Ajoy Opal

Analysis of nonlinear networks with inconsistent initial conditions

Inconsistent initial conditions and/or Dirac impulses can appear in networks with ideal switches, and in such cases simulators may give wrong results. To avoid errors, many simulators do not allow ideal switching. This paper presents simple CAD methods which can handle correctly, and automatically, inconsistent initial conditions of linear as well as nonlinear networks. For easy understanding, all explanations are done on simple examples, with the minimum of mathematics. >

Analysis and sensitivity of periodically switched linear networks

A completely general computer-oriented method for exact frequency-domain analysis of multiphase periodically switched linear networks is presented. Input signals can be either continuous or sample-and-held. The theory is valid even for cases where the network variables are discontinuous during switching. An algorithm to compute sensitivity of the response to element changes is also given. The method unifies analysis of general switched linear networks and ideal switched capacitor networks to a single algorithm. Equation formulation is based on the two-graph modified nodal analysis. The theoretical results presented are compared to previously published results. The theories have been implemented in a computer program. Numerical results of the analysis of three networks are given. They show the usefulness of the program in the analysis and design of switched networks. >

Sampled data simulation of linear and nonlinear circuits

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.

Distortion analysis of periodically switched nonlinear circuits using time-varying Volterra series

This paper presents a new frequency-domain method for distortion analysis of general periodically switched nonlinear circuits. It generalizes Zadehs time-varying network functions and bifrequency transfer functions from linear time-varying systems to nonlinear time-varying systems. The periodicity of time-varying network functions of linear and nonlinear periodically time-varying systems is investigated using time-varying Volterra series. We show that a periodically switched nonlinear circuit can be characterized by a set of coupled periodically switched linear circuits. Distortion of the periodically switched nonlinear circuit is obtained by solving these linear circuits. This result is a generalization of the multi-linear theory known for nonlinear time-invariant circuits. We also show that the aliasing effect encountered in noise analysis of switched analog circuits exists in distortion analysis of periodically switched nonlinear circuits. Computation associated with the folding effect can be minimized by using the adjoint network of periodically switched linear circuits, in particular, the frequency reversal theorem. The method presented in this paper has been implemented in a computer program. Distortion of practical switched circuits is analyzed and the results are compared with SPICE simulation.

Computer methods for switched circuits

This paper presents a state-of-the-art review of the recent advances in computer methods for analysis and design of switched circuits in both time and frequency domains. It also presents new research results on time-domain analysis and sensitivity of switched nonlinear circuits, time- and frequency-domain statistical analysis of switched linear and nonlinear circuits, and efficient modeling and analysis of clock feedthrough and charge injection in switched linear circuits. In time-domain analysis, the modeling of switches and its effect on the simulation of switched circuits are investigated. Formulation methods for these circuits are examined. Inconsistent initial conditions arising from ideal switching are investigated and numerical methods that derive the consistent initial conditions are examined. Sampled-data simulation (SDSIM) of switched linear circuits including clocked sigma-delta modulators is investigated. SDSIM is extended to switched nonlinear circuits. Time-domain sensitivity of switched linear and nonlinear circuits is analyzed using SDSIM. Efficient time-domain statistical analysis of switched linear and nonlinear circuits is introduced, and their effectiveness is assessed using Monte Carlo simulation. Methods that compute the effect of the clock jitter of periodically switched linear (PSL) circuits are examined. Time-domain noise analysis of PSL circuits is investigated. In frequency-domain analysis, exact frequency analysis of multiphase PSL circuits is reviewed. Sensitivity analysis of these circuits is examined in detail. Adjoint network theory and its usefulness in noise and sensitivity analysis of switched linear circuits are studied. Group delay of PSL circuits is investigated briefly. Efficient modeling and analysis of clock feed-though and charge injection of PSL circuits are introduced. Distortion and sensitivity of periodically switched nonlinear circuits with mild nonlinearities are investigated. Finally, frequency-domain noise analysis of PSL circuits is examined.

An efficient transient analysis algorithm for mildly nonlinear circuits

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.

Analysis and Design of On-Chip Decoupling Capacitors

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 ~25%.

Analog functional simulator for multilevel systems

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. >

Adjoint network of periodically switched linear circuits with applications to noise analysis

In this paper, Tellegens theorem for multiphase periodically switched linear (PSL) circuits in phasor domain and the adjoint network of PSL circuits are developed. Two new theorems are introduced and theoretical proofs are given. The first theorem, called the transfer function theorem, gives an efficient way to calculate the transfer functions from multiple inputs to a single output of PSL circuits. This theorem is the generalization of a similar result known for linear time-invariant and ideal switched capacitor networks. A major contribution of this paper is the second theorem, called the frequency reversal theorem, which gives an efficient way to compute the aliasing transfer functions of linear periodically time-varying circuits. The use of both of these theorems results in an efficient algorithm for noise analysis of linear periodically time-varying circuits in the frequency domain. The algorithm handles general PSL circuits, including switched capacitor and switched current networks with both white and 1/f noise sources. It has been implemented in a computer program. The output noise power of practical PSL circuits is analyzed and the results are compared with published measurement data.

Noise and sensitivity analysis of periodically switched linear circuits in frequency domain

This paper presents new theories and efficient computational methods for noise and sensitivity analysis of multiphase periodically switched linear (PSL) circuits in frequency domain. Tellegens theorem for PSL circuits in the phasor domain, frequency reversal theorem, and transfer function theorem, are introduced. The adjoint network of PSL circuits is developed using a frequency-domain approach. An adjoint network-based noise analysis algorithm for PSL circuits is proposed. It is shown that the computational overhead associated with multiple noise sources is eliminated by using the transfer function theorem. It is also shown that the excessive cost of computation due to aliasing effects is significantly reduced when the frequency reversal theorem is employed. In sensitivity analysis, the incremental form of Tellegens theorem for PSL circuits in the phasor domain is introduced and frequency-domain sensitivity of PSL circuits Is obtained. It is shown that frequency-domain sensitivity of PSL circuits is a series summation of the network variables. Both the baseband and sideband frequency components of the network variables contribute to baseband sensitivity. The method yields sensitivities of one output with respect to all circuit elements in one frequency analysis. Sensitivity networks of PSL circuits are introduced. It is demonstrated that both the adjoint and sensitivity network approaches give the same sensitivity. Numerical results computed using the proposed methods are compared with measurement data and those from other CAD tools.