Seeking Maximum Linearity of Transfer Functions

TL;DR

This paper introduces a method to identify the most linear region of a transfer function using least squares regression, applicable to both analytical and real-world electronic systems, enhancing device characterization and system optimization.

Contribution

The paper presents a novel systematic approach to find the most linear operating region of transfer functions, including in noisy environments and for complex device characteristics.

Findings

Successfully identified optimal linear regions in analytical and real-world systems

Estimated local device constants from experimental data

Revealed complex structures in transistor characteristic surfaces

Abstract

Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function, identifying the respective most linear region of operation with a fixed width. This methodology, which is based on least squares regression and systematic consideration of all possible regions, has been illustrated with respect to both an analytical (sigmoid transfer function) and real-world (low-power, one-stage class A transistor amplifier) situations. In the former case, the method was found to identity the theoretically optimal region of operation even in presence of noise. In the latter case, it was possible to identify an amplifier circuit configuration providing a good compromise between linearity, amplification and output resistance. The transistor amplifier application, which was addressed in terms of transfer functions derived from its experimentally obtained characteristic surface, also yielded contributions such as the estimation of local constants of the device, as opposed to typically considered average values. Moreover, the obtained characteristic surfaces of the considered transistor (a generic, low signal device) revealed a surprisingly complex structure. The reported method and results paves the way to several other applications in other types of devices and systems, intelligent control operation, and other areas such as identifying regions of power law behavior.