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Hajimiri_MOTC - TRANSACTIONS ON CIRCUITS AND SYSTEMS VOL XX...

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TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. XX, NO. XX, DECEMBER 2009 1 Generalized Time- and Transfer-Constant Circuit Analysis Ali Hajimiri, Abstract —The generalized method of time and transfer con- stants is introduced. It can be used to determine the transfer function to the desired level of accuracy in terms of time and transfer constants of first order systems using exclusively low frequency calculations. This method can be used to determine the poles and zeros of circuits with both inductors and capacitors. An inductive proof of this generalized method is given which subsumes special cases, such as methods of zero- and infinite- value time constants. Several important and useful corollaries of this method are discussed and several examples are analyzed. Index Terms —Circuit Analysis, method of time and trans- fer constants (TTC), determination of poles and zeros, zero- value time constants (ZVT), infinite-value time constants (IVT), Cochran-Grabel method, bandwidth enhancement techniques. I. I NTRODUCTION A NALOG circuit design depends on analysis as a beacon to provide qualitative and quantitative input on how we can improve circuit performance by modifying its topology and/or parameters. A great deal of effort goes into improving the accuracy of device models and circuit simulators to predict the expected experimental outcome accurately on a computer before testing going to the lab. However, these absolutely nec- essary tools are not sufficient for analog circuit design, which by its nature is open-ended and divergent. This necessitates analytical techniques that can provide insight into how and where the circuit can be modified for design purposes. The identification of the dominant source of a problem is at the core of design as it focuses creative energy on critical parts of the circuit and more importantly identify what kind of modifications will improve it. Generally, this is done by reducing the analysis into smaller more straightforward calculations that allow one to arrive at progressively more accurate approximations without performing the full analysis. Although mesh and nodal analysis provide a systematic framework to apply Kirchhoff’s current and voltage laws (KCL and KVL) to the circuit problem and convert them to a linear algebra problem (e.g., works of Bode [1] and Guillemin [2]) that can be solved numerically using a computer, they are not effective design tools. The analysis must be carried to the end before approximate results can be obtained and even then it is hard to obtain design insight from the resultant algebraic expressions particularly in terms of identifying the dominant A. Hajimiri is with the Department of Electrical Engineering, Cali- fornia Institute of Technology, Pasadena, CA, 91125 USA e-mail: ha- [email protected]
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