# 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.

## 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.
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$_o$.
${\begin{matrix}{\hat {Z}}_{o}=&\left[{\frac {R_{p}L_{t}^{2}R_{t}+\omega ^{2}R_{p}(M_{c}+L_{t}^{2}M_{t})^{2}+{\frac {R_{t}}{w^{2}C_{p}^{2}}}}{\left(R_{p}L_{t}^{2}R_{t}+{\frac {M_{c}+L_{t}^{2}M_{t}}{C_{p}}}\right)^{2}+\left(\omega (M_{c}+L_{t}^{2}M_{t})R_{p}-{\frac {L_{t}^{2}R_{t}}{\omega C_{p}}}\right)^{2}}}\right]\\&\\&+j\left[{\frac {\omega (M_{c}+L_{t}^{2}M_{t})\left({\frac {M_{c}+L_{t}^{2}M_{t}}{C_{p}}}-R_{p}^{2}\right)-{\frac {1}{\omega C_{p}}}\left({\frac {M_{c}+L_{t}^{2}M_{t}}{C_{p}}}-L_{t}^{4}R_{t}^{2}\right)}{\left(R_{p}L_{t}^{2}R_{t}+{\frac {M_{c}+L_{t}^{2}M_{t}}{C_{p}}}\right)^{2}+\left(\omega (M_{c}+L_{t}^{2}M_{t})R_{p}-{\frac {L_{t}^{2}R_{t}}{\omega C_{p}}}\right)^{2}}}\right]\end{matrix}}$

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