB. Your setting on your limiter would be -1 dB for the thermal protection of the speaker.

Now, dBu using a reference of .775 for the denominator for the equation 20*Log(Voltage/.775) and I could not relate to that at first. Then I finally found something to answer that question.

Now we will still use the voltage for this calculation but we will use 20*Log(Voltage/.775) where this voltage will be the speaker or amplifier voltage as we did before and find the result for each device.

Speaker Program Voltage 80V would be 20*Log(80/.775) = 40.3 dBu
Amplifier Voltage 89V would be 20*Log(89/.775) = 41.2 dBu
In this case the amplifier sensitivity is .775

Now using the difference between these two dBu values (Speaker dBu minus Amplifier dBu) will provide you with the Threshold setting in dBu. Now looking at this, the dB calculation and the dBu calculation will be the same because the reference for the dBu calculation is .775 and the amplifier sensitivity is also .775.

Now there is a snag. What if the sensitivity is 1.4 or 1.7 that I found in some of these amplifiers? Instead of the .775 in the amplifier voltage calculation, you would use the sensitivity of the amplifier.

Amplifier Voltage would be 20*Log(Voltage/1.4) = 36.1 dBu for a 4.17 dBu
Amplifier Voltage would be 20*Log(Voltage/1.7) = 32.4 dBu for a 5.86 dBu

FYI – Reference Selecting the limiter threshold for a loudspeaker power limiter.


Speaker Sensitivity

Amplifier power vs Speaker Sensitivity
There are many aspect that would dictate the selection of an amplifier and speaker application. One of these aspect that I wish to address is the selection is the speaker sensitivity. The graph below shows the requirements in reference to the sensitivity of a speaker. In my case I already have my existing amplifiers and I wish to select my speakers to be used for my application. The first thing is to decide the dB level that you wish to provide for your application. The choices that I have provided in the graph below is 30, 50, 70 and 90 feet. These could represent:

• The 30 feet would address a small club
• The 50 feet would address a large club
• The 70 feet might address a small hall
• The 90 feet might address an outdoor event

Using the Crown calculation, the results provides the power requirement for each of conditions. For each distance the dB level requirement was selected to be 90 dBs. In my case, I have a 300 watt RMS amplifier that I used in my application and will use this value as a reference for the explanation that I am trying to provide. Since I have the amplifier, my speaker rating should be in the range of 150 watt RMS / 300 watt program power.

No automatic alt text available.

Now the question is, what will be my minimum speaker sensitivity for each of these requirements.
• For the 30 feet for a small club, I would select one that is greater than 88 dB.
• For the 50 feet for a small club, I would select one that is greater than 93 dB.
• For the 70 feet for a small club, I would select one that is greater than 96 dB.
• For the 90 feet for a small club, I would select one that is greater than 98 dB.

Note: For every 3 dB increase in sensitivity the power requirement is decreased by 50%.

Notice that the greater the speaker sensitivity the less power that is required. So it would be in your best interest to select one that is as large as possible to provide the additional headroom for your application.

This is only addressing the typical bass reflux speaker that manufactures have most of their focus on. In my case, my focus is concentrating on the loading of the speaker as well. Last year I build a couple of folded horn subwoofers and the sensitivity of these cabinet increased by 8 to 10 dBs. 

I loaded these cabinets with a speaker that was rated at sensitivity 90 dBs and the result of cabinet loading increased this speaker application up to 98 to100 dBs. The end result decreased my power requirement 2 to 3 times. To explain further, this 90 dB speaker could provide a 50 foot application but would require 487 watts to do this. Now with the loading of these subwoofers with this same speaker, I can provide a 90 foot application and would only require 158 at 100 dB to 250 at 98 dB.

Lloyd Perkins – PerkAudio – Live Sound Consulting & Custom Speaker Design.

Speaker Sensitivity

Speaker Sensitivity represents one of the most useful specifications published for any transducer.
Loudspeaker manufacturers follow different rules to obtaining this value with most expressing this value as the average output across the usable frequency when applying 1W/1M into a nominal impedance.

This represents the efficiency and volume that can be expected from a speaker when applying 1 watt into the nominal impedance and measuring the dBSPL at a distance of 1 meter with a reference voltage for this measurement is 2.83V into 8 ohms.

Why is this so important? When selecting a speaker or speaker cabinet, if I can increase the sensitivity by 3 dB, you will reduce my power requirement by half and this can be a considerable cost savings when purchasing a power amplifier.

This value can be used to determine the required amplifier wattage required to provide a certain given dB level at a given distance for an application.

This equations can be used to calculate the required wattage by first using:
dBW = Lreq – Lsens + 20 * Log (D2/Dref) + HR

Then using the dBW result to get the required wattage with:
Watts = 10 to the power of (dBW / 10)

Lreq = required SPL at listener
Lsens = loudspeaker sensitivity (1W/1M)
D2 = loudspeaker-to-listener distance
Dref = reference distance
HR = desired amplifier headroom
dBW = ratio of power referenced to 1 watt
W = power required

I do this in a spreadsheet for comparison calculations.

Doing this calculation yourself is not required, an app is provided the Crown site at: www.crownaudio.com/en/tools/calculators
and select the Amplifier Power Required.

This calculation will give you the ratio, in decibels, between two power values. For example, you can calculate the difference in…