Noise Considerations in Circuit Optimization

Noise can cause digital circuits to switch incorrectly and thus produce spurious results. Noise can also have adverse power, timing and reliability e ects. Dynamic logic is particularly susceptible to charge-sharing and coupling noise. Thus the design and optimization of a circuit should take noise considerations into account. Such considerations are typically stated as semi-in nite constraints. In addition, the number of signals to be checked and the number of sub-intervals of time during which the checking must be performed can potentially be very large. Thus, the practical incorporation of noise constraints during circuit optimization is a hitherto unsolved problem. This paper describes a novel method for incorporating noise considerations during automatic circuit optimization. Semi-in nite constraints representing noise considerations are rst converted toordinary equality constraints involving time integrals, which are readily computed in the context of circuit optimization based on time-domain simulation. Next, the gradients of these integrals are computed by the adjoint method. By using an augmented Lagrangian optimization merit function, the adjoint method is applied tocompute all the necessary gradients required for optimization in a single adjoint analysis, no matter how many noise measurements are considered and irrespective of the dimensionality of the problem. Numerical results are presented.

Circuit Optimization via Adjoint Lagrangians

The circuit tuning problem is best approached by means of gradient-based nonlinear optimization algorithms. For large circuits, gradient computation can be the bottleneck in the optimization procedure. Traditionally, when the number of measurements is large relative to the number of tunable parameters, the direct method [2] is used to repeatedly solve the associated sensitivity circuit to obtain all the necessary gradients. Likewise, when the parameters outnumber the measurements, the adjoint method [1] is employed to solve the adjoint circuit repeatedly for each measurement to compute the sensitivities. In this paper, we propose the adjoint Lagrangian method, which computes all the gradients necessary for augmented-Lagrangian-based optimization in a single adjoint analysis. After the nominal simulation of the circuit has been carried out, the gradients of the merit function are expressed as the gradients of a weighted sum of circuit measurements. The weights are dependent on the nominal solution and on optimizer quantities such as Lagrange multipliers. By suitably choosing the excitations of the adjoint circuit, the gradients of the merit function are computed via a single adjoint analysis, irrespective of the number of measurements and the number of parameters of the optimization. This procedure requires close integration between the nonlinear optimization software and the circuit simulation program. The adjoin

Optimization of Custom MOS Circuits by Transistor Sizing

Optimization of a circuit by transistor sizing is often a slow, tedious and iterative manual process which relies on designer intuition. Circuit simulation is carried out in the inner loop of this tuning procedure. Automating the transistor sizing process is an important step towards being able to rapidly design high-performance, custom circuits. JiffyTune is a new circuit optimization tool that automates the tuning task. Delay, rise/fall time, area and power targets are accommodated. Each (weighted) target can be either a constraint or an objective function. Minimax optimization is supported. Transistors can be ratioed and similar structures grouped to ensure regular layouts. Bounds on transistor widths are supported. JiffyTune use

Halotropism Is a Response of Plant Roots to Avoid a Saline Environment

International audienceTropisms represent fascinating examples of how plants respond to environmental signals by adapting their growth and development. Here, a novel tropism is reported, halotropism, allowing plant seedlings to reduce their exposure to salinity by circumventing a saline environment. In response to a salt gradient, Arabidopsis, tomato, and sorghum roots were found to actively prioritize growth away from salinity above following the gravity axis. Directionality of this response is established by an active redistribution of the plant hormone auxin in the root tip, which is mediated by the PIN-FORMED 2 (PIN2) auxin efflux carrier. We show that salt-induced phospholipase D activity stimulates clathrin-mediated endocytosis of PIN2 at the side of the root facing the higher salt concentration. The intracellular relocalization of PIN2 allows for auxin redistribution and for the directional bending of the root away from the higher salt concentration. Our results thus identify a cellular pathway essential for the integration of environmental cues with auxin-regulated root growth that likely plays a key role in plant adaptative responses to salt stress