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Loudspeaker Measurements Standard: Sensitivity

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Loudspeaker sensitivity is a measure of sound pressure level at a given distance when a specific sinusoidal voltage is applied across the loudspeaker terminals. The sound pressure level at the given voltage, say 2.83V, has to be inspected across the entire audio band.  Looking at frequency response, it is easy to see that for a constant voltage input, sound output varies with frequency.  It is easy to impress with this number by taking the peak in the loudspeaker frequency response and stating it as the loudspeaker sensitivity.  Unfortunately, this does not help anyone understand how loud the speaker will sound to the average listener.  Making all things fair, it is better to find the average SPL from 300Hz to 3kHz representing the mid-band of a typical full range loudspeaker. 

Editorial Note about Sensitivity Frequency Range by Dr. Floyd Toole:

This frequency range was selected because it embraces most of the significant frequencies in human voices and much music.

This is the method accepted by the well-respected National Research Council of Canada, so we are sticking with it!  In the rare case where 300Hz to 3kHz is not in the mid-band of the speaker under test, additional information will be included in the review assessing the sensitivity based on the mid-band range of the speaker.

The sensitivity measurement is obtained from the on-axis frequency response measurement.  Prior to the measurement, the microphone is calibrated at 94dB and 114dB reference points established by an acoustical calibrator.  A 2.83VRMS MLS signal is applied to the loudspeaker and the measurement captures the SPL calibrated frequency response.  The output is exported to mathematical software capable of working with matrices for averaging the SPL.  Since SPL is a logarithmic scale, the average of the inverse logarithm of each value must be equated and converted back to decibels.

For more information on this topic, see:  Loudspeaker Sensitivity Specifications & Measurements Explained

Listening Window

Unfortunately, there is only one sweet spot and sometimes the listening chair does not position the listener at the same height as that sweet spot.  That is why listening window measurements are so important.  A listening window measurement Audioholics style is simply an average of loudspeaker measurements at the reference distance from 7 different locations. 

  • On-axis
  • +/- 15 Degrees Horizontal
  • +/- 30 Degrees Horizontal
  • +/- 15 Degrees Vertical

 listeningwindow.jpg

Listening Window Sample

This gives you an idea of the power response of the system.  If on-axis measurements look great but the listening window is not even close, then the sweet spot will be relatively narrow.  The published listening window graph shows the response at each angle independently so that you will have an idea of how the speaker will sound in typical listening positions.

The results for a listening window measurement are obtained using 2.83VRMS at the reference distance and moving the measurement microphone to the specified angle.  The low frequency response below the window frequency is typically relatively uniform so it is not included in the measurement.

Polar Response

Polar response measurements are obtained by measuring the loudspeaker from 0 to 180 degrees in 7.5 degree increments following the same methods used to obtain on-axis frequency response at the reference distance.  The vertical axis of rotation is the acoustic center of the baffle.  In cases where the loudspeaker does not have vertical symmetry, the measurement is taken from 0 to 360 degrees.  Polar response measurements from 0 to 90 and 90 to 180 degrees are contour plotted in software for a clear representation of polar response versus frequency for the forward plane and rear plane of the loudspeaker.  This information can be used to determine loudspeaker directivity, room interactions, off-axis listening and gives a general idea about the power response of the loudspeaker in the horizontal plane.

 polarresponse.jpg

Polar Response Sample

Impedance and Electrical Phase

Impedance measurements are conducted using a very simple technique.  A resistor of a known (measured) value is placed in line with the positive speaker terminal.  Two voltage probes connected to a soundcard are connected to the amplifier side of the resistor.  A 1kHz test tone is sent to the loudspeaker and the difference in the sensed voltage is automatically calibrated out in the measurement software.  Next, one of the measurement probes is moved to the speaker side of the known resistor and an MLS sequence is generated.  The impulse response of the impedance and phase is captured and converted to the frequency domain using the same techniques discussed in the on-axis frequency response section.

 Loudspeaker Impedance

Impedance and Electrical Phase Sample

The impedance of a loudspeaker is important when trying to mate a loudspeaker with an amplifier.  An ideal audio amplifier should output a constant voltage regardless of the impedance of the speaker.  However, no amplifier can produce infinite current.  Using Ohm’s law, it is clear that as impedance decreases the current must go up in order to hold voltage constant.  Many amplifiers are not designed to handle impedances below 6 ohms due to the increased current draw.

The lowest impedance is measured at DC, which is also known as the DC resistance. The IEC 26-8 method of specifying nominal loudspeaker impedance is set such that minimum impedance must not fall below 80% of nominal, so for an 8 ohm speaker this would be 6.4 ohms minimum, and for 4 ohms would be 3.2 ohms.

The impedance phase is an important factor to look at as well, because it relates to how efficiently the amplifier can deliver power to the loudspeaker.  When the phase angle of the impedance is greater than 0 degrees, the loudspeaker is presenting a partially inductive impedance to the amplifier which typically does not pose much threat to amplifiers.  When the phase angle is less than 0 degrees, the loudspeaker is presenting a partially capacitive impedance to the amplifier.  A large capacitive load can cause instability in some amplifiers.

Distortion Testing

Harmonic distortion components are generated by exposing a loudspeaker to a stepped sinusoid excitation signal and measuring the system’s response. To reduce the effects of noise on harmonic distortion measurements, the software uses heterodyne filters to select the harmonic frequency being measured.  The total harmonic distortion measurement is displayed in percent representing the percentage amplitude of harmonic distortion present compared to the fundamental.

This measurement is conducted on axis with a stepped sinusoid excitation signal at 90dB measured from 2-meters.  The 2nd through 5th harmonics are graphed together with the total harmonic distortion (THD) showing the constituent parts of the total harmonic distortion.

Analysis of the THD results should be taken in the context of the loudspeaker under test. Note that the distortion percentage is a logarithmic scale. The components listed as D2-D5 represent the 2nd through 5th harmonic of the fundamental.  The graph shows the amount of each harmonic present at the given fundamental frequency.  So the contribution to distortion from the 2nd harmonic of a 1kHz signal is visible by finding the line for D2 at 1kHz.  In this case, D2 represents two times the fundamental frequency, which is 2kHz.  Due to the limitations of the measurement/playback system and human hearing, harmonic frequencies above 24kHz will not be measured.  Since a harmonic is an integer multiple of the fundamental frequency, the harmonic distortion plot for each harmonic stops when the product of the harmonic order number and the fundamental frequency equals 24kHz.

harmonicdistortion.jpg 

Harmonic Distortion % Sample

Harmonic distortion is a standard test applied to many systems handling signals.  However, the correlation between harmonic distortion numbers and the human perception of sound quality is very poor.  This is because harmonics are typically masked in the broadband music signal.  Additionally, harmonics do not sound as bad as frequencies that are not integer multiples of the fundamental.  Inter-modulation distortion is another type of distortion that is produced when a loudspeaker plays multiple frequencies simultaneously.  Inter-modulation distortion is particularly offensive because it creates distortion at frequencies that are sums and differences of a mixed signal.  The frequencies produced are not musically correlated with the fundamentals that produced them.  Audioholics is actively researching methods to measure and display inter-modulation distortion that are presentable and useful to readers.

Cumulative spectral decay is a very easy way to identify loudspeaker resonance issues.  If a cabinet or driver has an issue with resonance in the audible band, the cumulative spectral decay plot shows how the response of the loudspeaker decays from an impulse excitation signal versus frequency.  As was discussed in the On-Axis Frequency Response section, the discrete Fourier transform of a gated impulse response generates frequency response.  To see the decay, the window is simply moved forward a certain amount of time and the discrete Fourier transform is calculated using the fast Fourier transform successively until the reflection free window time is reached.  This measurement is obtained at 2.83VRMS at the reference distance discussed in the on-axis frequency response section.  The sample results show the low frequency data cutoff curling to higher frequencies, this is due to the moving window. 

Editorial Note Regarding CSD by Dr. Floyd Toole:

Because of the time gating, necessary to see into the time domain, frequency resolution is sacrificed – note the smoothness of the curves. This means that energy in a high-Q resonance is spread over a wider frequency range, resulting in an artificially low level.  Besides all of this decorous displaying of data, the fact is that, except at very low frequencies, humans do not hear the ringing, we hear the spectral bump (which, ironically in these displays cannot be accurately seen).  See Section 9.2.1 in my book [1]. See also Figure 13.23 p. 246 for examples of the “uncertainty” principle as applied to waterfall displays of data.  You have a choice of seeing high resolution in time or frequency domains, not both.  They are pretty, though.

In perceptual terms, the audibility of ringing is substantially reduced by a phenomenon known as “forward temporal masking” – the initial sound reduces the audibility of sounds that immediately follow it.

[1] F. Toole, Sound Reproduction: Loudspeakers and Rooms. Burlington, MA: Elsevier, 2008

CSDsample.jpg

CSD Sample

The group delay of loudspeakers is also analyzed.  Group delay can be derived from the impulse response measurement and represents the time delay of amplitude envelopes of sinusoidal components through a loudspeaker.  While harmonic distortion is typically displayed in the frequency domain, group delay distortion is displayed in the time domain.  The group delay measurement defines the rate of change of the slope of the loudspeaker phase.  Group delay values between 1.6 to 2.0 ms [1] in the mid to high frequencies are detectable but their effect on the perception of sound quality is not well established.

groupdelay.jpg 

Group Delay Sample

 

Additional Tests

As part of the review process, each loudspeaker is disassembled.  The loudspeaker drivers, cabinet construction, and crossover components are inspected.  Each individual driver is measured independently in the cabinet to determine crossover frequencies, crossover slope and each driver’s contribution to the system response.  If anything interesting or out of the ordinary is determined, additional graphs will be generated.

 

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Recent Forum Posts:

Paul womble dung posts on September 13, 2016 17:45
i guess that some people don't understand why many of the technical technicalities can be very important to some other people.

not everyone only uses or needs good speakers at home to listen to music, or use a home theater/entertainment suite.

some people work with music, either in sound engineering, production, or are themselves musicians.
in which case they need speakers which are suited to them, and need to know WHY those particular speakers are suited to them, so they can recreate this wherever they are (obviously within the context of the average spaces they intend to do it in, even if they intend to use hired gear, it is wise to have even a basic understanding of all of this).

some musicians for example play acoustic instruments, and when they need amplified for some spaces, then generally certain set ups work much better for them.
other musicians may work purely electronically/digitally (like a techno music musician) so certain other set ups may suite them.

and you will find this will be similar for their home,perhaps, in that their domestic set up may reflect their work. although some of us like to leave work at work!

other folk need audio gear for research purposes and may be buying it on behalf of their university department so certain criteria may need to be fulfilled in various qualities.

i was quite impressed by how much detail the written stuff linked to from this page was, despite much of the language as yet being a bit over my head. but liked how it gave me a load of terms to look up and become familiar with.
although the algebra took a few reads through to grasp, it actually was not too difficult and was on a level with secondary education (middle school in U.S.?) and online calculators can help, or any basic calculator that has “scientific” settings on it.
my main interest at the moment is in deciding shapes and proportions with which to build cabinets for a slightly large sound system for mainly outdoor use, so i will need a little maths to work out the best proportions to get the best out of the materials used.

then that whole minefield of resistance, amps, etc etc etc, to get it all clean and efficient (with all of those taken into account and sorted, then even a 1500watt setup can rip the back-side off a much larger setup up, and save money, and weight.)



i think i will enjoy being a member of this forum!
DannyA posts on March 20, 2014 19:02
exlabdriver, post: 1024402
Danny:

If your system sounds good to you then don't worry about it. Why care about what other's subjective opinions are? Yours is the only one that counts.

It's best just to enjoy…

TAM

Agreed. Sometime that curiosity bug gets the better of me though.
exlabdriver posts on March 20, 2014 18:34
Danny:

If your system sounds good to you then don't worry about it. Why care about what other's subjective opinions are? Yours is the only one that counts.

It's best just to enjoy…

TAM
DannyA posts on March 20, 2014 16:26
At one point I was determined to know how my speakers stack up against other speakers in the same price/quality range. I eventually let the idea go. I like how my system sounds after all of the work I put in to placement and tuning. With that said, I've seen enough posts and comments about my speakers and their advertised specs to know that I would most likely be disappointed with the results. I could be wrong and I guess now I'm curious again but I don't want to ask “the question” if I can't live with the answer. What I don't know won't make my system sound any better or worse. But if I do know and the results stink, I'll be grinding my brain thinking about how to build a new system (that I can't afford right now).
Somehow I know my curiosity is going to get the best of me.
ira posts on March 20, 2014 13:10
Please keep in mind that if the multimeter you use is not a “true RMS” meter, it will have material errors in its RMS measurements. I could not tell the exact model number of the DMM you are using, so please make sure you look up its exact specs, and I recommend junking it if it's not a true RMS DMM - no need to include avoidable errors in your reviews.
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