Comparative Analyses of Phase Noise in 28 nm CMOS LC Oscillator Circuit Topologies: Hartley, Colpitts, and Common-Source Cross-Coupled Differential Pair

This paper reports comparative analyses of phase noise in Hartley, Colpitts, and common-source cross-coupled differential pair LC oscillator topologies in 28 nm CMOS technology. The impulse sensitivity function is used to carry out both qualitative and quantitative analyses of the phase noise exhibited by each circuit component in each circuit topology with oscillation frequency ranging from 1 to 100 GHz. The comparative analyses show the existence of four distinct frequency regions in which the three oscillator topologies rank unevenly in terms of best phase noise performance, due to the combined effects of device noise and circuit node sensitivity

Mathematical Modeling of Electronic Systems: From Oscillators to Multipliers

The ubiquity of electronics in modern technology is undeniable. Although it is not feasible to design or analyze circuits in an exhaustively detailed fashion, it is still imperative that circuit design engineers understand the pertinent physical tradeoffs and are able to think at the appropriate level of mathematical abstraction. This thesis presents several mathematical modeling techniques of common electronic systems. First, we derive, ab initio, a general analytical model for the behavior of electrical oscillators under injection without making any assumptions about the type of oscillator or the size or shape of the injection. This model provides novel insights into the phenomena of injection locking and pulling while subsuming existing theories found in the literature. Next, we focus on the familiar scenario of an inductor-capacitor (LC) oscillator locked to a sinusoidal signal. An exact analysis of this circuit is carried out for an arbitrary injection strength and frequency, a task which has not been executed to fruition in the existing literature. This analysis intuitively illuminates the fundamental physics underlying the synchronization of electrical harmonic oscillators, and it generalizes the notion of the lock range for such oscillators into separate necessary and sufficient conditions. We then turn to the classical estimate of the bandwidth of a linear time-invariant (LTI) system via the sum of its zero-value time constants (ZVTs), and we show that this sum can actually be used to tightly bound the bandwidth—both from above and from below—in addition to simply estimating it. Finally, we look at a natural generalization of the Gilbert cell topology: an analog multiplier for an arbitrary number of inputs; we then analyze its large- and small-signal characteristics as well as its frequency response. Throughout, we will demonstrate how infusing physical intuition with mathematical rigor whilst seeking a balance between detailed analysis and abstract modularity results in models that are conceptually insightful, sufficiently accurate, and computationally feasible.</p

Efficient Calculation of the Impulse Sensitivity Function in Oscillators

This paper describes a simple method to compute the impulse sensitivity function of oscillators by means of the periodic transfer function analysis that is available in most of the commercial circuit simulators. The proposed calculation method, relying on linear-time variant simulations, is at least an order of magnitude more efficient than a conventional direct computation of the impulse sensitivity function based on transient analyses