A cutterhead can be considered an electromagnet, similar in principle to those used in traditional telephone systems, but operating with significantly greater power.
In stereo cutterheads, two main coils and two feedback coils are arranged at ±45° angles relative to the modulation plane of the lacquer disc — positioned 90° apart from each other. This configuration allows the cutting stylus to encode both vertical and lateral information into the groove simultaneously(1).
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 illustrated in the earlier figure, if we imagine rotating the modulation plane’s axis forwards or backwards by 45°, stereo cutting would still be feasible. However, one channel would then move the stylus exclusively along the vertical axis, creating a groove geometry that is much more complex.
The Westrex system avoids this issue by balancing lateral and vertical components through its 45° rotation, simplifying the groove geometry.
Figure (2) illustrates a groove during cutting, with the cutterhead moving from right to left toward the disc’s center.
The angle and depth of the groove’s V-shape are determined by the stylus facets and the preset cutting depth.
Horizontal and Vertical Modulation
When no current is applied to the main coils, the groove appears under a microscope as a straight V-shaped lane. The stylus tip forms the groove’s base, while the stylus facets form the groove’s outer edges.
When an audio signal is fed into the amplifier, the coils energize and vibrate the stylus. The resulting groove shape reflects the volume, frequency content, and stereo image of the audio.
The accompanying image illustrates two scenarios:
- Left groove: a sinewave at 1kHz and equal amplitude on both channels. The stylus vibrates 1000 times per second, producing a horizontal modulation with a period of 1ms.
- Next three grooves to the right: the same sinewave is applied only to the right channel. The left channel remains silent.
In the first scenario:
identical signals on both channels result in pure horizontal modulation — the stylus moves only laterally, and the groove depth remains constant.
In the next three grooves to the right (second scenario):
the right channel produces modulation while the left does not. This asymmetry introduces vertical modulation — a variation in groove depth corresponding to the difference between the silent and active channels.
Close observation reveals that the groove’s bottom shifts slightly toward the active channel — where voltage (and stylus motion) is greater.
Thus:
- horizontal modulation = V(L) + V(R)
- vertical modulation = V(L) - V(R)
Phase effects
When two sinewaves of equal amplitude but opposite phase (180° shift) are fed to each channel, their sum is zero, cancelling each other out horizontally. However, this phase difference causes significant vertical stylus movement, which translates into groove depth variations based on V(L) - V(R).
If the dominant frequency has a high time constant, the depth variation may become excessive. To counteract this, frequencies below 150–300Hz are often converted to mono before cutting.
If the polarity of one speaker is reversed, its cone is pulled inward instead of pushed outward. When both channels operate with inverted polarity, extreme vertical modulation may occur. The automatic depth control of the cutting lathe compensates by adjusting the head suspension to avoid excessively shallow grooves.
Without such control, the groove could theoretically disappear, as depicted in the figure below (3).
Although this is an extreme case, polarity inversion can occur in some recordings.
More commonly, partial phase shifts affect only specific frequency ranges.
These can be managed with pre-cutting techniques:
- elliptical filters: characterized by a very steep curve, preserve stereo above a crossover frequency and sum to mono below it;
- MS equalisation: allows frequency-specific adjustment of stereo width, particularly effective in minimizing groove depth variation without affecting audible quality;
- stereo image adjustment: narrows stereo width across the spectrum, gradually summing to mono. This is effective but more audibly noticeable
Time Constants
At 1kHz, the stylus completes 1000 vibrations per second, each with a 1ms cycle. At 6kHz, the period shortens to about 0.17ms.
Based on the relationship between frequency and period, it has also been observed that the latter is 1ms, therefore the cyclic sequence of these 1000 vibrations will repeat every 1ms.
It is therefore easy to calculate that if the waveform had been — for example — 6kHz, the vibrations per second would have been 6000, and the period would have been shorter (0.17ms).
It can therefore be stated that — regardless of the signal volume — the “groove velocity”, that is, the time in which the excursion of the stylus vibration reaches its peak and returns to its starting point, is directly proportional to the predominant frequency of the signal.
Regardless of volume, lower frequencies produce wider stylus excursions than mid or high frequencies.
For example, a 200Hz sinewave at the same volume as a 1kHz tone generates 1/5 the vibrations but with 5× the excursion, due to the same energy being spread over fewer cycles. Thus, low frequencies:
- generate greater lateral excursions, according to the V(L)+V(R) logic;
- potentially generate greater vertical excursions, according to the V(L)-V(R) logic.
The time constant is therefore a transfer function of the inverse of the frequency in the time domain.
It can be considered as a measure of how quickly a system responds, and it is inversely proportional to frequency:
Each frequency is in relation with a specific time constant, which is denoted by the Greek letter "tau":
and as stated before, high frequencies have smaller (faster) time constants and low frequencies vice versa.
Converting seconds into microseconds, we derive the following conditional equation:
This equation, when applied to a frequency of 1kHz, gives a result of 59.23µs, and to a frequency of 200Hz, a result of 796.18µs.
By repeating the same calculation for the edges of the range of frequencies that can be reproduced by a cutterhead (from 20Hz to 20kHz), the following is obtained:
- 20Hz: 7957.75µs
- 20kHz: 7.95µs
This thousandfold difference makes it physically impossible to transcribe the full frequency range onto vinyl without correction. Low frequencies would produce overly wide modulations, while high frequencies would result in poor signal-to-noise ratios.
To resolve this, the 1950s saw the introduction of equalisation curves that attenuated low frequencies and boosted highs during recording.
The playback system then applied the inverse curve to restore balance.
The RIAA Curve
In the 1960s, the RIAA (Recording Industry Association of America) standardised this approach. The RIAA curve is still used in modern phono preamps.
The RIAA equalisation curve uses 3 key time constants:
where
- t1 is the time constant of high frequencies (≈75µs);
- t2 is the time constant of medium frequencies (≈318µs);
- t3 is the time constant of low frequencies (≈3180µs).
These time constants are implemented in passive equalisation circuits using precision resistors and capacitors.
1,3 Larry Boden, Basic Disc Mastering, USA 1981
2 Jvo
Studer, Pitchbox98 user manual, StuKa Engineering, Switzerland 2003
How grooves work