Power and Decibel

The decibel is one unit that you will hear used (and misused) quite often in electronics. I have two examples here recently that I have seen.

The first one was in a music shop where they were selling speakers. The sign on of these said 600 Watts RMS and 1300 Watts Peak but the box said it was a powered speaker. In the electronics of the amplifier, if the RMS rating is 600 Watts then the Peak Watts is only 1.414 times the RMS value or 848 Watts Peak. It is NOT 2x RMS.

Now one of the other cabinets was a passive speaker (no power) and said 500 Watts RMS and 2000 Watt Peak.

First, there is no RMS in a passive speaker because it is tested for continuous power. 500 Watts with a 3 dB Crest Factor will allow 1000 Watts peaks during a test with pink noise. Now 6 dB above the 500 Watts continuous shall be 4 times the continuous power or 2000 Watts.

Another example is with the continuous decibel specification. The specifications defines this single line array cabinet at 127 dB continuous. In addition, it defines 4 of these cabinets as 139 dB continuous and this is incorrect.

The reason this is incorrect is because 4 times the increase of power will provide you with 6 dB increase for a value of 133 dB not 139 dB.

To summarize, in electronics every time an increase the power by a factor of 2 times, the result will be a 3 dB increase of power. Every time an increase the power by a factor of 4 times, the result will be a 6 dB increase of power. To add to that, an increase the power by 10 times, will provide an increase of 10 dB.

On the passive note as with a raw speaker, a speaker that has been tested and defined as having a power rating of 500 Watts continuous, an increase of 3 dB in the power rating will define the program power rating of 1000 Watts Program. An increase of 6 dB in the continuous power rating will define the peak power rating of 2000 Watts Peak.

And last, an amplifier with a 500 Watt RMS rating will have a peak rating of 1.414 times RMS or 707 Watt peak. Use caution when you are evaluating the specification of an amplifier. To impress you, vendors and manufacturers will provide the peak power not RMS and will also give the rating in 4 ohms and not 8 ohms.

3000 Watts Peak at 4 ohms is only 1500 Watts Peak at 8 ohms. This 1500 Watts Peak at 8 ohms is only 1060 Watts RMS at 8 ohms. The larger numbers looks impressive but is deceiving.

Speaker reference efficiency relationship

Speaker Efficiency or Reference Efficiency, is a calculated parameter in percent that uses the electro-mechanical parameters of a speaker that include the resonance frequency (Fs), the speaker’s electrical damping (Qes) and the equivalent volume compliance (Vas).

The relationship that I have found is that if the resonance frequency (Fs) or the equivalent volume compliance (Vas) was to increase, the Reference Efficiency will increase.

The odd one is the speaker’s electrical damping (Qes), so if this parameter was to increase, the Reference Efficiency will decrease.

The Reference Efficiency numbers will be in a range of 1 to 4 %.

This is why I have seen many times that it has been recommended that the Qes parameter should be 0.40 or less when selecting a speaker.

Trying to provide some relationship with four variables will require that two of these be constants.

I have chosen for the Reference Efficiency to be 3.00 +.02 and the Qes parameter to be .40.

This will allow for me to plot the resonance frequency (Fs) and the equivalent volume compliance (Vas).

The relationship shows that a decrease in the equivalent volume compliance (Vas) will require an increase in resonance frequency (Fs) to maintain the Reference Efficiency of 3.0.

Speaker sensitivity vs Speaker Efficiency

Something I have seen recently, is the parameter SPLO that I have never seen before. I cannot get a straight answer from anyone because they do not know, and all I get is bullshit. These same people is trying to tell me that the sensitivity parameter is the efficiency of the speaker and this is another bullshit statement.

First, the only thing that I found is that this is a SPLO measurement is specific to subwoofers with a measurement in the range with the application (40 to 250 Hz). This parameter is sometimes larger than the sensitivity and can be deceiving. This is because averaged test output for sensitivity is from 500 Hz to 2.5 kHz vs the focus on subwoofers low frequency.

Now the important thing, is to understand the differences between sensitivity and efficiency, and how these are derived.

Sensitivity, sound pressure in dB, is a physical measurement of the on-axis output, using the reference of 1 watt of pink noise in the range of the resonance frequency (Fs) times 10 with a Crest Factor of 6 dB applied and measuring the average sound pressure level at 1 meter. This parameter may not relate to the low-frequency efficiency level of a speaker.

η0 or Efficiency, is referred to as the  Reference Efficiency and specified in percent. Comparing drivers by the calculated reference efficiency is more useful than the sensitivity parameter. This reference efficiency, is a calculated function of the electro-mechanical parameters of the loudspeaker and represents the low frequency output range of 300 to 400 Hz range for 12 to 18 inch speaker drivers that directly correlates with the efficiency ratings.

This efficiency calculation used the electro-mechanical parameters that include the resonance frequency (Fs), the speaker’s electrical damping (Qes) and the equivalent volume compliance (Vas).

Cabinet Port Parameters Relationship

What are the effects of the parameters associated with port sizing and the tuning of a ported speaker cabinet? I was using an app on my tablet and thought I would improve on my understanding of these parameters.

Speaker Cabinet Port Parameters Relationship

For explanation, the first port length effect is saying that a decrease in cabinet volume, a decrease in tuning frequency, a increase in port diameter or increase in the number of ports will effect the port length by increasing length requirements of that port.

As I found some online calculations that can be used for design or to double check yourself as I do from time to time.

Great online calculations for Speaker Design that I recommend.

Calculate Length of Vent or Port
Calculate Volume of Box
Calculate Tunning Frequency
Calculate End Correction Factor

Calculate Minimum Port Vent Diameter
Calculate Maximum Air Volume
Calculate Tuning Frequency

Calculate Enclosure Volume or for Box
Calculate Speaker Total at f_s
Calculate Air Compliance

Calculate for Box Enclosure Tuning Frequency
Calculate Speaker Resonance Frequency
Calculate Enclosure Volume or for Box

Lloyd Perkins & PerkAudio’s House of Horns

Speaker Power Ratings

Manufacture Test Rating

• This is the thermal limit using pink noise to define the continuous power rating.
• Standards include AES2-1984 (r2003), EIA-426-B (2001), IEC 60268-5 and AES2-2012
• Most vendor will label this RMS and is totally incorrect.
• Will see defined as Pc, Continuous, RMS, IEC 60268-5, EIA-426-B. IEC Continuous or AES Continuous rating.

Thermal Limits

• This is the thermal limit using random frequencies of music reproduction
• This is defined as 2 x Pc, Continuous or RMS Power
• Will see this defined as Pe, PMax, Peak, Program, Music or System Power
• Caution! Some vendors will label this as peak power.
• If Peak defined as 2 x RMS then this is Max Thermal Limits not Peak
• Thermal capacity is related to coil temperature, adhesives and insulation melting point.

Mechanical Limits

• Pm or PLim or Peak Power is the mechanical limitation
• An excursions greater than the Xmax parameter can damage the component.
• This is defined by 2 x Pe, Pmax, Program, Music or System Power
• Can be defined by 4 x Pc, Continuous or RMS Power

PerkHorns