### Abstract

Electrical networks consisting of linear passive elements and many nonlinear resistors are often used to model the basilar membrane. The inputs to these networks are typically a sum of sinusoids switched on at t = 0, and the resulting quantities of interest because of their interpretation as analogs of experimental observables are the steady‐state response components of a certain current and of certain voltages. In this paper, recently obtained mathematical results concerning the input‐output representation of nonlinear systems are used to give, for the first time, a locally convergent expansion for all of the steady‐state quantities of interest. Also given is a good deal of information concerning general properties of the expansion, and this establishes important properties of the nonlinear network's response. Of particular practical interest is a term in the expansion that contains a component whose frequency is (2f_{1} — f_{2}) when the network's input consists of a sum of two sinusoids, with frequencies f_{1} and f_{2}. One of our main results is an explicit expression for this (2f_{1} — f_{2}) component.

Original language | English (US) |
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Pages (from-to) | 1775-1786 |

Number of pages | 12 |

Journal | AT&T Technical Journal |

Volume | 64 |

Issue number | 8 |

DOIs | |

State | Published - Oct 1985 |

Externally published | Yes |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*AT&T Technical Journal*,

*64*(8), 1775-1786. https://doi.org/10.1002/j.1538-7305.1985.tb00036.x