Power supply noise management continues to be a challenge with the scaling of CMOS technologies. Use of on-chip decoupling capacitors (decaps) is the most common noise suppression technique and has significant associated area and leakage costs. There are numerous methods of implementing decaps and it is not always clear which implementation is the most optimal for the given design constraints. This paper characterizes various decap implementations including MOS-based decaps, multilayer metal decaps, and metal-insulator-metal decaps using postlayout simulations in a 65-nm CMOS technology, and provides an outline for determining the most optimal selection and design of decaps based on area, leakage, and location. Hybrid structures are further shown to boost the area efficiency of conventional nMOS decaps by an additional${\sim}{25\%}$.

Decomposition of distortion on per nonlinear element basis is crucial in design optimization, symbolic analysis and nonlinear model reduction. However, traditional methods cannot provide efficient and accurate distortion decomposition, for even moderate size analog circuits, because they are based on symbolic analysis. Analysis is normally possible by using simplified transistor models; however, even the most popular compact models are still inadequate for high frequency (HF) distortion analysis. To achieve both, insight of traditional symbolic analysis, and the handling capability, efficiency and accuracy of commercial numerical simulators, this work proposes an advanced distortion decomposition technique based on nonlinearity transfer matrix.

Volterra series (VS) is frequently used in the analysis of mildly nonlinear circuits. In this approach, nonlinear circuit analysis is converted into the analysis of a series of linear circuits. The main benefit of this approach is that linear circuit analysis is well established and direct frequency domain analysis of a nonlinear circuit becomes possible. In this paper, we present for the first time the sensitivity analysis of mildly nonlinear circuits in the frequency domain as an extension of the VS approach. Sensitivity analysis is useful in comparing the quality of two different designs and in gradient based optimization methods. One example circuit is analyzed and the sensitivity of the output to circuit parameters is given.

This paper presents a new and efficient transient analysis method for mildly nonlinear circuits. The method is based on Volterra series representation of nonlinear circuits. It characterizes nonlinear circuits using a set of linear circuits called Volterra circuits. The input of the first-order Volterra circuit is identical to that of the nonlinear circuit, whereas that of higher order Volterra circuits is obtained from the response of lower order Volterra circuits. Fourier series interpolation is employed to approximate the input of higher order Volterra circuits. These circuits are analyzed using the sampled-data simulation of linear circuits for computational efficiency and the response of nonlinear circuits is obtained at equally spaced intervals of time. The accuracy of the method is. controlled by the order of Volterra and interpolating Fourier series. Various sources contributing to the error are analyzed. The method has been implemented in a computer program. Numerical results on example circuits demonstrate that the accuracy of the method is comparable to that of linear multistep predictor-corrector algorithms, but with greatly improved speed.

This paper presents an accurate and efficient algorithm for simulating the effects of thermal noise in time-domain. The algorithm presented in this paper is based on Monte Carlo methods and is applicable to linear time invariant circuits. In addition to linear time invariant elements, the algorithm can easily be extended to include clock controlled switches and single or multibit quantizers. This expands the thermal noise analysis capability to switched capacitor circuits and oversampled delta-sigma modulators. Thermal noise generated by different elements is modeled, in the time-domain, by a random pulse waveform having a desired power spectral density. Typically the noise power level is much smaller than that of other desired signals in the circuit and accurate simulation is needed to obtain correct results. In addition, random noise waveforms require the computation of many time points in each transient analysis and efficient simulation methods are needed. In this paper, a new method for computing the transient response of linear time invariant circuits is used. This method accurately and efficiently computes the response to the random pulse waveforms. In addition to thermal noise, the method can also be used to simulate the effect of random dither signals in delta-sigma modulators. Examples of noise simulation are given and, when possible, comparison with measurements, previously published results, or analytical expressions is done.

The state transition matrix /spl Phi/(t)=e/sup At/ plays an important role in the state variable analysis of linear time-invariant circuits. In this paper, we give a method to compute the equivalent matrix for a set of differential-algebraic equations. Specifically, the algorithm is illustrated for the modified nodal analysis (MNA). A benefit of using MNA formulation is that equation formulation is straightforward and computer-aided analysis of large circuits is simplified. Another benefit is that inconsistent initial conditions in the analysis of switched circuits is automatically and correctly handled by the algorithm. Comparison with the state variable approach is made, and application to the simulation of linear circuits is given. The method is based on circuit theory concepts accessible to all electrical engineers. In addition to the transition matrix, a numerical method to compute the zero state response of linear circuits for a restricted set of inputs is given. The transition matrix along with the zero state response results in a special algorithm that is used to compute the time response of lumped linear time-invariant circuits at equally spaced intervals of time. This method is compared with the solution of linear circuits by SPICE-like simulators.

In this paper, an efficient, accurate, stable, and explicit method for transient analysis of lumped linear time invariant circuits is given. The method formulates a set of finite difference equations in the analog domain for sampled data simulation of the circuit. The solution of these equations gives the network response at fixed and equally spaced discrete instants of time. The fixed-time interval between each solution can be chosen arbitrarily and does not depend on the circuit time constants. The transient solution at each time point requires one matrix/vector multiplication and vector addition only. The algorithm is a general computer oriented formulation method that can be applied to any linear circuit. In addition to linear time invariant circuits, the method can be applied to a restricted class of time varying and/or nonlinear circuits. It is directly applicable to linear networks containing periodically clocked ideal switches, for example, switched capacitor and switched current circuits. In these networks, the circuit is linear inside each phase and changes its topology at fixed discrete instants of time. All nonlinear elements allowed in analysis must be clocked, such that their characteristics change only at discrete instants of time. For example, clocked digital circuits, such as, ideal comparators, A/D and D/A blocks are allowed. In particular, the method is applied to the simulation of oversampled delta-sigma modulators. The method can be used to study the effect of clock feed through, finite switch resistance, and finite gain bandwidth of operational amplifiers on the performance of these modulators. In addition, the algorithm can be used for analysis of continuous time delta-sigma modulators. Examples of simulation results are given.

In this paper an efficient method for calculating the zero state response of linear time invariant circuits is given. The input, in general, is a complex exponential function of time, of which step and sinusoidal functions are special cases. The method gives an algebraic relationship between the response due to two arbitrary exponential inputs. If the transient response due to one input is known, then the response due to the other input can be computed by the solution of a system of linear equations. No approximation is made in the derivation, and they are valid for all time and all exponential inputs. The method is useful in reducing the computational costs of analyzing periodically switched linear networks, such as, switched capacitor and switched current circuits.

The authors describe a high-level functional analog simulator for hybrid logic/analog networks. it forms one level of an experimental multilevel simulation system which is currently under development. The functional simulator is described in detail, and the structure of the multilevel simulator is briefly outlined. It can be used as a stand-alone system but was developed specifically for coupling with other levels of simulation which also use time responses (or voltage waveforms). Since Boolean algebra cannot operate with time responses, a new algebra is developed. It eliminates the unknown state, the main obstacle in coupling analog simulation to logic simulation. Logic states are replaced by operations on time functions, in this case represented by piecewise linear segments. High-level analog operations are also possible. The simulator based on these ideas was used to solve several high-level analog problems. The examples presented demonstrate its application.>