# Engineering Acoustics/Phonograph Sound Reproduction

## Phonograph Sound Reproduction

The content of this article is intended as an electro-mechanical
analysis of phonograph sound reproduction. For a general history and
overview of phonograph technology refer to Wikipedia entries on
Phonograph and Magnetic
Cartridges.

## A Simplified Phono Model for Phono (Magnetic) Cartridges

The basic principle of phonograph sound reproduction stems from a small
diameter diamond needle follows a groove cut into the surface of a
record. The resulting needle velocity is mechanically coupled to one
element of an electrical coil transducer to produce an electrical
current.

Two main variants of cartage design exist. Moving Magnet (MM) designs
couple a permanent magnet to the needle, causing the magnet to move near
an electrical coil solenoid. Moving Coil (MC) cartridges couple an
electrical coil to the needle, causing the coil to move in a fixed
permanent magnetic field. In both cartridge designs the relative motion
of the magnetic flux field induces current flow in the electrical coil.

Figure 1 demonstrates this process with a simplified MM cartridge
schematic. In this configuration the position of the magnet alters the
magnetic domains of the surrounding
ferromagnetic transducer
core. Similarly, the velocity of the magnet induces a change in the
magnetic flux of the
transducer core, and according to the principle of electromagnetic
induction, a
current in the electrical coil is produced.

\
!Figure 1: Top view of simplified (MM) phono cartridge
schematic. phono cartridge schematic."){width="600"}

## Electro-Mechanical Analogy of a Phono Cartridge

Figure 2 gives an electrical analogue model for the simplified MM
cartridge show in Figure 1. This circuit representation of the system
was obtained according to the Mobility Analogue for
Mechanical-Acoustical
Systems.
The following assumptions are included in this model:

-   Motion is limited to the horizontal plane.
-   Angular velocities are proportional to linear velocities according
    to the small angle assumption.
-   The stylus cantilever and tonearm are perfectly rigid acting only as
    mechanical transformers.
-   All compliant and damping elements are represented by ideal
    linearized elements.
-   The MM transducer element is represented by an ideal transformer
    with an aggregate coefficient *μBl*.

\
!Figure 2: Mechanical mobility circuit analogy for MM phonograph
system.{width="600"}

As an estimate of the phonograph system frequency response can be
obtained by calculating the complex input impedance, $Z_o$. An
analytical expression for $Z_o$ is more easily obtained by neglecting
the stylus mass *M~s~* and electrical system influence. These
assumptions are consistent with a low frequency approximaiton of the
system, shown in Figure 2. The resulting system input impedance is given
by the equation for *Z~o~*.

\
!Figure 3: Simplified low frequency circuit analogy for MM phonograph
system.{width="400"}\

```{=html}
<center>
```
$\begin{matrix}
\hat{Z}_o = &

            \left[\frac{
                  R_pL_t^2R_t + \omega^2R_p(M_c+L_t^2M_t)^2 + \frac{R_t}{w^2C_p^2} 
                 }{
                 \left( R_p L_t^2 R_t + \frac{M_c+L_t^2M_t}{C_p} \right)^2 + 
                 \left(\omega (M_c+L_t^2M_t) R_p - \frac{L_t^2 R_t}{\omega C_p} \right)^2
                 }\right]
            \\
            &
            \\
            &
            +j \left[\frac{
                 \omega(M_c+L_t^2M_t)\left(\frac{M_c+L_t^2M_t}{C_p} - R_p^2\right) 
                 - \frac{1}{\omega C_p}\left(\frac{M_c+L_t^2M_t}{C_p} - L_t^4 R_t^2\right)
                 }{
                 \left( R_p L_t^2 R_t + \frac{M_c+L_t^2M_t}{C_p} \right)^2 + 
                 \left(\omega (M_c+L_t^2M_t) R_p - \frac{L_t^2 R_t}{\omega C_p} \right)^2
                 }\right]
\end{matrix}$

```{=html}
</center>
```
## References

The technique of applying a lumped element system analysis was a
standard method used in the development of phonograph cartridges. In
addition to the low frequency analysis shown it is also possible to
conduct a simplified high frequency analysis for which the properties of
the stylus mass and vinyl surface compliance dominate the response.
Interestingly, poor performance in the low frequency extreme of a
phonograph cartridge response can have substantial and detrimental
effects on the high frequency response capability. For further reading
on this topic a list of relevant reference material is given below.

1.  Hunt, F. V. (1962). \"The Rational Design of Phonograph
    Pickups.\" J. Audio Eng. Soc 10(4): 274-289.
2.  Bauer, B. B. (1963). \"On the Damping of Phonograph Arms.\" J. Audio
    Eng. Soc 11(3): 207-211.
3.  Walton, J. (1963). \"Stylus Mass and Reproduction Distortion.\" J.
    Audio Eng. Soc 11(2): 104-109.
4.  Bauer, B. B. (1964). \"On the Damping of Phonograph Styli.\" J.
    Audio Eng. Soc 12(3): 210-213.
5.  Anderson, C. R. K., J. H.; Samson, R. S., (1965). Optimizing the
    Dynamic Characteristics of a Phonograph Pickup. Audio Engineering
    Society Convention 17.
6.  Anderson, C. R. K., James H.; Samson, Robert S., (1966).
    \"Optimizing the Dynamic Characteristics of a Phonograph
    Pickup.\" J. Audio Eng. Soc 14(2): 145-152.
7.  White, J. V. (1972). \"Mechanical Playback Losses and the Design of
    Wideband Phonograph Pickups.\" J. Audio Eng. Soc 20(4): 265-270.
8.  Nakai, G. T. (1973). \"Dynamic Damping of Stylus Compliance/Tone-Arm
    Resonance.\" J. Audio Eng. Soc 21(7): 555-562.
9.  Kates, J. M. (1976). \"Low-Frequency Tracking Behavior of Pickup
    Arm-Cartridge Systems.\" J. Audio Eng. Soc 24(4): 258-262.
10. Bauer, B. B. (1977). \"The High-Fidelity Phonograph Transducer.\" J.
    Audio Eng. Soc 25(10/11): 729-748.
11. Kogen, J. H. (1977). \"Record Changers, Turntables, and Tone Arms-A
    Brief Technical History.\" J. Audio Eng. Soc 25(10/11): 749-758.
12. Barlow Donald A.; Garside, G. R. (1978). \"Groove Deformation and
    Distortion in Recordings.\" J. Audio Eng. Soc 26(7/8): 498-510.
13. Lipshitz, S. P. (1978). \"Impulse Response of the Pickup
    Arm-Cartridge System.\" J. Audio Eng. Soc 26(1/2): 20-35.
14. Takahashi, S. T., Sadao; Kaneko, Nobuyuki; Fujimoto, Yasuhiro,
    (1979). \"The Optimum Pivot Position on a Tone Arm.\" J. Audio Eng.
    Soc 27(9): 648-656.
15. Happ, L. R. (1979). \"Dynamic Modeling and Analysis of a Phonograph
    Stylus.\" J. Audio Eng. Soc 27(1/2): 3-12.
16. Pardee, R. P. (1981). \"Determination of Sliding Friction Between
    Stylus and Record Groove.\" J. Audio Eng. Soc 29(12): 890-894.

## References

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