Table of Contents
VLSI Design
Volume 2010, Article ID 297083, 12 pages
Research Article

Local Biasing and the Use of Nullator-Norator Pairs in Analog Circuits Designs

Department of Electrical Engineering, Northern Illinois University, DeKalb, IL 60115, USA

Received 9 April 2009; Accepted 8 December 2009

Academic Editor: Benjamin J. Blalock

Copyright © 2010 Reza Hashemian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new technique is presented for biasing of analog circuits. The biasing design begins with local biasing of the nonlinear components (transistors), done according to the pre-specified operating points (OPs) and for the best performance of the circuit. Next, the transistors are replaced with their linear models to perform the AC design. Upon finishing with the AC design we need to move from the local biasing to global (normal) biasing while the OPs are kept unchanged. Here fixators—nullators plus sources—are shown to be very instrumental and with norators—as the place holders for the DC supplies in the circuit—they make pairs. The solution of the circuit so prepared provides the DC supplies at the designated locations in the circuit. The rules to engage in circuit analysis with fixator-norator pairs are discussed, and numerous pitfalls in this line are specified. Finally, two design examples are worked out that clearly demonstrate the capability and power of the proposed technique for biasing any analog circuit.