transfer impedances and are hybrid ratios of an electrical and mechanical quantity. Transformers The mechanical analogy of a transformer is a simple machine such as a pulley or a lever. The force applied to the load can be greater or less than the input force depending on whether the mechanical advantage of the machine is greater or less than unity respectively. Mechanical advantage is analogous to transformer turns ratio in the impedance analogy. A mechanical advantage greater than unity is analogous to a step-up transformer and less than unity is analogous to a step-down transformer. Power and energy equations Examples Simple resonant circuit The figure shows a mechanical arrangement of a platform of mass that is suspended above the substrate by a spring of stiffness and a damper of resistance The impedance analogy equivalent circuit is shown to the right of this arrangement and consists of a series resonant circuit. This system has a resonant frequency, and may have a natural frequency of oscillation if not too heavily damped. Model of the human ear The circuit diagram shows an impedance analogy model of the human ear. The ear canal section is followed by a transformer representing the eardrum. The eardrum is the transducer between the acoustic waves in air in the ear canal and the mechanical vibrations in the bones of the middle ear. At the cochlea there is another change of medium from mechanical vibrations to the fluid filling the cochlea. This example thus demonstrates the power of electrical analogies in bringing together three domains (acoustic, mechanical and fluid flow) into a single unified whole. If the nerve impulses flowing to the brain had also been included in the model then the electrical domain would have made four domains encompassed in the model. The cochlea portion of the circuit uses a finite element analysis of the continuous transmission line of the cochlear duct. An ideal representation of such a structure would use infinitesimal elements, and there would thus be an infinite number of them. In this model the cochlea is divided into 350 sections and each section is modelled using a small number of lumped elements. Advantages and disadvantages The principal advantage of the impedance analogy over its alternative, the mobility analogy, is that it maintains the analogy between electrical and mechanical impedance. That is, a mechanical impedance is represented as an electrical impedance and a mechanical resistance is