Using the Best Linear Approximation in circuit design

The need for faster and more efficient electronic circuits pushes the devices more and more into their non-linear operating regions. The amount of non-linear distortion generated by a circuit becomes an increasingly important part of the circuit’s specifications. Most of the designers of analog electronic circuits use a linear framework to build their circuits. When the design is finished, the distortion levels are determined by simulations on the global circuit. If distortion specifications are not met, the origin of the distortion is not easily identified.

Current solutions to finding the dominant source of distortion rely on Volterra theory. These techniques are complex and lie far from the classical linear framework. Hence, they are not widely used during the design of electronic circuits.
Our goal is to introduce the Best Linear Approximation (BLA) into the design of analog circuits. The BLA allows the approximation of a non-linear block by a linear block where the distortion introduced by the system is modelled as noise. Linear systems and noise are concepts designers are very familiar with, so they would be able to adapt quickly to BLA-based methods. Using the BLA, information about the non-linear behaviour of the circuit can be introduced early into the design flow, preventing problems at the end.
There are two main research goals:

  1. Develop a simulation-based Distortion Contribution Analysis (DCA) that determines the dominant source of non-linear distortion in a complex circuit.
  2. Build a set of design rules to give a designer hints on how to decrease the amount of nonlinear distortion generated by a circuit.

We started by looking into the DCA for operational amplifiers and continuous-time filters [1]. The method works fine at low frequencies but, at higher frequencies, the terminal impedances of the stages come into play and limit the use of the method developed in [1]. An extension of the method to include the full port representation of the stages already shows nice results [2], but the fast extraction of the BLA is a current issue.
In a next stage, we will study how the methods can be extended for the design of mixers, power amplifiers, Phase Locked Loops and finally: a full transceiver.

References

[1] A. Cooman, G. Vandersteen and Y. Rolain. “Finding the dominant source of distortion in two-stage opamps” Analog Integrated Circuits and Signal Processing, vol. 78, no. 1, Jan. 2014
[2] A. Cooman, G. Vandersteen. “Distortion Contribution Analysis by combining the Best Linear Approximation and noise analysis” Proc. of the 2014 IEEE International Symposium on circuits and systems (ISCAS). pp. 2772-275, June 2014

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