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6 - CONTROL BY MASS, RESISTANCE OR COMPLIANCE

The overall profile of the frequency response curve of a microphone is also determined by certain physical quantities that influence the velocity/frequency or amplitude/ frequency characteristics of the vibratory system - mass, compliance and friction. The study of the influence of each of these parameters on the frequency response of each type of microphone can be facilitated by the representation of each system as an equivalent electrical circuit based on analogies between electrical and mechanical quantities. However a detailed mathematical analysis of the influence of these specific quantities on the response of the microphone system is not absolutely necessary if we accept simply that each microphone type can be associated with a particular and characteristic fundamental resonance frequency - every vibratory system has in fact a fundamental resonance frequency.

The fundamental resonant frequency of a vibrating system is determined by the ratio of mass to elasticity of the suspension. A simple demonstration of a vibrating system is possible using a weight or mass suspended on the end of a spring. If the other end of the spring is moved slowly up and down the mass will follow the movement with about the same amplitude. With increasing speed of movement of the spring support, the mass will increase its amplitude of oscillation, reaching a maximum amplitude when the frequency of movement corresponds with the fundamental resonant frequency of the system.

The precise frequency of resonance will depend on the specific values of mass and elasticity of the spring. At this frequency, very little amplitude of movement is necessary to impart a considerable amplitude of movement to the mass. At higher frequencies of excitation, the amplitude of movement decreases, eventually remaining almost stationary. The amplitude of movement, especially at resonance, can be reduced by placing the weight against an almost vertical surface - the friction with the surface will introduce a certain quantity of friction or resistance to movement called damping. Placing the weight on the end of the spring into water will also introduce damping on the amplitude of movement, as will increasing the surface of the weight with a sheet of thin cardboard causing viscous air-flow damping - this last experiment being the nearest illustration of the type of damping used in the design of a microphone.

With this simple experiment we have introduced the three fundamental parameters of a vibrating system. A graphical representation of this resonant system is shown in Figure 23. To the left of the resonance frequency it is stiffness or compliance (the inverse function of elasticity) that is the dominant parameter, to the right it is mass that predominates, whereas around the resonant frequency especially when highly damped it is the damping caused by friction that is the predominant controlling parameter.

Figure 23 - The Amplitude/Frequency Response of a Vibrating System

This nomenclature is used to classify the dominant parameter in the frequency response of the microphone system. If the fundamental resonance of a microphone is in the high frequency range we consider the microphone to be compliance controlled - if the resonance is in the low frequencies we consider the microphone to be mass controlled - if the resonance is in the middle of the frequency range and highly damped then the microphone is said to be resistance controlled. A mathematical analysis of the equivalent electrical/mechanical circuit analogy will obviously give a clearer understanding of these functions, and can found in a book called ‘Microphones’ by A.E.Robertson^[7] (downloadable on the BBC website) or in any good textbook on electro-acoustics.

In the case of different microphone types we can say that

 an electrodynamic moving coil microphone has a highly damped fundamental resonance in the medium frequency range (between about 1kHz and 8kHz) – this type of microphone is classified as having control by resistance

 an electrodynamic ribbon microphone has a fundamental resonance frequency in the bass frequencies (well below 50Hz) – the major part of the response curve is dominated by the mass of the ribbon - this is said to be control by mass

 an electrostatic condenser measurement microphone with pressure acoustic coupling has a fundamental resonance in the high frequency range (above about 20kHz) – the major part of the response curve is dominated by the stiffness of the diaphragm suspension - this is said to be control by compliance.

 On the other hand an electrostatic condenser microphone with pressure-gradient acoustic coupling can have a fundamental resonant frequency anywhere between about 1kHz and 8kHz – this is then control by resistance

Each microphone type has a specific way of introducing damping into the basic oscillatory system in order to reduce the amplitude of the fundamental resonance. Additionally in certain types of microphone a flat frequency response can only be attained by the use of extra resonating cavities to boost the frequency response in the low and/or high frequency range.

[7] 1951/1963 - "Microphones - Chapter 5: Diffraction and Dimensional Effects" by A.E.Robertson published by Iliffe books in 1951/63 now available at BBC Website