Here is a visual breakdown of the engineering sequence and mathematical logic defined by the standards (AVIXA, CEDIA, AES).

1. The Design Sequence Graphic (AVIXA/CEDIA Workflow)

The industry standards dictate a specific engineering linear workflow. You cannot select an amplifier until the environment has defined the speaker, and the speaker has defined the load.

The Workflow Logic:

1. Needs Analysis: The room's use defines the required Volume (SPL).

2. Environment: The room size and ambient noise set the performance baseline.

3. Speaker Selection (Transducer): We choose speakers that physically fit the room and can achieve the coverage and target volume. This establishes the electrical requirement.

4. Amplifier Selection: We choose an amplifier whose output can satisfy the speaker's load requirement (Z) plus necessary headroom.

2. The Power Calculation Graphic (Inverse Square Law)

This image illustrates why a standard calculation (rather than a rule of thumb) is required. Audio professionals must calculate the loss of sound energy over distance to ensure the speaker has enough power from the amplifier to meet the system goals at the furthest seat.

If you know the speaker's sensitivity (dB SPL at 1W / 1m), you calculate how much power (Preq) is needed to overcome the Inverse Square Law loss (the 20log(D) component) and achieve your target SPL.



3. The Core Equation: Finding Required Amplifier Power (Preq)

This is the exact mathematical description of the required amplifier output (gain). It is utilized during the CTS-D (Design) phase.

Preq = 10^ ((SPLtarget − Sens + 20·log10(D) + Headroom)/10)

Where:

• Preq: Required Amplifier Output Power (Watts).

• SPLtarget: The target Sound Pressure Level (dB) at the listener’s ear (e.g., 75dB continuous for speech). This target is derived from the room's ambient noise plus a defined Signal-to-Noise Ratio (SNR).

• $Sens$ (Sensitivity): The speaker's efficiency rating, specified by the manufacturer as dB SPL output with 1Watt of power at 1 meter distance (e.g., 87dB at 1 W /1 m).

• 20log10(D): This represents the Inverse Square Law loss. It calculates the necessary increase in power (in dB) to overcome the attenuation of sound over distance, where 'D' is the distance in meters to the furthest listener (as shown in the attenuation graphic above).

• Headroom: The extra power capacity needed to handle sudden peak signals (dynamic peaks) without clipping the amplifier (typically 3 dB for compressed background music, up to 20dB for dynamic cinema performance, per CEDIA/AES).

• The divisor '10' and base '10' exponent: These convert the final result from the decibel domain back into linear power (Watts).

Because decibels (dB) use a logarithmic scale rather than a linear scale, you cannot simply add the Sound Pressure Level (SPL) values together. For example, two speakers playing at 80dB each do not equal 160dB.

According to AVIXA, CEDIA, and AES standards, the calculation for total SPL depends entirely on whether the acoustic signals coming out of the speakers are uncorrelated (incoherent) or correlated (coherent).

Now what if 2 speakers have identical SPL level how total SPL will be calculated?