Transistors vs. Tubes/Valves: A good little reminder

I was leafing through some old editions of Wireless World magazine this week and came across an article in the July, 1968 issue called “Computing Distortion: Method for low-power transistor amplifiers” by L. B. Arguimbau and D.M. Fanger.

I was immediately intrigued by the first sentence, which read:

Unlike those of thermionic valves, the non-linearities in junction transistors for low collector currents are highly uniform and predictable, hardly differing from one transistor to another.

Now, as an “audio professional”, I’m very used to seeing the “±” sign in data sheets. Any production line of anything has some tolerance limits within which the product will fall.

For example, the (on-axis, where applicable) magnitude response of a loudspeaker or headphone is typically spec’ed something like ± 3 dB within some frequency range. This would mean that, at some frequency within that range, when measured under identical conditions, two “identical” products (e.g. with the same brand and model name) might be as much as 6 dB apart.

For different devices and components inside those devices, the tolerance values are different.

This is why, for example, when I read that someone says “headphone model A has more bass than headphone model B”, I know that if you included the missing information, it would actually read “my sample of headphone model A has more bass than my sample of headphone model B”.

However, when it comes down to the component level, I’m used to seeing tighter tolerances. Of course, if you save money on resistors, they might be within 20% of the stated value. However, if I look at the specs of a decent DAC (which, in my case, is a chip that would be used inside a product – not a big DAC-in-a-box that sits on your desk), I’m used to seeing numbers like < ±1 dB within pragmatically usable frequency ranges.

Since I’m only a young person, I’ve only really worked with transistor-based equipment, both when I worked in studios and also since I started working in home audio. So, I’ve always taken it for granted, and never even considered that the distortion characteristics of a transistor would vary from one to another. This is because, as the article from 1968 states: they don’t… much…

However, I’ve never thought about the (now obvious) possibility that two “identical” tubes/valves will have different distortion behaviour, even at low levels, due to manufacturing differences.

So, the next time someone tells you that this tube amp is better than that tube amp (which I translate in my head to actually mean “I prefer the sound of this tube amp over the sound of that tube amp” since “better” is multi-dimensional with different weightings of the different dimensions by person), remind them that the full sentence should be:

“I prefer My sample of this tube amp with the tubes that are currently in it to that tube amp with the tubes that are currently in it.”

Wow

This article, from The Gramophone magazine, August 1932 foretells the future of turntables with platters driven by electric motors. Note that, to test this particular one, they increased what we would today call the “tracking force” to 3.5 pounds (about 1.6 kg) on the outside groove of a 10″ record without reducing the speed. Try that on a turntable today…

Sad to see a familiar mantra here though: “the motor is remarkably efficient, very well made and ridiculously expensive.”

Fibre needles

Reading through some old magazines again…

This time, it’s The Gramophone magazine from October, 1930. In the editorial, Compton Mackenzie says

What caught my eye was the discussion of gramophone needles made of “hard wood”, and also the prediction that “the growth of electrical recording steps … to grapple with that problem of wear and tear.”

The fact that electrical (instead of mechanical) recording and playback was seen as a solution to “wear and tear” reminded me of my first textbook in Sound Recording where “Digital Audio” was introduced only within the chapter on Noise Reduction.

Later in that same issue, there is a little explanation of the “Electrocolor” and “Burmese” needles.

The March 1935 issue raises the point of wear vs. fidelity in the Editorial (which starts by comparing players with over-sized horns).

I like the comment about having to be in the “right mood” for Ravel. Some things never change.

What’s funny is that, now that I’ve seen this, I can’t NOT see it. There are advertisements for fibre, thorn, and wood needles all over the place in 1930s audio magazines.

Vinyl info and calculators

This is just a collection of information about turntables and vinyl for anyone wanting to dig deeper into It (which might mean that it’s just for me…). I’ll keep adding to this (and completing it) as time goes by.

Glossary

Cantilever

  • The rod or arm that connects the stylus on one end to the “motor” on the other.

Effective Length

  • The straight-line distance between the pivot point of the tonearm and the top of the stylus

Equivalent Mass

  • definition to come

Flutter

  • Higher-frequency modulation of the audio frequency caused by changes in the groove speed. These may be the result of changes in problems such as unstable motor speed, variable compliance on a belt, issues with a spindle bearing, drive wheel eccentricity, and other issues.
  • Flutter describes a modulation in the groove speed ranging from 6 to 100 times a second (6 Hz to 100 Hz).

Frequency Drift

  • Very long-term (or low-frequency) changes in the audio frequency, typically caused by slow changes in the platter rotation speed.
  • Typically, changes with a modulation frequency of less than 0.5 Hz (a period of no less than 2 seconds) are considered to be frequency drift. Faster changes are labelled “Wow”

Groove

  • The v-shaped track pressed into the surface of the vinyl record, in which the stylus sits

Linear Tracking

  • A tonearm that moves linearly, following a path that is parallel to the radius line traced by the stylus. This (in theory) ensures that the tracking error is always 0º, however, in practice this error is merely small.

Modulation Width

  • The distance measured on a line through the spindle from the start of the modulated groove to the end of the modulated groove. This is approximately 3″ or 76 mm.

Mounting Distance

  • The distance between the spindle and the pivot point of the tonearm.

Needle

  • Also known as the stylus. The point that is placed in the groove of the vinyl record.
    Some persons distinguish between the “stylus” (to indicate the chisel on the mastering lathe that creates the groove in the master record), and the “needle” (to indicate the portion of the pickup on a turntable that plays the signal).

Null Radius

  • The radius (distance between the spindle and the stylus) where the tracking error is 0º. A typically-designed and correctly installed radial tracking tonearm has two null radii (see this posting).

Offset Angle

  • The angle between the axis of the stylus and a line drawn between the tonearm pivot and the stylus. See the line diagram below.

Overhang

  • The difference between the Effective Length of the tonearm and the Mounting Distance. This value is used in some equations for calculating the Tracking Error.

Pickup, Electromagnetic

  • Includes three general types: Moving Coil, Moving Magnet, and Variable Reluctance (aka Moving Iron). These produce an output proportional to the velocity of the stylus movement.

Pickup, Piezoelectic

  • Produces an output proportional to the displacement of the stylus.

Pitch

  • The density of the groove count per distance in lines per inch or lines per mm. The pitch can vary from disc to disc, or even within a single track, according to the requirements of the mastering.

Radial Tracking

  • A tonearm that rotates on a pivot point with the stylus tracing a circular path around that pivot.

Radius

  • The distance between the centre of the vinyl disc and the pickup stylus.

RIAA

  • A pre-emphasis / de-emphasis filter designed to fill two functions.
    • The first is a high-frequency attenuation de-emphasis that reduces the playback system’s sensitivity to surface noise. This requires a reciprocal high-frequency pre-emphasis boost.
    • The second is a low-frequency attenuation pre-emphasis that maintains a constant modulation amplitude at lower frequencies to avoid over-excursion of the playback stylus. This requires a reciprocal low-frequency de-emphasis boost.
  • The first of the two plots below, show the theoretical (black lines) and typical (red) response of the pre-emphasis filter. The second of the two plots shows the de-emphasis filter response.

Side Thrust

  • definition to come

Skating Force

  • definition to come

Spindle

  • The centre of the platter around which the record rotates

Stylus

  • Also known as the needle. The point that is placed in the groove of the vinyl record.
    Some persons distinguish between the “stylus” (to indicate the chisel on the mastering lathe that creates the groove in the master record), and the “needle” (to indicate the portion of the pickup on a turntable that plays the signal).

Stylus, Bonded vs. Nude

  • Although the tip of the stylus is typically made of diamond today, in lower-cost units, that diamond tip is mounted or bonded to a metal pin (typically steel, aluminium, or titanium) which is, in turn, connected to the cantilever (the long “arm” that connects back to the cartridge housing). This bonded design is cheaper to manufacture, but it results in a high mass at the stylus tip, which means that it will not move easily at high frequencies.
  • In order to reduce mass, the metal pin is eliminated, and the entire stylus is made of diamond instead. This makes things more costly, but reduces the mass dramatically, so it is preferred if the goal is higher sound performance. This design is known as a nude stylus.

Tracking Error

  • The angle between the tangent to the groove and the alignment of the stylus. In a perfect system, the stylus would align with the tangent to the groove at all radii (distances from the spindle), since this matches the angular rotation of the cutting head when the master was made on a lathe. A linear tracking arm minimises this error. A radial tracking arm can be designed to have two radii with no tracking error (each called a “Null Radius”) but will have some measurable tracking error at all other locations on the disk.
  • One side-effect of tracking error is distortion of the audio signal, typically calculated and expressed as a 2nd-harmonic distortion on a sinusoidal audio signal. However, higher order distortion and intermodulation artefacts also exist.

Warp Wow

  • A modulation of the frequency of the audio signal caused by vertical changes in the vinyl surface (a warped record). This typically happens at a lower frequency, which is why it is “warp wow” and not “warp flutter”.

Wow

  • Low-frequency modulation of the audio frequency caused by changes in the groove speed. These may be the result of changes in problems such as rotation speed of the platter, discs with an incorrectly-placed centre hole, or vertical changes in the surface of the vinyl, and other issues.
  • Wow is a modulation in the groove speed ranging from once every 2 seconds to 6 times a second (0.5 Hz to 6 Hz). Note that, for a turntable, the rotational speed of the disc is within this range. (At 33 1/3 RPM: 1 revolution every 1.8 seconds is equal to approximately 0.556 Hz.)

Disk size limits

Outside starting diameter

  • 7″ discs
    • 6.78″, +0.06″, -0.00″
    • 172.2 mm, +1.524 mm, – 0.0 mm
  • 10″ discs
    • 9.72″, +0.06″, -0.00″
    • 246.9 mm, +1.524 mm, – 0.0 mm
  • 12″ discs
    • 11.72″, +0.06″, -0.00″
    • 297.7 mm, +1.524 mm, – 0.0 mm

Start of modulated pitch diameter

  • 7″ discs
    • 6.63″, +0.00″, -0.03″
    • 168.4 mm, +0.0 mm, – 0.762 mm
  • 10″ discs
    • 9.50″, +0.00″, -0.03″
    • 241.3 mm, +0.0 mm, – 0.762 mm
  • 12″ discs
    • 11.50″, +0.00″, -0.03″
    • 292.1 mm, +0.0 mm, – 0.762 mm

Minimum inside diameter

  • 7″ discs
    • 4.25″
    • 107.95 mm
  • 10″ discs
    • 4.75″
    • 120.65 mm
  • 12″ discs
    • 4.75″
    • 120.65 mm

Lockout Groove diameter

  • 7″ discs
    • 3.88″, +0.00, -0.08
    • 98.552 mm, +0.0 mm, -2.032 mm
  • 10″ discs
    • 4.19″, +0.00, -0.08
    • 106.426 mm, +0.0 mm, -0.762 mm
  • 12″ discs
    • 4.19″, +0.00, -0.08
    • 106.426 mm, +0.0 mm, -0.762 mm

Unmodulated (silent) groove width

  • 2 mil minimum, 4 mil maximum
  • 0.0508 mm minimum, 0.1016 mm maximum

Modulated groove depth

  • 1 mil minimum, 5 mil maximum
  • 0.0254 mm minimum, 0.127 mm maximum
  • The figure below shows the typical, minimum, and maximum groove depths, drawn to scale (with a 13 µm spherical stylus)

Signal levels

  • A typical standard reference level is a velocity of 35.4 mm/sec on one channel.
  • This means that a monophonic signal (identical signal in both channels) with that modulation will have a lateral (side-to-side) velocity of 50 mm/sec.

Calculators and Measurements

Conversion

  • 1 mil = 1 “thou” = 1/1000 inch
  • Lengthmm = Lengthmil * 127/5000

Revolutions per Second

  • RevolutionsPerSecond = RevolutionsPerMinute / 60
  • e.g.
    • 0.556 Rev/Sec @ 33 1/3 RPM
    • 0.75 Rev/Sec @ 45 RPM
    • 1.3 Rev/Sec @ 78 RPM

Seconds per revolution

  • SecondsPerRevolution = 60 / RevolutionsPerMinute
  • e.g.
    • 1.8 Sec/Rev @ 33 1/3 RPM
    • 1.333 Sec/Rev @ 45 RPM
    • 0.769 Sec/Rev @ 78 RPM

Modulation Width

  • MaximumModulationWidth = (StartOfModulatedPitch – MinimumInsideDiameter) / 2
  • e.g. for a 12″ disc
    • (292.1 mm – 120.65 mm) / 2 = 85.725 mm
    • Typically approximately 3″ = 76 mm

Pitch (assuming constant pitch)

  • (RunningTime * RPM) / ModulationWidth
  • e.g.
    • (20 minutes * 33.333 RPM) / 76 mm = 8.77 lines per mm
    • (20 minutes * 33.333 RPM) / 3″ = 222.22 lines per inch

Groove Width

  • GrooveWidthInMil = (1000 / PitchInLinesPerInch + 1) / 2
  • e.g.
    • (1000 / 222 LPI + 1) / 2 = 2.75 mil = 2.75 x 10-3 inches = 0.07 mm

Angular Frequency (of the audio)

  • abbreviated ω (unit: radians per second)
  • ω = 2 * π * FrequencyHz

Angular Speed of Rotation (of of the disk)

  • commonly abbreviated ωr (unit: radians per second)
  • ωr = 2 * π * RevolutionsPerSecond

Displacement Amplitude

  • DisplacementAmplitudePeak = Velocitypeak / ω
  • e.g.
    • 50 mm/sec / (2 * pi * 1000 Hz) = 0.008 mm (peak)

Groove Speed

  • 2 * π * Radius * RevolutionsPerSecond
  • e.g.
    • at the Start of modulated pitch on a 12″ disk turning at 33 1/3 RPM
      • 2 * π * (292.1 mm / 2) * (33.333 / 60) = 509.8 mm/sec
    • at the Minimum inside diameter on a 12″ disk turning at 33 1/3 RPM
      • 2 * π * (120.65 mm / 2) * (33.333 / 60) = 210.6 mm/sec
  • The plot below shows the groove speeds of 12″ 33 1/3 RPM and 7″ 45 RPM for all possible radii.

Wavelength

  • GrooveSpeed / Frequency
  • e.g.
    • 20 Hz at the Start of modulated pitch on a 12″ disk turning at 33 1/3 RPM
      • 509.8 / 20 = 25.5 mm
    • 20 kHz at the Start of modulated pitch on a 12″ disk turning at 33 1/3 RPM
      • 509.8 / 20000 = 0.0255 mm
    • The plot below shows wavelengths of 4 different frequencies for 12″ 33 1/3 RPM records (the longer curves) and 7″ 45 RPM records (the shorter curves)

Tracking Error

  • Tracking Error =
    OffsetAngle – asin ((EffectiveLength2 + Radius2 – MountingDistance2) / (2 * EffectiveLength * Radius))
  • see this posting for an explanation and example

Distortion caused by tracking error

  • Equation is for calculating percentage of second-harmonic distortion of a laterally-modulated monophonic sinusoidal audio signal
  • DistortionPercent = 100 * (PeakVelocity * tan(TrackingError)) / (GrooveSpeed)
  • see this posting for an explanation and examples

Wow and Flutter

  • Typically measured with a 3150 Hz sinusoidal tone, played from the vinyl surface
  • This signal is then de-modulated to determine its change over time. That modulation is then filtered through the response shown below which approximates human sensitivity to frequency modulation of an audio signal. More detailed information is given below
  • The AES6-2008 standard, which is the currently accepted method of measuring and expressing the wow and flutter specification, uses a “2σ” or “2-Sigma” method, which is a way of looking at the peak deviation to give a kind of “worst-case” scenario. In this method, the tone is played from a disc and captured for as long a time as is possible (or feasible). Firstly, the average value of the actual frequency of the output is found (in theory, it’s fixed at 3,150 Hz, but this is never true). Next, the short-term variation of the actual frequency over time is compared to the average, and weighted using the filter shown above. The result shows the instantaneous frequency variations over the length of the captured signal, relative to the average frequency (however, the effect of very slow and very fast changes have been reduced by the filter). Finally, the standard deviation of the variation from the average is calculated, and multiplied by 2 (hence “2-Sigma”, or “two times the standard deviation”), resulting in the value that is shown as the specification. The reason two standard deviations is chosen is that (in the typical case where the deviation has a Gaussian distribution) the actual Wow & Flutter value should exceed this value no more than 5% of the time.

References

All of these are available online. Some of them require you to purchase them (or be a member of an organisation).

  • “Tracking Angle in Phonograph Pickups”
    B. B. Bauer. Electronics magazine, March 1945
  • “Minimising Pickup Tracking Error”
    Dr. John D. Seagrave, Audiocraft Magazine, December 1956, January 1957, and August 1957
  • “Understanding Phono Cartridges”
    S.K. Pramanik, Audio magazine, March 1979
  • “Tonearm Geometry and Setup Demystified”
    Martin D. Kessler and B.V.Pisha, Audio magazine, January 1980
  • “Understanding Tonearms”
    S.K. Pramanik, Audio magazine, June 1980
  • “Analytic Treatment of Tracking Error and Notes on Optimal Pick-up Design”
    H.G.Baerwald, Journal of the Society of Motion Picture Engineers, December 1941
  • “Pickup Arm Design”
    J.K. Stevenson, Wireless World magazine, May 1966, and June 1966
  • “The Optimum Pivot Position on Tonearm”
    S. Takahashi et. al., Audio Engineering Society Preprint no. 1390 (61st Convention, November 1978)
  • “Audible Effects of Mechanical Resonances in Turntables”
    Brüel and Kjær Application Note (1977)
  • “Basic Disc Mastering”; “
    Larry Boden (1981)
  • “Cartridge / Arm / Turntable Followup: Loose Ends and New Developments”
    The Audio Critic, 1:43 (Spring/Fall, 1978)
  • “Have Tone Arm Designers Forgotten Their High-School Geometry?”
    The Audio Critic, 1:31 (Jan./Feb. 1977).
  • “How the Stereo Disc Works”
    Radio-Electronics, (July 1958)
  • “Manual of Analogue Sound Restoration Techniques”
    Peter Copeland (2008)
  • “On the Mechanics of Tonearms”
    Dick Pierce (2005)
  • “Reproduction of Sound in High-Fidelity and Stereo Phonographs”
    Edgar Villchur (1966)
  • Journal of the Audio Engineering Society (www.aes.org)
    • “Centennial Issue: The Phonograph and Sound Recording After One-Hundred Years”
      Vol. 25, No. 10/11 (Oct./Nov. 1977)
    • “Factors Affecting the Stylus / Groove Relationship in Phonograph Playback Systems”
      C.R. Bastiaans; Vol. 15 Issue 4 (Oct. 1967)
    • “Further Thoughts on Geometric Conditions in the Cutting and Playing of Stereo Disk”
      C.R. Bastiaans; Vol. 11 Issue 1 (Jan. 1963)
    • “Record Changers, Turntables, and Tone Arms-A Brief Technical History”
      James H. Kogen; Vol. 25 (Oct./Nov. 1977)
    • “Some Thoughts on Geometric Conditions in the Cutting and Playing of Stereodiscs and Their Influence on the Final Sound Picture”
      Ooms, Johan L., Bastiaans, C. R.; Vol. 7 Issue 3 (Jul. 1959)
    • “The High-Fidelity Phonograph Transducer”
      B.B. Bauer; Vol. 25 Issue 10/11 (Nov. 1977)
  • DIN Standards
    • 45 500: Hi-Fi Technics: Requirements for Disk Recording Reproducing Equipment
    • 45 507: Measuring Apparatus for Frequency Variations in Sound Recording Equipment
    • 45 538: Definitions for Disk Record Reproducing Equipment
    • 45 539: Disk Record Reproducing Equipment: Directives for Measurements, Markings, and Audio Frequency, Connections, Dimensions of Interchangeable Pickups, Requirements of Playback Amplifiers
    • 45 541: Frequency Test Record St 33 and M 33 (33 1/3 rev/min; Stereo and Mono)
    • 45 542: Distortion Test Record St 33 and St 45 (33 1/3 or 45 rev/min; Stereo)
    • 45 543: Frequency Response and Crosstalk Test Record
    • 45 544: Rumble Measurement Test Record St 33 and M 33 (33 1/3 rev/min; Stereo and Mono)
    • 45 545: Wow and Flutter Test Records, 33 1/3 and 45 rev/min
    • 45 546: Stereophonic Disk Record St 45 (45 rpm)
    • 45 547: Stereophonic Disk Record St 33 (33 1/3 rpm)
    • 45 548 Aptitude for Performance of Disk Record Reproducing Equipment
    • 45 549: Tracking Ability Test Record
  • IEC Publications
    • 98: Recommendations for Lateral-Cut Commercial and Transcription Disk Recordings
    • 98: Processed Disk Records and Reproducing Equipment
    • 386: Method of Measurement of Speed Fluctuations in Sound Recording and Reproducing Equipment

Tonearm tracking error and distortion

In the last posting, I reviewed the math for calculating the tracking error for a radial tonearm. The question associated with this is “who cares?”

In the March, 1945 issue of Electronics Magazine, Benjamin Bauer supplied the answer. An error in the tracking angle results in a distortion of the audio signal. (This was also discussed in a 3-part article by Dr. John D. Seagrave in Audiocraft Magazine in December 1956, January 1957, and August 1957)

If the signal is a sine wave, then the distortion is almost entirely 2nd-order (meaning that you get the sine wave fundamental, plus one octave above it). If the signal is not a sine wave, then things are more complicated, so I will not discuss this.

Let’s take a quick look at how the signal is distorted. An example of this is shown below.

In that plot, you can see that the actual output from the stylus with a tracking error (the black curve) precedes the theoretical output that’s actually on the vinyl surface (the red curve) when the signal is positive, and lags when it’s negative. An intuitive way of thinking of this to consider the tracking error as an angular rotation, so the stylus “reads” the signal in the groove at the wrong place. This is shown below, which is merely zooming in on the figure above.

Here, you can see that the rotation (tracking error) of the stylus is getting its output from the wrong place in the groove and therefore has the wrong output at any given moment. However, the amount by which it’s wrong is dependent not only on the tracking error but the amplitude of the signal. When the signal is at 0, then the error is also 0. This is not only the reason why the distortion creates a harmonic of the sine wave, but it also explains why (as we’ll see below) the level of distortion is dependent on the level of the signal.

This intuitive explanation is helpful, but life is unfortunately, more complicated. This is because (as we saw in the previous posting), the tracking error is not constant; it changes according to where the stylus is on the surface of the vinyl.

If you dig into Bauer’s article, you’ll find a bunch of equations to help you calculate how bad things get. There are some minor hurdles to overcome, however. Since he was writing in the USA in 1945, his reference was 78 RPM records and his examples are all in inches. However, if you spend some time, you can convert this to something more useful. Or, you could just trust me and use the information below.

In the case of a sinusoidal signal the level of the 2nd harmonic distortion (in percent) can be calculated with the following equation:

PercentDistortion = 100 * (ω Αpeak α) / (ωr r)

where

  • ω is 2 * pi * the audio frequency in Hz
  • Apeak is the peak amplitude of the modulation (the “height” of the groove) in mm
  • α is the tracking error in radians
  • ωr is the rotational speed of the record in radians per second, calculated using 2 * pi * (RPM / 60)
  • r is the radius of the groove; the distance from the centre spindle to the stylus in mm

Let’s invent a case where you have a constant tracking error of 1º, with a rotational speed of 33 1/3 RPM, and a frequency of 1 kHz. Even though the tracking error remains constant, the signal’s distortion will change as the needle moves across the surface of the record because the wavelength of the signal on the vinyl surface changes (the rotational speed is the same, but the circumference is bigger at the outside edge of the record than the inside edge). The amount of error increases as the wavelength gets smaller, so the distortion is worse as you get closer to the centre of the record. This can be see in the shapes of the curves in the plot below. (Remember that, as you play the record, the needle is moving from right to left in those plots.)

You can also see in those plots that the percentage of distortion changes significantly with the amplitude of the signal. In this case, I’ve calculated using three different modulation velocities. The middle plot is 35.4 mm / sec, which is a typical accepted standard reference level, which we’ll call 0 dB. The other two plots have modulation velocities of -3 dB (25 mm / sec) and + 3 dB (50 mm / sec).

Sidebar: If you want to calculate the Amplitude of the modulation

Apeak = (ModulationVelocity * sqrt(2)) / (2 * pi * FrequencyInHz)

Note that this simplifies the equation for calculating the distortion somewhat.

Also, if you need to convert radians to degrees, then you can multiply by 180/pi. (about 57.3)

Of course, unless you have a very badly-constructed linear tracking turntable, you will never have a constant tracking error. The tracking error of a radial tonearm is a little more complicated. Using the recommended values for the “well known tonearm” that I used in the last posting:

  • Effective Length (l) : 233.20 mm
  • Mounting Distance (d) : 215.50 mm
  • Offset angle (y) : 23.63º

and assuming that this was done perfectly, we get the following result for a 33 1/3 RPM album.

You can see here that the distortion drops to 0% when the tracking error is 0º, which (in this case) happens at two radii (distances between the centre spindle and the stylus).

If we do exactly the same calculation at 45 RPM, you’ll see that the distortion level drops (because the value of ωr increases), as shown below. (But good luck finding a 12″ 45 RPM record… I only have two in my collection, and one of those is a test record.)

Important notes:

Everything I’ve shown above is not to be used as proof of anything. It’s merely to provide some intuitive understanding of the relationship between radial tracking tonearms, tracking error, and the resulting distortion. There is one additional important reason why all this should be taken with a grain of salt. Remember that the math that I’ve given above is for 78 RPM records in 1945. This means that they were for laterally-modulated monophonic grooves; not modern two-channel stereophonic grooves. This means that the math above isn’t accurate for a modern turntable, since the tracking error will be 45º off-axis to the axis of modulation of the groove wall. This rotation can be built into the math as a modification applied to the variable α, however, I’m not going to complicate things further today…

In addition, the RIAA equalisation curve didn’t get standardised until 1954 (although other pre-emphasis curves were being used in the 1940s). Strictly speaking, the inclusion of a pre-emphasis curve doesn’t really affect the math above, however, in real life, this equalisation makes it a little more complicated to find out what the modulation velocity (and therefore the amplitude) of the signal is, since it adds a frequency-dependent scaling factor on things. On the down-side, RIAA pre-emphasis will increase the modulation velocity of the signal on the vinyl, resulting in an increase in the distortion effects caused by tracking error. On the up-side, the RIAA de-emphasis filtering is applied not only to the fundamentals, but the distortion components as well, so the higher the order of the unwanted harmonics, the more they’ll be attenuated by the RIAA filtering. How much these two effects negate each other could be the subject of a future posting; if I can wrap my own head around the problem…

One extra comment for the truly geeky:

You may be looking at the last two plots above and being confused in the same way that I was when I made them the first time. If you look at the equation, you can see that the PercentDistortion is related to α: the tracking error. However, if you look at the plots, you’ll see that I’ve shown it as being related to | α |: the absolute value of the tracking error instead. This took me a while to deal with, since my first versions of the plots were showing a negative value for the distortion. “How can a negative tracking result in distortion being removed?” I asked myself. The answer is that it doesn’t. When the tracking error is negative, then the angle shown in the second figure above rotates counter-clockwise to the left of the vertical line. In this case, then the output of the stylus lags for positive values and precedes for negative values (opposite to the example I gave above), meaning that the 2nd-order harmonic flips in polarity. SINCE you cannot compare the phase of two sine tones that do not have the same frequency, and SINCE (for these small levels of distortion) it’ll sound the same regardless of the polarity of the 2nd-order harmonic, and SINCE (in real-life) we don’t listen to sine tones so we get higher-order THN and IMD artefacts, not just a frequency doubling, THEN I chose to simplify things and use the absolute value.
Post Script to the comment for geeks: This conclusion was confirmed by J.K. Stevenson’s article called “Pickup Arm Design” in the May, 1966 edition of Wireless World where he states “The sign of φ (positive or negative) is ignored as it has no effect on the distortion.” (He uses φ to denote the tracking error angle.)

Penultimate Post Script:

J.K. Stevenson’s article gives an alternative way of calculating the 2nd order harmonic distortion that gives the same results. However, if you are like me, then you think in modulation velocity instead of amplitude, so it’s easier to not convert on the way through. This version of the equation is

PercentDistortion = 100 * (Vpeak tan(α)) / (μ)

where

  • Vpeak is the peak modulation velocity in mm/sec
  • α is the tracking error in radians
  • μ is the groove speed of the record in mm/sec calculated using 2*pi*(rpm/60)*r
  • r is the radius of the groove; the distance from the centre spindle to the stylus in mm

Final Post-Script:

I’ve given this a lot of thought over the past couple of days and I’m pretty convinced that, since the tracking error is a rotation angle on an axis that is 45º away from the axis of modulation of the stylus (unlike the assumption that we’re dealing with a monophonic laterally-modulated groove in all of the above math), then, to find the distortion for a single channel of a stereophonic groove, you should multiply the results above by cos(45º) or 1/sqrt(2) or 0.707 – whichever you prefer. If you are convinced that this was the wrong thing to do, and you can convince me that you’re right, I’ll be happy to change it to something else.

Tonearm alignment and tracking error

The June 1980 issue of Audio Magazine contains an article written by Subir K. Pramanik called “Understanding Tonearms”. This is a must-read tutorial for anyone who is interested in the design and behaviour of radial tonearms.

One of the things Pram talked about in that article concerned the already well-known relationship between tonearm geometry, its mounting position on the turntable, and the tracking error (the angular difference between the tangent to the groove and the cantilever axis – or the rotation of the stylus with respect to the groove). Since the tracking error is partly responsible for distortion of the audio signal, the goal is to minimise it as much as possible. However, without a linear-tracking system (or an infinitely long tonearm), it’s impossible to have a tracking error of 0º across the entire surface of a vinyl record.

One thing that is mentioned in the article is that “Small errors in the mounting distance from the centre of the platter … can make comparatively large differences in angular error” So I thought that I’d do a little math to find out this relationship.

The article contains the diagram shown below, showing the information required to do the calculations we’re interested in. In a high-end turntable, the Mounting Distance (d) can be varied, since the location of the tonearm’s bearing (the location of the pivot point) is adjustable, as can be seen in the photo above of an SME tonearm on a Micro Seiki turntable.

The tonearm’s Effective Length (l) and Offset Angle (y) are decided by the manufacturer (assuming that the pickup cartridge is mounted correctly). The Minimum and Maximum groove radius are set by international standards (I’ve rounded these to 60 mm and 149 mm respectively). The Radius (r) is the distance from the centre of the LP (the spindle) to the stylus at any given moment when playing the record.

In a perfect world, the tracking error would be 0º at all locations on the record (for all values of r from the Maximum to the Minimum groove radii) which would make the cantilever align with the tangent to the groove. However, since the tonearm rotates around the bearing, the tracking error is actually the angle x (in the diagram above) subtracted from the offset angle. “X” can be calculated using the equation:

x = asin ((l2 + r2 – d2) / (2 l r))

So the tracking error is

Tracking Error = y – asin ((l2 + r2 – d2) / (2 l r))

Just as one example, I used the dimensions of a well-known tonearm as follows:

  • Effective Length (l) : 233.20 mm
  • Mounting Distance (d) : 215.50 mm
  • Offset angle (y) : 23.63º

Then the question is, if I make an error in the Mounting Distance, what is the effect on the Tracking Error? The result is below.

If we take the manufacturer’s recommendation of d = 215.4 mm as the reference, and then look at the change in that Tracking Error by mounting the bearing at the incorrect distance in increments of 0.2 mm, then we get the plot below.

So, as you can see there, a 0.2 mm error in the location of the tonearm bearing (which, in my opinion, is a very small error…) results in a tracking error difference of about 0.2º at the minimum groove radius.

If I increase the error to increments of 1 mm (± 5mm) then we get similar plots, but with correspondingly increased tracking error.

If you go back and take a look at the equation above, you can see that the change in the tracking error is constant with the Offset Angle (unlike its relationship with an error in the location of the tonearm bearing, which results in a tracking error that is NOT constant). This means that if you mount your pickup on the tonearm head shell with a slight error in its angle, then this angular error is added to the tracking error as a constant value, regardless of the location of the stylus on the surface of the vinyl, as shown below.

B&O Pickup stylus comparison

Below are four photos taken with the same magnification.

The top two photos are a Bang & Olufsen SP2 pickup, compatible with the 25º tonearm on a Type 42 “Stereopladespiller”.

The bottom two are a rather dirty Bang & Olufsen MMC 1/2 pickup, compatible with a range of turntables including the Beogram 4500, for example.

The yellow grid lines have a 0.50 mm spacing.

Keep your needle clean

One of my jobs at Bang & Olufsen is to do the final measurements on each bespoke Beogram 4000c turntable before it’s sent to the customer. Those measurements include checking the end-to-end magnitude response, playing from a vinyl record with a sine sweep on it (one per channel), recording that from the turntable’s line-level output, and analysing it to make sure that it’s as expected. Part of that analysis is to very that the magnitude responses of the left and right channel outputs are the same (or, same enough… it’s analogue, a world where nothing is perfect…)

Today, I was surprised to see this result on a turntable that was being inspected part-way through its restoration process :

Taken at face value, this should have resulted in a rejection – or at least some very serious questions. This is a terrible result, with unacceptable differences in output level between the two channels. When I looked at the raw measurements, I could easily see that the left channel was behaving – it was the right channel that was all over the place.

The black curve looks very much like what I would expect to see. This is the result of playing a track that is a sine sweep from 20 Hz to 20 kHz, where the signal below 1 kHz follows the RIAA curve, whereas the signal above 1 kHz does not. This is why, after it’s been filtered using a RIAA preamp, the low frequency portion has a flat response, but the upper frequency band rolls off (following the RIAA curve).

Notice that the right channel (the red curve) is a mess…

A quick inspection revealed what might have been the problem: a small ball of fluff collected around the stylus. (This was a pickup that was being used to verify that the turntable was behaving through the restoration – not the one intended for the final customer – and so had been used multiple times on multiple turntables.)

So, we used a stylus brush to clean off the fluff and ran the measurement again. The result immediately afterwards looked like this:

which is more like it! A left-right channel difference of something like ± 0.5 dB is perfectly acceptable.

The moral of the story: keep your pickup clean. But do it carefully! That cantilever is not difficult to snap.

Beograms side-by-side

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

On the left: a “Stereopladespiller” (Stereo Gramophone) Type 42 VF.
On the right, a Beogram 1000 V Type 5203 Series 33, modified with a built-in RIAA preamp (making it a Beogram 1000 VF)

Some history today – without much tech-talk. I just finished restoring my 42VF and I thought I’d spend an hour or two taking some photos next to my BG1000.

According to the beoworld.org website, the Stereopladespiller was in production from 1960 to 1976. Although Bang & Olufsen made many gramophones before 1960, they were all monophonic, for 1-channel audio. This one was originally made to support the 2-channel “SP1 / SP2” pickup developed by Erik Rørbæk Madsen after having heard 2-channel stereo on a visit to the USA in the mid-1950s (and returned to Denmark with a test record).

Sidebar: The “V” means that the players are powered from the AC mains voltage (220 V AC, 50 Hz here in Denmark). The “F” stands for “Forforstærker” or “Preamplifier”, meaning that it has a built-in RIAA preamp with a line-level output.

Internally, the SP1 and SP2 are identical. The only difference is the mounting bracket to accommodate the B&O “ST-” series tonearms and standard tonearms.

There were 4 variants in the ST-series of tonearms:

[table]

Name, Pivot – Platter Centre, Pivot – Stylus, Pickup

ST/M,190 mm, 205 mm, SP2

ST/L, 209.5 mm, 223.5 mm, SP2

ST/P, 310 mm, 320 mm, SP2

ST/A, 209.5 mm, 223.5 mm, SP1

[/table]

(I’ll do another, more detailed posting about the tonearms at a later date…)

Again, according to the beoworld.org website, the Beogram 1000 was in production from 1965 to 1973. (The overlap and the later EoP date of the former makes me a little suspicious. If I get better information, I’ll update this posting.)

The tonearm seen here on the Stereopladespiller is the ST/L model with a Type PL tonearm lifter.

Looking not-very-carefully at the photos below, you can see that the two tonearms have a significant difference – the angle of the pickup relative to the surface of the vinyl. The ST/L has a 25º angle whereas the tonearm on the Beogram 1000 has a 15º angle. This means that the two pickups are mutually incompatible. The pickup shown on the Beogram 1000 is an SP14.

This, in turn, means that the vertical pivot points for the two tonearms are different, as can be seen below.

The heights of both tonearms at the pivot are adjustable by moving a collar around the post and fixing its position with a small set screw. A nut under the top plate (inside the turntable) locks it in position.

The position of the counterbalance on the older tonearm can be adjusted with the large setscrew seen in the photo above. The tonearm on the Beogram 1000 gently “locks” into the correct position using a small spring-loaded ball that sets into a hole at the end of the tonearm tube, and so it’s not designed to have the same adjustability.

Both tonearms use a spring attached to a plastic collar with an adjustable position for fine-tuning the tracking force. At the end of this posting, you can see that I’ve measured its accuracy.

The Micro Moving Cross (MMC) principle of the SP1/2 pickup can easily be seen in the photo above (a New-Old-Stock pickup that I stumbled across at a flea market). For more information about the MMC design, see this posting. In later versions of the pickup, such as the SP14, seen below, the stylus and MMC assembly were attached to the external housing instead.

A couple of later SP-series pickups in considerably worse shape. These are also flea-market finds, but neither of them is behaving very well due to bent cantilevers.

This construction made it easier to replace the stylus, although it was also possible to do so with the SP1-2 using a replacement such as the one shown below.

A replacement stylus for the SP1/2 shown on the bremdal-radio.dk website.

Just to satisfy my own curiosity, I measured the tracking force at the stylus with a number of different adjustments on the collar. The results are shown below.

Tracking force on the Stereopladespiller with the collar aligned to each side of the gradations on the tonearm. Right-click on the photo and open it in a new window or tab to zoom in for more details.
Tracking force on the Beogram 1000 with the collar aligned to each side of the gradations on the tonearm. Right-click on the photo and open it in a new window or tab to zoom in for more details.

As you can see there, the accuracy is reasonably good. This is not really surprising, since the tracking force is applied by a spring. So, as long as the spring constant hasn’t changed over the years, which it shouldn’t have unless it got stretched for some reason (say, when I was rebuilding the pivot on the tonearm, for example…) it should behave as it always did.