Electrical Engineering

, Volume 100, Issue 2, pp 1159–1181 | Cite as

Negative feedback, linearity and parameter invariance in linear electronics

  • Luciano da F. CostaEmail author
  • Filipi N. Silva
  • Cesar H. Comin
Original Paper


Negative feedback is a powerful approach capable of improving several aspects of a system. In linear electronics, it has been critical for allowing device invariance. Negative feedback is also known to enhance linearity in amplification, which is one of the most important foundations of linear electronics. At the same time, thousands of transistors types have been made available, suggesting that these devices, in addition to their assumed variability of parameters, have distinguishing properties. The current work reports a systematic approach to quantifying the potential of negative feedback, with respect to bipolar transistors, as a means of providing device invariance and linearity. Several approaches, including concepts and methods from signal processing, multivariate statistics and complex systems, are applied at the theoretical as well as experimental levels, and a number of interesting results are obtained. For instance, it has been verified that transistor types have well-defined characteristics which clearly segregate them into groups. The addition of feedback at moderate and intense levels promoted uniformization of the properties of these transistors when used in a class A common emitter configuration. However, such effect occurred with different efficiencies regarding the considered device features, and even intense feedback was unable to completely eliminate device dependence. This indicates that it would be interesting to consider the device properties in linear design even when negative feedback is applied. We also verified that the linearization induced in the considered experiments is relatively modest, with effects that depend on type of transfer function of the original devices.


Negative feedback Transistor properties Pattern recognition Total harmonic distortion 



L. da F. Costa thanks CNPq (Grant No. 307333/2013-2) for the support. F. N. Silva acknowledges FAPESP (Grant No. 15/08003-4). C. H. Comin thanks FAPESP (Grant No. 15/18942-8) for financial support. This work has been supported also by FAPESP Grant 11/50761-2.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Luciano da F. Costa
    • 1
    Email author
  • Filipi N. Silva
    • 1
  • Cesar H. Comin
    • 1
  1. 1.São Carlos Institute of PhysicsUniversity of São PauloSão CarlosBrazil

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