Kai Bittner

Adaptive Multi-Rate Wavelet Method for Circuit Simulation

In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The circuit ordinary differential equations are first rewritten by a system of (multi-rate) partial differential equations (MPDEs) in order to decouple the different time scales. Second, a semi-discretization by Rothes method of the MPDEs results in a system of differential algebraic equations (DAEs) with periodic boundary conditions. These boundary value problems are solved by a Galerkin discretization using spline functions. An adaptive spline grid is generated, using spline wavelets for non-uniform grids. Moreover the instantaneous frequency is chosen adaptively to guarantee a smooth envelope resulting in large time steps and therefore high run time efficiency. Numerical tests on circuits exhibiting multi-rate behavior including mixers and PLL conclude the paper.

Optimal frequency sweep method in multi-rate circuit simulation

Purpose – Radio-frequency circuits often possess a multi-rate behavior. Slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit. Frequency modulated signals pose a particular challenge. The paper aims to discuss these issues. Design/methodology/approach – The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations in order to decouple the different time scales. For an efficient simulation the paper needs an optimal choice of a frequency-dependent parameter. This is achieved by an additional smoothness condition. Findings – By incorporating the smoothness condition into the discretization, the paper obtains a non-linear system of equations complemented by a minimization constraint. This problem is solved by a modified Newton method, which needs only little extra computational effort. The method is tested on a phase locked loop with a frequency modulated input signal. Originality/value – A new optimal ...

Grid Size Adapted Multistep Methods for High

The numerical calculation of the limit cycle of oscillators with resonators exhibiting a high-quality factor Q such as quartz crystals is a difficult task in the time domain. Time domain integration formulas, when not carefully selected, introduce numerical damping that leads to erroneous limit cycles or spurious oscillations. A novel class of adaptive multistep integration formulas based on finite difference (FD) schemes is derived, which circumvent the aforementioned problems. The results are compared with the well-known harmonic balance (HB) technique. Moreover, the range of absolute stability is derived for these methods. The resulting discretized system by FD methods is sparser than that of HB and, therefore, easier to solve and easier to implement.

Q

In this paper we present an algorithm for analog simulation of electronic circuits involving a spline Galerkin method with wavelet-based adaptive refinement. Numerical tests show that a first algorithm prototype, build within a productively used in-house circuit simulator, is completely able to meet and even surpass the accuracy requirements and has a performance close to classical time-domain simulation methods, with high potential for further improvement.

Oscillators

New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline expansions (differentiation, Oslo algorithm, etc.). Due to inherent properties of the spline wavelets, the algorithm can be modified for spline grid refinement or coarsening. The performance of the algorithms is demonstrated by numerical tests of the adaptive spline methods in circuit simulation.

Adaptive Wavelet-Based Method for Simulation of Electronic Circuits

The numerical calculation of the limit cycle of oscillators with resonators exhibiting a high quality factor such as quartz crystals is a difficult task in the time domain. Time domain integration formulas introduce numerical damping which leads asympotically to erroneous limit cycles or spurious oscillations. The numerical problems for solving the underlying differential algebraic equations are studied in detail. Based on these results a class of novel integration formulas is derived and the results are compared with the well-known Harmonic Balance (HB) technique. The discretized system is sparser than that of the HB method, therefore easier to solve and slower run time.

Fast Algorithms for Adaptive Free Knot Spline Approximation Using Nonuniform Biorthogonal Spline Wavelets

The project nanoCOPS (http://www.fp7-nanocops.eu) is a collaborative research project within the FP7-ICT research program funded by the European Union. The consortium comprises experts in mathematics and electrical engineering from seven universities (BU Wuppertal, HU Berlin, Brno UT, TU Darmstadt, FH OO Hagenberg, U Greifswald, KU Leuven), one research institute (MPI Magdeburg), two industrial partners (NXP Semiconductors Netherlands, ON Semiconductor Belgium) and two SMEs (MAGWEL—Belgium, ACCO Semiconductor—France).

Simulation of the steady state of oscillators in the time domain

We present an analysis of the stability characteristics of the discretized Maxwell-Ampere equations that result from a finite integration of the potential formulation. We demonstrate that the derivation of the discrete versions of these equations will result into unstable formulations unless, in the conversion from a continuous expression to a discrete expression, one accounts for the original motivation of the presence of the prior form.

The European Project nanoCOPS for Nanoelectronic Coupled Problems Solutions

We introduce multirate shootings methods to compute the response of radio frequency (RF) circuits with frequency modulated stimuli. The multirate technique is based on reformulating the system of ordinary differential algebraic equations (DAE) by partial differential equations (PDE). The PDE is semi-discretized by Rothe’s method, i.e. by first discretizing the initial value problem. The resulting periodic boundary value problems are then solved by shooting techniques. Second, the instantaneous frequency is an additional unknown and concurrently estimated.

Stability Analysis of Electromagnetic Transient Simulations

The goal of coupled circuit-field simulation is to test a complex device described by a full 3D field model in the environment of a larger circuit. We present here an approach, which treats the field model as device with a large number of internal unknowns and equations.