The Technology of Electrical Recording

(The reader may find this section highly technical).

The key to Maxfield and Harrison's work was the acoustical research of Arthur Gordon Webster between 1914 and 1919. Webster, whose field initially was ballistics, had studied the physics of gas pressures in the confinement of a gun barrel when it was fired. He noted that the concept of "impedance" as applied to electrical circuits by British scientist Oliver Heaviside, could be extrapolated to describe certain physical behaviors in the fields of mechanics and acoustics. Applying this concept to the work of G.W. Stewart, who had set about designing more efficient horn-type loudspeakers for the British government during WWI, Webster deduced three fundamental formulas that would mathematically describe the most efficient horn shape for a given desired response curve.

Maxfield and Harrison correctly reasoned that if the electrical force called "impedance" had a mechanical force equivalent, then other electrical forces must have a mechanical equivalent as well. The theory they developed is known as the 'Maxfield-Harrison Electro-Mechanical Model', or the 'Theory of Matched Impedance'. By using the electrical formula that describes the electrical forces of the recording process, it is possible to derive a mechanical formula that is equivalent. From the mechanical side of the equation, an optimal mechanical playback model may be inferred. A table to better understand the equivalence of electrical and mechanical forces is given below:

Maxfield-Harrison Electro- A graphic representation of correspondences between electrical and mechanical amplification stages per the Theory of Matched Impedance.

Mechanical Table of Correspondences

Force (dynes) = Electromotive Force (volts)
Velocity (cm/Second) = Current (amperes)
Displacement (cm) = Charge (coulombs)
Impedance (dyne sec/cm) = Impedance (ohms)
Resistance (dyne sec/cm) = Resistance (ohms)
(or mechanical ohms)
Reactance (dyne sec/cm) = Reactance (ohms)
(or mechanical ohms)
Mass (gms) = Compliance (cm/dyne)
Inductance (henries) = Capacity (farads)

This cutaway of an Orthophonic soundbox illustrates that compliance between two moving elements in direct connection is represented as a parallel capacity; compliance between a moving element and a fixed or rigid element in direct connection as a series capacity.

Here are the two equations upon which the whole theory of the design is based:

When . . . Then . . .

The record surface is to be considered an approximate equivalent of a constant current electrical generator of infinite impedance.

fc = transmission system cut-off frequency in cycles per second
C = shunt compliance per section in cm/dynes
M = series mass per section
zo = characteristic impedance over the largest portion of the band range.

Confused yet?

The value of M is a diaphragm of 13.5 cm with a mass of .186 gms.
Cut-off frequency chosen was 5,000 hz after which surface noise becomes a real nuisance.
In this particular example, the characteristic impedance is calculated at 2920 mechanical ohms.

Maxfield and Harrison ultimately settled upon a final design that resulted in a characteristic impedance of about 4500 mechanical ohms to produce acceptable volume.

Using those two numbers, a lever/transformer ratio of 4500/2920 was determined as necessary to produce the required resistance in the system.