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 Ms 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 Zo.

$$ \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} $$