A New Transformation in Alternating-Current Theory with an Application to the Theory of Audition

A mathematical transformation of the elements of an impedance, called a j-transformation is considered whereby the complex impedance of each of the constituents is multiplied by j, j
²
and j
³
and thereupon the physical meaning of such a transformed system is investigated. Thus new circuits can be derived from known circuits and special properties of the former are transformed into new special properties of the latter. Further negative capacities and negative inductances are considered which are independent of frequency. Next several a-c circuits are described having the property that the modulus of their impedances is independent of frequency. Hence a complicated "wave" form, such as speech, retains in such a circuit all its higher harmonics with their former amplitudes, though the phases of these harmonics are shifted. Oscillograms of vowels thus obviously show a very marked distortion, though the ear is unable to detect this phase distortion. The experiments confirm the well-known acoustical law of Ohm stating that within limits the ear is not able to detect phase shifts of the components of a complicated sound.