Assessment of Thermal Instabilities and Oscillations in Multifinger Heterojunction Bipolar Transistors Through a Harmonic-Balance-Based CAD-Oriented Dynamic Stability Analysis Technique

Abstract

We present a novel analysis of thermal instabilities and oscillations in multifinger heterojunction bipolar transistors (HBTs), based on a harmonic-balance computer-aided-design (CAD)-oriented approach to the dynamic stability assessment. The stability analysis is carried out in time-periodic dynamic conditions by calculating the Floquet multipliers of the limit cycle representing the HBT working point. Such a computation is performed directly in the frequency domain, on the basis of the Jacobian of the harmonic-balance problem yielding the limit cycle. The corresponding stability assessment is rigorous, and the efficient calculation method makes it readily implementable in CAD tools, thus allowing for circuit and device optimization. Results on three-and four-finger layouts are presented, including closed-form oscillation criteria for two-finger devices.

Selective Determination of Floquet Quantities for the Efficient Assessment of Limit Cycle Stability and Oscillator Noise

“…The HB determination of the FEs leads to the computation of a large number of eigenvalues, that, in principle, should be distributed in the complex plane in sets characterized by having the same imaginary part [1], [14]; the n − m exponents are chosen by maximizing the accuracy in the associated eigenvectors [16]. The electrothermal system is based on the two-finger HBT model discussed in detail in [2]; each HBT finger is described by a temperature-dependent Gummel-Poon electrical model, and the corresponding temperature increase is calculated as the result of power dissipation on a thermal impedance matrix. Both the electrical and thermal device descriptions take into account capacitive effects, and device physics suggests that the time constants governing the two phenomena (electrical and thermal) are widely separated, since thermal transients are normally much longer than electrical time constants; this should be reflected in the appearance of widely separated FEs.…”

“…Interest in the Floquet theory has been recently revived in the area of analog electronic circuit analysis and design, mainly because of the central role it plays in the assessment of the stability properties of nonlinear circuit periodic limit cycles [1], [2] and of the phase and amplitude perturbations of oscillators [3]- [7]. For lumped circuits, Floquet's theorem for index-1 differential-algebraic equations (DAEs) [8] defines the properties of a small change perturbation of the circuit periodic working point.…”

Improved harmonic balance implementation of Floquet analysis for nonlinear circuit simulation

“…Nevertheless, sinceĈ is made of diagonal blocks (deriving from the time-sampling of the elements of C(t)),C T can easily be built from the components ofC avoiding any further calculation [20]. In summary, the Floquet quantities can be calculated as the solution of the generalized eigenvalue problems in (11) and (12), whose matrices correspond to the jacobians of the HB problem defining the limit cycle, and therefore are available as a byproduct of the Newton iterations normally exploited for the determination of x S (t).…”

“…The solution of the generalized eigenproblems (11) and (12) yields n(2N H + 1) FEs (and the corresponding direct and adjoint eigenvectors). In an ideal system, i.e.…”

“…Floquet analysis, although a classical topic in the mathematical literature [1,2], is the object of a renewed interest in the circuit simulation community because of the central role played in two important areas of nonlinear circuit performance assessment: the rigorous study of phase and amplitude noise in oscillators [3,4,5,6,7,8], and the appraisal of the stability of the time-periodic working point solution of a nonlinear circuit, either driven or autonomous [1,2,9,10,11,12,13].…”