  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.
