Bob Lehman, a classically-educated retired electrical engineer and long-term audiophile, asked some very good questions upon reading my column in Issue 110, “Vinyl and Absolute Polarity: A Technical Exposition.”
What follows are my detailed answers to his questions, combining science and practical examples to hopefully keep it interesting both for engineers and for normal people!
Bob Lehman: All magnet-and-coil acoustic-to-electrical transducers [including] dynamic microphones (I’m not sure about powered or electret condenser types), tape heads, and most phono cartridges (moving magnet, moving coil and moving iron I believe, but again, I’m not sure about electret condenser types) produce their electrical signal as a function of (i.e., in proportion to) the rate of change of the mechanical motion of the moving part of the transducer – right? E.g., my old Shure test record, for the trackability sections would announce each [section] with a phrase such as “velocity 5 centimeters per second, frequency 1,000 Hertz.” For that example, the velocity is a reference to that of the vibrating stylus – right?
J.I. Agnew:
Both mechanical grooved-media reproducer (record player/phonograph) and magnetic media reproducer(tape machine) transducers respond to the rate of change of mechanical displacement or magnetic flux. When motion is stopped, such as keeping the needle down on a stationary record, or having a tape machine in “edit” mode (tape stationary, head in contact, reproducer electronics activated), there will be no signal output from the transducer. There may still be a non-zero value of absolute groove displacement (relative to the spiral pitch or depth), or magnetic flux, at the point of contact between transducer and medium, but the transducer will not produce any output.
On magnetic tape transducers operating on the Faraday principle (as is the case with most common tape heads), this is because the electrical output is generated by a coil wound on a core of a suitable magnetic material, which generates an electrical signal when the flux through the core changes. Mathematically speaking, a periodic change of any parameter (displacement, flux, etc.) has a certain frequency of repetition and therefore different values over time. A static value (no rate of change) has a zero frequency of repetition.
The operating principle of magnet-and-coil transducers can be mathematically expressed as e = N (dφ/dt), where e = electromotive force (EMF, or voltage), N = number of turns of a coil linked by magnetic lines of flux, φ = flux and t = time. If the flux is constant, then regardless of its numerical value, the rate of change of flux over time (dφ /dt) does not exist, which will always result in e = 0. Zero voltage effectively means no signal output.
As such, if non-zero flux on tape remains stationary in front of the repro head, the core would assume an equivalent non-zero value of DC magnetization, but since the frequency/rate of change would be zero, there would be no electrical output. A Hall-effect sensor (a device used to measure the magnitude of a magnetic field), on the other hand, would be able to detect DC magnetization, which is why Hall-effect probes are commonly used in instrumentation for measuring permanent magnets, and Faraday-principle heads are used to reproduce audio. Faraday principle tape heads cannot be used to measure the magnitude of a permanent magnetic flux. Once the tape starts rolling, the flux keeps on changing and the rate of change is converted to an electrical signal, since dφ/dt exists.
Phono cartridges have more effects at play. The Faraday principle of coil EMF (electromotive force) applies just the same as for tape heads. But as this is a mechanical medium, the electrical output is proportional to ds/dt, where s = stylus displacement. Inside the cartridge, however, the mechanical displacement moves a magnet (or coil) relative to a coil (or magnet), creating a dφ/dt, (variations in flux linking the coil, over time). Relative motion between the magnet and coil at f ≠ 0 introduces a rate of change which produces an electrical signal. On the other hand, when the cartridge is lowered onto the record, the vertical tracking force will result in cantilever displacement. If lowered on a stationary record, this displacement is static, and despite the magnet inside the cartridge still causing a non-zero value of flux, dφ/dt does not exist (there is no difference in the value of φ over time).
Initially, at the moment it drops, there will be a short impulse where dφ/dt exists. But then it will reach an equilibrium where dφ/dt no longer exists and the displacement depends entirely on the static compliance (in μm/mN) of the cantilever suspension and the effective vertical tracking force (in mN). This static displacement does not produce any output from the cartridge. This is not a sudden effect; the output starts dropping gradually below a certain frequency. By 0 Hz (DC), it is certainly zero. But it already starts dropping at a frequency defined by the transducer design parameters.
This is because in a practical cartridge, the rate of change of flux does not remain proportional to the rate of change of displacement, at large amplitudes of displacement, due to finite magnet dimensions, weight and strength.
Especially below the lower 3180 μs/50.05 Hz RIAA curve point, where the recording is in constant velocity mode, the amplitude of displacement increases as the frequency decreases. As amplitude increases, the time interval also increases in proportion (being the inverse of frequency), keeping the velocity (ds/dt) constant.
The flux swing increases along with amplitude swing, up until the limits of zero flux and maximum flux linking the coil are reached, at which point the flux cannot increase any further, even if the amplitude keeps on increasing. In practice, even before any hard limits of flux are reached, the relationship between flux variations and amplitude variations stops being linear and flux increases progressively less than amplitude, so the electrical output starts falling.
A cut-off frequency between 1 – 3 Hz is common for the cartridge alone, below which the output would gradually fall.
But the cartridge is not alone! It is held on a tonearm. If we move the tonearm to the start of our favorite song on a record, it will stay there, absorbing the “DC” displacement. Likewise, if the spiral groove leads the tonearm across the record surface from the beginning to the end of the record, it is allowing a very slow displacement to be transferred directly to the tonearm, instead of bending the cartridge cantilever as far as it will go! Imagine if you would hold the tonearm still with your hand while the record is playing! The cantilever would just bend more and more, trying to follow the groove, up until it would skip or snap! But if we let it operate as intended, slow, large displacements, such as vertical warps and normal tracking along the record, are transferred to the tonearm pivots, allowing the cartridge to concentrate on reproducing the intentional groove modulation as audio.
This is due to the mass/compliance resonance of the tonearm/cartridge system, which effectively creates a mechanical crossover filter at the resonant frequency, typically between 8 – 12 Hz. This functions similarly to the crossover in your loudspeakers, but it is accomplished entirely by mechanical means. As the frequency is lowered, the entire cartridge and tonearm start to follow the displacement, while the cantilever remains stationary and the entire cartridge moves, below the “crossover” frequency. Under these conditions, there is no electrical output from the cartridge. Therefore, while the cartridge itself could, in theory, respond to frequencies much lower than the mechanical crossover, in practice the low-frequency response of the system is determined by the mass/compliance resonance frequency.
This is a good thing in disk record reproduction, as it filters out all the strange sounds that would otherwise creep in as a result of even the slightest warp. It does, however, adversely affect the low-frequency phase response, if not adequately dealt with by disk mastering engineers at the time of cutting the masters, and by designers of audio equipment (such as phono stages) to be used with turntables.
So, disk reproducers respond to the rate of change of displacement over time, above the mechanical crossover frequency of around 10 Hz. The rate of change of displacement over time, ds/dt, is the definition of velocity, which is why velocity is used to measure recorded levels on disk. This is the velocity of the vibrating stylus.
BL: To be picky, is that RMS velocity? Or average, or peak velocity?
JIA: The old NAB monophonic standard was an RMS lateral velocity of 5 cm/s at 1 kHz, which is equal to a peak lateral velocity of 7 cm/s at 1 kHz, which is equal to a peak velocity per stereophonic channel of 5 cm/s at 1 kHz, which is equal to an RMS velocity per channel of 3.54 cm/s at 1 kHz. But if we measure the velocity per channel in the actual geometric plane of the channel (45 degrees to the record surface), then it is 5 cm/s RMS or 7 cm/s peak per channel at 1 kHz.
Which is why it is essential to specify if the reference velocity figure given is peak or RMS, and lateral or per channel, along with the frequency. Looking through the dozens of different standards (and yes, there are dozens), these values (7 cm/s, 5 cm/s, 3.54 cm/s) all show up regularly in different contexts, without usually specifying what exactly is meant. This hints suspiciously in the direction of a generally poor understanding of the issue by many of the standards organizations and test record manufacturers.
BL: That would be a function of the amplitude and the frequency of the test signal engraved into the groove – right (which is, I assume, why both are stated)?
JIA: The frequency is important because of the RIAA curve. A quick, simplified explanation for readers who may not know: the RIAA curve is an equalization curve applied to vinyl records, which reduces the lows and boosts the highs on the record and does the reverse on playback equipment. The result is a flat frequency and phase response. The RIAA curve enables improved sound quality and longer cutting times.
The RIAA curve. Courtesy of Wikimedia Commons.
A record could be recorded at constant velocity, but the amplitude (groove excursion) would be too large at low frequencies and too small at high frequencies. Constant amplitude recording, on the other hand, implies that the velocity is no longer constant with frequency.
To better understand constant amplitude versus constant velocity, take a 12-inch record sleeve as a reference and slowly move your hand back and forth by 12 inches. Now do it faster, as fast as you can. It gets harder the faster you go.
Now allow your hand to reduce the amplitude to less than 12 inches, and you will notice that the faster you go, the lower the amplitude will tend to be. This is constant velocity, or as an over-simplification, constant effort. Constant amplitude requires that the amplitude remains constant (the full 12 inches) as your hand velocity increases (you’re moving it faster), which requires increasing effort, but keeps that motion clearly visible relative to the background, even from a distance. This results in an improved signal to noise ratio. Records are cut at constant velocity up to 50.05 Hz, constant amplitude from 50.05 Hz to 500.05 Hz, constant velocity once again from 500.05 Hz to 2122 Hz and constant amplitude yet again from 2122 Hz upwards, as defined by the RIAA curve.
This is unrelated to the linear velocity of the medium (the disk record) which is diameter-dependent, since the speed of rotation (rpm) is steady.
It is practically impossible to implement the RIAA pre-emphasis curve at the time of cutting, as it would imply infinite amplification to keep on increasing the drive to the cutter head at a rate of 6 dB/octave from 2122 Hz upwards, with no defined upper limit! The cutter head would certainly not survive this, even if the cutting amplifier system could do it. This is a topic worthy of a dedicated article, perhaps in a future issue.
BL: Move the stylus to a greater maximum amplitude displacement at a given frequency, or move it at a higher frequency at the same amplitude, or increase the amplitude displacement and the frequency, and the electrical amplitude of the phono cartridge will increase – right?
JIA: Electrical amplitude is proportional to velocity, ds/dt, in Faraday-principle cartridges. At a given frequency, increasing the amplitude of displacement, s, increases the velocity, since the variation in displacement values is made larger while the time (inverse of frequency) remains the same. Keeping the amplitude of displacement steady and increasing frequency reduces the time, while keeping the displacement values steady, which again increases the velocity. Increasing displacement values and reducing the time simultaneously increases the velocity to a much greater extent, as we are now changing both terms in the direction of increased velocity! For constant velocity, as the frequency goes up, the amplitude of displacement must go down. Since most phono cartridges generate an electrical output that is proportional to velocity, an increase in velocity will result in a proportional increase of the electrical output level.
BL: However, a reproduction transducer cannot output a DC signal [a signal of a steady non-zero value rather than alternating between positive and negative value]. If a microphone is presented with a constant air pressure, or if a tape head is presented with a constant magnetic field, or if a phono cartridge is presented with a constant physical displacement shift, the transducer is not capable of producing a DC electrical signal as an analog of what the “media” is doing. It will produce an impulse, and perhaps (probably) some “ringing,” [overshoot] but no DC, right? And this has nothing to do with AC vs. DC coupling of the signal path between the electrical components – even if all of the electrical components are DC coupled, these transducers cannot produce DC signals.[1]
JIA: Exactly. These transducers cannot produce a DC output. If they could, then microphones would produce a DC output proportional to atmospheric pressure, which would vary with altitude and weather phenomena. Phono cartridges would produce a DC output proportional to vertical tracking force, groove depth changes and groove pitch changes. Tape heads would produce a DC output as a result of the earth’s magnetic field, or any other permanent magnetic fields nearby. If the DC outputs of such devices would be accurately preserved all the way to the loudspeakers upon reproduction, then all we would achieve would be a displacement of the coil in proportion to parameters unrelated to sound.
This would cause an increase in distortion due to coil misalignment (since it would be displaced). Most listening rooms are not air-tight and practical loudspeaker drivers are not as efficient in pressurizing a room as they are in radiating sound waves.
Even if we would set up an airtight listening room with a loudspeaker system capable of DC pressurization of the room (at which point I suspect that both Underwriters Laboratories and your insurance company would take exception, in fear of your impending claim for the costs of your emergency medical treatment for self-inflicted divers’ disease), since the room would start with a given atmospheric pressure. If the microphone would have registered the exact same value of atmospheric pressure during the recording, the recorded DC would instruct the loudspeakers to pressurize the room even more, unless we also establish a complex feedback loop to sense the actual atmospheric pressure in the control room and ensure it matches the conditions under which the recording was made.
Apart from being unnecessarily complex, I wouldn’t want to know what would happen when trying to enjoy whale recordings under realistic conditions…something along the lines of what happened to the aliens in Mars Attacks upon hearing the yodeling of Slim Whitman! SPLAT!
Even worse, the orientation of the tape machine with respect to the earth’s magnetic field and the automatic groove depth/pitch control system found on many disk mastering lathes, along with record warps, would be translated into extreme pressurization of the listening room, which is far from a truthful recreation of the actual performance! [My head is ready to explode just contemplating this. – Ed.]
Fortunately, regardless of the transducer type and its ability to produce a DC output, typical microphone diaphragms are not mechanically sensitive to the static atmospheric pressure. Both sides of the diaphragm are open to the atmosphere (unlike the vacuum-operated power assisted braking servo mechanism in a passenger car), so a change in the static pressure would apply to both sides equally, preventing any displacement forces from being set up, even if we put the entire microphone in a pressure chamber.
Which leaves us with the great philosophical question of our century: how perfectly sealed should a sealed box loudspeaker really be?
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[1] AC coupling vs DC coupling: Electronic circuits are said to be DC-coupled when they can pass DC. AC-coupled circuits only respond to AC signals, blocking DC. If an AC signal exists superimposed on a DC bias, an AC-coupled circuit would still pass the AC, removing the DC offset. A DC-coupled circuit would pass both the DC and AC components.
Header image courtesy of Wikimedia Commons/Joost Dicker Hupkes.
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