Discussion in 'Audio Hardware' started by dianos, Nov 7, 2014.
Thanks for this. I'll read it again more closely later, but it makes sense. I was confused by how long the wavelength of light is compared to these grooves, thinking only about the frequency, forgetting how fast it's travelling!
Thanks. Make sure you catch my correction a couple of posts after the explanation, plus quadjoe's correction a little further still.
When you say "It has to be smaller than the smallest wiggle in the record" you are saying the stylus is smaller than the groove. The groove is larger than the stylus. I agree with this.
In the next paragraph you say "That means that a 20 kHz signal can't be any larger than 2.5 microns. " Here you are saying that the groove must be smaller than the stylus. This is the contradiction that leads to your flawed conclusion.
To put it another way: You are correct to note that the size of the stylus imposes a lower limit on traceable grooves. Grooves have to be bigger than a certain size in order to be trackable. (Or should I say traceable?) Starting from here, you cannot argue that the grooves get so small that they approach the wavelength of light.
I agree and corrected this point a few posts later. The sentence should have read, "That means that a 20 kHz signal can't be any smaller than 2.5 microns."
This is a more interesting objection and one I thought of as I was falling asleep last night. It's wonderful how much thinking we do as we sleep. I woke up feeling that yes, it is a lower limit, as you say, but also is a good indicator of the size of the wiggles in the groove. You only build a door tall enough for most people to walk through. Doors aren't in general nine feet tall. You make a chair big enough for the average person's butt. Why make a stylus capable of tracing a wiggle as small as 6 microns (let's use the larger size of a Shibata stylus although it doesn't really make that much difference) if it doesn't have to trace bumps in that range? I can't see any point in over-engineering the design. It can't be easy to cut a diamond 6 x 75 microns. Why do it if a bigger diamond would work just as well? A bigger diamond with a larger contact area would cause less wear. There would be advantages to a bigger diamond but those in the know have chosen to use smaller ones. Why? I think that's because it needs to be that small to read the wiggles in the groove, which means the bumps it's reading are also that small. It's logical to assume the wiggles in the groove approach 6 microns.
There's one other indicator. As quadjoe pointed out upthread, a Shibata stylus, which was developed specifically to trace CD4 quad records, has to read frequencies up to 45 kHz. Why did manufacturers spend time and money to develope the intricate shape of a Shibata diamond, with a cross section of 6 x 75 microns, if that wasn't the size necessary to read a 45,000 Hertz signal in a record groove? It only makes sense if a 6 micron contact area was the maximum size that could reliably trace a 45 kHz wiggle.
It would be a huge help to learn the size of the cutting edge of a stylus in a record cutting lathe. I've tried to find out that figure in the past and have been unable to discover it. I've found specs on the size of the overall stylus in a cutting lathe, and while I can't pull up the numbers from memory, they are in the ballpark of what we are talking about here. But that's not the determining factor. A large knife can make a very tiny cut. What is the size of the cutting edge of that stylus? That's the issue, along with dexterity of the motors behind it. How fine can a record cutting lathe cut? If we knew that, we'd know the answer to this question.
I'll continue to work on this. I've been cogitating over this problem since the early 1980s. It's not going away tomorrow. Thank you for your input.
I've been looking it up because you've made me curious, and light waves (the visible spectrum at least) range from 700 nanometres (µm)(red light) to 390 µm (violet). The thickness of the membrane of a soap bubble is about 480 µm in thickness. Nanometres are billionths of a millimetre, so light waves are very small. We can convert nanometres to Terahertz, so if violet is 390 µm it can be expressed as 769 THz. We can then convert THz to kHz: 769 THz = 7.69e+11 kHz or 76,900,000,000,000 kHz. However, light waves are considerably different from sound waves in that sound waves need a medium to be transmitted, whereas light (and other forms of electromagnetic radiation) require no medium. (Check my calculation here since 1 THz = 1012Hz .)
Here are the sites I looked up for the information I used, hope this helps in your calculations:
ggergm, I was thinking about how small a groove could be made (and thus the accompanying stylus), and I had an epiphany: the RCA Selectavision CED videodisc system used a spiral groove that was 657 nm wide. Here's the pertinent part from Wikipedia:
CEDs are conductive vinyl platters that are 30.0 cm (11.8 in) in diameter. To avoid metric names they are usually called "12 inch discs". A CED has a spiral groove on both sides. The groove is 657 nm wide and has a length of up to 12 miles (19 km). The discs rotate at a constant angular speed during playback (450 rpm for NTSC, 500 rpm for PAL) and each rotation contains several full frames (four frames for NTSC, three for PAL). This meant that freeze frame was impossible on players without an expensive electronic frame store facility.
A keel-shaped needle with a titanium electrode layer rides in the groove with extremely light tracking force (65 mg or a little over a grain), and an electronic circuit is formed through the disc and stylus. Like an audio turntable, the stylus reads the disc, starting at the outer edge and going towards the center. The video and audio signals are stored on the Videodiscs in a composite analog signal which is encoded into vertical undulations in the bottom of the groove, somewhat like pits. These undulations have a shorter wavelength than the length of the stylus tip in the groove, and the stylus rides over them; the varying distance between the stylus tip and the conductive surface due to the depth of the undulations in the groove under the stylus directly controls the capacitance between the stylus and the conductive carbon-loaded PVC disc. This varying capacitance in turn alters the frequency of a resonant circuit, producing an FM electrical signal which is then decoded into video and audio signals by the player's electronics.
"The capacitive stylus pickup system which gives the CED its name can be contrasted with the technology of the conventional phonograph. Whereas the phonograph stylus physically vibrates with the variations in the record groove, and those vibrations are converted by a mechanical transducer (the phono pickup) to an electrical signal, the CED stylus normally does not vibrate and moves only to track the CED groove (and the disc surface—out-of-plane), while the signal from the stylus is natively obtained as an electrical signal. This more sophisticated system, combined with a high revolution rate, is necessary to enable the encoding of video signals with bandwidth of a few megahertz, compared to a maximum of 20 kilohertz for an audio-only signal—a difference of two orders of magnitude. Also, while the undulations in the bottom of the groove may be likened to pits, it is important to note that the spacing of vertical wave crests and troughs in a CED groove is continuously variable, as the CED is an analog medium. Usually, the term "pits," when used in the context of information media, refers to features with sharply defined edges and discrete lengths and depths, such as the pits on digital optical media such as CDs and DVDs.
In order to maintain an extremely light tracking force, the stylus arm is surrounded by coils which sense deflection, and a circuit in the player responds to the signals from these coils by moving the stylus head carriage in steps as the groove pulls the stylus across the disc. Other coils are used to deflect the stylus, to finely adjust tracking. This system is very similar to—yet predates—the one used in Compact Disc players to follow the spiral optical track, where typically a servo motor moves the optical pickup in steps for coarse tracking and a set of coils tilts the laser lens for fine tracking, both guided by an optical sensing device which is the analogue of CED stylus deflection sensing coils. For the CED player, this tracking arrangement has the additional benefit that the stylus drag angle remains uniformly tangent to the groove, unlike the case for a phonograph tonearm in which the stylus drag angle and consequently the stylus side force varies with the tone arm angle, which in turn depends on the radial position on the record of the stylus. Whereas for a phonograph, where the stylus has a pinpoint tip, linear tracking is merely ideal to reduce wear of records and styli and to maximize tracking stability, for a CED player linear tracking is a necessity for the keel-shaped stylus, which must always stay tangent to the groove. Furthermore, the achievement of an extremely light tracking force on the CED stylus enables the use of a fine groove pitch (i.e. fine spacing of adjacent revolutions of the spiral,) necessary to provide a long playing time at the required high rotational speed, while also limiting the rate of disc and stylus wear."
Something I saved from the stereo store.
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A spherical diamond tip bonded to a metal shaft, which is then mounted into the cantilever.
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An elliptical diamond bonded to a metal shaft. An elliptical diamond has facets cut into its leading and trailing edges, with the sides, where it hits the groove, left round. It contacts the groove at two small points that grow as the cartridge wears.
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A nude elliptical diamond, where the diamond goes into the cantilever. The square shank gives better alignment. It's also stronger and lighter.
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A Shibata stylus, which has two facets cut into its trailing edge, giving it a vertical, skinny line of contact with the groove. The leading edge is left round. In this picture, the leading edge is on the left. As a Shibata stylus contacts more area than an elliptical, it wears better.
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CED was really pretty remarkable technology. If internal bickering and stupidity at RCA hadn't slowed its development they might have been able to roll out in the mid-'70s, possibly beating the VCR to mass adoption.
They really should have developed audio-only discs as well. It would have greatly expanded the market for the technology, lowering the cost of manufacture in the process. With that kind of bandwidth CED would have allowed for awesome audio reproduction - it would essentially have been FM radio with CD-like specifications in terms of dynamic range and frequency response, if not beyond CD specs. Quad would have easily been accommodated with no discernible reduction in fidelity. They would have been a potent replacement for the vinyl LP - and might have also delayed or even completely scrapped the introduction of the Compact Disc.
Maybe the first successful consumer digital format would have been DAT...
What frequence that can be traced is also very much depending on amplitude, of course.
The only issue (or failing if you want to call it that) was the the CED disc surface was extremely delicate and touching it could render it unplayable, or so I heard it said. That was why the disk was placed in a caddy that you inserted into the player, releasing the disc without the risk of it being touched. When you think about it, it was amazing what was possible in those days with analog technology. When I play quadradiscs for people, they are often amazed that it was possible to get 4 channels of sound from a stereo groove 40 years ago. Quite remarkable, really.
Then no one would have had to invent the $5K record cleaning machine...
Maybe we can just work out it directly:
At radius R the circumference of the groove (approximating it by a circle) is 2*Pi*R or about 6.28R. If the rotation is 33rpm = 0.55 revs per second then the stylus travels through a distance of about 3.5R every second. If the signal is a 35kHz tone then that second contains 35,000 squiggles. Each one covers a distance of 3.5R / 35,000 = 1/10000R. If R is 7cm then that gives 7 microns for a 35kHz tone. Pretty close to what you estimated actually. At more distant grooves the size of each squiggle would increase in proportion to radius, so at 20cm it would be 20 microns per squiggle.
Cutting styli are basically triangular. The front face is flat and at right angles to the rotation. The sides taper sharply back.
Take a block of Toblerone chocolate (or a Pono player ) and stand it on end. Now shape the bottom end to the profile of a groove. That's it. The cutting occurs at the "knife edge" where the front face meets the sides. The sides are sloped sharply back into the triangular profile to allow clearance when the stylus moves from side to side. (If the cutter moves too fast, the sides may contact and damage the walls just cut.)
Here's a FAQ page with an image about half way down the page, showing an overhead representation of a groove with the profile of a cutting stylus, and elliptical and spherical playback styli:
Yeah...it's hard to wrap your head around the idea that the groove is a miniture version of the entire sound wave.
Wright90, yes, but with a longer wavelength at the outside of a record than at the inner part of the record.
The calculations ronankeane did, plus the fascinating website Don Hills brought to the table - lots of great info there - bring up a fact that's painfully obvious in retrospect. For a given frequency, the wiggles of the groove grow shorter as the tone arm tracks in. Duh...too bad I never considered that before. It helps explain why inner groove distortion can be such a problem.
It also might allow me to declare victory. Maybe the stylus is tracking vibrations as tiny as the wavelength of light. Given ronankeane's calculations, toward the record label a 35kHz signal is about 7 microns long. Let's use audible frequencies and cut the tone in half. A 17kHz tone is about 14 microns long. The wavelength of light is one thirtieth of that. What if I were to take that 14 micron wiggle and break it into 30 separate segments? If I measured each of those segments, wouldn't the voltage coming out of the phono cartridge have changed from the previous segment? If we could measure things accurately enough, wouldn't we find 30 separate states of the phono cartridge as it tracked that 14 micron long tone?
I've got to think about this for a while. It seems like cheating to me to look at the question this way, to break up a sound into smaller segments simply to prove a point. And yet, if this was digital, we wouldn't think twice about doing just that. A CD would sample that 17kHz tone two or three times. If we were to convert the 17kHz analog signal into a 24/96 digital stream, it would sample it 5 times.
Can I look at a stylus and phono cartridge in the same way for the purpose of justifying the phrase, "a stylus has to track vibrations as tiny as the wavelength of light?"
My gut says no.
But I'll ponder this for a bit. I've only been trying to answer this question for 30 years. There's no rush.
I'm not sure about the tracking the wavelength of light thing. If you can't track the groove perfectly you will get distortion on playback though. This will require tracking well beyond the signal cut in the groove . The distortion can be mild but when you hear a cartridge that tracks and traces well the difference is obvious.
You pulled that conclusion out of a hat.
To relate the wavelength of the modulations in the vinyl to a frequency you NEED the speed at which the stylus is moving in the groove. It is the only way to make the calculation. I didn't quote your entire post, but you made no mention of the speed in the groove. How did you come up with 2.5 um?
The velocity of the stylus in the groove varies from roughly 50 to 25 cm/sec. This assumes 33.3 rpm or 0.55 rev/sec, multiply this by the circumference at the outer edge of the record and the inner edge to get the speed range. Now divide this speed by 20 kHz (20000 1/sec) and you get the modulation length scale for 20 kHz.
This comes out to 25 to 13 um.
Also, this thread has been very loose with units like force, acceleration and mass. Its easy to confuse mass and force. If I have a 100 kg mass, it doesn't matter if I'm on Mars, Earth, or the Moon, it is still 100 kg. If I say it weighs less on Mars, that is a statement that it exerts less force on Mars. English units are really screwed up because pound is used as force and mass, yuck.
A G is an acceleration, not a force. 1 G equals the acceleration of gravity at sea level on Earth. If I'm on a roller coaster and experience 2 Gs, it feels like a force because of my mass, the more massive I am the more force I will feel.
Pressure is force divided by area, like pounds per square inch.
So a stylus exerts a pretty small force on the groove because there is only a couple of grams of effective mass, but because the contact area is so small, its a large pressure. But this has nothing to do with a ton, because that is not a unit of pressure.
So if me and Jack take your maths correctly a 20kHz sign wave occupies 13um of length at the inner grooves. The sign wave must pass through zero so each excursion would be 6.5um long. If this was a perfect arc the diameter would be 6.5um or 3.25um radius. Depending on the level of cut the actual radius that the diamond must fit into would be larger or smaller than 3.25um.
Maybe I don't understand though.
What distortion? Lol!
I think the tip would have to be smaller than 3.25 um. And smaller by a generous margin, since a tip of exactly the same radius as the radius of a groove would not be able to track it smoothly. But something doesn't seem right. Conversion of 3.25 um = 0.127 mil (0.13 mil) So, a 0.2 x 0.7 elliptical would have a larger effective tip radius than the 0.127 mil groove radius at 20 kHz on a 33 RPM record. That can not be right, since a 0.2 elliptical tip has no problem tracking 20kHz. (or does it have a problem?) The above is referenced to the stylus velocity of 25 cm/sec at the innermost groove on a 33 1/3 RPM record. (I assume is correct)
Doesn't the physical radius of the groove vary with the pitch of the groove? (modulation of the groove) A lower modulated groove would have a larger radius than a more highly modulated groove would it not? And the stylus velocity increases too. (increased modulation increases the distance the stylus must travel) I have to think about this!
Also, a 20kHz groove modulation replicates sine wave oscillations. A sine wave is not of a constant radius. I need to brush up on my trig, all this beyond me at the moment.
Nice pics thanks for posting. SEM of course. Note that groove walls have random features/grain ie aren't smooth at this detail. The stylus simply has to follow the path of the base of the V groove, and is held by the walls and only VTF holds it down. In a sense it's wonderfully simple - I find it amazing how small it is, on the scale of bacteria and viruses hangs issues that affect performance. Imagine if it was scaled up to be like a 1m wide bob-sleigh track, and you're a passenger on the stylus. I make the straight line speed about mach 12 on that scale, and accelerations would be instantly lethal - it only works because it is so small and parts so light !
Physically, the groove doesn't represent what people commonly think in terms of shape. At any moment, groove deviation angle from 'straight' represents programme level or amplitude. Groove curvature represents 'slew rate' of programme material. This is because grooves are cut so that velocity (ie angle) represents level - ie not amplitude as commonly imagined I think.
So working out what stylus shape fits accurately into grooves involves the slew rate and level of programme material, rather than simply frequency content. ie level plays an important role too. If stylus doesn't fit curvature, cartridge output is slew rate limited, rather than necessarily rolled off at high frequencies (depending on level). In practice curvature of real records is typically intentionally limited during mastering (citation needed from the boss !) or during programme material post production so that styli do fit, and it works.
When it come to trackability, it's typically simply programme level or 'groove deviation angle' which is limiting. Though acceleration or 'G forces' due to curvature can also be limiting depending on mastering and content. Just my 2p worth.
I'm still having trouble visualizing the process but it seems only half as bad as I thought. There is only one zero crossing per period so only one radius to trace. The positive and negative peaks seen on a scope are caused by the acceleration of the tip and the groove modulation looks nothing like that nice curve.
Still the peaks and valleys on a groove wall can get can get too tight for a conical or big elliptical tip to fit or trace well. A ortofon STY30 has a minor radius of 8um. I imagine there are grooves that are too severe for that to trace accurately.
Is that the "binary solo" from Flight of the Conchord's "The Humans Are Dead"?
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