In a perfect sound system, all loudspeakers are identical, and they are all able to play a full frequency range at any listening level. However, most often, this is not a feasible option, either due to space or cost considerations (or both…). Luckily, it is possible to play some tricks to avoid having to install a large-scale sound system to listen to music or watch movies.
Humans have an amazing ability to localise sound sources. With your eyes closed, you are able to point towards the direction sounds are coming from with an incredible accuracy. However, this ability gets increasingly worse as we go lower in frequency, particularly in closed rooms.
In a sound system, we can use this inability to our advantage. Since you are unable to localise the point of origin of very low frequencies indoors, it should not matter where the loudspeaker that’s producing them is positioned in your listening room. Consequently, many simple systems remove the bass from the “main” loudspeakers and send them to a single large loudspeaker whose role it is to reproduce the bass for the entire system. This loudspeaker is called a “subwoofer”, since it is used to produce frequency bands below those played by the woofers in the main loudspeakers.
The process of removing the bass from the main channels and re-routing them to a subwoofer is called bass management.
It’s important to remember that, although many bass management systems assume the presence of at least one subwoofer, that output should not be confused with an (Low-Frequency Effects) LFE (Low-Frequency Effects) or a “.1” input channel. However, in most cases, the LFE channel from your media (for example, a Blu-ray disc or video streaming device) will be combined with the low-frequency output of the bass management system and the total result routed to the subwoofer. A simple example of this for a 5.1-channel system is shown below in Figure 1.
Figure 1: A simple example of a bass management system for a 5.1 channel system.
Of course, there are many other ways to do this. One simplification that’s usually used is to put a single Low Pass Filter (LPF) on the output of the summing buss after the signals are added together. That way, you only need to have the processing for one LPF instead of 5 or 6. On the other hand, you might not want to apply a LPF to an LFE input, so you may want to add the main channels, apply the LPF, and then add the LFE, for example. Other systems such as Bang & Olufsen televisions use a 2-channel bass management system so that you can have two subwoofers (or two larger main loudspeakers) and still maintain left/right differences in the low frequency content all the way out to the loudspeakers.
However, the one thing that older bass management systems have in common is that they typically route the low frequency content to a subset of the total number of loudspeakers. For example, a single subwoofer, or the two main front loudspeakers in a larger multichannel system.
In Bang & Olufsen televisions starting with the Beoplay V1 and going through to the Beovision Harmony, it is possible to change this behaviour in the setup menus, and to use the “Re-direction Level” to route the low frequency output to any of the loudspeakers in the current Speaker Group. So, for example, you could choose to send the bass to all loudspeakers instead of just one subwoofer.
There are advantages and disadvantages to doing this.
The first advantage is that, by sending the low frequency content to all loudspeakers, they all work together as a single “subwoofer”, and thus you might be able to get more total output from your entire system.
The second advantage is that, since the loudspeakers are (probably) placed in different locations around your listening room, then they can work together to better control the room’s resonances (a.k.a. room modes).
One possible disadvantage is that, if you have different loudspeakers in your system (say, for example, Beolab 3s, which have slave drivers, and Beolab 17s, which use a sealed cabinet design) then your loudspeakers may have different frequency-dependent phase responses. This can mean in some situations that, by sending the same signal to more loudspeakers, you get a lower total acoustic output in the room because the loudspeakers will cancel each other rather than adding together.
Another disadvantage is that different loudspeakers have different maximum output levels. So, although they may all have the same output level at a lower listening level, as you turn the volume up, that balance will change depending on the signal level (which is also dependent on frequency content). For example, if you own Beolab 17s (which are small-ish) and Beolab 50s (which are not) and if you’re listening to a battle scene with lots of explosions, at lower volume levels, the 17s can play as much bass as the 50s, but as you turn up the volume, the 17s reach their maximum limit and start protecting themselves long before the 50s do – so the balance of bass in the room changes.
Beosound Theatre
Beosound Theatre uses a new Bass Management system that is an optimised version of the one described above, with safeguards built-in to address the disadvantages. To start, the two low-frequency output channels from the bass management system are distributed to all loudspeakers in the system that are currently being used.
However, in order to ensure that the loudspeakers don’t cancel each other, the Beosound Theatre has Phase Compensation filters that are applied to each individual output channel (up to a maximum of 7 internal outputs and 16 external loudspeakers) to ensure that they work together instead against each other when reproducing the bass content. This is possible because we have measured the frequency-dependent phase responses of all B&O loudspeakers going as far back in time as the Beolab Penta, and created a custom filter for each model. The appropriate filters are chosen and applied to each individual outputs accordingly.
Secondly, we also know the maximum bass capability of each loudspeaker. Consequently, when you choose the loudspeakers in the setup menus of the Beosound Theatre, the appropriate Bass Management Re-direction levels are calculated to ensure that, for bass-heavy signals at high listening levels, all loudspeakers reach their maximum possible output simultaneously. This means that the overall balance of the entire system, both spatially and timbrally, does not change.
The total result is that, when you have external loudspeakers connected to the Beosound Theatre, you are ensured the maximum possible performance from your system, not only in terms of total output level, but also temporal control of your listening room.
There’s one last thing that I alluded to in a previous part of this series that now needs discussing before I wrap up the topic. Up to now, we’ve looked at how a filter behaves, both in time and magnitude vs. frequency. What we haven’t really dealt with is the question “why are you using a filter in the first place?”
Originally, equalisers were called that because they were used to equalise the high frequency levels that were lost on long-distance telephone transmissions. The kilometres of wire acted as a low-pass filter, and so a circuit had to be used to make the levels of the frequency bands equal again.
Nowadays we use filters and equalisers for all sorts of things – you can use them to add bass or treble because you like it. A loudspeaker developer can use them to correct linear response problems caused by the construction or visual design of the device. They can be used to compensate for the acoustical behaviour of a listening room. Or they can be used to compensate for things like hearing loss. These are just a few examples, but you’ll notice that three of the four of them are used as compensation – just like the original telephone equalisers.
Let’s focus on this application. You have an issue, and you want to fix it with a filter.
IF the problem that you’re trying to fix has a minimum phase characteristic, then a minimum phase filter (implemented either as an analogue circuit or in a DSP) can be used to “fix” the problem not only in the frequency domain – but also in the time domain. IF, however, you use a linear phase filter to fix a minimum phase problem, you might be able to take care of things on a magnitude vs. frequency analysis, but you will NOT fix the problem in the time domain.
This is why you need to know the time-domain behaviour of the problem to choose the correct filter to fix it.
For example, if you’re building a room compensation algorithm, you probably start by doing a measurement of the loudspeaker in a “reference” room / location / environment. This is your target.
You then take the loudspeaker to a different room and measure it again, and you can see the difference between the two.
In order to “undo” this difference with a filter (assuming that this is possible) one strategy is to start by analysing the difference in the two measurements by decomposing it into minimum phase and non-minimum phase components. You can then choose different filters for different tasks. A minimum phase filter can be used to compensate a resonance at a single frequency caused by a room mode. However, the cancellation at a frequency caused by a reflection is not minimum phase, so you can’t just use a filter to boost at that frequency. An octave-smoothed or 1/3-octave smoothed measurement done with pink noise might look like you fixed the problem – but you’ve probably screwed up the time domain.
Another, less intuitive example is when you’re building a loudspeaker, and you want to use a filter to fix a resonance that you can hear. It’s quite possible that the resonance (ringing in the time domain) is actually associated with a dip in the magnitude response (as we saw earlier). This means that, although intuition says “I can hear the resonant frequency sticking out, so I’ll put a dip there with a filter” – in order to correct it properly, you might need to boost it instead. The reason you can hear it is that it’s ringing in the time domain – not because it’s louder. So, a dip makes the problem less audible, but actually worse. In this case, you’re actually just attenuating the symptom, not fixing the problem – like taking an Asprin because you have a broken leg. Your leg is still broken, you just can’t feel it.
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:
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.
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.
Let’s go back to something I said in the last post:
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.
If you consider that signal flow from the position of an end-consumer playing a digital recording, this was pretty easy to accomplish in the “old days” when we were all playing CDs. That’s because (in a theoretical, oversimplified world…)
the output of the mixing/mastering console was analogue
that analogue signal was converted to digital in the mastering studio
the resulting bits were put on a disc
you put that disc in your player which contained a DAC that converted the signal directly to analogue
you then sent the signal to your “processing” (a.k.a. “volume control”, and maybe some bass and treble adjustment.).
So, that flowchart in Figure 1 was quite often true in 1985.
These days, things are probably VERY different… These days, the signal path probably looks something more like this (note that I’ve highlighted “alterations” or changes in the bits in the audio signal in red):
The signal was converted from analogue to digital in the studio (yes, I know… studios often work with digital mixers these days, but at least some of the signals within the mix were analogue to start – unless you are listening to music made exclusively with digital synthesizers)
The file was transferred to a storage device (let’s say “hard drive”) in a large server farm renting out space to your streaming service
The streaming service encodes the file
If the streaming service does not offer an lossless option, then the file is converted to a lossy format like MP3, Ogg Vorbis, AAC, or something else.
If the streaming service offers a lossless option, then the file is compressed using a format like FLAC or ALAC (This is not an alteration, since, with a lossless compression system, you don’t lose anything)
You download the file to your computer (it might look like an audio player – but that means it’s just a computer that you can’t use to check your social media profile)
You press play, and the signal is decoded (either from the lossy CODEC or the compression format) back to LPCM. (Still not an alteration. If it’s a lossy CODEC, then the alteration has already happened.)
That LPCM signal might be sample-rate converted
The streaming service’s player might do some processing like dynamic range compression or gain changes if you’ve asked it to make all the songs have the same level.
All of the user-controlled “processing” like volume controls, bass, and treble, are done to the digital signal.
The signal is sent to the loudspeaker or headphones
If you’re sending the signal wirelessly to a loudspeaker or headphones, then the signal is probably re-encoded as a lossy CODEC like AAC, aptX, or SBC. (Yes, there are exceptions with wireless loudspeakers, but they are exceptions.)
If you’re sending the signal as a digital signal over a wire (like S/PDIF or USB), the you get a bit-for-bit copy at the input of the loudspeaker or headphones.
The loudspeakers or headphones might sample-rate convert the signal
The sound is (finally) converted to analogue – either one stream per channel (e.g. “left”) or one stream per loudspeaker driver (e.g. “tweeter”) depending on the product.
So, as you can see in that rather long and complicated list (it looks complicated, but I’ve actually simplified it a little, believe it or not), there’s not much relation to the system you had in 1985.
Let’s take just one of those blocks and see what happens if things go horribly wrong. I’ll take the “volume control” block and add some distortion to see the result with two LPCM systems that have two different sampling rates, one running at 48 kHz and the other at 194 kHz – four times the rate. Both systems are running at 24 bits, with TPDF dither (I won’t explain what that means here). I’ll start by making a 10 kHz tone, and sending it through the system without any intentional distortion. If we look at those two signals in the time domain, they’ll look like this:
Figure 1: Two 10 kHz tones. The black one is in a 48 kHz, 24 bit LPCM system. The red one is in a 192 kHz, 24 bit LPCM system.
The sine tone in the 48 kHz system may look less like a sine tone than the one in the 192 kHz system, however, in this case, appearances are deceiving. The reconstruction filter in the DAC will filter out all the high frequencies that are necessary to reproduce those corners that you see here, so the resulting output will be a sine wave. Trust me.
If we look at the magnitude responses of these two signals, they look like Figure 2, below.
Figure 2: The magnitude responses of the two signals shown in Figure 1.
You may be wondering about the “skirts” on either side of the 10 kHz spikes. These are not really in the signal, they’re a side-effect (ha ha) of the windowing process used in the DFT (aka FFT). I will not explain this here – but I did a long series of articles on windowing effects with DFTs, so you can search for it if you’re interested in learning more about this.
If you’re attentive, you’ll notice that both plots extend up to 96 kHz. That’s because the 192 kHz system on the bottom has a Nyquist frequency of 96 kHz, and I want both plots to be on the same scale for reasons that will be obvious soon.
Now I want to make some distortion. In order to make things obvious, I’m going to make a LOT of distortion. I’ve made the sine wave try to have an amplitude that is 10 times higher than my two systems will allow. In other words, my amplitude should be +/- 10, but the signal clips at +/- 1, resulting in something looking very much like a square wave, as shown in Figure 3.
Figure 3: Distorted 10 kHz sine waves. The black one is in a 48 kHz, 24 bit LPCM system. The red one is in a 192 kHz, 24 bit LPCM system.
You may already know that if you want to make a square wave by building it up using its constituent harmonics, you need to have the fundamental (which we’ll call Fc. In our case, Fc = 10 kHz) with an amplitude that we’ll say is “A”, you then add the
3rd harmonic (3 times Fc, so 30 kHz in our case) with an amplitude of A/3.
5th harmonic (5 Fc = 50 kHz) with an amplitude of A/5
7 Fc at A/7
and so on up to infinity
Let’s look at the magnitude responses of the two signals above to see if that’s true.
Figure 4: The magnitude responses of the two signals shown in Figure 3.
If we look at the bottom plot first (running at 192 kHz and with a Nyquist limit of 96 kHz) the 10 kHz tone is still there. We can also see the harmonics at 30 kHz, 50 kHz, 70 kHz, and 90 kHz in amongst the mess of other spikes we’ll get to those soon…)
Figure 5. Some labels applied to Figure 4 for clarity, showing the harmonics of the square waves that are captured by the two systems
Looking at the top plot (running at 48 kHz and with a Nyquist limit of 24 kHz), we see the 10 kHz tone, but the 30 kHz harmonic is not there – because it can’t be. Signals can’t exist in our system above the Nyquist limit. So, what happens? Think back to the images of the rotating wheel in Part 3. When the wheel was turning more than 1/2 a turn per frame of the movie, it appears to be going backwards at a different speed that can be calculated by subtracting the actual rotation from 180º (half-a-turn).
The same is true when, inside a digital audio signal flow, we try to make a signal that’s higher than Nyquist. The energy exists in there – it just “folds” to another frequency – its “alias”.
We can look at this generally using Figure 6.
Figure 6: A general plot of aliasing, showing the intended frequency in black and the actual output frequency in red.
Looking at Figure 6: If we make a sine tone that sweeps upward from 0 Hz to the Nyquist frequency at Fs/2 (half the sampling rate or sampling frequency) then the output is the same as the input. However, when the intended frequency goes above Fs/2, the actual frequency that comes out is Fs/2 minus the intended frequency. This creates a “mirror” effect.
If the intended frequency keeps going up above Fs, then the mirroring happens again, and again, and again… This is illustrated in Figure 7.
Figure 7: An extension of Figure 5 to a higher intended frequency.
This plot is shown with linear scales for both the X- and Y-axes to make it easy to understand. If the axes in Figure 7 were scaled to a logarithmic scaling instead (which is how “Frequency Response” are normally shown, since this corresponds to how we hear frequency differences), then it would look like Figure 8.
Figure 8: The same information shown in Figure 7, plotted on a logarithmic scale instead. Note that this example is for a system running at 48 kHz (therefore with a Nyquist frequency of 24 kHz), and an intended input frequency (in black) going up to 3 times 48 kHz = 144 kHz.
Coming back to our missing 30 kHz harmonic in the 48 kHz LPCM system: Since 30 kHz is above the Nyquist limit of 24 kHz in that system, it mirrors down to 24 kHz – (30 kHz – 24 kHz) = 18 kHz. The 50 kHz harmonic shows up as an alias at 2 kHz. (follow the red line in Figure 7: A harmonic on the black line at 48 kHz would actually be at 0 Hz on the red line. Then, going 2000 Hz up to 50 kHz would bring the red line up to 2 kHz.)
Similarly, the 110 kHz harmonic in the 192 kHz system will produce an alias at 96 kHz – (110 kHz – 96 kHz) = 82 kHz.
If I then label the first set of aliases in the two systems, we get Figure 9.
Figure 9: The first set of aliased frequency content in the two systems.
Now we have to stop for a while and think about what’s happened.
We had a digital signal that was originally “valid” – meaning that it did not contain any information above the Nyquist frequency, so nothing was aliasing. We then did something to the signal that distorted it inside the digital audio path. This produced harmonics in both cases, however, some of the harmonics that were produced are harmonically related to the original signal (just as they ought to be) and others are not (because they’re aliases of frequency content that cannot be reproduced by the system.
What we have to remember is that, once this happens, that frequency content is all there, in the signal, below the Nyquist frequency. This means that, when we finally send the signal out of the DAC, the low-pass filtering performed by the reconstruction filter will not take care of this. It’s all part of the signal.
So, the question is: which of these two systems will “sound better” (whatever that means)? (I know, I know, I’m asking “which of these two distortions would you prefer?” which is a bit of a weird question…)
This can be answered in two ways that are inter-related.
The first is to ask “how much of the artefact that we’ve generated is harmonically related to the signal (the original sine tone)?” As we can see in Figure 5, the higher the sampling rate, the more artefacts (harmonics) will be preserved at their original intended frequencies. There’s no question that harmonics that are harmonically related to the fundamental will sound “better” than tones that appear to have no frequency relationship to the fundamental. (If I were using a siren instead of a constant sine tone, then aliased harmonics are equally likely to be going down or up when the fundamental frequency goes up… This sounds weird.)
The second is to look at the levels of the enharmonic artefacts (the ones that are not harmonically related to the fundamental). For example, both the 48 kHz and the 192 kHz system have an aliased artefact at 2 kHz, however, its level in the 48 kHz system is 15 dB below the fundamental whereas, in the 192 kHz system, it’s more than 26 dB below. This is because the 6 kHz artefact in the 48 kHz system is an alias of the 30 kHz harmonic, whereas, in the 192 kHz system, it’s an alias of the 190 kHz harmonic, which is much lower in level.
As I said, these two points are inter-related (you might even consider them to be the same point) however, they can be generalised as follows:
The higher the sampling rate, the more the artefacts caused by distortion generated within the system are harmonically related to the signal.
In other words, it gives a manufacturer more “space” to screw things up before they sound bad. The title of this posting is “Mirrors are bad” but maybe it should be “Mirrors are better when they’re further away” instead.
Of course, the distortion that’s actually generated by processing inside a digital audio system (hopefully) won’t be anything like the clipping that I did to the signal. On the other hand, I’ve measured some systems that exhibit exactly this kind of behaviour. I talked about this in another series about Typical Problems in Digital Audio: Aliasing where I showed this measurement of a real device:
Figure 10: A measurement of a real device showing some kind of distortion and aliased artefacts of a swept sine tone. Half of the aliasing is immediately recognizable as going downwards when the tone is going upwards.
However, I’m not here to talk about what you can or can’t hear – that is dependent on too many variables to make it worth even starting to talk about. The point of this series is not to prove that something is better or worse than something else. It’s only to show the advantages and disadvantages of the options so that you can make an informed choice that best suits your requirements.
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…
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).
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!
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…
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!
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…
