A cutterhead can be considered an electromagnet, similar to those found in conventional telephone systems, but with greater power involved.
In stereo heads, the two main coils and the two feedback coils are positioned at angles of ±45° relative to the modulation plane of the disc. Consequently, they are spaced 90° apart from each other. This configuration ensures that the grooves created by the cutting stylus always contain both vertical and lateral information¹.
This system, first introduced by Westrex in the United States over 50 years ago, quickly became the industry standard. At the time, monophonic records were still the norm. The 45° rotation of the vertical axis enabled the encoding of stereo signals for the first time while maintaining compatibility with mono playback systems.
As shown in the previous figure, if we imagine rotating the axis of the modulation plane forwards or backwards by 45°, we notice that one of the two channels causes the stylus to move only along the vertical axis, generating grooves with very complex geometry.
The Westrex system, with its 45° rotation of the vertical axis, avoids this problem by balancing the lateral and vertical components, resulting in simpler groove geometry.
The previous figure² illustrates the logic of groove engraving, assuming the head moves from right to left, toward the center of the disc.
First, it’s clear that the right channel is always engraved on the groove side facing the outer edge of the disc. Also, the polarities of the two channels are opposite:
- on the right channel, a “+” phase causes the stylus to move deeper along the 45° inclined axis, and vice versa.
- on the left channel, the same occurs with a “−” phase.
So, if a mono-frequency stereo signal with the same amplitude on both channels is engraved, there will be only lateral excursions of the stylus and no (or negligible) vertical movement.
If the two channels have signals with different amplitudes, then in addition to lateral movement, there will also be vertical movement, resulting in changes to groove depth.
As seen in the previous figure³, let VL and VR be the modulated voltages of the two channels, keeping in mind they have opposite polarities. Then:
- when their algebraic sum (±VL) + (±VR) decreases, the stylus engraves with greater depth;
- when the sum (±VL) + (±VR) increases, the stylus engraves more shallowly.
It should be noted that groove width and depth are not the same. Groove width can always be measured under a microscope, while depth is not as easily measurable. However, since the two groove walls form an angle of about 90°, it can be reasonably approximated that groove depth is half of its width.
Time Constants
A time constant can be defined as a transfer function of the inverse of frequency in the time domain.
If we divide the frequency spectrum used for cutting into an infinite number of RC filters, the time constant of each filter indicates the typical response time of the RC circuit it is made from.
If a signal with a frequency of 1 kHz is engraved, the stylus vibrates 1000 times per second, following the waveform. Based on the relationship between frequency and period, the period is 1 ms, meaning this vibration cycle repeats every 1 ms.
It’s easy to calculate that, if the waveform were — for example — 6 kHz, the stylus would vibrate 6000 times per second, and the period would be shorter (0.17 ms).
Thus, we can say that the “groove speed”— that is, the time in which the stylus reaches its maximum excursion and returns to its starting point — is directly proportional to the dominant signal frequency.
Moreover, regardless of the signal volume, low frequencies produce wider vibrations than mid and high frequencies, and mid frequencies produce wider vibrations than high frequencies.
For example, if a 1 kHz and a 200 Hz sine wave are recorded at the same volume, the 200 Hz wave will generate only 1/5 of the vibrations per second (200) compared to the 1 kHz wave. But since the volume is the same, each of the 200 vibrations will have excursions five times larger than the 1000, requiring slightly more time to complete.
So, at the same volume, the lower the frequency, the greater the energy in terms of stylus vibration amplitude, both horizontally and vertically.
Each frequency thus has an associated time constant, represented by the Greek letter “tau”:
and as stated before, high frequencies have smaller (faster) time constants and low frequencies vice versa.
By converting seconds to microseconds, the following conditional equation is obtained:
This equation, applied to 1 kHz, yields 59.23 µs, and for 200 Hz, 796.18 µs.
Repeating the same calculation for the extremes of the frequency range reproducible by a head (typically 20 Hz to 20 kHz), results are 7957.75 µs at 20 Hz and 7.95 µs at 20 kHz.
So, the 20 Hz time constant is 1000 times higher than that of 20 kHz, making it physically impossible — without corrective equalization — to cut a flat-line signal containing the full frequency spectrum onto disc. Low frequencies would cause excessive stylus excursions, while high frequencies would barely register, resulting in an unacceptable signal-to-noise ratio.
Due to this issue, several equalization curves were proposed in the 1950s. These curves attenuated low frequencies and boosted high frequencies during recording to counteract the imbalance.
Whichever curve was used, the same (but inverted) equalization had to be applied by the phono playback circuitry to restore correct frequency response.
The RIAA Curve
In the 1960s, the Recording Industry Association of America (RIAA) standardized several previously proposed curves into the “RIAA curve” (see the following figure), which remains the standard for phono amplification today.
the dB(f) function includes, besides the frequency f, three time constants:
where
- t₁ is the high-frequency time constant (≈75 µs);
- t₂ is the mid-frequency time constant (≈318 µs);
- t₃ is the low-frequency time constant (≈3180 µs).
RIAA passive equalization circuits can be implemented using properly sized resistor-capacitor networks.
Phase
Based on what has been discussed so far, stereo signal phase is also important.
If two signals of equal amplitude and frequency but opposite phase are added together, the result is null. This is also when the magnitude of the stylus’s vertical excursion reaches its maximum peak.
The impact of this excursion also depend on the time constant of the dominant frequency. The larger the time constant (i.e., the lower the dominant frequency), the greater the stylus excursion in all directions, including vertical. If the algebraic sum (±VL) + (±VR) produces a sufficient voltage difference and the time constant is high enough, the groove can become very deep and then immediately very shallow.
Consequences include:
- groove too wide: if a certain depth is exceeded, the stylus may contact the aluminum substrate beneath the lacquer, causing irreparable damage.
- groove too shallow: the groove becomes untrackable (a playback stylus has a radius of about 15 µm, so the groove width must not drop below ~30µm).
Typically, there is an automatic depth control — almost always present in professional cutting systems — that adjusts the action of the head’s moving coils in real-time to keep groove depth above a safety threshold. Without such intervention, the result could look like the figure below⁴.
Although some cutting systems’ Pitch & Depth Control includes built-in depth control, it’s now common to prepare and/or adjust the signal before it reaches amplification. Common interventions include:
- Elliptical filter: characterized by a very steep curve, it preserves the stereo image above the crossover frequency and converts it to mono below it.
- MS equalization: allows separate equalization of the mono component (center of the stereo image) and the stereo component (sides). This is particularly useful when identifying the frequency at which depth variation occurs. Only the stereo component around the frequency of interest is equalized — just enough to reduce the variation. This method can yield highly effective results that are very difficult to detect audibly when compared to the original recording.
1, 4 Larry Boden, Basic Disc Mastering, USA 1981
2, 3 Struck, Polygram Pitch Control IV user manual, internal files, UK-Europe 1977-82
How grooves work