10Log(Amp Power) = SPL - Sens - 6 + 20*log(Distance to the speaker)
 
SPL:
Sound Pressure Level (dB) you like at your listening position
 
Sens:
Loudspeaker Sensitivity
 
W: Distance between 2 loudspeakers
D: Distance between your position to the center of 2 speakers
Distance to the speaker: 
Your position to one of speaker

How Much Amplifier Power Is Needed? 

For amplifier pairing, the calculator above gives the minimum amount of wattage required to drive the loudspeakers. The key equation employed by the algorithm is:

 

SPL = Sens - 20 Log( Meter Distance to one speaker) + 10 Log(Power Watt) +6

 

Where Sens: Loudspeaker Sensitivity = Sound Pressure measured one meter from the speaker when driven by one Watt of power. And because there are 2 speakers, the intensity is doubled and 6dB added to the total.

 

Whenever Amplifier power is doubled, SPL increases by 3dB

Whenever Distance is doubled, SPL decreases by 6 dB

 

Example 1

 

An 88dB/1W/1m sensitivity speaker like the W5-1880-SP full range driver, driven by 1 Watt Amplifier power, will result in 88dB SPL measured at one meter distance. When the same speaker is driven by 2 Watts, the SPL will be 91dB (SPL adds 3dB when the power is doubled.). Driven by 4 Watts, the SPL will be 94dB, and so on. If it is driven by 8 Watts at 2 meters, the SPL will be 91dB (= 94 + 3dB due to doubled power – 6dB due to doubled distance).
 

Example 2

Let’s take another example. Imagine a 200W x 2 Solid-State amplifier with a pair of bookshelf loudspeakers (sensitivity: 91 dB/1W/1m) operating in a room four meters by five meters. What will the SPL system deliver in this case?

We must first clarify the term ‘Distance’: Here, distance refers to the distance from the listening position to the loudspeakers — the size of the room is irrelevant. So, if the distance to the speaker is 5 meters, then the SPL is 106 dB.

Is this level too big? Too small? For long-term, comfortable listening, 90dB SPL suits most listeners whereas 106dB is not sustainable. This is why some audiophiles love low power, as with delicate Single-Ended Tube amplifiers like EL34-10W paired with higher sensitivity speakers like the W5-1880-SP full ranger with 88 dB sensitivity for living rooms, or paired with 84dB sensitivity 2-way LS35-SP speakers for smaller rooms.
 

 

The SE Class A EL34-10W amplifier with a pair of W5-1880-SP bookshelf speakers can provide 95dB SPL @3 meter away. It is more than enough.

 

Note: Room size and decoration materials affect the music reverberation time and the reflective sound wave. The calculator only considers and calculates the direct sound level to the listener. For the impact of room size and materials, please go to the other “Home effect calculator” for reverberation influence. 

 

Other factors may affect optimum amplifier power: the sensitivity of the listener’s ears for example or their tolerance of distortion, the dynamic of the tracks you're listening to, the acoustics (including the absorber, diffuser, and reverberation in your room), and psychoacoustics. And the unavoidable fact that our ears do not hear exactly the same sound when responding to bass and high frequency. Also, speakers' impedance varies according to changes in frequency. We'll try to elaborate more in the FAQ session.

Frequently asked questions

How much SPL do I need?


The table below gives us a list of common sound level and its dB level for your easy reference. (Source: Information from S. S. Stevens, F. Warshofsky, and the Editors of Time-Life Books) Or, you can find many mobile APP’s, such as Decibel X, or Sound Meter, to physically do the field test. Try to carry out tests on the different types of music you like and adjust the volume to the most comfortable level. Last but not the least, before you decide your SPL for the calculator, please read through the rest… A THFC Sound Sense program report (http://canadianaudiologist.ca/the-hearing-foundation-of-canada-sound-sense/ ) indicated that two hours of exposure to sound levels under 91dB will damage hearing. Anna Gilmore Hall, Executive Director of the Hearing Loss Association of America, recommends that: “You shouldn’t have exposure to 80 decibels for longer than 60 minutes,” (https://www.huffingtonpost.com/2015/03/06/music-hearing-loss_n_6755058.html ) Listening to music is one of most enjoyable things to do. Choose the sound level most comfortable for you and don’t waste your money on overly powerful amplifiers that exceed your needs.




How the Human Ears "hear" sound?


- The left ear differs from right Studies of 3000 newborn children carried out by US researchers have shown that the right ear is better than the left at receiving sounds from speech, whereas the left ear is more sensitive to sounds such as music and song (Source: http://www.ucla.edu and www.channelnewsasia.com, and https://www.hear-it.org/Your-ears-differ- ). - We “hear” different loudness of bass and treble by nature From the new revision of equal-loudness contours below, our ears are less sensitive to bass and treble compared to mid-range vocals. The lower the volume, the less we hear bass and treble. So ‘loudness’ features intended to boost or, rather, manipulate what we hear, are absent in high-end amps designed to deliver high fidelity musical sounds. (source: https://en.wikipedia.org/wiki/Equal-loudness_contour) Adding an amplitude factor into equal-loudness contours as above, the chart below graphically depicts the range of human hearing. Outside the boundaries you either cannot hear the sound or it becomes painful. (Source: http://sound.whsites.net/articles/fadb.htm)
The chart shows that the human ear is most sensitive at 3-4 Khz or whistle register in the vocal range and doesn't have to be loud to be heard. In the orchestral range, we hear around the 45-17Khz range. So, when choosing an amplifier or speakers, a smoother frequency response and lower distortion (THD) of this range (45 Hz -20 Khz) should be your most important considerations. Now that we know the limits of human hearing, what does this tell us about our perception of musical instruments? The chart below shows a frequency range of instruments to map to. Remember, some individuals might not be able to experience the full spectrum of orchestra, especially males over 50, who will be limited by natural hearing loss to 14-15Khz., Frequencies below 25Hz are felt rather than heard, but the conditions under which we experience such low frequencies make a big difference to how we perceive them. At very low frequencies, there is little difference between the threshold of hearing and the threshold of pain, which can make low frequency noises especially troublesome (http://sound.whsites.net/articles/fadb.htm). You can also refer to http://www.independentrecording.net/irn/resources/freqchart/main_display.htm for more detailed instrument frequency chart.




Why bigger power of Solid-State Amplifier is required than Tube Amplifier?


From the Power calculator formula, it’s clear that a 100W tube amplifier is exactly same as a 100W Solid-State amplifier which can deliver the same 100W of power over a specified impedance load. But if this is true, what’s the point of adding a Tube/Solid-state amplifier factor into the calculator? Why do many people claim to experience tube amplifiers as being louder than SS(solid-state) amplifiers with the same power? Implying that tube amplifiers can deliver higher power than SS amps. Why do so many people suggest that you double the power if you plan to use solid-state amplifier? What’s missing? * The load impedance of Speakers is not constant The key phrase here is ‘specified impedance load’. The truth is that loudspeakers have different impedance loads under different frequencies. Take the 5" full-range speaker driver of the W5-1880-SP for example (without the influence of a crossover circuit). The impedance of the driver on the spec is 8 Ohms. The resonant frequency is at 48 Ohms where the impedance rises to 32 Ohm — over 4 times the difference. And 4-8 times difference in impedance of loudspeakers is quite common in the real world. Take LS3/5a 2-way speakers for another example (with cross-over. Impedance curve shown below). The impedance is 34 Ohm at 75Hz and 8 Ohm at 180Hz/10KHz, over 4 times difference across the whole frequency range. Due to design differences between tube amps and SS amps, the actual power required to drive the speakers makes a big difference (source: https://www.stereophile.com/content/bbc-ls35a-loudspeaker-1989-follow ) * Higher output impedance of Tube Amp than SS Amp

For SS amps to achieve high efficiency levels, a feedback circuit is designed to have the output impedance as low to 0.1 Ohm so as to have most of the power applied to the speaker load efficiently.

Then when the impedance rises to 32 Ohm, the output power is only 1/4 of output power @8 Ohm. So to match the output requires 4 times as much power. Because of the high impedance output of vacuum tube amps, a transformer is required to match to a lower output impedance. Taking 8 Ohms as an example, output power is calculated according to the formula below. And the power required to drive 32 Ohm to have same output power level as 8 Ohm is 1.55 times (=1/0.64), much less than 4 times required for SS Amp. (in this case, it's 2.58 times difference = 4/1.55) EL34-10W Single-Ended Tube Amplifier has a lower output impedance due to "Ultra Linear" circuit design using 43% of primary turns to connect back to Screen grid of EL34 to decrease the distortion, and the impedance measured is from 1 Ohm to 3 Ohm. For most of the music you listen to, the power delivered in low-frequency Bass range is usually much higher than higher frequency, which makes things worse while most high load impedance happens at low frequency around 50-100 Hz of loudspeakers, so you hear much louder bass on Tube Amp than SS Amp. * Hard Clipping vs. Soft Clipping

SS amps usually trigger hard clipping when driving over the amplifier’s power rating (overdrive). This hard clipping of sound waves generates a high amplitude of high frequency harmonics that is painful on the ears. So it's better to choose a higher rated power SS amp to make sure you have some more room before hitting the hard clipping point.

Yet in tube amps, which have important soft clipping characteristics, generating lower amplitudes of high frequency harmonics makes for a warmer sound which our ears are more tolerant of. We will elaborate more on next topic.

In summary, We have taken the above factors into consideration and tested many speakers to establish the multiplier factor that Solid-state amplifiers might need to out-perform tube amplifiers on power.




Can I use 250W or even higher power Amplifier to drive peak power 200W speakers?


Yes. In fact this is something that we highly recommend.

250W is the power measured under 10% distortion, so it can deliver much less distorted power to 200W rated speakers. High quality speakers such as the M1, AP1 and LS35-SP can usually handle more transient power than listed.




Can 30W Amplifier delivers 60W power?


1. RMS power vs. Peak Power Amplifier spec sheet usually specifies RMS Power (or Continuous Mean Power Output), for example A60 can deliver 30 Watt continuous power, while some might state Peak Power (or Max / Dynamic Power), which is the maximum power the amplifier can deliver occasionally. 2. Impedance matters A 30W@8 Ohm can drive 60W power if it connects to a 4 Ohm speaker. 3. Human Ear Tolerance matters A 30W amplifier delivers 30W of power under 10% distortion. But this doesn't mean the amplifier cannot deliver 40W or even 60W if the distortion is within acceptable bounds. If you are insensitive to distortion, then 30W actually can deliver 60W power. I know what you’re thinking now, so just for your reference, most of people cannot detect 30% bass distortion.




How come the Calculator didn't consider "headroom" factor in Amp power calculation?


Headroom" is the difference between the maximum power an amplifier can deliver and the power required for your choice of music. Some recommend at least 3dB headroom, so in general you need to choose twice the power needed (calculated from the calculator above) to play safe. This means that to play safe you need deeper pockets for more amplifier power. And for tube amplifiers, playing safe means a lot heavier. Is this really necessary?

For high-end amplifier makers, the maximum power can sometimes be up to 10 times of RMS power listed in the spec, which also means the RMS power marked on the Amplifier is the power needed for your music, with headroom already factored in. To avoid confusing the customer we didn’t consider headroom.

Yet, if you’re looking for an entry-level amplifier from no brand, you can consider adding a headroom factor, or simply double/triple the power in case you purchase the Peak Power instead of RMS power.

And, because speaker impedance is not constant across the frequency range, which will affect the actual output power of the amplifier, especially solid-state amplifiers, more power will be required. We’ll elaborate more on this issue in the next topic





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