Index VinylCartridge Alignment

Cartridge Alignment

Overhang, offset angle and tracking error for three classic geometries.

Overhang18.05mm

Offset angle23.97°

Pivot to spindle211.95mm

Null points66.0 / 120.9mm

Error at the stylus−0.96°

Worst error on the side1.89°

Plan view

Cartridge
Groove tangent at the stylus
Null radii

Dashed circles are the two null radii, where the cartridge sits exactly tangent to the groove.

Tracking error across the side

Baerwald (Löfgren A)
Löfgren B
Stevenson

Input

Common arm lengths

Effective length

L

Pivot to stylus tip, from the arm's specification.

Alignment

Innermost groove

Stylus position on the recordmm

Radius from the spindle. Moves the arm in the drawing.

How it works

The compromise of a pivoted arm

A record is cut by a head that moves in a straight line, always tangent to the groove. A pivoted arm swings in an arc, so the cartridge can only be tangent at two radii. By making the arm overhang the spindle and angling the headshell, the error everywhere else is kept to a degree or two.

With effective length $L$ , pivot-to-spindle distance $D$ and offset angle $\beta$ , the tracking error at radius $r$ is

\varepsilon(r) = \arcsin\!\left(\frac{r^{2} + L^{2} - D^{2}}{2\,r\,L}\right) - \beta

From null points to settings

Each alignment is a choice of two null radii $N_1$ and $N_2$ . Everything else follows:

\beta = \arcsin\!\left(\frac{N_1 + N_2}{2L}\right)

D = \sqrt{L^{2} - N_1 N_2}

\text{overhang} = L - D

Three classic answers

Baerwald (Löfgren A) makes the distortion peaks at the inner groove, between the nulls and at the outer groove all equal. For inner and outer radii $r_1, r_2$ the nulls are $N = \dfrac{2 r_1 r_2}{(1 \mp \tfrac{1}{\sqrt2})\,r_1 + (1 \pm \tfrac{1}{\sqrt2})\,r_2}$ . The usual all-round choice.
Löfgren B keeps the same offset angle and adjusts overhang to minimise average distortion across the side, at the price of more at the very start and end.
Stevenson puts the inner null on the innermost groove, favouring the end of the side, where classical crescendos tend to fall and distortion is otherwise worst.

Distortion is proportional to error divided by radius, so the same angle hurts more near the label. A longer arm lowers the whole curve: compare 230 mm with 305 mm.

Setting up

Set the overhang first by sliding the cartridge in the headshell, then twist it until the body is square to a protractor grid at both null radii. Half a millimetre of overhang error moves the nulls by several millimetres, so take your time.

References

E. Löfgren, “Über die nichtlineare Verzerrung bei der Wiedergabe von Schallplatten infolge Winkelabweichungen des Abtastorgans,” Akustische Zeitschrift, vol. 3, pp. 350–362, 1938. English translation
H. G. Baerwald, “Analytic Treatment of Tracking Error and Notes on Optimal Pick-Up Design,” J. Soc. Motion Picture Eng., vol. 37, pp. 591–622, 1941. SMPTE
J. K. Stevenson, “Pickup Arm Design,” Wireless World, May 1966, p. 214 and June 1966, p. 314. May issue· June issue