Loop-Based and Device-Based Algorithms for Stability Analysis of Linear Analog Circuits in the Frequency Domain

TL;DR: Based on Bode’s definition of return ratio with respect to a single controlled source, the loop-based two-port algorithm and device-based gain-nulling algorithm are proposed for small-signal stability analysis and produce accurate stability information for single-loop networks.

Abstract: N egative feedback techniques are widely used in analog and RF design to improve circuit properties such as variation tolerance, bandwidth, impedance matching, and output waveform distortion. In practice, unwanted local return loops also exist around individual transistors through parasitic capacitance. As the size of transistors continues to shrink and the bandwidth of transistors continues to broaden, these local return loops degrade circuit performance significantly in the high-frequency regime. Stability is always a serious concern for feedback circuits. Self-oscillations have been found above and/or beyond the bandwidth in such diversified circuits as optical fiber system receivers, power amplifiers, and distributed microwave amplifiers. It is critical to evaluate stability and stability margin of a feedback circuit. Such information can be used for optimization in the early design stage and for diagnosis in physical realization stage. Single-loop theory/multiloop reality is the state-of-the-art of stability analysis [8]. All physical networks in the frequency band of interest are intrinsically multiloop structures, yet it is still common practice to assess stability from single-loop theory. In this article, based on Bode’s definition of return ratio with respect to a single controlled source, the loop-based two-port algorithm and device-based gain-nulling algorithm are proposed for small-signal stability analysis. These two algorithms are complementary in terms of applicability, and they produce accurate stability information for single-loop networks. After a brief primer on feedback and stability, we review Bode’s feedback theory, where the return difference and return ratio concepts are applicable to general feedback configurations and avoid the necessity of identifyingμ andβ. Middlebrook’s null double-injection technique, which provides a laboratory-based way to measure return ratio, is then discussed in the modern circuit analysis context. We then extend the unilateral feedback model used in Middlebrook’s approach to accommodate both normaland reverse-loop transmission and characterize the return loop using a general two-port analysis. This loop-based two-port algorithm determines the stability of a feedback network in which a critical wire can be located to break all return loops. The device-based gain-nulling algorithm is then discussed to evaluate the influence of the local return loops upon network stability. This algorithm determines the stability of a feedback network in which a controlled source can be nulled to render the network to be passive. Conditions under which these two algorithms can be applied are discussed, and numerical results are provided.