Equivalent circuit of the dynamic system of a phono cartridge

Back in the 1960s when record quality had advanced in leaps and bounds with the invention of the LP and stereo, the first serious attempts were made to analyse fully the requirements of a phono cartridge; especially in terms of its ability to track the groove modulation accurately at a downforce below that which would damage the PVC material.

In this work, the developments (and publications) of the American company Shure Brothers, Inc. of Evanston, Illinois stand out. Not only did the Shure development team do so much to understand the dynamical system of the phono cartridge but also, they took the time and trouble to transmit that understanding to the wider audio community.

Shure's "analog"

Various methods of investigation are available to the engineer to investigate the dynamic system of the phono cartridge: Mathematical analysis, physical measurements, and equivalent circuit techniques. Because a study of optimization requires a great many variations (and presumably because most of the engineering team were, at heart, electrical engineers), Shure chose an analogue equivalent circuit as their analytical tool¹.

To anyone who has a similar background, this analogue circuit model of the physical, dynamic system is enormously helpful in understanding the engineering compromises inherent in phono cartridge design.

This page presents a simplified model which eliminates the cantilever effects; essentially this element is treated as massless and infinitely stiff.

The simplified model is illustrated. The various mechanical elements are represented by the electrical components as follows:

C1, represents - Record tip compliance µF = µ(cm/dyne)
C2 represents - Bearing compliance µF = µ(cm/dyne)
L1 represents - Inertia of armature (tip, cantilever and magnet) mH = mg
R represents - Viscous damping of bearing ohms = dyne-sec/cm
Ii represents - Recorded velocity Amperes = cm/s
Io represents - Output velocity of stylus Amperes = cm/s
Vab represents - Tracking force volts = grams

Now the last of these quantities (Vab) is a little tricky to understand. Effectively, it is the force of reaction from the groove upon the stylus as it tracks the modulation. It is thereby more or less equivalant (by a small margin) with the force required to hold the stylus in the groove provided by the tracking weight. Vab is thereby a direct measure of the downforce (expressed as a weight) required by the cartridge at various frequencies. Generally, we want this to be a small as possible to avoid unnecessary wear to the record.

The quantity Io (the output velocity of the stylus magnet) is easiest to visualise as the voltage generated across the damping (R) expressed as a voltage (V). This gives us the frequency-response of the dynamic system (ignoring the electrical circuit of the motor part of the cartridge.) Generally we want this to be as flat as possible across the audio band.

Concentrating of the circuit itself, we can see that it simpy two resonant circuits formed by L1 resonating in series with C2 and in parallel with C1; each being damped by R. Because of the huge difference in the values of C1 and C2, the two resonance frequencies will be widely separated and, to all intents and purposes they have little effect upon one another. Translating this back to a mechanical model, the mass of the armature (stylus, cantilever and magnet = L1) resonates with the main bearing compliance (C2) at an mid-band audio frequency, in this case at,

   [2 × π × (L1 × C2)½ ]-1 = 1125Hz, ....... (1)

and again with the compliance of the record material (C1) at a high frequency, in this case at,

   [2 × π × (L1 × C1)½ ]-1 = 25kHz....... (2)

Plotting voltage Vab and altering the value of R we get the following set of curves.


Because one resonance is series and the other parallel, they work in opposite directions in terms of the tracking downforce required. The resonance due to the main bearing compliance and the armature mass tends to make the stylus easier to drive and thereby requires less downforce to keep the stylus engaged with the groove. On the other hand, the parallel resonance due to the armature and the vinyl compliance makes the cartridge much harder to drive and thereby demands more downforce to keep it in the groove.

We can see that the critical component here is the damping (R) because it is "shared" between the two resonances. Too little damping and the high-frequency peak becomes very significant. Too much and, although the HF peak is "tamed", the cartridge needs more tracking downforce in the mid-range.

This is the core of the designer's dilemma.

The role of each part

Now let's consider the effects of the various components (mechanical and electrical) across the frequency band.

R - If you consider the point of series resonance due to the armature (L1) and the compliance of the main bearing (C2), it's obvious that when their reactances are equal and opposite, they "disappear" electrically and the only load the generator "sees" is the damping (R). So R represents the limiting factor in the midrange. This is also the frequency range we know contains the greatest velocities, so we must not over-damp or we will sacrifice mid-range tracking. In real life C2 and R are not separable, they are both part of the characteristic of an elastomer³.

C2 - The bearing compliance (C2) is what "decouples" R from the stylus at very low frequencies which is the equivalent of saying that the compliance of the bearing must be large enough to allow for the large amplitude groove excursions at low-frequencies.

In order to track a record with maximum modulation amplitude of about 0.002" (50µm) at a maximum tracking force of 1 g, the required compliance for C2 is 5µ(cm/dyne). Viscoelastic bearings decrease in compliance as frequency increases so a considerable safety margin needs to be provided at the lowest frequency of interest, say 20Hz. That is why this component is set at 25 × 10-6 cm/dyne (or 25µF) in the equivalent circuit. But neither must the compliance of C2 be so great that sub-audio movements (due to warps etc) cause the armature to move relative to the pole-pieces.

L1 - The resonance due to the mass of the armature (L1) and the record-surface compliance (C1) has a number of side-effects over and above its effect on tracking. The increased current in the circuit mesh including R indicates that the transfer-function of IoIi will peak at this point and this will lead to a frequency-response peak. And, in the stereo cartridge, the resonance also leads to interchannel crosstalk as the movement of the armature becomes uncontrolled.

In the 1960s, it was believed the best the cartridge designer could do was simply to postpone this resonance to as high a frequency as possible and then damp adequately to keep the tracking demand down without over-damping the midrange. It seemed that keeping this resonance in abeyance could only be achieved by reducing mass of the armature (L1) because the cartridge designer had no control over the compliance of the record surface (C1). This was uncomfortable because, even with the selection of the lightest (and sometimes exotic) materials, this was inevitably a game of diminishing returns.

The birth of CD-4 quadraphonic in the 1970s placed excrutiating demands on the phono cartridges at the time. Shure's solution to the problems fostered by CD-4 quadraphonic was to add a parasitic compliance and mass to the moving armature tuned to a frequency close to the main L1/C1 resonance. In terms of the equivalent circuit, this involved adding a parallel resonant circuit in series with L1. Shure called this innovation the Dynamic Vibration Absorber² and it acted rather like the port in a bass-reflex loudspeaker, sucking energy out of the system and controlling the main resonance.

In Japan, Norio Shibata of JVC realised that if he could increase the contact area of the stylus in the groove, he could vary the effective springiness of the record surface and do the equivalent of altering the value of C1 in the model. The Shibata stylus has a contact area about 4× greater than an elliptical type stylus and thus this resonance was "stepped up" an entire octave; a very great accomplishment at the time. (Remember, resonance is related to the square-root of the product of L1 and C1, see equation 2).



References

1. Optimizing the Dynamic Characteristics of a Phonograph Pickup. Anderson, C.R., et al. Journal of the Audio Engineering Society April 1966, volume 14, number 2

2. The Dynamic Vibration Absorber Principle Applied to a High-Quality Phonograph Pickup. GROH, A.R. Presented October 31, 1976, at the 55th Convention of the Audio Engineering Society, New York. Journal of the Audio Engineering Society June 1977, volume 25, number 6

3. Elastomers are not perfectly elastic and lose energy during the compression (or tension) and subsequent recovery. Unlike purely elastic substances, elastomers are viscoelastic which means that a substance has an elastic component and a viscous component. A viscoelastic element may be modelled as a perfect spring with a damper; or, in electrical terms, as a capacitance and a resistor.


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