Calculating power drawn at typical listening levels

Dave MacKay

Dave MacKay

Active Member
I've been trying to get a handle on how many watts I'm drawing from my amps at differing volumes and listening positions. I'm getting answers, but they don't seem right to me. I thought I'd post what I've been doing in the hope that someone could point out any error(s) that I've made.

Situation
  • I have tri-amped La Scala speakers. The La Scala is rated as delivering approximately 105 dB SPL @ 2.83V @ 1m (i.e., 1 W at 1m when going into an 8 ohm load).
  • All of the drivers in the system are also rated at roughly 105 dB SPL @ 2.83V @ 1m
  • My listening positions are about 3m (10 feet) from the speakers.
  • I seldom listen at much more than 90 dB SPL.
Calculation

Recall that while dB power is calculated as 10log(P2/P1), dB amplitude (such as SPL) is calculated as 20log(A2/A1).

105 dB SPL --- SPL produced from 1W
- 9.5 dB SPL --- SPL reduction at 3m distance (i.e., 20log(3/1) = -9.5 dB SPL)
- 5.5 dB SPL --- to get down to typical listening volume
90 dB SPL --- upper limit of typical listening

It is important to realize that the -9.5 dB SPL comes from distance, not from lower power. Consequently I think that --- from where I sit --- I must be listening at about -5.5 dB SPL below the SPL the La Scala would produce when drawing 1 W.

Some "back of the envelope" figuring makes me believe that my typical listening levels would require about 280 mW (i.e., 10log(.28W/1W) = -5.5 dB).

The amps that I am using deliver roughly 50W (before clipping) when driven by a 0.5V input (the measured input sensitivity of the amp) into 8 ohms. That would be about 17 dB more than what the La Scala delivers at 1W (i.e., 10log(50W/1W)=17 dB). Since I typically listen at less than 90 dB SPL (which I've calculated as requiring 0.28W), I ought to have about 22.5 dB "headroom" (i.e., 10log(50W/0.28W) = 22.5 dB) above my typical listening level.

I can't help thinking that 280 mW is too small so that I must have made errors somewhere in my process. I invite your comments and corrections.

One more thing

I came across a rule of thumb that power is typically apportioned roughly 60% woofer, 30% midrange, and 10% tweeter. If that's valid, the power would be apportioned:
  • 168 mW to the woofer
  • 84 mW to the midrange
  • 28 mW to the tweeter
Is there any validity to that rule of thumb?
 
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I used an online "SPL" calculator...

105db/W/m sensitivity
2 speakers positioned in corners
10ft distance

Playing with power (WPC) input, 0.04W (40mW per channel) gives 90.1dB according to that calculator.

Of course, it can be looked at two ways; as average SPL or peak SPL.

If the 90dB is peak SPL then the 40 mWPC is peak power and average power would be less.

If the 90dB is average SPL then the 40 mWPC would be average power and peak power would be more.
 
whoaru99 said:
I used an online "SPL" calculator...

105db/W/m sensitivity
2 speakers positioned in corners
10ft distance

Playing with power (WPC) input, 0.04W (40mW per channel) gives 90.1dB according to that calculator.

Of course, it can be looked at two ways; as average SPL or peak SPL.

If the 90dB is peak SPL then the 40 mWPC is peak power and average power would be less.

If the 90dB is average SPL then the 40 mWPC would be average power and peak power would be more.
Click to expand...
@whoaru99 Thanks. You pointed out an omission and also reinforced that very little power is involved.

I neglected to consider that there are two speakers. That should increase the SPL by 6 dB and reduce the amount of power I’m drawing even more! That sure seems like a lot of volume for a tiny amount of power.

I’d love to find a power meter that I could sit on top of my amps to show the power being drawn. It would mostly be eye candy, but I’d find it fascinating.
 
My amps have a no gain option. Voltage gain of one. The dac can output 5 volts.
Using four ohms for woofers, sixteen for K55, and eight for DE-120 the power available to each driver is six watts to Kappa 15C, 1.6 watts to K55, and 3 watts to DE-120.
This is at 0dB digital signal and no attenuation. I usually listen at -15 to -20dB so peaks are about one tenth the numbers above.
People using the 1 watt SET amps should be fine.
 
Dave MacKay said:
I can't help thinking that 280 mW is too small so that I must have made errors somewhere in my process. I invite your comments and corrections.

One more thing

I came across a rule of thumb that power is typically apportioned roughly 60% woofer, 30% midrange, and 10% tweeter. If that's valid, the power would be apportioned:
  • 168 mW to the woofer
  • 84 mW to the midrange
  • 28 mW to the tweeter
Is there any validity to that rule of thumb?
Click to expand...
280 doesn't seem too small at all. remember, power and SPL is exponential. Also, you're using three amps, without a passive dividing network, so power output would be per amp; I do suspect your woofer/mid/tweeter estimates are actually quite high. try this calculator and reduce the wattage until you hit your listening level. it is surprising how few watts are needed. Peak SPL Calculator
 
This is where most amplifiers struggle. The industry standard seems to be THD+N at 5 watts. For our use that measurement at 50mW would be more applicable.
A few manufactures show sweeps of THD+N vs output power. Most stop at 50mW. A few take it down to uW levels.
That is what I look at. The SET supporters have always touted low level linearity as a strength. Every note goes through zero twice.
Somehow my amps Class B. Measure fantastic at levels even below Klipsch output requirements. Should be the worst at low level. Shows engineering can overcome.
 
I've been referred to another resource that has provided a different means to calculate power usage from SPL. Here are my updated results.

Situation
  • I have tri-amped La Scala speakers. Klipsch rates the La Scala as delivering approximately 105 dB SPL @ 2.83V @ 1m (i.e., 1 W at 1m when going into an 8 ohm load).
  • All of the drivers in the system are also rated at roughly 105 dB SPL @ 2.83V @ 1m
  • I am listening to 2 speakers
  • My listening positions are about 3m (10 feet) from the speakers.
  • I seldom listen at much more than 90 dB SPL.
Since I lack power meters on my amps (boy, would I ever like some), I’ve had to estimate the power. Here's how I've calculated it:

Calculation

Recall:
  • while dB power is calculated as 10log(P2/P1), dB amplitude (such as SPL) is calculated as 20log(A2/A1).
  • adding a second speaker increases SPL between +3 dB (for incoherent/out-of-phase sources) and +6 dB SPL (for coherent/in-phase sources)
105 dB SPL --- SPL produced from 1W
+ 3 dB SPL --- additional SPL from second speaker (worst case, assumes speakers are incoherent)
108 dB SPL --- total SPL from both speakers
- 9.5 dB SPL --- SPL reduction at 3m distance (i.e., 20log(3/1) = -9.5 dB SPL)
98.5 dB SPL --- SPL at 3m when both speakers are driven with 1 watt

From information provided by Crown alongside one of their calculators, we find two formulae that can help us:
1) dBW = Lreq - Lsens + 20 * Log (D2/Dref) + HR
2) W = 10 to the power of (dBW / 10)

Where:
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

If we remove the contribution of the second speaker, the SPL at the listening position should drop from 90 dB SPL to 87 dB SPL.

Populating formula 1, we get:
dbW = 87 - 105 + 20log(3/1)+0 (since we are not interested in amplifier headroom at this time, HR can be ignored)
= 90 -105 + 9.5
= -8.5

Using that result, we populate formula 2 as follows:
W = 10^(-8.5/10)
= ~ .141

Therefore, my speakers should each be drawing about 140 mW to produce 90 dB SPL at my listening position.

The amps that I am using delivers roughly 50W (before clipping) when driven by a 0.5V input (the measured input sensitivity of the amp) into 8 ohms. That would be about 17 dB more than what the La Scala delivers at 1W (i.e., 10log(50W/1W)=17 dB). Since I typically listen at less than 90 dB SPL (which I've calculated as requiring 0.14W), I ought to have about 25.5 dB "headroom" (i.e., 10log(50W/0.14W) = 25.5 dB) above my typical listening level. That should be loads.
 
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Sounds like 'plenty'.

re: THD+N at low power levels, there's a point at the low-power end where the self-noise of the amplifier takes over and the THD+N line starts to climb up just due to the signal and especially distortion getting buried in the noise floor. Below that, the THD+N number becomes 'unmarketable', and probably unimportant.

And you just found out why 1.5-10w tube amps are such a valid option with these speakers.
 
Perhaps my approach is wrong, but...

My Fluke 115 has a Min/Max/Avg setting. I attach the meter across the amplifier outputs, set it to AC voltage and Max, and play a song at a normal listening level. It will record the maximum voltage across the amplifier outputs during the song. I then run DATS to measure the impedance of the speaker/network to determine the minimum impedance of the load.

Even though I don't know at what frequency the maximum voltage occurred, I use the MAX voltage and the MIN impedance to determine the MAX current drawn during the song.

Thoughts?

Mike
 
mboxler said:
Thoughts?

Mike
Click to expand...
My initial reaction is I think you can't presume min impedance and max voltage gives the correct result because instantaneous power is contingent on the voltage & current/impedance at any given instantaneous point.

I think what I did in the past was use low resistance precision shunt resistor in series with speaker to get the current (based on voltage drop across the shunt) as one input and used the voltage across the speaker as a 2nd input. Those two inputs to a DSO with a math channel to calculate and plot power based on the current and speaker voltage. From that, came away with this -
20201209_172749.jpg

If I recall correctly, that trace is using a Yamaha pro amp, Bose 901 V (or are they VI?) and playing an early part of Porcupine Tree's Nil Recurring or maybe Cheating the Polygraph track.
 
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whoaru99 said:
My initial reaction is I think you can't presume min impedance and max voltage gives the correct result because instantaneous power is contingent on the voltage & current/impedance at any given instantaneous point.
Click to expand...

Just so I understand, let's say that during playback the maximum voltage is 2.4 volts, and the speaker's minimum impedance is 5.7 ohms. I'm saying the power needed never exceeded 1 watt, and most likely was less. Are you saying it can exceed 1 watt?

Thanks, Mike
 
mboxler said:
My Fluke 115 has a Min/Max/Avg setting. I attach the meter across the amplifier outputs, set it to AC voltage and Max, and play a song at a normal listening level. It will record the maximum voltage across the amplifier outputs during the song. I then run DATS to measure the impedance of the speaker/network to determine the minimum impedance of the load.

Even though I don't know at what frequency the maximum voltage occurred, I use the MAX voltage and the MIN impedance to determine the MAX current drawn during the song.

Thoughts?

Mike
Click to expand...
@mboxler I did something like that, but using a 1 kHz sine wave from my waveform generator instead of a music track. There was a bit of a complication.

I found that my Brymen DMM and my Rigol 'scope gave different RMS voltage readings and I couldn't figure out why. Not knowing which to trust, I went with the readings I got from the DMM.

I used the lowest impedance of the driver along with the measured voltage to calculate current (I=V/R) and power (P=V^2/R).

I didn't find a convincing explanation as to why the two instruments would report different voltages. The best guess had to do with the speed with which the DMM presented readings: although the DMM is a 6000 count unit, it only updates its display 5 times a second. The person who offered that explanation thought that the scope readings ought to be more accurate. I don't know if that's right or not.
 
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whoaru99 said:
My initial reaction is I think you can't presume min impedance and max voltage gives the correct result because instantaneous power is contingent on the voltage & current/impedance at any given instantaneous point.

I think what I did in the past was use low resistance precision shunt resistor in series with speaker to get the current (based on voltage drop across the shunt) as one input and used the voltage across the speaker as a 2nd input. Those two inputs to a DSO with a math channel to calculate and plot power based on the current and speaker voltage. From that, came away with this -
View attachment 3729077

If I recall correctly, that trace is using a Yamaha pro amp, Bose 901 V (or are they VI?) and playing an early part of Porcupine Tree's Nil Recurring or maybe Cheating the Polygraph track.
Click to expand...
@whoaru99 Neat!

How did you do that? Did you hook a computer up to the 'scope and have it take the two readings every so often (e.g., every second)? If so, what did you use to program the data acquisition?

My amps have differential output so that I would use a differential probe on my 'scope to measure voltage. I could pass the voltage readings to Excel and do math and graphing with it. Since I don't (yet) have a current probe, I would take the voltage measurement and the impedance (nominal or lowest) to calculate a reasonable approximation of the power (using P=V^2/R).
 
mboxler said:
Just so I understand, let's say that during playback the maximum voltage is 2.4 volts, and the speaker's minimum impedance is 5.7 ohms. I'm saying the power needed never exceeded 1 watt, and most likely was less. Are you saying it can exceed 1 watt?

Thanks, Mike
Click to expand...

I'm saying the instantaneous value is whatever it is at that point in time, dependent on the voltage and impedance/current at that point in time.

Generalizations can come in any number of forms.
 
This is a hopeless task unless you're a true metrology nutcase. It's taken me decades to recover from that affliction. First, there's electrical power dissipated in/by the speaker. You can measure that if you know the instantaneous voltage and current, which you can get with a 2-channel digital scope. A good scope can probably do the conversion and give you an answer in real time. Or, use a scope with deep memory and process a block of time later. Forget anything involving DMMs; you need to get down to very short time slices. Expect a number in the tens to hundreds of milliwatts for normal not-too-loud levels. Then there's the actual acoustic power radiated out from the speaker. That can be calculated from an average SPL at a known distance from the speaker, preferably outdoors or in an anechoic chamber. I don't know what a typical number would be, but it's going to be small. Dividing that by the previous electrical power measurement will give you the actual efficiency of the speaker, which is usually a surprise to people, typically below 1%. A full size Klipschorn might be 10% or something similar.
 
Dave MacKay said:
@whoaru99 Neat!

How did you do that? Did you hook a computer up to the 'scope and have it take the two readings every so often (e.g., every second)? If so, what did you use to program the data acquisition?
Click to expand...

It was done with a PicoScope, which is a DSO that connects to a computer. It inherently writes to "pages" (I presume more technically something like waveform buffers/frames) that you can save one or all. I do not recall the sample rate I used but it would have been orders of magnitude faster than every second. Well into the kS/s if not MS/s rate.
 
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Missed this. There was an epic related thread at diyA by pano and I think a follow-up maybe, too. I think this is the first one...it's worth a look, IMO, if only because it was all beaten-up fairly-well. Like a lot of things over there that grow big, it takes some seat-time to go through.
 
grindstone said:
Missed this. There was an epic related thread at diyA by pano and I think a follow-up maybe, too. I think this is the first one...it's worth a look, IMO, if only because it was all beaten-up fairly-well. Like a lot of things over there that grow big, it takes some seat-time to go through.
Click to expand...
@grindstone Thanks for the link to the lengthy thread (73 pages, 1451 posts) on diyAudio. I don’t typically go there so that I wouldn’t have come across it otherwise. I’ve skimmed a few pages already.

Although I can calculate the power drawn by my (stock) speakers at any particular dB SPL level and listening distance, perhaps the diyAudio thread will give insight into how to measure the speakers in their modded state. I’ve tri-amped my speakers and used a DSP in lieu of the original passive crossover. Because I’ve:
  • applied different crossover frequencies, filters, and slopes
  • implemented PEQs to boost and cut different frequencies (boosting LF should draw more power)
  • cut the amplitude of the output signal differently for each driver
  • implemented different house curves that boost and cut different frequencies
the “stock” efficiency rating is likely not valid any more.

Figuring what power is actually being drawn won’t be easy.
 
Dave MacKay said:
Figuring what power is actually being drawn won’t be easy.
Click to expand...
I think measuring it isn't too hard with appropriate gear, e.g. like a couple previous posts mentioned.

If you don't have the gear to do it, is it really worth getting the gear to do more than what calculations such as yours in post #8 and others have already suggested? It's pretty small power required even if including massive headroom. To what end is it you're driving that you don't generally understand already?
 
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