SPL Ratings & Power Response - In the Land of Confusion Again

[radiogram]

Loudspeaker sensitivity ratings are specified based on Power and (@ 1 Watt/meter) and not Voltage. This would imply that the SPL will increase with increased power into the speaker and decrease with decreased power into the speaker.

This would mean that two different speakers with same SPL rating but different impedences will have the same SPL at different voltages across the speakers for the same wattage.

So here is my confusion. If this is indeed the case then would not a speaker’s acoustic frequency response be the inverse of the impedence curve? Let us assume we a have high current solid state amplifier with high damping factor (voltage source) capable of supplying enough current at the lowest impedence and can maintain same voltage.

Now, wherever the impedence is lower, the amplifier is going to supply enough current so as to maintain the same voltage. Thus, the lower the impedence more the power and if SPL is based on Watts then, consequently more SPL. This again would then imply an acoustic frequency response that cannot be flat but one that will track the inverse of the impedence curve.

If the SPL sensitivity were instead based on Voltage and not power, then it will result in same SPL at any impedence.

So here are my confusion questions:

1. If the above is true then it would seem that an amplifier that actually lowers the voltage to maintain same power at lower impedence is preferable so as to have the same acoustic output since SPL is Watt based? – Totally against well established design that a low impedence voltage source is the way to go.

2. Is any of my above analysis correct if we base SPL as dependent on Wattage ? If not, then where did my understanding or application going wrong?

[Al Klappenberger]

Radiogram,

You are right on again!

There are actually two measures of speaker efficiency. The one to consider is "sensitivity". It assumes 1 W in 8 Ohms which is 2.83V applied. This is the one to consider. You simply measure the output of the speaker at 1 meter with 2.83 V applied and to heck with the actual power delivered by the amp. No speaker is a constant 8 Ohm load. The Khorn with the AA network actually looks like 30 Ohms at 2 KHz! Sensitivity is actually a fixed ratio input to output. With this method, the Khorn is actually about 99 to 100 dB SPL at 1 meter sensitivity. I have measured several of them using a 2-channel analyzer (HP 3563a) with a calibrated mike on one channel and an voltage divider from the amp output to the other channel. The voltage divider is set to cut 2.83 V down to EXACTLY the level the mike produces at 100 dB SPL. This way, with the analyzer set to compare channels (transfer function) 100 dB SPL at the mike is displayed as 0 dB on the display no matter what voltage is being applied to the speaker. I can measure absolute sensitivity without having to wear ear plugs!

Remember too that sensitivity is an average over the frequency rage involved. The level will be about 100 dB +- 5 dB or so.

AL K.

[jacksonbart]

You also have to consider what type of A/C power cords you are using.....???..... .... .. . . . . .. . ... .. . . .. .. nah

[Al Klappenberger]

Here is an example of the “sensitivity” method. It’s a study of a JBL 2426H driver on a wood Trachrix horn. It’s old, so it was done on my older analyzer (Spectral dynamics SD375) using the voltage divider on channel “A” from the amp. Notice the analyzer identifies the scale as +20 to -60 dB and the display is “TF LOG B/A”. TF stands for Transfer Function. Note that the 0 dB point is actually 100 dB SPL at 1 meter (39 Inches). The sensitivity is about 108 dB on axis below 6KHz where I am using it as a squawker. That driver needs some major EQ-ing to compensate for the mass roll-off if you wanted to use it in a 2-way system. BTW: I did that for a while and it sounded quite good.

Al K.

[Arkytype]

Radiogram,

Loudspeaker sensitivity ratings are specified based on Power and (@ 1 Watt/meter) and not Voltage. This would imply that the SPL will increase with increased power into the speaker and decrease with decreased power into the speaker.

While the International Electrotechnical Commission (IEC) sets the standards for loudspeaker measurements under part 60268-5, not all manuafacturers specify their products according to the "book".

For example, a perusal of JBL spec sheets shows sensitivity ratings of both 2.83 V @ 1m and 1W @ 1m for their products. To be fair, they do state that the nominal impedance rating of the loudspeaker.

One of the more detailed loudspeaker sensitivity rating will be found on the Eminence web site.

http://www.eminence.com/proaudio_speaker_detail.asp?web_detail_link=KAPPAPRO-10A&speaker_size=10&SUB_CAT_ID=1

A related article by Charlie Hughes goes even further to clarify loudspeaker sensitivity ratings. His recommendation is to apply the same voltage to every loudspeaker. That way the acoustic output will vary depending upon the rated impedance of the loudspeaker.

http://www.prosoundweb.com/article/print/loudspeaker_sensitivity_whats_a_watt_anyway

This would mean that two different speakers with same SPL rating but different impedences will have the same SPL at different voltages across the speakers for the same wattage.

Yep. All things being equal (they never are!), if loudspeaker A has a nominal impedance rating of 8 ohms and loudspeaker B is rated at 4 ohms and both output 98 dB SPL with 1 watt input, then the voltage read across the voice coils would be 2.83 and 4.0 volts respectively.

So here is my confusion. If this is indeed the case then would not a speaker’s acoustic frequency response be the inverse of the impedence curve? Let us assume we a have high current solid state amplifier with high damping factor (voltage source) capable of supplying enough current at the lowest impedence and can maintain same voltage.

Now, wherever the impedence is lower, the amplifier is going to supply enough current so as to maintain the same voltage. Thus, the lower the impedence more the power and if SPL is based on Watts then, consequently more SPL. This again would then imply an acoustic frequency response that cannot be flat but one that will track the inverse of the impedence curve.

The problem with your premise is that the efficiency of a loudspeaker is not constant. As the complex electrical impedance of the loudspeaker increases or decreases, its acoustic efficiency increases or decreases. All things being equal, while the "constant voltage" amplifier will vary its output current to mirror the load, the acoustic output of the loudspeaker may remain constant.

Nelson Pass has written an article extolling the virtues of a constant current amplifier when driving full-range high efficiency loudspeakers. He also shows how to convert your constant voltage amp to a constant current device.

http://www.firstwatt.com/pdf/art_cs_amps.pdf

Lee

[Al Klappenberger]

Lee,

Interesting info.

I'm curios about what you think of a constant current source with respect to "damping factor". A constant current source is an infinite Zo. No damping at all! It would seem a speaker would ring like a Christmas bell. Try tapping the cone of a cheap loudspeaker, then short the terminals and tap it again. The difference is dramatic!

Al K.

[radiogram]

Deleting post due to issues with line feed.

[radiogram]

Lee:

Please ignore previous post. Issues with New Line when I post which Preview does not show.

The problem with your premise is that the efficiency of a loudspeaker is not constant. As the complex electrical impedance of the loudspeaker increases or decreases, its acoustic efficiency increases or decreases. All things being equal, while the "constant voltage" amplifier will vary its output current to mirror the load, the acoustic output of the loudspeaker may remain constant.

]

That is quite interesting and makes some sense now. While it is not clear to me regarding mathematical relationship of impedence vs speaker efficiency, there has to be some truth in what you are saying, since otherwise many speakers with wild swinging impedence curves will sound utterly terrible with modern sold state amplifiers which are closer to a voltage source.

Now let us look at this with some numbers taking the example of a B&W 801N speaker. I have taken the values as was published by Stereophile measurements. I am completely ignoring the impedence phase here.

Impedence = 19.5 @ 35Hz; Impedence = 3.0 @ 100Hz.

Driven by a Voltage Source Amplifier – Let us for practical purposes assume its source impedence is 0 since many SS amps have impedence as low as .01 ohms.

Source Voltage Freq Load Impedence Power at Load (Watts)

2.83V 35 19.5 0.41

2.83V 100 3.0 2.67

So, the power delivered is 6.5 times (8dB) at 100Hz compared with at 35Hz.Now, if the speaker had the same efficiency or sensitivity based on Watts at all frequencies, it will have an acoustic output at 100Hz that will be about 8 dB louder than at 35Hz. Now this cannot be really the case as the 801s supposed to sound good driven by SS Amps.

Now, if we assume that in reality the speaker’s real efficiency at same power is actually between +/- 5dB across the frequency spectrum and if we further assume what you said that real efficiency will be higher at higher impedences, then let us make an assumption that at 35Hz its true efficiency is 5dB higher than at 100Hz - and in the end the net effect when driven by the same voltage, becomes a difference in acoustic output at 100Hz being more by 8 – 5 = 3 dB compared with 35Hz, which is a lot better than a difference of 8 dB. But again it is a huge assumption that at 35Hz its real efficiency at same power is 5dB more than that at 100Hz.

Now let us take an Amp with a high source impedence (like a Tube Amp) and let us assume it has an output impedence of 3 Ohms and let us increase the source voltage so as to have the same power at the load at 35Hz (0.41 Watts) as in the above case.

Source Voltage Src Imp Freq Load Impedence Total Imp Current (I) Power at Load

3.26V 3 35 19.5 22.5 .145 .41 Watts

3.26V 3 100 3.0 6.0 .543 .885 Watts

Now, while the voltage freq response at the load will track the impedence curve of the load and not be flat like a voltage source solid state, LOOK at the power response at the load. The power difference is only 2.16 times i.e. 3.35 dB and not 8 dB between F1 & F2.

Now, if SPL were a function of purely Watts, does it mean DEPENDING on the speaker’s true efficiency differences at various frequencies, a high source impedence amp MAY actually result in a subjectively flatter acoustic output?

[Al Klappenberger]

Guys,

This a very interesting point. It would not be difficult to test this out. I have all the equipment needed to do it. Lee does too. I suggest running a frequency repose plot from a good solid state amp on some speaker as a reference, then connecting a resistor between the amp and the speaker and running the plot again. You could start with your 3 Ohm example.

Below is a complex Zo plot of the an actual AA network. The network is designed to reduce the level to the squawker but the nearly 30 Ohm peak in the middle of the midrange would seem to yield excessive attenuation considering the transformer used to do it is also yielding 3 dB of attenuation due to its turns ratio. My Universal network provides a flat 6-8 Ohm resistive load to the amp and the usual transformer setting is 5.5 dB. That's only a 2.5 dB difference.

Power into 30 Ohms = 2.83 * 2.83 / 30 = 0.27W

Power into 7 Ohms = 2.83 * 2.83 / 7 = 1.14W

db = 10 * log10(1.14 / 0.27) = 6.26 dB

Add in the transform ratio and you get 9.26 dB.

I don't think that is really what is happening especially considering the actual Zo is more like 28 ohms than 30 Ohms.

BTW: Several years ago I had Dean Wescott (DEANG) connect a resistor in series with his amp and his Khorn (AK-4 network) to test out a theory I had about the AK-4 at the time. I asked him to listen to it. His conclusion was that is didn't sound very good!

Al K.

[radiogram]

Al:

There is one thing I may have overlooked here. In my B&W 801 Example I have given, the impedence is not that of just the driver, it is with the crossover and driver as a whole. So while my calculation that at 100Hz, 6.5 times more power is being fed is correct, it is power fed into the crossover. Does it necessarily mean the same power is being drawn by the load (Driver) ? Is it possible that the power consumed by the network @ 100Hz is more than that at 35Hz and what is at the load @ 100Hz is actually not higher by 8dB but lower ? In other words, is it possible the crossover network can be consuming different power at different frequencies and somehow this needs to be taken into account?

[Al Klappenberger]

I tend to doubt that the crossover is causing anything like that. I am thinking that any peak in the impedance around 35 Hz would be the resonance of the woofer driver. I see peaks like that on every speaker I have tested. In fact, there are usually two peaks. I have never run test on a B&W though.

Here's a Zo plot on a K24 in a ported box. It has two peaks around that frequency

Al K.

[Arkytype]

If you have access to the late Richard C. Heyser's collection of papers entitled Time Delay Spectrometry published by the Audio Engineering Society, I think you will find not only some answers to your inquiries, but answers to questions you didn't know you needed to ask! The link is to the second part of a two-part article someone posted earlier on this forum.

http://forums.klipsch.com/forums/storage/3/1027018/6904heyser.pdf

He concludes this article by stating, in part, A loudspeaker, when considered as a transducer of electrical signals to acoustic pressure, has a transfer function which has a frequency-dependent amplitude and phase response. The effect of these amplitude and phase variations may be considered to be the introduction of a time delay distortion in the reproduced pressure response.

To sum up Heyser's many articles on the subject (no mean feat!), an on-axis "frequency response" is virtually meaningless without the attendant phase response. This discovery was the impetus for his invention of Time Delay Spectrometry (TDS).

Whether you are using a Mitey Mike or a Bruel & Kjaer microphone to measure your loudspeaker, neither instrument is capable of measuring more than air pressure modulations. They are "deaf" to complex impedance, time delay, etc..

To get back to your overarching theme, keep in mind that in addition to the crossover network's complex impedance vs. frequency, you have the individual driver's acoustic delay due to offset voice coils as well as their complex impedance characteristics. Don't forget to factor in the back EMF generated by the drivers. Heck, it's a wonder that any loudspeaker works!

Lee

[WMcD]

Just to revisit this. The actual spec used is "voltage sensitivity." So we use 2.828 volts for some SPL output. That is based on the assumption that the speaker has an impedance of 8 ohms. P = V^2 / R. So we assume R = 8. 2.82 x 2.82 = 8 and therefore P = 1 watt.

We basically have to use this assumption because, when a speaker is tested, we apply a constant voltage and sweep it across the freq band. We just pretend there is 1 watt being absorbed. It ain't so.

Stepping back a bit more, there is an assumption in the whole scheme in the recording chain. If we sweep through acoustic tones at a constant SPL at the microphone, that should result in a constant voltage at the amp output thoughout the sweep. That is good in that it is fixed goal.

You really have to disregard the notion that the amp output, given the above, is constant power. The amp is not smart enough to do that. It does not sense the impedance of the load in a way to maintain constant power output as the impedance of the speaker input terminal changes.

The other question or assumption seems to be whether a bass system has has the same efficiency at all freqs. The answer is very much, no.

One overall reason for this is that the woofer diaphragm is shrinking, in terms of wavelenght, as we go down in freq. It is a more and more poorer radiator. So to some extent, the woofer is always acoustically more effective at high freqs. There is a work around. This arises from the fact that it is more difficult for the motor to move the mass of the diaphragm at high freqs. So this mass loading essentially kills off high freqs. A type of equalization.

There is still, though the issue of getting the diaphragm to move more easily at low freqs. (From the above we've killed off high freqs with mass loading.) Is there anything which can help goose up low freqs?

Yes. Let's assume we have a woofer in a sealled box at the rear. At some low freq, the box and suspension of the woofer hit a resonance. At resonance, the diaphragm moves fairly freely, like a tuning fork. In a larger sense, as we go down toward resonance the is a curve where the diaphragm is becoming more and more easy to move, and it does move more and more.

So, now we have a neat equalization as we go down toward resonance of the box combination. The acoustic efficency is dropping but the diaphragm is moving more. And it is easier mechanically for the electric motor to move it.

These last item means two things which are wrapped up together. The motor draws less current (I). Recall Z = V/I. And V applied is constant. And I is going up. So Z goes up. Also the moving diaphragm and motor start acting like a generator to add voltage. Essentially, the V goes up and Z goes up again. It is odd but the power drawn is less, but the acoustic output is greater. So we see that there is no straigh line conversion efficency at all. It is working inversely.

This is why we see a hump in electical impedance around resonance. It means that the amp is delivering less current and therefore less power. However, the acousic output is being goosed up just where it is needed. This is because the diaphragm is moving more. A lot of this is the built-in equalization of a well designed sealled box system. Mass rollof kills the highs and resonance gooses the lows. Below resonance, the motion decreases and acoustic output drops. If you look at specs for sealled box systems, the -3 dB acoustic output is just below the system resonance. We've goosed up diaphragme motion just at the last minute as we slide down the freq scale

The other design for the box is a ported system. Here, again we are searching for some acousic mechanism to goose up bass as it dropping off. In the sealed box system we have a simple "tuned" system of resonance. Let's do something more complicated.

In the tuned box, bass reflex, system we have a port in the box which can harvest some additional acoustic energy. A sealed box is a tuning fork and now we have another which is potentially more effective. There is a mass of air in the port which can cause another resonance and it is somewhat easy to pump air in and out of the port. The back of the driver will drive this.

Yet, we must be wise with this second tuning fork which potentially efficient acoustically.

There is one setting of the two resonances which is easy to understand. It is to put the resonance and Q (size and slope of the hump) of the box at the same point as the resonance and Q of the driver. (A B3 alignment?) Here we set things up so that the box and port is a doppleganger (?) dual of the speaker driver. Therefore, just as the driver is trying to resonate, the box and port is resonating too and loading it exactly the same. And the acoustic power is sent to the port.

So you say, what does this have to do with conversion efficency and electical impedance? We see the doppleganger effect in the graph of electrical impendance which Al K put up. It looks like two peaks. But not so, it is hump of the resonance of the driver with the imposed valley of the box-port loading it just in the middle.

Here we have something interesting. The electrical motor has to work harder because the box and port is loading it acoustically. The excusion of the diaphragm is reduced because it is acoustically loaded by the box-port. The acoustic efficency is increased because pressure is coming out of the port and there is far less SPL off the front of the driver.

Going back to the question. (Ahem) In this design, we see that over a narrow range (the valley in the middle of what would otherwise be the hump of a sealled box) we have succeeded in drawing more power out of the amp (Z is low and therefore current is high). We've again goosed up bass just when it is falling off, at least for narrow range. There is a downside. When this two-tuning-fork system gets below resonance, the output drops very quickly.

Okay, that is a lot to understand without diagrams. However, it just shows how electrical power to acoustic power conversion is played with in box design. To re-cap The sealed box increased acoustic output with less electrical power at resonance in a smooth hump of impedance (less current), just when we need it. The ported box gives an increase in acoustic output, just when it is needed, by drawing more electrical power at the valley (more current).

We see, therefore, that conversion efficency is by no means constant over a freq range.

Wm McD

[DrWho]

If this is indeed the case then would not a speaker’s acoustic frequency response be the inverse of the impedence curve?

Keep in mind that an SPL measurement (frequency response) is a measure of intensity, not
power. You would need to integrate the SPL over 360 degrees in every
direction in order to obtain the total power output of the speaker.

With almost every transducer, you see a rising impedance as you go higher in frequency due to the inductance of the voice coil. When fed with a perfect voltage source and the frequency response is measured on-axis, you often see a flat frequency response in the region where the impedance is rising. However, if you measured on every axis, you would notice that it only remained flat in the on-axis, and off-axis the highs were rolling off. What's happening is that less acoustic power is being delivered by the driver, but that acoustic power is being focused such that the on-axis intensity is higher. So in a way, this is an example of where the output power is following the inverse of the impedance response.

However, in the lower bandwidth of the transducer you're going to see a peak in the impedance response that correlates with its Fs. In a completely lossless system, the driver would resonate forever at its resonant frequency once stimulated...which requires the impedance to be infinity so that the law of conservation of energy is preserved. Since there are some resistive losses in the coil, heat losses in the suspension, and heat losses from moving air around, the magnitude of the impedance is finite and often less than 100 ohms even. But like the lossless system, the transducer wants to resonate at that frequency and is therefore easier to move. Because of this, the driver is more efficient at its Fs than it is at other frequencies, which is convenient because for a given voltage input, the current is less because the impedance is higher. And in a transducer, the amount of force generated by the voice coil is proportional to the current, which means there is naturally less current flowing at the frequency where the driver is easiest to move.

Depending on how the driver is designed, the Fs impedance peak could result in a flat frequency repsonse when fed with a perfect voltage source, or it could result in a peak in the frequency response too. Either way, the actual power output from the system at the Fs peak of the system is not inversely proportional to the impedance response.

The difference between the Fs related impedance shape and the inductance impedance shape is where in the driver these effects are manifesting themselves. The inductance is really part of the electrical components and limits the current, but the Fs is related to the acoustic side of the transducer.

All that said, if you had a perfect current source feeding your speakers and they were designed to not beam the high frequencies, then you would actually end up with a flat on-axis response where with a perfect voltage source you would have a 6dB/octave slope (it attenuates on-axis as you go higher in frequency).

The problem with a current source, however, is that at the lower frequency Fs bump, you're going to get too much output.

At the end of the day, it's easier to approximate a perfect voltage source (which is what a good audio amplifier does) and it's also easier to model the behavior of speakers assuming a perfect voltage source (which is the "Thiele Small Model").

One thing I've been really interested in is coming up with a Thiele Small type model that assumed a perfect current source instead. I've had the opportunity to work on electric motor controllers and my roommate was employed to design super high end motor controllers for a year or so, and I thought it was really interesting that they stick to current based models because it makes the torque control loops easier to stabilize when using Class D topologies. You also get the cycle-by-cylce current limiting with it too. Anyways, I think it would be really interesting to employ some of these technique to a loudspeaker motor....basically turning it into a high-speed/high-accuracy servo instead of the open-loop control we typically see today.

Anyways, the easiest way to grasp these variations is to understand how the speaker efficiency isn't the same at every frequency. I might also add that it gets a bit more complicated when you start looking at ports/horns/etc... instead of just the classic sealed box. One interesting thing about a reactance anulled horn is that it has no impedance peak at the lower frequencies...and it is quite possible to come up with a constant coverage pattern, which means the perfect current source would naturally lend itself towards a flat acoustical power response without having to deal with the low frequency peaks.

Well that's my take on it...I'll have to review my comments sometime when I'm not dozing off at the keyboard to make sure I didn't get something backwards.