The impedance analogy is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. By converting to an electrical representation, these tools in the electrical domain can be directly applied to a mechanical system without modification. A further advantage occurs in electromechanical systems: Converting the mechanical part of such a system into the electrical domain allows the entire system to be analysed as a unified whole. The mathematical behaviour of the simulated electrical system is identical to the mathematical behaviour of the represented mechanical system. Each element in the electrical domain has a corresponding element in the mechanical domain with an analogous constitutive equation. All laws of circuit analysis, such as Kirchhoff's circuit laws, that apply in the electrical domain also apply to the mechanical impedance analogy. The impedance analogy is one of the two main mechanical–electrical analogies used for representing mechanical systems in the electrical domain, the other being the mobility analogy. The roles of voltage and current are reversed in these two methods, and the electrical representations produced are the dual circuits of each other. The impedance analogy preserves the analogy between electrical impedance and mechanical impedance whereas the mobility analogy does not. On the other hand, the mobility analogy preserves the topology of the mechanical system when transferred to the electrical domain whereas the impedance analogy does not. Applications The impedance analogy is widely used to model the behaviour of mechanical filters. These are filters that are intended for use in an electronic circuit, but work entirely by mechanical vibrational waves. Transducers are provided at the input and output of the filter to convert between the electrical and mechanical domains. Another very common use is in the field of audio equipment, such as loudspeakers. Loudspeakers consist of a transducer and mechanical moving parts. Acoustic waves themselves are waves of mechanical motion: of air molecules or some other fluid medium. A very early application of this type was to make significant improvements to the abysmal audio performance of phonographs. In 1929 Edward Norton designed the mechanical parts of a phonograph to behave as a maximally flat filter, thus anticipating the electronic Butterworth filter. Elements Before an electrical analogy can be developed for a mechanical system, it must first be