Sound Engineers, Let's Talk System Gain the 'Standard' Way
In the early days of the PA industry, achieving sound gain using speakers and amplifiers was arduous. Back then, when a power amplifier could deliver 100W or even 150W, connecting it to a speaker was truly a powerhouse! That is, the mainstream discussion focused on wattage ratings, not today's standard measure of sound pressure gain.
Today, 100W amplifiers are no longer mainstream. High-tech speaker manufacturing processes have deeply penetrated the consumer market, with amplifiers reaching 1000W or higher wattages. With current industrial technology, gain is easily achievable if you have sufficient funds. However, once the rules of the game are established, people's conceptual understanding hasn't kept pace. Knowledge gaps often arise, especially since we aren't a standards-declaring body here, and language issues lead to a higher rate of 'User Bugs'.
In our audio industry today, how many people use the standard logarithmic laws of electrical physics to calculate the required number of speakers for a venue or the amplifier gain? It's almost always based on price to roughly estimate the speaker quantity. This issue has never been seriously discussed openly. Now, let's understand our system capabilities in a standard way.
Preface
Many people struggle to grasp the concept of structuring a sound reinforcement system. There are significant reasons why support is needed in sound transmission. Face-to-face conversation is direct and clear. But what if we are 30 meters apart? To speak effortlessly and clearly, support is needed. Via what? That's the electroacoustic system—using electronic equipment to extend the listening required on-site. This necessitates calculations for combining sound equipment. (As usual, we'll minimize mathematics to keep the article engaging. The data introduced here are based on existing physical laws and the logarithmic characteristics of the human ear, not new 'array' algorithms.)
How Much Gain Do We Need?
A good Sound Man always clearly defines the sound system for the show, understanding the entire SPL situation from start to finish. This allows them to manage the dynamics of the music program. Without this pre-established operational sound pressure framework, you'll find yourself constantly below or exceeding the total gain requirements of the system—a common occurrence in the industry.
Crucially: Never force a system with insufficient sound gain conditions. You risk damaging equipment and your technical competence will be questioned. Conversely, when the total sound gain exceeds the venue's requirements, the Sound Man at the panel will enjoy a smooth and pleasant process.
Let's assume a working scenario: An indoor medium-sized venue (a common situation). We aim for a normal music program sound pressure level of 95dB at the listener's position relative to the speaker. The corresponding dynamic peak would be 101dB. Then, we add our desired 10dB of dynamic peak Headroom to meet instantaneous performance dynamic sound pressure demands on-site.
We know that sound radiates from speakers in a roughly spherical pattern. Sound pressure attenuation from the source point with distance is proportional to the square of the distance. According to this conversion, for every doubling of distance, the sound pressure level decreases by 6dB (Note: This conversion does not apply to vertical arrays).
Also, assume the sound console is positioned at 80 feet. Speaker sensitivity is referenced to the international AES (Audio Engineering Society) standard: the test value obtained at 1 meter with 1W input. The formula for level loss due to distance is:
Formula 1
SPL Distance Loss Value = 20log(Distance in feet / 3.3)
SPL Distance Loss Value = 20log(Distance in meters)
The first line of Formula 1 is for converting if distance is measured in feet to meters. Plugging in our assumed data (don't forget the engineering calculator), using "Formula 1": 80 feet converts to approximately 24.242424... meters, so 24 meters. Taking log (logarithm) of 24 meters gives ≈1.38457.... Multiplying by 20 gives ≈27.6915..., rounded to 28dB.
Therefore, the story tells us: At the listener position 80 feet (24 meters) from the sound source, there will be a 28dB SPL loss. Okay! Add this to the dynamic peak of 101dB from our example plus the preset 10dB Headroom: 101dB + 10dB + 28dB = 139dB. Now we know the maximum SPL required from the mixing console to the speaker position is 139dB. Of course, if a single speaker could produce 139dB at 80 feet from its origin, one speaker would suffice. However, technology isn't that advanced yet. Therefore, we must dutifully select a speaker that meets the AES standard of 139dB peak SPL at 1 meter @1W. Then, we increase the quantity of speakers with this specification. That's why main speaker counts are so high. Understood?
Today's main speakers are rarely full-range (single-way); most are three-way (3-way), divided into High Frequency (HF), Mid Frequency (MF), and Low Frequency (LF) ranges.
AES declared minimum power rating specifications for each frequency range are:
Speaker Frequency Range —— HF —— MF —— LF
1W@1m Value ———————— 112dB —— 109dB —— 103dB
AES Power Rating ————— 200W —— 400W —— 1000W
Calculated Max SPL ———— 141dB —— 141dB —— 139dB
Calculating Speaker MAX SPL:
Assume a brand's speaker with sensitivity (1W@1m): HF 112dB, MF 109dB, LF 110dB. We can calculate its maximum SPL (peak) using this formula:
Formula 2:
Max SPL = Speaker 1W@1m Sensitivity + 10log(AES Declared Min Rated Power) + 6dB Peak
SPL = HF 112 + 10log(200W) + 6dB
SPL = 112 + 23 + 6
SPL = 141dB
On an engineering calculator, you can compute it step-by-step to see the total. On a standard business calculator, first take log of 200W for HF, multiply that value by 10 ≈ 23.010299..., add 112dB ≈ 135.0102..., then add the 6dB peak factor. This speaker's HF component is 141dB, exceeding our 139dB requirement.
Here, helpful math emerges: To convert any wattage amplifier output to dBW, use:
Formula 3:
10log(Wattage)
Similarly, apply Formula 2 for the MF component. Since the LF component's calculated SPL is below standard, we must double the number of LF speakers with the same frequency response to meet the target SPL.
The second approach is to reduce the energy in the MF/HF ranges to match the overall frequency band SPL, effectively lowering the initial SPL target.
Reducing from 141 dBSPL to 139 dBSPL isn't just a 3dB matter. Previous articles mentioned that human perception of loudness changes by ±3dB, and this ±3dB change already corresponds to a ±10 times change in amplifier power!
The above example used 8 Ohms. In practical investment applications, parallel connection at 4 Ohms is common, meaning two speakers per amplifier channel. Let's see the difference. One HF speaker at 112dB, plus another equals 115dB.
10log(10^(112/10) + 10^(112/10)) = 115
Additionally, a 200W amplifier generally delivers about 75% more power into 4 Ohms (not 100% due to power supply demands, line loss, etc.), so it becomes roughly 300W driving these two HF units.
Apply Formula 2:
Max SPL = Speaker 1W@1m Sensitivity + 10log(AES Declared Min Rated Power) + 6dB Peak
Max SPL = 115dB + 10log(300) + 6dB
Max SPL = 115 + 24.7 + 6
Max SPL = 145.7 ≈ 146dB
This result satisfies our target SPL. Without increasing the amplifier power, SPL increased. The difference? We increased the speaker count. More importantly, every power amplifier now consumes double the current. Crucially, watch thermal protection! Many amplifiers reduce output or shut down when temperature rises to cool the circuit quickly—this is an issue.
OK, back to the earlier 8-ohm content. Seasoned professionals already know that to perceive a doubling of loudness requires nearly a 10dB difference.
So let's be practical. We now know the Max SPL values for each frequency band of the example speaker. We need to select appropriately powered amplifiers. Use this formula to find the required power rating for each band:
Formula 4:
dBW = Sound Peak Level - Frequency Band Component Sensitivity + Distance Loss
Here, (Sound Peak Level) is our earlier derived dynamic peak: 101dB (95dB listening level + 6dB dynamic peak), plus the desired 10dB Headroom: 101dB + 10dB = 111dB. (Frequency Band Component Sensitivity) is the 1W@1m value for each component within the speaker. (Distance Loss) is the 28dB SPL loss calculated earlier for 80 feet (24 meters). Ok, plug in the values for each band to find its power requirement:
HF: (111dB - 112dB) + 28dB = 27 dBW
MF: (111dB - 109dB) + 28dB = 30 dBW
LF: (111dB - 103dB) + 28dB = 36 dBW
Convert dBW back to Watts (see table for reference):
HF 27 dBW = 500W
MF 30 dBW = 1000W
LF 36 dBW = 4000W
After organizing, we see a key difference: The LF data requires significant reinforcement. We can use multiple 1000W amplifiers with LF speakers or employ the 4-Ohm method mentioned earlier to achieve the target standard.
After reading this, you've gained a few simple formulas. They help pre-plan calculations for required SPL, dynamic range usage, etc. Check your main speakers' specifications. Take my own MARTIN VRS-1000 as an example:
1m@1W = 106dB, using a 1000W amplifier: 106 + 30 = 136dB
At 1m. Then, with a typical 4-Ohm connection: 109 + 31.5 ≈ 140.5dB (at 1m).
The purpose of this article is to help you understand the potential energy of your amplifiers and speakers. This doesn't even touch on sound quality (good/bad sound). This is just about amps and speakers. Extending forward is the preamp section—where should levels be adjusted? What are the standards? These are adjustments and understandings needed after establishing a system.
Mixing Console & Processors
The signal level between the mixer's output and downstream processors, and finally connecting to the power amplifier, requires clear understanding. You must know at what indicated signal level from the mixer your power amplifier reaches full load, and at what level clipping occurs. This is extremely important.
Most mixers handle output levels between +18dBu to +24dBu. Simply put, if you calibrate +4dBu (1.23V) = 0VU; and your digital processor is set to -18dBFS or -20dBFS = +4dBu, then if your amplifier is configured for full load at 0.775V or 1.4V, you'll clearly understand the operational range of the amplifier. Therefore, understanding the relationship between amplifier clipping levels, amplifier gain in dB, and voltage is crucial.
Today, 100W amplifiers are no longer mainstream. High-tech speaker manufacturing processes have deeply penetrated the consumer market, with amplifiers reaching 1000W or higher wattages. With current industrial technology, gain is easily achievable if you have sufficient funds. However, once the rules of the game are established, people's conceptual understanding hasn't kept pace. Knowledge gaps often arise, especially since we aren't a standards-declaring body here, and language issues lead to a higher rate of 'User Bugs'.
In our audio industry today, how many people use the standard logarithmic laws of electrical physics to calculate the required number of speakers for a venue or the amplifier gain? It's almost always based on price to roughly estimate the speaker quantity. This issue has never been seriously discussed openly. Now, let's understand our system capabilities in a standard way.
Preface
Many people struggle to grasp the concept of structuring a sound reinforcement system. There are significant reasons why support is needed in sound transmission. Face-to-face conversation is direct and clear. But what if we are 30 meters apart? To speak effortlessly and clearly, support is needed. Via what? That's the electroacoustic system—using electronic equipment to extend the listening required on-site. This necessitates calculations for combining sound equipment. (As usual, we'll minimize mathematics to keep the article engaging. The data introduced here are based on existing physical laws and the logarithmic characteristics of the human ear, not new 'array' algorithms.)
How Much Gain Do We Need?
A good Sound Man always clearly defines the sound system for the show, understanding the entire SPL situation from start to finish. This allows them to manage the dynamics of the music program. Without this pre-established operational sound pressure framework, you'll find yourself constantly below or exceeding the total gain requirements of the system—a common occurrence in the industry.
Crucially: Never force a system with insufficient sound gain conditions. You risk damaging equipment and your technical competence will be questioned. Conversely, when the total sound gain exceeds the venue's requirements, the Sound Man at the panel will enjoy a smooth and pleasant process.
Let's assume a working scenario: An indoor medium-sized venue (a common situation). We aim for a normal music program sound pressure level of 95dB at the listener's position relative to the speaker. The corresponding dynamic peak would be 101dB. Then, we add our desired 10dB of dynamic peak Headroom to meet instantaneous performance dynamic sound pressure demands on-site.
We know that sound radiates from speakers in a roughly spherical pattern. Sound pressure attenuation from the source point with distance is proportional to the square of the distance. According to this conversion, for every doubling of distance, the sound pressure level decreases by 6dB (Note: This conversion does not apply to vertical arrays).
Also, assume the sound console is positioned at 80 feet. Speaker sensitivity is referenced to the international AES (Audio Engineering Society) standard: the test value obtained at 1 meter with 1W input. The formula for level loss due to distance is:
Formula 1
SPL Distance Loss Value = 20log(Distance in feet / 3.3)
SPL Distance Loss Value = 20log(Distance in meters)
The first line of Formula 1 is for converting if distance is measured in feet to meters. Plugging in our assumed data (don't forget the engineering calculator), using "Formula 1": 80 feet converts to approximately 24.242424... meters, so 24 meters. Taking log (logarithm) of 24 meters gives ≈1.38457.... Multiplying by 20 gives ≈27.6915..., rounded to 28dB.
Therefore, the story tells us: At the listener position 80 feet (24 meters) from the sound source, there will be a 28dB SPL loss. Okay! Add this to the dynamic peak of 101dB from our example plus the preset 10dB Headroom: 101dB + 10dB + 28dB = 139dB. Now we know the maximum SPL required from the mixing console to the speaker position is 139dB. Of course, if a single speaker could produce 139dB at 80 feet from its origin, one speaker would suffice. However, technology isn't that advanced yet. Therefore, we must dutifully select a speaker that meets the AES standard of 139dB peak SPL at 1 meter @1W. Then, we increase the quantity of speakers with this specification. That's why main speaker counts are so high. Understood?
Today's main speakers are rarely full-range (single-way); most are three-way (3-way), divided into High Frequency (HF), Mid Frequency (MF), and Low Frequency (LF) ranges.
AES declared minimum power rating specifications for each frequency range are:
Speaker Frequency Range —— HF —— MF —— LF
1W@1m Value ———————— 112dB —— 109dB —— 103dB
AES Power Rating ————— 200W —— 400W —— 1000W
Calculated Max SPL ———— 141dB —— 141dB —— 139dB
Calculating Speaker MAX SPL:
Assume a brand's speaker with sensitivity (1W@1m): HF 112dB, MF 109dB, LF 110dB. We can calculate its maximum SPL (peak) using this formula:
Formula 2:
Max SPL = Speaker 1W@1m Sensitivity + 10log(AES Declared Min Rated Power) + 6dB Peak
SPL = HF 112 + 10log(200W) + 6dB
SPL = 112 + 23 + 6
SPL = 141dB
On an engineering calculator, you can compute it step-by-step to see the total. On a standard business calculator, first take log of 200W for HF, multiply that value by 10 ≈ 23.010299..., add 112dB ≈ 135.0102..., then add the 6dB peak factor. This speaker's HF component is 141dB, exceeding our 139dB requirement.
Here, helpful math emerges: To convert any wattage amplifier output to dBW, use:
Formula 3:
10log(Wattage)
Similarly, apply Formula 2 for the MF component. Since the LF component's calculated SPL is below standard, we must double the number of LF speakers with the same frequency response to meet the target SPL.
The second approach is to reduce the energy in the MF/HF ranges to match the overall frequency band SPL, effectively lowering the initial SPL target.
Reducing from 141 dBSPL to 139 dBSPL isn't just a 3dB matter. Previous articles mentioned that human perception of loudness changes by ±3dB, and this ±3dB change already corresponds to a ±10 times change in amplifier power!
The above example used 8 Ohms. In practical investment applications, parallel connection at 4 Ohms is common, meaning two speakers per amplifier channel. Let's see the difference. One HF speaker at 112dB, plus another equals 115dB.
10log(10^(112/10) + 10^(112/10)) = 115
Additionally, a 200W amplifier generally delivers about 75% more power into 4 Ohms (not 100% due to power supply demands, line loss, etc.), so it becomes roughly 300W driving these two HF units.
Apply Formula 2:
Max SPL = Speaker 1W@1m Sensitivity + 10log(AES Declared Min Rated Power) + 6dB Peak
Max SPL = 115dB + 10log(300) + 6dB
Max SPL = 115 + 24.7 + 6
Max SPL = 145.7 ≈ 146dB
This result satisfies our target SPL. Without increasing the amplifier power, SPL increased. The difference? We increased the speaker count. More importantly, every power amplifier now consumes double the current. Crucially, watch thermal protection! Many amplifiers reduce output or shut down when temperature rises to cool the circuit quickly—this is an issue.
OK, back to the earlier 8-ohm content. Seasoned professionals already know that to perceive a doubling of loudness requires nearly a 10dB difference.
So let's be practical. We now know the Max SPL values for each frequency band of the example speaker. We need to select appropriately powered amplifiers. Use this formula to find the required power rating for each band:
Formula 4:
dBW = Sound Peak Level - Frequency Band Component Sensitivity + Distance Loss
Here, (Sound Peak Level) is our earlier derived dynamic peak: 101dB (95dB listening level + 6dB dynamic peak), plus the desired 10dB Headroom: 101dB + 10dB = 111dB. (Frequency Band Component Sensitivity) is the 1W@1m value for each component within the speaker. (Distance Loss) is the 28dB SPL loss calculated earlier for 80 feet (24 meters). Ok, plug in the values for each band to find its power requirement:
HF: (111dB - 112dB) + 28dB = 27 dBW
MF: (111dB - 109dB) + 28dB = 30 dBW
LF: (111dB - 103dB) + 28dB = 36 dBW
Convert dBW back to Watts (see table for reference):
HF 27 dBW = 500W
MF 30 dBW = 1000W
LF 36 dBW = 4000W
After organizing, we see a key difference: The LF data requires significant reinforcement. We can use multiple 1000W amplifiers with LF speakers or employ the 4-Ohm method mentioned earlier to achieve the target standard.
After reading this, you've gained a few simple formulas. They help pre-plan calculations for required SPL, dynamic range usage, etc. Check your main speakers' specifications. Take my own MARTIN VRS-1000 as an example:
1m@1W = 106dB, using a 1000W amplifier: 106 + 30 = 136dB
At 1m. Then, with a typical 4-Ohm connection: 109 + 31.5 ≈ 140.5dB (at 1m).
The purpose of this article is to help you understand the potential energy of your amplifiers and speakers. This doesn't even touch on sound quality (good/bad sound). This is just about amps and speakers. Extending forward is the preamp section—where should levels be adjusted? What are the standards? These are adjustments and understandings needed after establishing a system.
Mixing Console & Processors
The signal level between the mixer's output and downstream processors, and finally connecting to the power amplifier, requires clear understanding. You must know at what indicated signal level from the mixer your power amplifier reaches full load, and at what level clipping occurs. This is extremely important.
Most mixers handle output levels between +18dBu to +24dBu. Simply put, if you calibrate +4dBu (1.23V) = 0VU; and your digital processor is set to -18dBFS or -20dBFS = +4dBu, then if your amplifier is configured for full load at 0.775V or 1.4V, you'll clearly understand the operational range of the amplifier. Therefore, understanding the relationship between amplifier clipping levels, amplifier gain in dB, and voltage is crucial.