## Some notes on gramophones.

### Introduction.

This is a collection of notes for gramophone / pick-up cartridge calculation.
They are in no particular order.

### Units.

All levels are rms values unless stated.
V p or V peak is peak voltage. In some documents, the character is used to denote peak value.
V pp is peak-peak voltage.

All formulas use absolute metric units unless noted.

### Tonearm resonance frequency.

The effective moving mass of the tonearm system and the compliance of the pick-up forms a high-pass filter. This is ideally a critically damped filter at a frequency below the audio range, but this is rarely possible, so the frequency response will have a peak. This peak must be below the audio range, but above the VLF output components from the gramophone so a general rule-of-thump is to aim for 10 Hz.

The effective moving mass is the moving (some times called dynamic mass) of the tonearm plus the mass of the pick-up cartridge and its mounting hardware. These values can normally be found in the product's data sheets.

The pick-up compliance is normally specified as Static compliance, compliance at 10 Hz or compliance at 100 Hz. The value to use for arm resonance calculation is the 10 Hz value. Mørch [4] suggest you can use the Static value divided by 2 or the 100 Hz value multiplied by 1.5-2. For a more detailed discussion on this subject, see this Vinylengine forum thread on the subject of pick-up compliance [5].
Pick-up compliance is normally specified in 1 of 3 units (or with no unit): µm/mN (micrometer/millinewton), x10-6cm/dyn (centimeters/dyne) (micro-centimeters/dyne to be exact), cu or CU (compliance units). Luckily these units are identical so "15 µm/mN", "15 x10-6cm/dyn", "15 cu", "15 CU" or "15" are the same value.

The tonearm resonance frequency is calculated by:
fres=1000 / ( 2 * π * √M * C ), where:
fres is the resonance frequency in Hz.
M is the effective moving mass in grams.
C is the pick-up compliance in one of the units listed above.

### Record modulation.

Fig.1: Record groove modulation.
L:Left channel.
R: Right channel.
M: Mono signal (L+R).
S: Side signal (L-R). Mono signal for vertically cut records.
The arrows indicates the phase.

How to pack a stereo signal in one record groove (animation) [7].

### Pick-up.

This table lists some characteristics of the most common pick-up types used today.

 Type High Output Moving Coil (HOMC) Moving Coil (MC) Moving Iron (MI) Moving Magnet (MM) Output voltage @ 5 cm/s 1 mV to 3.5 mV 0.04 mV to 0.7 mV 0.4 mV to 5 mV 2.5 mV to 13 mV Coil resistance 20 Ω to 150 Ω 1 Ω to 100 Ω 10 Ω to 600 Ω 500 Ω to 1.5 kΩ Coil inductance 1 µH to 100 µH 1 µH to 100 µH 2 mH to 50 mH 300 mH to 1 H Recommended load resistance 250 Ω to 47 kΩ 5 Ω to 500 Ω 500 Ω to 47 kΩ 47 kΩ Recommended load capacitance Uncritical Uncritical Uncritical 150 pF to 600 pF User replaceable stylus No No On some models Yes

#### Nominal output voltage.

A pick-up's output voltage is proportional to the stylus velocity and is specified in V at some reference velocity (typically 3.84 cm/s or 5 cm/s).

#### Maximum output voltage.

The maximum output voltage from a pick-up depends on its tracking ability. This is specified as velocity in cm/s or as amplitude in µm at a specified frequency (typically 315 Hz). Incidentally, very few manufacturers specify tracking ability.

If the specification is in µm, the maximum velocity is calculated:
vmax = 2 * π * f * tmax, where
vmax is the maximum velocity.
f is the tracking measurement frequency.
tmax is maximum peak tracking amplitude.
Example:
Tracking ability: 60 µm peak @ 315 Hz.
vmax = 2 * π * 315 * 60E-6 = 1.19E-1 or 11.9 cm/s.

When the maximum velocity is known, the maximum output voltage is calculated:
Umax = Unom / vnom * vmax, where
Umax is maximum output voltage.
Unom is the nominal output voltage.
vnom is the reference velocity for Unom.
Example:
Nominal output level: 3 mV @ 5 cm/s.
Maximum velocity: 25 cm/s.
Umax = 3E-3 / 5E-2 * 25E-2 = 1.5E-2 or 15 mV.

Another approach is to take the data from a recording head and calculate the maximum pick-up output from that.
From Neumann SX 74 data sheet:
Maximum continuous velocity: 28.5 cm/s peak vertical.
Maximum short-term velocity (10 kHz, 10 ms): 105 cm/s peak vertical.
Maximum stylus excursion: ± 150 µm.
As the values are for a vertical (mono) groove, they must be divided by √2 to obtain the velocity for each of left and right channels, giving a velocity of 20 cm/s continuous or 74 cm/s short term. For half-speed-mastered records, these numbers will double at playback.
20 cm/s is a peak amplitude of 100 µm at 315 Hz. 74 cm/s is a peak amplitude of 375 µm at 315 Hz, but this number exceeds the recording heads maximum stylus excursion.
The maximum stylus excursion of 150 µm peak limits the lowest frequency that can be recorded to 215 Hz for 20 cm/s or 790 Hz for 74 cm/s.

### Tonearm wire.

The tone arm wire is normally not very critical from an electrical point of view, but in a few applications with very low pick-up impedance it should be considered.

#### Wire resistance.

The resistance of the wire is normally not specified, but is easy to calculate.
If the wire size is given i AWG, convert to meters:
d = 127E-6 * 92 ˆ ( ( 36 - AWG ) / 39 ), where
d is the wire diameter.
AWG is the wire AWG number.
A = π * ( d / 2 )², where
A is the wire cross-sectional area.
Rw = ρ * l / A, where
Rw is the wire resistance.
l is the wire length.
ρ is the wire material's resistivity ( Silver: 1.59E-8 Ωm, Aluminum: 2.82E-8 Ωm, Gold: 2.44e-8 Ωm, Copper: 1.68E-8 Ωm ).
Example:
60 cm AWG30 wire.
d = 127E-6 * 92 ˆ ( ( 36 - 30 ) / 39 ) = 2.55E-4 or 0.255 mm.
A = π * ( 2.55E-4 / 2 )² = 5.10E-8 or 0.051 mm².
Rw = 1.68E-8 * 0.6 / 5.10E-8 = 0.20 Ω.

#### Signal loss due to the wire.

Signal loss = 20 * log ( 1 + Rw / (Rl + Rp) ) (in dB), where
Rl is the pick-up load resistance.
Rp is the pick-up internal resistance.
Rw is the wire resistance.
Example:
Rg = 3 Ω, Rl = 30 Ω, Rw = 0.2 Ω
Signal loss = 20 * log ( 1 + 0.2 / ( 30 + 3 ) ) = 0.05 dB.

#### Wire noise.

vn1 = √4 * kB * T * Rp
vn2 = √4 * kB * T * ( Rp + Rw ) , where
vn1 and vn2 are the thermal noise for the pick-up without and with the tone arm wire.
kB is Boltzmann's constant = 1.38E-23.
T is temperature in kelvin. 300k is 27C.
NF = 20 * log ( vn2 / vn1 ), where
NF is the noise figure ( noise added due to the wire ).
Example:
Rg = 3 Ω, Rw = 0.2 Ω
vn1 = √4 * 1.38E-23 * 300 * 3 = 2.28E-10 or 0.228 nV/√Hz.
vn2 = √4 * 1.38E-23 * 300 * (3 + 0.2) = 2.30E-10 or 0.230 nV/√Hz.
NF = 20 * log ( 2.30e-10 / 2.28E-10 ) = 0.28 dB.
The short version:
NF = 20 * log ( √( Rg + Rw ) / Rw ).

 Wire AWG 28 30 32 34 Wire cross-sectional area 0.08 mm² 0.05 mm² 0.03 mm² 0.02 mm² Wire resistance for 60 cm copper 0.12 Ω 0.20 Ω 0.31 Ω 0.50 Ω Signal loss due to wire 0.03 dB 0.05 dB 0.08 dB 0.13 dB Added thermal noise due to wire 0.18 dB 0.28 dB 0.43 dB 0.67 dB
Wire influence for a pick-up with 3 Ω internal resistance and a 30 Ω load.
Changing the wire material from copper to silver will reduce the resistance by 5% and does not have any significant influence on signal loss or thermal noise.

### Pick-up DC current.

Pick-up DC current is not normally considered, but should be if you design an amplifier with a DC coupled input stage.
A 3 mV signal into a 47 kΩ load is a signal current of 64 nA.
Compare this with the typical 500 nA (2 µA worst case) bias current of a NE5534 OP-AMP.
With a pick-up with an internal resistance of 1 kΩ, 10 nA will pass through the 47 kΩ input ground resistor and 490 nA through the pick-up, resulting in 490 µV across the pick-up.
In this case the DC current in the pick-up is 7 times the nominal signal current. This will not harm the pick-up, but it is audible with some MM pick-ups.

Some MC pick-ups are wound with very thin wire (down to 8 µm).
I have not been able to find any data for so thin wire, but some extrapolation from existing data suggest a fusing current around 50 mA in free air.

### Gramophone VLF Output.

Gramophone VLF output is generally caused by record groove eccentricity and is at 0.56 Hz (33 1/3; rpm) or at 0.75 Hz (45 rpm).
Maximum eccentricity of the groove with reference to the center-hole is 0.2 mm [2].
The center-hole diameter is 7.24 -0 +0.09 mm [2].
I have not been able to find any specification for the spindle, so I have assumed a total maximum eccentricity of 0.4 mm.
As this is a horizontal signal, it must be divided by √2 to obtain the output for left and right channels.
This is a needle velocity of 0.099 cm/s at 33 1/3; rpm and 0.13 cm/s at 45 rpm.
This signal is attenuated by the filter formed by the tonearm mass and the pick-up compliance. Assuming a critical damped filter at 10 Hz, the output levels will be 3.3 µm/s at 33 1/3 rpm and 7.5 µm/s at 45 rpm (-84 dB and -76 dB ref. 5 cm/s).

### Pick-up Wire Colors.

Gramophone pick-up wire colors [2].

 Red Right + Green Right GND (Often also the pick-up shielding) White Left + Blue Left GND

### Strobo disc.

Record label area [2]:
25 cm and 30 cm records: label diameter: 95..101.6 mm, center-hole diameter: 7.24 -0 +0.09 mm.
17 cm records: label diameter: 90..91.5 mm, center-hole diameter: 7.24 -0 +0.09 mm or 38.15 -0 +0.1 mm.

Number of lines:
n = 60 * f / rpm, where
n is number of lines.
f is the strobo flash frequency (this is 100 Hz for 50 Hz mains, 120 Hz for 60 Hz mains)
rpm is rotational speed.
100 Hz, 33 1/3 rpm: 180 lines.
100 Hz, 45 rpm: 133 1/3; lines.
120 Hz, 33 1/3 rpm: 216 lines.
120 Hz, 45 rpm: 160 lines.

A disc with 133 lines will indicate 45 1/9 rpm at 100 Hz. A disc with 133 1/3 lines can be made by placing a gap in one place. This gives a stable read-out that shifts for each revolution.

The mains frequency in Europe is typically within ±0.2 % depending on the load on the power-grid.
The mains frequency right here and now is 49.92 Hz.

### References.

 [1] IEC 60098:1987 "Analogue audio disk records and reproducing equipment". This standard os often referred to as IEC98. Available for download from IEC for a fee. Also available from some technical libraries. [2] DIN IEC 98 "Analoge Schallplatten und -Abspielgeräte; Identisch mit IEC 60098:1987". A german translation of IEC 60098:1987. Available for download from Beuth Verlag GmbH for a fee. Also available from some technical libraries. [3] Stanley P. Lipshitz "On RIAA Equalization Networks", Journal of the Audio Engineering Society, 1979 June, Volume 27, Number 6, Page 458. Available for download from Audio Engineering Society for a fee. Search for "On RIAA Equalization Networks". Also available from some technical libraries. [4] Cartridge/Armtube Combination List from Mørch. [5] Vinylengine forum thread on the subject of pick-up compliance. [6] A lot of mixed notes on gramophones.I do not know who the author is as most of the web-site is in Japanese. [7] How to pack a stereo signal in one record groove (animation).

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