Thread: imputing speaker impedance curve | volume level to generate 1-watt

today, i conducted the following tests / experiments in order to 1) determine how high the volume on my amp had to be turned up so that a continuous 1 kHz tone would generate 97 dB from my speakers measured at a 1-meter distance and 2) get an approximate idea of the impedance curve of my speakers. sound level measurements were taken using an uncalibrated smart-phone app.

by no means are these rigorous, scientific tests conducted with proper, professional equipment, however i thought the results would at least be informative.

- stated speaker efficiency: 97 dB / 1 watt / 1 meter | impedance 8 ohms

- amp power rating: 18 watts / channel
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test #1

the volume had to be turned up to just shy of the the 10:30 position in order to generate 97 dB. i have never listened to my system at that level, ever. the highest i listen has the volume around the 9:00 position. zero volume is at the 7:00 position.

note: my amp has a shallow volume taper.

question: given that speaker efficiency is measured at 97-dB per 1-watt into 8-ohms measured at 1-meter, is it correct to infer from this test that my amp has to have the volume turned up to 10:30 before it sends 1-watt of power to the speakers?

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test #2

keeping the volume at the 10:30 position determined in test #1, i took sound level readings for 8 different frequencies:

50 Hz........... 83 dB
100 Hz......... 84 dB
150 Hz......... 88 dB
200 Hz......... 92 dB
500 Hz......... 97 db
1,000 Hz...... 97 dB
2,500 Hz...... 95 dB
5,000 Hz...... 89 dB

note: at least subjectively, the lower frequencies did not sound as loud as the mid frequencies ...but, that may be psycho-acoustics, not sure.

question: is this a logical way to impute the character of the speaker impedance curve?

question: what do others here make of these results?

thanks!!

Performing a frequency sweep at a given volume level is only going to tell you the in-room frequency response, and as such isn't very useful for figuring out anything about the speaker's electrical characteristics. The room is going to make the frequency response go all over the place, and even an anechoic measurement only tells you the "pure" frequency response, or voltage sensitivity assuming your amplifier during the test is not acting as a limiter, and nothing else. Although you are measuring at 1 meter, it kind of looks like you're not avoiding the room interactions (what's your measurement window?) and/or the smart phone microphone isn't reliable for this use, otherwise your SPL readings wouldn't be so far apart; the manufacturer claims 28Hz - 35kHz ±1.5dB for your Berlin R MkII.

Measuring impedance has to be done by actually measuring the speaker load. Searching Google for how to measure a speaker impedance graph (not just the nominal impedance) can provide you with some methods to do so. Room EQ Wizard also has some impedance measurement instructions, and note the warning about potential damage to your input interface.

What I take away from your posted results is the potential benefit of adding room treatments or room correction DSP, assuming a similar wide swing in the frequency response at your listening position.

Sensitivity should be viewed is a voltage function, e.g. 97dB @ 1 meter @ 2.83 volts. When the load is 8 ohms, that equals 1 watt. When the load is 4 ohms, it equals 2 watts. That's why specifications might use 1 watt instead of 2.83 volts, particularly for a speaker that isn't 8 ohms. An audio amplifier is a voltage amplifier. In other words, an amplifier might have a 23dB gain and if the preamp is feeding it 1V, then the amplifier will output ~14V. Whether or not it can do that is where impedance and phase kicks in.

Efficiency is technically something else but often used interchangeably in casual conversation.

Originally Posted by NekoAudio

Performing a frequency sweep at a given volume level is only going to tell you the in-room frequency response, and as such isn't very useful for figuring out anything about the speaker's electrical characteristics. The room is going to make the frequency response go all over the place, and even an anechoic measurement only tells you the "pure" frequency response, or voltage sensitivity assuming your amplifier during the test is not acting as a limiter, and nothing else. Although you are measuring at 1 meter, it kind of looks like you're not avoiding the room interactions (what's your measurement window?) and/or the smart phone microphone isn't reliable for this use, otherwise your SPL readings wouldn't be so far apart; the manufacturer claims 28Hz - 35kHz ±1.5dB for your Berlin R MkII.

Measuring impedance has to be done by actually measuring the speaker load. Searching Google for how to measure a speaker impedance graph (not just the nominal impedance) can provide you with some methods to do so. Room EQ Wizard also has some impedance measurement instructions, and note the warning about potential damage to your input interface.

What I take away from your posted results is the potential benefit of adding room treatments or room correction DSP, assuming a similar wide swing in the frequency response at your listening position.

Sensitivity should be viewed is a voltage function, e.g. 97dB @ 1 meter @ 2.83 volts. When the load is 8 ohms, that equals 1 watt. When the load is 4 ohms, it equals 2 watts. That's why specifications might use 1 watt instead of 2.83 volts, particularly for a speaker that isn't 8 ohms. An audio amplifier is a voltage amplifier. In other words, an amplifier might have a 23dB gain and if the preamp is feeding it 1V, then the amplifier will output ~14V. Whether or not it can do that is where impedance and phase kicks in.

Efficiency is technically something else but often used interchangeably in casual conversation.

thanks so much for this thoughtful and informative response!! i am just trying to understand my speakers and amp and how they interact with each other. you have given me some quite useful and practical information.

the test results in the OP have been updated and now show a much flatter response curve than initially reported*

there is still a decent dB fall-off seen in the lower frequencies. this may very well be room interactions, particularly as there are many sound absorbing materials in the room -- soft furniture, thick rugs, and fabric shades.

one remaining question is whether test #1 is a good or at least ballpark estimate of the amp volume level where 1-watt is being sent to the speakers?

i would like to use this to help estimate a minimum level of amp power (wpc) that will pair with my speakers yet still provide ample headroom. if so, it would seem that an 8 wpc amp would certainly be more than enough power?


* i was wearing ear protection during the initial test and accidentally took the measurement in front of the wrong speaker

If your initial measurements were accurate, my first thought was a subwoofer is in order.
Scientific or not looks like a fun project.

Originally Posted by aKnyght

one remaining question is whether test #1 is a good or at least ballpark estimate of the amp volume level where 1-watt is being sent to the speakers?

Maybe, given the 1kHz reading. If the manufacturer's 97dB @ 1m @ 1W is based on a 1kHz measurement and the speaker impedance is actually 8 ohms at 1kHz. The nominal impedance could be 8 ohms but the actual impedance at 1kHz could be higher or lower.

Originally Posted by aKnyght

i would like to use this to help estimate a minimum level of amp power (wpc) that will pair with my speakers yet still provide ample headroom. if so, it would seem that an 8 wpc amp would certainly be more than enough power?

Also maybe. The two limiting characteristics of an audio amplifier are voltage and current. An amplifier that is able to feed 8 watts (i.e. 8 volts at 1 amp) into an 8 ohm resistive load may not be able to maintain the 8 volts into a 2 or 4 ohm load (requiring 4 amps and 2 amps), and your speaker may have drops in its impedance for some frequencies. Plus the speaker's electrical phase at a given frequency may increase the difficulty at that frequency.

In other words, giving yourself some headroom by picking an amplifier that is rated at a higher wattage (usually at least double) than what you'll likely need is one way to make some assumptions about the drive capability of the amplifier. As well as to keep the amplifier distortion low since an amplifier's rated power output tends to be based on 1% THD. Assuming the manufacturer's claims are accurate. Plus, if you did end up adding some room+speaker correction DSP, there will likely be some significant PEQ boosts applied which could require a lot more extra output in a few places.

thanks again for the thoughtful response -- very helpful information and discussion of all the relevant factors involved here.

this just goes to illustrate that no matter how hard one tries to use manufacturer specifications to evaluate components and to judge their synergy with one's system, the only foolproof method is an actual home demo.

unfortunately, even in the best of times it is difficult to hear many components at a dealer let alone get a home demo. this is almost universally true for the smaller boutique/exotic manufacturers. nowadays with the pandemic, forget about it.

Originally Posted by NekoAudio

...Although you are measuring at 1 meter, it kind of looks like you're not avoiding the room interactions (what's your measurement window?) and/or the smart phone microphone isn't reliable for this use, otherwise your SPL readings wouldn't be so far apart; the manufacturer claims 28Hz - 35kHz ±1.5dB for your Berlin R MkII...

just finishing up on this project...

i have no reason not to believe the bandwidth specs on my speakers. so, other than room interactions and the obvious inaccuracy of any results obtained from an uncalibrated smartphone and SPL app, that leaves the amp.

on paper at least, the amp is clearly the "weak link" in my system. in looking at the specs in the manual i noticed that the frequency range is listed at 20Hz ~ 20kHz / -6dB !

from my research, one standard is to measure the frequency range as lo-freq ~ hi-freq / -3dB ; the frequencies where the power falls by 50%. in comparison, the frequency range listed for my amp are at the points where the power falls by 75%, halving again. this is most likely a significant factor driving the fall-off seen in the results i show in the OP.

to get a little more perspective here, i looked up the frequency range listed on some other SET amps:

- air tight ATM 300R : 30Hz ~ 40kHz (−1dB / 1W)
- luxman mq-300 : 20Hz ~ 20kHz (+0.3,-1.5dB)
- yamamoto 300B A-09S : 15Hz ~ 22 kHz (-3dB)
- sophia electric 91-03 : 12Hz ~ 35kHz (+/- 3dB)
- audio tekne TM-9501PCS 6AS7G : 10Hz ~ 20KHz (-1dB / -3dB)

and just to include a class A solid state amp:

- first watt sit-3 : 10H ~ 50kHz (-0.5 dB / – 3.0dB)

anyway, not sure this tells me anything that i don’t already know: amplification is probably the area where the biggest increase in the SQ of my system is to be had.

however… specs are only numbers and make absolutely no statement about the contribution to overall system sound that any particular component is capable of contributing.

in terms of my litte almarro amp, i have always just loved its sweet, rich sound …and, it has responded to every system upgrade i have made with ever richer, fuller, more detailed / textured sound. for an amp i paid $2,250 for 8 years ago, i just may have stumbled across the one true david in a world of goliaths. in any event, it is a beloved family member and has been the gateway drug into this hobby.

@aKnyght I missed looking at the amplifier you are using.

The 20Hz - 20kHz (-6dB) measurement was most likely done with a resistive load, and is not indicative of what the frequency response would look like with a real world speaker. Tube amplifiers generally have higher output impedance, and sometimes a non-flat output impedance, which will result in wider swings in the frequency response than a solid state amplifier. That's why Stereophile has that "simulated speaker load" line in their frequency response measurement graphs.

So unless the amplifier is a typical solid state design that also uses the typical amount of negative feedback, that specification won't necessarily be accurate in use.

thanks again for the post and clarifying information.

assuming the frequency range of the other amps listed are similarly measured with a resistive load, then it is at least a comparative measure where the almarro could be decently less "linear" in its frequency response curve.

in any event, there are certainly a lot of layers of this onion to peel back! thus far, i think the one thing i learned from this exercise is: specs are great, but trust your ears.

Originally Posted by Speedskater

A long informative thread:

A Test. How much Voltage (power) do your speakers need? - diyAudio

thanks for posting... great thread which details a test designed to determine the power (wpc) necessary to drive a speaker at the highest playback volume one would ever use.

based on this test, i performed the following:

test #1

i set the amp volume to the maximum level that i would ever listen at. i then took the Vac reading at that volume level using a 1-kHz sine wave from the 8 ohm tap on the amp which was was 0.575 Vac ...which when converted to watts using ohm's law is way below 1 watt.

this is pretty much as expected and consistent with SPL measurements i took and reported above
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test #2

next, i set the volume such that it generated 1.0 Vac at the 8 ohm speaker tap from a 1-kHz sine wave. that volume level was at approximately at the 10:30 position. this is the same volume position that generated 97 dB on a smart-phone app measuring SPLs that i reported in the OP.

since 1.0 Vac convert to 1.0 watt and as my speakers have a 97 dB sensitivity, nice to see that these two measurements are consistent.
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test #3

finally, keeping the volume at the 1.0-Vac / 1-watt level, i then took readings at a number of other frequencies with these results which are posted alongside the SPL results from the OP:

50 Hz ........... 83 dB ..... 1.015 Vac
100 Hz ......... 84 dB ..... 1.038 Vac
150 Hz ......... 88 dB ..... 0.979 Vac
200 Hz ......... 92 dB ..... 0.979 Vac
500 Hz ......... 97 db ..... 1.000 Vac
1,000 Hz ...... 97 dB ..... 1.003 Vac
2,500 Hz ...... 95 dB ..... 0.947 Vac
5,000 Hz ...... 89 dB ..... 0.500 Vac

a-priori, i expected the Vac readings to mimic the SPL readings and trail off in the extremes, especially in the lower frequencies -- indicating that the SPL results were generated by the amp rather than the speakers. however, the Vac readings are pretty much dead-on constant up until the 2.5-kHz level where they drop off in concert with the SPL readings.

one interpretation is that the SPL fall-off in the lower frequencies is an indication of a "non-benign" speaker impedance curve rather than the frequency response of the amp. although this seems unlikely as the stated amp frequency response is 20Hz - 20kHz / -6dB and the speaker bandwidth is listed at 28Hz - 35kHz ±1.5dB

curious what others make of the Vac / SPL readings in the lower frequencies?

thanks!

edit: i have read that the accuracy of inexpensive multi-meters (such as mine) falls off for high frequencies. makes sense as they are typically used to measure at 50-60 Hz and are optimized for that point. this might explain the drop off at 2.5 kHz and above ...nonetheless, the low frequency observations are still puzzling. must be something i am missing here.