“High-Res” Audio: Part 13: Wrapping up

As I’ve stated a couple of times through this series, my reason for writing this stuff was not to prove that high res audio is better or worse than normal res audio (whatever that is…). My reason was to highlight some of the advantages and disadvantages associated with LPCM audio at different bit depths and sampling rates. Just as a bullet-point summary of things-to-remember/consider (with some loose grouping):

  • “High resolution audio” could mean
    • “more than 16 bits per sample”
      or
    • “a sampling rate higher than 44.1 kHz”
      or
    • both.
  • These two dimensions of the specifications have different implications on the signal

  • Doubling the sampling rate only increases your audio bandwidth by 1 octave.
    Yes, it’s twice as much information, but that’s only one octave. If you add an extra octave on top of a piano, you don’t get twice as many notes.
  • Just because you have more bits per sample doesn’t mean that you are actually getting more resolution.
    There are examples out there where a “24-bit recording” is just a 16-bit recording with 8 zeros stuck on the end.
  • Just because you have a higher sampling rate doesn’t mean that you are actually getting a recording that was done at that sampling rate.
    There are examples out there where, if you do a spectral analysis of a “high-res” recording, you’ll see the cutoff filter of the original 44.1 kHz recording.
  • Just because you have a recording done at a higher sampling rate doesn’t mean that the extra information you get is actually useful.



  • There are many cases where you want equipment that has higher specifications than your audio signal.
  • If you have a volume control after the conversion to analogue, then 93 dB of dynamic range (16 bits, TPDF dithered) might be enough – especially if you listen to music with a limited dynamic range. However, if your volume control is in the digital domain, and you have a speaker that can play loudly, then you’ll probably want more dynamic range, and therefore more bits per sample hitting the DAC.

Like I said, I’m not here to tell you that one thing is better or worse than another thing.

As I said, my intention in writing all of this is to help you to never fall into the trap of assuming that “high resolution audio” is better than “normal resolution audio” in all respects.

More is not necessarily better, sometimes, it’s not even more. Don’t fall victim to misleading advertising.

“High-Res” Audio: Part 12: Outputs

Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 7
Part 8a
Part 8b
Part 9
Part 10
Part 11

This series has flipped back and forth between talking about high resolution audio files & sources and the processing that happens in the equipment when you play it. For this posting, we’re going to deal exclusively with the playback side – regardless of the source content.

I work for a company that makes loudspeakers (among other things). All of the loudspeakers we make use digital signal processing instead of resistors, capacitors, and inductors because that’s the best way to do things these days…

Point 1: This means that our volume control is a gain (a multiplier) that’s applied to the digital signal.

We also make surround processors (most of our customers call them “televisions”) that take a multichannel audio input (these days, this is under the flag of “spatial audio”, but that’s just a new name on an old idea) and distribute the signals to multiple loudspeakers. Consequently, all of our loudspeakers have the same “sensitivity”. This is a measurement of how loud the output is for a given input.

Let’s take one loudspeaker model, Beolab 90, as an example. The sensitivity of this loudspeaker is set to be the same as all other Bang & Olufsen loudspeakers. Originally, this was based on an analogue signal, but has since been converted to digital.

Point 2: Specifically, if you send a 0 dB FS signal into a Beolab 90 set to maximum volume, then it will produce a little over 122 dB SPL at 1 m in a free field (theoretically).

Let’s combine points 1 and 2, with a consideration of bit depth on the audio signal.

If you have a DSP-based loudspeaker with a maximum output of 122 dB SPL, and you play a 16-bit audio signal with nothing but TPDF dither, then the noise floor caused by that dither will be 122 – 93 = 29 dB SPL which is pretty loud. Certainly loud enough for a customer to complain about the noise coming from their loudspeaker.

Now, you might say “but no one would play a CD at maximum volume on that loudspeaker” to which I say two things:

  1. I do.
    The “Banditen Galop” track from Telarc’s disc called “Ein Straussfest” has enough dynamic range that this is not dangerous. You just get very loud, but very short spikes when the gunshots happen.
  2. That’s not the point I’m trying to make anyway…

The point I’m trying to make is that, if Beolab 90 (or any other Bang & Olufsen loudspeaker) used 16-bit DACs, then the noise floor would be 29 dB SPL, regardless of the input signal’s bit depth or dynamic range.

So, the only way to ensure that the DAC (or the bit depth of the signal feeding the DAC) isn’t the source of the noise floor from the loudspeaker is to use more than 16 bits at that point in the signal flow. So, we use a 24-bit DAC, which gives us a (theoretical) noise floor of 122 – 141 = -19 dB SPL. Of course, this is just a theoretical number, since there are no DACs with a 141 dB dynamic range (not without doing some very creative cheating, but this wouldn’t be worth it, since we don’t really need 141 dB of dynamic range anyway).

So, there are many cases where a 24-bit DAC is a REALLY good idea, even though you’re only playing 16-bit recordings.

Similarly, you want the processing itself to be running at a higher resolution than your DAC, so that you can control its (the DAC’s) signal (for example, you want to create the dither in the DSP – not hope that the DAC does it for you. This is why you’ll often see digital signal processing running at floating point (typically 32-bit floating point) or fixed point with a wider bit depth than the DAC.

“High-Res” Audio: Part 11: How high can you go?

Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 7
Part 8a
Part 8b
Part 9
Part 10

If you you get an audiometry test done, you’ll be shown into a small room, about the size of a public bathroom stall. Someone will put a pair of headphones on you, and pass you a small handle with a button. Your instructions are to press the button if you hear a tone. Then the audiometrist will leave the room, closing the door, and you’ll suddenly realise that if there’s any noise in this room, it’s because you’re making it.

Then you hear a beep in your left ear. You press the button. You hear a quieter beep. Press. Quieter beep. Press…. …. …. Beep, press… …. …. …. Beep, press…. New frequency beep, loud again. Press… and so on.

What’s happening here is that you’re presented with a sine tone at some frequency, probably loud enough for you to hear. You press. The tone gets quieter, and you press again. Eventually, the tone is so quiet that you cannot hear it (this is normal) so you don’t press. So, the tone gets louder, and you press. Then it gets quieter again, until you can’t hear it again.

By crossing over that threshold of “can hear” and “can’t hear” a couple of times, the audiometrist finds out whether or not you got lucky… If you bottom out at the same level a couple of times in a row, then that’s your threshold of hearing at that frequency in that ear.

The frequency changes (usually by 1 octave, but sometimes less), and the whole process is repeated.

If you get a full test done, then this is probably done at 9 frequencies (250, 500, 1k, 1.5k, 2k, 3k, 4k, 6k, and 8kHz) in both ears individually – 18 tests in all.

You’ll then be given a sheet of paper, or at least shown a plot of your hearing threshold. Typically, if you have “normal” hearing (whatever that means) your thresholds will all be sitting on a horizontal line marked 0 dB. If you’re “better than normal” then you get a negative score, if you’re “worse than normal” you get a positive score.

What does this mean?

Let’s start over.

If a lot of people do this test, and we only test at 1 kHz, we’ll find out that, after the results are averaged, the group can hear the 1 kHz sine tone when the change in air pressure at the ear entrance is 20 µPa. We’re not going to talk about what this means other than to say that “sound is a change in air pressure over time, and that pressure is measured in pascals, abbreviated Pa”. Needless to say, 20 µPa is pretty quiet, since it’s the quietest sound a group of people can hear at 1 kHz when you take their average.

If you did that test at a much lower frequency, you would find out that people aren’t as good at hearing quiet sounds. In other words, at 100 Hz, the sine tone has to be louder than 20 µPa for people to hear it.

The same is true if you repeated the test at a much higher frequency – say, 10,000 Hz.

If you did this test at a lot of frequencies, then you’d find out that, on average, the threshold of hearing for a human follows the bottom red line of the plot in Figure 1, borrowed from Wikipedia.

Figure 1: The bottom red curve is the average threshold of hearing for a human being.

That bottom plot shows the threshold of hearing for different frequencies, plotted in dB SPL. Notice that, at 1 kHz, the line is at 0 dB SPL. This is because 0 dB SPL is defined to be the average threshold of hearing of a human at 1 kHz, which is 20 µPa. So, it’s not an accident…

Looking at that plot, you can see that, in order to hear a sine tone at 20 Hz, the tone has got to be more than 70 dB louder (that’s a LOT louder). So, a microphone “sees” a 73 dB SPL, 20 Hz sine tone as being louder than a 0 dB SPL, 1 kHz sine tone – but as far as you’re concerned, they’re both “the quietest sound you can hear” – therefore, they’re the same level.

If we take that threshold of hearing curve, and we play tones at those levels for those frequencies, then you should “just be able to” hear them. So, we’ll call those levels “0 dB” – since it’s the same as what is expected of you.

In other words, the piece of paper you got from the audiometrist tells you how much above or below that red threshold of hearing YOU sit.

Now, let’s back up a bit.

  1. I said that, in your test, you only went up to 8 kHz. This is because, above that (and possibly even before that) the headphones might not be trust-worthy, and even a tiny movement (say a couple of millimetres) in the position of the headphones will have a (relatively) big effect on the level at your eardrum. So, rather than get people worried about losing their hearing at 20,000 Hz (when, in fact, they were actually just wearing the headphones 1 mm too far forward), you won’t get tested.
  2. Notice how variable that threshold of hearing line is. There are big changes in level over the “audible” frequency range.
  3. Remember that the threshold of hearing curve is an AVERAGE of a lot of people. Just like no one has 2.6 children, no one has this exact response. And, if you are some freak of nature and you DO have exactly that response, you don’t for long… we all get old…
  4. Notice how that threshold of hearing curve only goes up to about 16 kHz, and above that it says “estimated”. See point #1.

Now, you should know that your ability to hear a sine tone at some frequency is defined as how your ability compares to an expectation based on an average, within a relatively small frequency band: 250 to 8 kHz.

Then you look at a textbook or you read a website that says “humans can hear from 20 Hz to 20 kHz”, which is not enough information to be either true or false… It’s like saying “humans are usually between 0 and 10 m tall” which is also sort of true, but also adequately vague to be potentially worse-than-useless information.

The truth is, unfortunately, much more complicated… However, it’s fair to say that, in order for you to just hear a sine tone at 20 kHz, it would have to be much, much louder than one at 1 kHz. In fact, if I played a 20 kHz sine tone loud enough for you to hear, measured that level, and then played a 1 kHz sine tone for you at the same level, you’d probably punch me – after you had passed out due to the pain, woken up, hunted me down, and found me… (I’d already have run away by then….)

So what?

We humans like nice, tidy, answers. “It will rain tomorrow” is preferable to “there is a 70 – 80% chance of scattered showers in the afternoon tomorrow”. We even get mad when the information is correct, but we interpret it tidily… For example, we’ll complain about getting rained on in the middle of our hike, when there was only a 10% chance of rain. On the other hand, if there was a 10% chance of winning 1 Million dollars in the lottery, we’d all buy a ticket.

Anyways, once-upon-a-time, when the committee for inventing the compact disc was holding meetings, they said “what should the sampling rate be?” and someone said “at least 40 kHz, because we can hear up to 20 kHz”. (The reason it’s 44100 is related to the fact that the bits were stored as black and white stripes on video tape, and NTSC and PAL come close to meeting each other close to that number, when you look at the numbers of lines per field and frames per second.)

Of course, like any first-generation thing, digital recording equipment wasn’t very good at the start (back around 1980 or so) – so the first DDD recordings that were released on CD sounded… well…. weird. There was quantisation distortion because they hadn’t figured out dither yet, only 12 or 13 of the bit values were working properly on the ADC’s, the anti-aliasing filters were implemented as analogue circuits, so they let some stuff through that aliased, and they rang (“sang along”) with the signal at a high frequency… All of that added up to “weird” – possibly even “bad”. Then, people who had good equipment (high-end turntables or, even better, 1/4″ tape running at 30 ips) listened to this new format, decided it was bad, and that was that.

Some of them asked “why is is bad?” and one answer they came up with was the band limiting… If the system can’t capture or store or play materials above 20 kHz, then it’s useless… Right? Maybe…

Then, instruments were put in front of measurement microphones and spectra were measured – and the proof was in. Trumpets with harmon (wah-wah) mutes, when pointing directly at the microphone, contain harmonics as high as 50 kHz! This must explain why CDs sound bad! Right? Maybe…

Then Rupert Neve did a demo at an AES (Audio Engineering Society) convention where he played people two tones. Both were at 7 kHz, but one was a sine wave and the other was a square wave (at some level). The question was: have a listen and tell me which is which. The results were the same as if everyone was just guessing. (Remember that, in order to make a square wave, you need to add odd harmonics – so the lowest-frequency content difference between a 7 kHz sine wave and a 7 kHz square wave is at 21 kHz.) Proof that we don’t need to go above 20 kHz, right? Maybe…

Some years ago, I took some “high resolution” audio files and measured their spectral content. One particularly interesting result is shown in Figures 2, below.

Figure 2: The spectral content of a 96/24 “high resolution” audio file I bought.

Look at that spike in the top end – around 20 kHz. What musical instrument makes that sound? The answer is “no musical instrument makes that sound – at least none of the baroque instruments in that recording make that sound. As I wrote back in 2014:

 If you’re wondering what it might be, I asked a bunch of smart friends, and the best explanation we can come up with is that it’s noise from a switched-mode power supply that is somehow bleeding into the recording. HOW it’s bleeding into the recording is a potentially interesting question for recording engineers. One possibility is that one of the musicians was charging up a phone in the room where the microphones were – and the mic’s just picked up the noise. Another possibility is that the power supply noise is bleeding electrically into the recording chain – maybe it’s a computer power supply or the sound card and the manufacturer hasn’t thought about isolating this high frequency noise from the audio path. Or, maybe it’s something else.

Interestingly, this is a conflict of two engineers. The designer of the power supply (assuming that’s what it is…) said “I’ll put the switching frequency above 20 kHz so that no one will hear it” and the recording engineer said “I’ll record this at 96 kHz so that people can get the content they’re missing…” The problem is that the content you’re missing is something you don’t want…

Similarly, if you listen to Eric Clapton’s “Unplugged” album with headphones or loudspeakers that have a low-enough low-frequency range, you’ll hear a loud thump, thump, thump going along with the music. This is the sound of someone tapping their foot on a temporary stage floor, shaking a vocal microphone. In my not-very-humble opinion, that should never have made it out to the public release. However, my guess is that the speakers it was mastered on didn’t go low enough… (OR, it was an artistic decision, and I would have done it differently.) Assuming that I’m right, then this is a second example where a “better” system sounds “worse”.

Of course, through all of this, I have assumed that your loudspeakers or headphones can produce the signals that we’re talking about in the direction that you’re sitting in, and that those signals are not being masked by other sounds in the room (like phone chargers singing…) However, to complicate things with reality would just be too far to go today…

Conclusions?

I don’t have any, but I have some questions and (as usual) some opinions…

  • Does a harmon mute on a trumpet produce energy at 50 kHz, if you’re sitting right in front of it?
    Yes.
  • Do you want to sit right in front of a trumpet with a harmon mute?
    Debatable.
  • Can a high-res audio recording include the sound of a phone charger?
    Yes.
  • Do you want to have an expensive recording of a baroque ensemble with obligato phone charger?
    Probably not – the charger is not in Buxtehude’s original score as far as I can see.
  • Can you hear the difference between a 7 kHz sine and a 7 kHz square wave?
    Depends on the speaker / headphone, the listening position, the background noise level, and whether or not you were out clubbing last night. Heads or tails?
  • Will you feel better by knowing that your file contains “audio” content above 20 kHz? Probably.
    Placebos have been known to work bigger miracles than this. (But don’t forget the stuff I said about sampling rate converters earlier…)

“High-Res” Audio: Part 4 – Know your limits

Part 1
Part 2
Part 3

If you’ve read the three introductory parts of this series, linked above; and if you’re still awake, then we are ready to start putting things together and jumping to incorrect conclusions…

Let’s say that you’ve been hired to specify a digital audio system for some reason (we’ll assume that it’s an LPCM system – nothing exotic). Using the information I’ve told you so far, you can make two decisions in your specification:

You select a bit depth to be enough to give you the dynamic range you desire. In this case, “dynamic range” means the “distance” in level between the loudest sound you can record / store / transmit (I isn’t say what the “digital audio system” was going to be used for) and the inherent noise floor of the system. If you’re recording the background noise on an airplane while it’s in flight, you don’t need a big dynamic range, because it’s always loud, and never changes. However, if you’re recording a Japanese Taiko Drummer group, you’ll need a huge usable dynamic range because the loud parts of the performance are a LOT louder than the quietest parts.

As we saw in Part 3, an LPCM digital audio system cannot record any audio that has a frequency higher than 1/2 the sampling rate. So, you select a sampling rate that is at least 2x the highest frequency you’re interested in. For example, if you believe the books that say you can hear from 20 Hz to 20,000 Hz, then you might decide that your sampling rate has to be at least 40,000 Hz. On the other hand, if you’re making a subwoofer that you know will never be fed a signal above 120 Hz, then you don’t need a sampling rate higher than 240 Hz.

Don’t get angry yet. I’m just keeping these numbers simple to make the math easy. Later on, I’ll explain why what I just said might not be correct.

Mistake #1

I just jumped to at least three conclusions (probably more) that are going to haunt me.

The first was that my “digital audio system” was something like the following:

Figure 1

As you can see there, I took an analogue audio signal, converted it to digital, and then converted it back to analogue. Maybe I transmitted it or stored it in the part that says “digital audio”.

However, the important, and very probably incorrect assumption here is that I did nothing to the signal. No volume control, no bass and treble adjustments… nothing.

Mistake #2

We assumed above that we can define the system’s dynamic range based on the dynamic range of the audio signal itself. However, this makes the assumption that the noise floor of the digital system and the noise floor of your audio signal are identical, which is probably not true. As we saw in Part 2, the noise generated by TPDF dither is white – it has the same probability of having a given amount of energy per Hertz. Since we hear sound logarithmically (meaning that, to us, octaves are equal widths. Equal spacings in Hz are not.) This means that the noise sound “bright” to us – because there’s just as much energy in the top octave (say, 10 kHz to 20 kHz, if you believe the books) as there is in all other frequencies combined from 0 Hz up to 10 kHz.

If, however, the noise floor in your concert hall where the taiko drummers are playing is caused by the air conditioning system, then this noise will be a lot louder in the low frequencies than the the highs – which is not the same.

Therefore it’s too simplistic to say “the noise floor of the digital system” and the “noise floor of the signal” – since these two noise floors are different. (As Steven Wright said: “It doesn’t matter what temperature the room is, it’s always room temperature.”)

Mistake #3

As we’ll see later, if you’re going to do anything to the signal while it’s in the “digital domain”, then you need to take that into consideration when you’re deciding on your sampling rate. It’s not enough to say “useful audio bandwidth times 2” because there are some side effects that need to be remembered…

However, counter-intuitively, it could be that, in order to improve your system, you’ll want to make the sampling rate LOWER instead of HIGHER – so this is not a simple case of “more is better”.

We’ll get to that topic later. For now, I’ll leave you in suspense.

Some details

One thing we saw in Part 3 was that, if we have an audio signal with energy at a frequency higher than 1/2 the sampling rate, and if that signal gets into the analogue-to-digital converter (ADC), then the output of the ADC will contain an error. We’ll get out energy at frequencies that were not in the original, due to the effect called “aliasing“.

Once that’s in the digital audio signal, there’s no removing it, so we need to make sure that the too-high-frequency signals don’t get into the ADC’s input in the first place. This is done using a low-pass filter that (in theory) removes all energy in the signal above the Nyquist frequency (which is equal to 1/2 the sampling rate). Since that low-pass filter prevents aliasing, we call it an anti-aliasing filter. Normally, these days, that antialiasing filter is built into the ADC itself.

As we also saw in Part 3, the digital-to-analogue converter (DAC) has to smooth out the digital signal to convert it from a “staircase” wave to a smoother one. That’s also done with a low-pass filter that eliminates all the harmonics that would be required to make the staircase have sharp corners. Since this is done to re-construct the analogue signal, it’s called a “reconstruction filter“.

This means that, if we pull apart some of the components in the signal chain I showed in Figure 1, it really looks more like this:

Figure 2.

On to Part 5.

What Use are Watts?

#83 in a series of articles about the technology behind Bang & Olufsen loudspeakers

Imagine water coming out of a garden hose, filling up a watering can (it’s nice outside, so this is the first analogy that comes to mind…). The water is pushed out of the hose by the pressure of the water behind it. The higher the pressure, the more water will come out, and the faster the watering can will fill.

If you want to reduce the amount of water coming out of the hose, you can squeeze it, restricting the flow by making a resistance that reduces the water pressure. The higher the resistance of the restriction to the flow, the less water comes out, and the slower the watering can fills up.

Electricity works in a similar fashion. There is an electrical equivalent of the “pressure”, which is called Electromotive Force or EMV, measured in Volts (which is why most people call it “Voltage” instead of its real name). The “flow” – the quantity of electrons that are flowing through the wire – is the current, measured in Amperes or Amps. A thing that restricts the flow of the electrons is called a resistor, since it resists the current. A resistor can be a thing that does nothing except restrict the current for some reason. It could also be something useful. A toaster, for example, is just a resistor as far as the power company is concerned. So is a computer, your house, or an entire city.

So, if we measure the current coming through a wire, and we want to increase it, we can increase the voltage (the electrical pressure) or we can reduce the resistance. These three are locked together. For example, if you know the voltage and the resistance, you can calculate the current. Or, if you know the current and the resistance, you can calculate the voltage. This is done with a very simple equation known as Ohm’s law:

V = I*R

Where V is the Voltage in Volts, I is the current in Amperes, and R is the resistance in Ohms.

For example, if you have a toaster plugged into a wall socket that is delivering 230 V, and you measure 2 Amperes of current going through it, then :

R = V / I

R = 230 / 4

R = 57.5 Ohms

However, to be honest, I don’t really care what the resistance of my toaster is. What concerns me most is how much I have to pay the power company every time I make toast. How is this calculated? Well, the power company promises to always give me 230 V at my disposal in the wall socket. The amount of current that I use is up to me. If I plug in a big resistance (like an LED lamp) then I don’t use much current. If I plug in a small resistance (say, to charge up the battery in the electric car) then I use lots. What they’re NOT doing is charging me for the current – although it does enter into another equation. The power company is charging me for the amount of Power that I’m using – because they’re charging me for the amount of work that they have to do to generate it for me.

When I use a toaster, it’s converting electrical energy into heat. The amount of heat that it generates is dependent on the voltage (the electrical pressure) and the current going through it. This can be calculated using another simple equation knowns as “Watt’s Law”:

P = V * I

So, let’s say that I plug my toaster into a 230 V outlet, and, because it is a 115 Ohm resistor, 2 Amperes goes through it. In this case, then the amount of Power it’s consuming is

P = 230 * 4

P = 920 Watts

If I’m going to be a little specific, then I should say that the Power (in Watts) is a measure of how much energy I’m transferring per second – so there’s an aspect of time here that I’m ignoring, but this won’t be important until the end of this posting.

Also, if I’m going to bring this back to the power company’s bill that they send me at the end of the month, it will be not only based on how much power I used (in Watts), but how long I used it for (in hours). So, if I make toast for 1 minute, then I used 920 Watts for 1/60th of an hour, therefore I have to pay for

920 / 60 = 15.33 Watt hours

Normally, of course, I do more than make toast once a month. In fact, I use a LOT more, so it’s measured in thousands of Watt hours or “kilowatt hours”.

For example, if I pull into the driveway with an almost-flat battery in our car, and I plug it into the special outlet we have for charging it to charge, I know that it’s using about 26 Amperes and the outlet is fixed at 380 V. This means that I’m using 10,000 Watts, and it will therefore take about 6.4 hours to charge the car (because it has a 64,000 Wh or 64 kWh battery). This means, at the end of the month, I’ll have to pay for those 64 kWh that I used to charge up the car.

So what? (So watt?)

When you play music in a loudspeaker driver, the amplifier “sees” the driver as a resistor.* Let’s say, for the purposes of this discussion, that the driver has a resistance of 8 Ohms. (It doesn’t, but today, we’ll pretend.) To play the music, the amplifier sends a signal that, on an oscilloscope, looks like the signal that came out of a microphone once-upon-a-time (yes – I’m oversimplifying). That signal that you’re looking at is the VOLTAGE that the amplifier is creating to make the signal. Since the loudspeaker driver has some resistance, we can therefore calculate the current that it “asks” the amplifier to deliver. As the voltage goes up, the current goes up, because the resistance stays the same (yes – I’m oversimplifying).

Now, let’s think about this: The amplifier is generating a voltage, and therefore it has to deliver a current. If I multiply those two things together, I can get the power: P = V*I. Simple, right?

Well, yes…. but remember that thing I said above about how power, in Watts, has an element of time. One watt is a measure of energy that is transferred into a thing (in our case, a loudspeaker driver) in one second. And this is where things get complicated, and increasingly irrelevant.

The problem is that power, measured in watts, has an underlying assumption that the consumption is constant. Turn on an old-fashioned light bulb or start making toast, and the power that you consume over time will be the same. However, when you’re playing Stravinsky on a loudspeaker, the voltage and the current are going up and down all the time – if they weren’t, you’d be listening to a sine wave, which is boring.

So, although it’s easy to use Watts to specify a the amount of energy an amplifier can deliver or a loudspeaker driver’s capabilities, it’s not really terribly useful. Instead, it’s much more useful to know how many volts the amplifier can deliver, and how many amperes it can push out before it can’t deliver more (and therefore distorts). However, although you know the maximum voltage and the maximum current, this is not necessarily the maximum power, since it might only be able to deliver those maxima for a VERY short period of time.

For example, if you measure the peak voltage and the peak current that comes out of all of the amplifiers in a Beolab 90 for less than 5 thousandths of a second (5 milliseconds), the you’ll get to a crazy number like 18,000 Watts. However, after about 5 ms, that number drops very rapidly. It can deliver the peak, but it can’t deliver it continuously (if it could, you’d trip a circuit breaker). (Similarly, you can drive a nail into wood by hitting it with a hammer – but you can’t push it in like a thumbtack. The amount of force you can deliver in a short peak is much higher than the amount you can deliver continuously.)

This is why, when we are specifying a power amplifier that we’ll need for a new loudspeaker at the beginning of the development process, we specify it in Peak Voltage and Peak Current (also the continuous values as well, of course) – but not Watts. Yes, you can use one to calculate the other, but consider this:

Amplifier #1: 1000 W amplifier, capable of delivering 10 V and 100 Amps

Amplifier #2: 1000 W amplifier, capable of delivering 100 V and 10 Amps

These are two VERY different things – so just saying a “1000 W amplifier” is not nearly enough information to be useful to anyone for anything. However, since advertisers have a long history of talking about a power amplifier’s capabilities in terms of watts, the tradition continues, regardless of its irrelevance. On the other hand, if you’re buying a toaster, the power consumption is a great thing to know…

* I’m pretending for this posting that a loudspeaker driver acts as a resistor to keep things simple. It doesn’t – but I’m not going to talk about phase or impedance today.

P.S. Yes, I cut MANY corners and oversimplified a LOT of issues in this posting – I know. Don’t send me hate mail because I didn’t mention reactance or crest factor…

What’s a woofer?

#82 in a series of articles about the technology behind Bang & Olufsen loudspeakers

Occasionally, a question that comes into the customer communications department to Bang & Olufsen from a dealer or a customer eventually finds its way into my inbox.

This week, the question was about nomenclature. Why is it that, on some loudspeakers, for example, we say there is a tweeter, mid-range, and woofer, whereas on other loudspeakers we say that we’re using a “full range” driver instead? What’s the difference? (Folded into the same question was another about amplifier power, but I’ll take that one in another posting.)

So, what IS the difference? There are three different ways to answer this question.

Answer #1: It’s how you use it.

My Honda Civic, the motorcycle that passed me on the highway this morning, and an F1 car all have a gear in the gearbox that’s labelled “3”. However, the gear ratio of those three examples of “third gear” are all different. In other words, if you showed a mechanic the gear ratio of one of those gearbox settings without knowing anything else, they wouldn’t be able to tell you “ah! that’s third gear…”

So, in this example, “third gear” is called “third” only because it’s the one between “second” and “fourth”. There is nothing physical about it that makes it “third”. If that were the case then my car wouldn’t have a first gear, because some farm tractor out there in the world would have a gear with a lower ratio – and an F1 car would start at gear 100 or so… And that wouldn’t make sense.

Similarly, we use the words “tweeter”, “midrange”, “woofer”, “subwoofer”, and “full range” to indicate the frequency range that that particular driver is looking after in this particular device. My laptop has a 1″ “woofer” – which only means that it’s the driver that’s taking care of the low frequencies that come out of my laptop.

So, using this explanation, the Beolab 90 webpage says that it has midranges and tweeters and no “full range” drivers because the midrange drivers look after the midrange frequencies, and the tweeters look after the high frequencies. However, the Beolab 28’s webpage says that it has a tweeter and full range drivers, but no midranges. This is because the drivers that play the midrange frequencies in the Beolab 28 also play some of the high-frequency content as part of the Beam Width control. Since they’re doing “double duty”, they get a different name.

Answer #2: Excruciating minutiae

The description I gave above isn’t really an adequate answer. For example, I said that my laptop has a 1″ “woofer”. Beolab 90 has a 1″ “tweeter” – but these two drivers are not designed the same way. Beolab 90’s tweeter is specifically designed to be used to produce high frequencies. One consequence of this is that the total mass of the moving parts (the diaphragm and voice coil, amongst other things) is as low as possible, so that it’s easy to move. This means that it can produce high frequency signals without having to use a lot of electrical power to push it back and forth.

However, the 1″ “woofer” in my laptop is designed differently. It probably has a much higher total mass for the moving parts. This means that its resonant frequency (the frequency that it would “ring” at if you hit it like a drum head) is much lower. Therefore it “wants” to move easily at a lower frequency than a tweeter would.

For example, if you put a child on a swing and you give them a push, they’ll swing back and forth at some frequency. If the child wanted to swing SLOWER (at a lower frequency), you could

  • move to a swing with longer ropes so this happens naturally, or
  • you can hold on to the ropes and use your muscles to control the rate of swinging instead.

The smarter thing to do is the first choice, that way you can keep sipping your coffee instead of getting a workout.

So, a 1″ woofer and a 1″ tweeter are not really the same thing.

Answer #3: Compromise

We live in a world that has been convinced by advertisers that “compromise” is a bad thing – but it’s not. Someone who does never accepts to compromise is destined to live a very lonely life. When designing a loudspeaker, one of the things to consider is what, exactly, each component will be asked to do, and choose the appropriate components accordingly.

If we’re going to be really pedantic – there’s really no such thing as a tweeter, woofer, or anything else with those kinds of names. Any loudspeaker driver can produce sound at any frequency. The only difference between them is the relative ease with which the driver plays a signal at a given frequency. You can get 20 Hz to come out of a “tweeter” – it will just be naturally a LOT quieter than the signals at around 5 kHz. Similarly, a woofer can play signals at 20 kHz, but it will be a lot quieter and/or take a lot more power than signals at 50 Hz.

What this means is that, when you make an active loudspeaker, the response (the relative levels of signals at different frequencies) is really a result of the filters in the digital signal processing and the control from the amplifier (ignoring the realities of heat and time…). If we want more or less level at 2 kHz from a loudspeaker driver, we “just” change the filter in the signal processing and use the amplifier to do the work (the same as the example above where you were using your muscle power to control the frequency of the child on the swing).

However, there are examples where we know that a driver will be primarily used for one frequency band, but actually be extending into another. The side-facing drivers on Beolab 28 are a good example of this. They’re primarily being used to control the beam width in the midrange, but they’re also helping to control the beam width in the high frequencies. Since, they’re doing double-duty in two frequency ranges, they can’t really be called “midranges” or “tweeters” – they’d be more accurately called “midranges that also play as quiet tweeters”. (They don’t have to play high frequencies loudly, since this is “only” to control the beam width of the front tweeter.) However, “midranges that also play as quiet tweeters” is just too much information for a simple datasheet – so “full range” will do as a compromise.

P.S.

I’ve got some extra things to add here…

Firstly, it has become common over the past couple of years to call “woofers” “subwoofers” instead. I don’t know why this happened – but I suspect that it’s merely the result of people who write advertising copy using a word they’ve heard before without really knowing what it means. Personally, I think that it’s funny to see a laptop specified to have a “1” subwoofer”. Maybe we should make the word “subtweeter” popular instead.

Secondly, personally, I believe that a “subwoofer” is a thing that looks after the frequency range below a “woofer”. I remember a conversation I had at an AES convention once (I think it was with Günther Theile and Tomlinson Holman) where we all agreed that a “subwoofer” should look after the frequency range up to 40 Hz, which is where a decent woofer should take over.

Lastly, if you find an audio magazine from the 1970s, you’ll see that a three-way loudspeaker had a “tweeter”, “squawker”, and “woofer”. Sometime between then and now, “squawker” was replaced with “midrange” – but I wonder why the other two didn’t change to “highrange” and “lowrange” (although neither of these would be correct, since all three drivers in a three-way system have limited frequency ranges).

Telefunken Lido: Repair (Day 6)

Day 5’s work can be seen here.

So, it was obvious that the speed regulation wasn’t working properly at the end of Day 5. So, last night was spent digging for information on how centrifugal speed governors work and I came across this excellent explanation.

So, my theory was that the disc was seized on the axle and not moving correctly with the rotational speed. This means that everything came apart again, and the axle had to come out.

In theory, as the governor spins faster, the three weights get pulled out. This in turn should pull the disc in to rub against the friction pad. When it came out of the motor, the disc was immovable – it was stuck to the axle as I guessed. So, the three springs+weights were removed from the axle and, after a lot of WD-40 and a little repeated gentle “persuasion”, I got to here:

This is after I polished the rust off the axle with sandpaper, starting at 400 and working up to 3200 (lubricated with more WD-40). I was sanding along the length of the axle, since that’s the direction of movement of the disc.

Then it was “just” a matter of putting it all back together again… However, before I put it back in the case, I checked that the governor was working, which you can see below. Notice how the disc moves sideways to meet the friction pad, keeping things at a constant speed.

Then it was just a matter of putting everything back together again… And I have a working Telefunken Lido for those Sunday afternoon garden parties!

Telefunken Lido: Repair (Day 5)

Back to Part 4.

This was nearly the last day of the restoration (sort of…)

The beechwood that will hold up the top plate. This is 21.4 mm from the lip of the casing, as are all of the other pieces.

The opposite side of the same part of the case. I’m hoping that the yellow leather will darken over time…

All of the wood in the case. Notice the bent wood at the top… Turns out that this didn’t work… There wasn’t enough room between the inside of the case and the horn, so it had to go.

The alternative solution, using large washers directly on the inside of the case.

The new mainspring, ready to be greased and wound into the barrel.

The mainspring in the barrel, with teflon grease applied. Notice that it winds clockwise. Also note that the hook on the inner sleeve is grabbing the spring end. This is important, and a little difficult to manage…

Closing up the mainspring barrel, rotating about 45 degrees each time, and tightening only a little at a time.

Teflon grease on all the inner parts. This was a good idea – except for the axles of the speed regulator. The grease was a little too viscous, so it was replaced with WD-40.

Everything’s back together. All those photos I took at the beginning helped a lot during re-assembly.

The thick rubber compression washers are used to help level everything later.

Motor’s back in… time to level things up.

The platter is a little high on the left (relative to the top side of the plywood) so two screws get loosened and two get tightened. The rubber washers keep things from vibrating, and allow for this adjustment.

The finished gramphone!

With the tonearm clipped back for transport. The crank is clipped into the lid on the right side.

Crank in place, ready to wind up the spring.

The tonearm out, but in its resting position.

Playing a record for the first time in a long time!!!!

Seems that I need to work on the speed regulator… But it works – which it hasn’t done, probably for many years…

Forward to Part 6 (The End!)

Telefunken Lido: Repair (Day 4)

Back to Part 3.

Some more bits and pieces of work this time, mostly leather work.

Yesterday was spent colour-testing the dye with some scraps first. The bottom piece is vegetable tanned leather without dye. The middle piece is with one light coat of dye. The top piece is thoroughly soaked with the same dye. The white balance in this photo is a bit weird – but the top one is the winner. It’s a yellow alcohol-based dye.

Then the remaining pieces were cut and dyed, the hardware is in, and the insert for the handle is formed. (At this stage, nothing was glued, since the leather was still wet.) The binder clips are there to shape the leather around the small piece of 2 mm thick leather inside the handle that creates the shape. The irregularity in the colour is due to the fact that the dye hasn’t finished drying yet.

All the stitching is done, and the handle is burnished. The handle and tabs are 2 mm leather, and the straps are 1.3 mm thick, give or take. I’ll punch the hole in the strap when it’s all assembled so as to ensure that it’s in the right place.

The above photo shows grease-proof paper glued to the inside of the bottom casing. This will protect the interior from any grease or oil that drops off the drivetrain. This is a pretty safe assumption, looking at the black grease stains that are there already.

The paper is cellulose-coated baking paper, and it’s glued in with water-based bookbinders glue. Once it’s dry (tomorrow), the white color will become transparent. Then I’ll put in another piece that wraps around the sidewall, since the player will often be set on its end.

In addition to this, the blocks of wood are ready to be inserted – almost all of them cut out of 10 mm thick beech. Instead of the canvas, I plan on using a 5 mm thick strip of beech, but this will have to be steam-bent to follow the curve of the top. We’ll see how well that works out – never tried steam-bending wood before… these will all be held in place with M3 Chicago Bolts with the non-slotted nut on the outside of the case. This will look almost exactly like the original rivets, but it will mean that everything will be much easier to disassemble in the future – just in case…

The new mainspring arrived in the mail today from Lindholts; it looks like it might need a couple of small modifications to work, but it’s a much better fit than the one I had on hand. So the next big days will be spent re-assembling the drive train and inserting the wood parts.

One small setback today. I found the right-shaped screws (to replace the random ones that were holding it together) at Birger A. Handel in Slagelse. The right shape – but the wrong colour. They’re brass, and the originals are all either nickel- or chrome-plated. A found a nickel-plating company near here in Herning, but they emailed me today to tell me that they’re not interested in plating 30 tiny screws for me. Not much profit in that I guess… Oh well. Hopefully, some day, I’ll find replacement screws. Until then, my Lido will be a lovely chrome / brass burst of colour!

Forward to Part 5

Telefunken Lido: Repair (Day 3)

Back to Part 2

Today was spent doing a bunch of small jobs while I wait for some replacement parts to arrive.

For starters, I found two needles under the hinge on the bottom half of the case. They’ll come in handy later!

The interior of the case, showing the four wood blocks to which the top screws on. Funnily, these are made of three different types of wood: pine, birch, and beech. I suspect that this was not strategic – but just a question of using whatever was on-hand. The lining is a waxy paper – the black stains are grease that has dripped down from the drive mechanism.

The four pieces of wood are two different heights from the top edge of the casing, although I suspect that this would have been custom-fitted. They’re attached to the outer casing using either tacks (the largest piece on the right) or split rivets that were bent over to lock the wood in place. The wood parts are not glued onto the case. All of the rivet and tack heads of these are badly rusted – so they’re coming out…

One of the split rivets after the wood has been removed. The wood did not survive the removal process. The hole on the far left is the opening for the crank.

The wood in the process of removal. I’ll just make new blocks to replace these…

The handle and strap are a different colour than the case, and are in quite bad shape. In addition, the hardware is badly rusted. This will all get replaced with new parts.

The handle and strap are attached with the same split rivets, but bent around a canvas material that’s glued to the inside of the case, as can be seen in the photo above. The canvas is the dark square and rectangle. This canvas can’t be seen normally, because it’s covered by the wax paper. I peeled this off, because I’ll be replacing it with something a little more sturdy.

The rust on the exterior metal parts was cleaned up with a small wire brush on my Dremel tool. The before-and-after can be seen above. This took some time so as to not slip and carve into the case covering.

I used Simichrome to polish the metal tonarm. This appears to be plated brass. I’m not going to take apart the reproducer (the black part that holds the needle and contains the diaphragm).

If you look carefully, you’ll see a small set screw sticking out of the half of the tonearm on the right. That’s used to stop the front portion of the tonearm from making a full rotation when it’s swivelled back and forth onto the record, by hitting the portion of the threaded pipe that can be seen below.

So, if you’re dismantling the tonearm, remember to back off the set screw before separating the two parts.

I also started the leather work to make a new handle and strap. The replacement hardware and dye were ordered from laederiet.dk, near Aarhus (which is where I buy all my leather supplies).

Apart from all of that, I washed the exterior of the case with dish soap and a soft cloth – not too wet because there are some places where the covering is worn through and I don’t want water getting in there.

I also sprayed the interior fabric (maybe taffeta?) with an enzyme spray and rubbed it gently to remove some of the stains. Too much rubbing frays the fabric, so I had to be gentle…

Forward to Part 4