Ernst Lüder

New structures for complex multipliers and their noise analysis

The realization and noise behavior of complex multipliers are examined. Using a systematic approach all multiplier structures which require the minimum number of three real multipliers are derived. Most of these structures are new. The two-dimensional probability density function of the complex error signal at the multiplier output is proposed for the description of the complex multiplier noise. A general approach to determine this density function is introduced and illustrated by some examples. Finally an overview of the noise properties of all structures is given. It turns out that the number of components and the noise behavior of a complex multiplier depend on the chosen realization.

Polycrystalline silicon-based sensors

Abstract This paper describes the processes now most often used to deposit polycrystalline, microcrystalline or amorphous Si films, and their applications for sensors. The processes are low pressure chemical vapour deposition (LPCVD), plasma enhanced-CVD (PECVD) and a chemical transport reaction. It is shown why the process in the above sequence require decreasing deposition temperatures ranging from 650°C to below 200°C. Lower temperatures allow for a wider selection of sensor substrates and membranes. Amorphous Si has to be laser recrystallized into poly-Si. Qualitative explanations are given for the adjustment of sensor properties such as temperature coefficient (TC) and gauge factor by doping with boron or phosphorus. Gauge factors of up to 27 with temperature coefficient of resistance (TCR) ≈ 0 are feasible. Temperature sensors will be presented as well as pressure sensors, the latter operating in the range of 0 to 1 bar or 2 bar and exhibiting sensitivities up to 10 mV/V bar. Remarks on radiation and magnetic field sensors and future trends conclude the paper.

Increasing the speed and saving multipliers in block parallel digital filters by a linear transformation

The linear transformation of flow graph matrices of block parallel digital filters can be applied to increase the speed of operation and to reduce the number of multipliers. To this aim we introduce a convenient matrix representation of block parallel digital filters and explain the transformation. As an example a second order block parallel filter with arbitrary block length L is generated which has the same high speed as an equivalent block-state space filter, but a multiplier complexity linear in block length L instead of square. For L=3 the number of multipliers is reduced by 32% compared with the block-state space filter and for L=6 by 26% compared with the structure proposed by Parhi.<<ETX>>

Synthesis of second-order digital filters with floating point arithmetic and maximum SNR

A lower bound for the roundoff-noise in second-order floating point digital filters is derived. Two filter structures are presented which exhibit this lowest noise power and in addition also the largest signal-to-noise ratio. Any given filter can be transposed into the low-noise structures by a linear transformation. Two more structures are shown to possess almost the lowest noise power.<<ETX>>

Discrete optimization by combining local search and design centering techniques

The authors propose a method for the discrete optimization of arbitrary objective functions subject to any constraints. Universality of the method is achieved by combining statistical design centering and deterministic local search techniques. An important application is the design of digital filters with prescribed accuracy or wordlength for the coefficients. Due to its general applicability, the method can be used for any type of digital filter (FIR, IIR, one-dimensional, multidimensional, etc.) with various number representations for the coefficients. Some examples demonstrate how the performance of digital filters can be enhanced while still maintaining a given wordlength of the coefficients.<<ETX>>

Analyse nichtlinearer Netzwerke mit Gebietsmethoden und adaptiven Funktionsansätzen

In this paper, we introduce domain methods for the analysis of nonlinear networks. A piecewise hermitian approximation with selfadaptive time intervals is proposed for the necessary function approach. This allows a good approxmation of functions with only a few parameters. With the described method it is possible to determine the periodic steady-state in nonlinear networks directly. For the given examples, especially the broadband driving of an LCD, our method shows a clear superiority compared to the popular harmonic balance.

Verbesserung des Rauschverhaltens von digitalen Filtern durch übertragungsfunktionsinvariante Transformation der Signalflussgraphmatrix

In order to reduce the roundoff noise and to enhance the dynamic range of general digital filters their flow graph matrix can be changed with transformation matrices. To do so, a suitable matrix representation of the filter is introduced and the constraints for the transformation matrices for a transfer function invariant alteration are listed. After that, a procedure of noise reduction on the basis of the introduced matrices is presented. As an example a block digital filter with 3 in- and outputs is used, for which the roundoff noise could be improved from 9.8 dB to 4.0 dB with the given method.

Ein analytischer Entwurf von digitalen Halbband-Filtern

A new, simple analytic method for the design of digital half-band filters is derived; for that, we introduce a closed form of the ideal half-band transfer function and apply polynomial approximations to the non-rational part. For the maximally flat half-band filter, we can find a new form especially suited for an implementation without multipliers, often using less than half the number of adders compared with the direct form. Furthermore, half-band filters with nearly perfect Chebyshev approximation can be generated; in general, the ripple exceeds the optimum value by less than 1% and is approximately halved compared to the Kaiser-window method.

Optimization of distributed parameter systems with a combined statistical-deterministic method

This paper describes an optimization method for nonlinear systems with properties that depend on functions instead of discrete parameters. The method is applied to the design of systems with spatially distributed parameters. The underlying mathematical problem of the calculus of variations is approximated by a finite dimensional constrained nonlinear minimax-problem. This is solved with a method that combines a deterministic algorithm for local optimisation with a statistical method for global optimization. The former is based on linearization and linear programming with adaptive trust region, while the latter uses elements from genetic methods and pattern recognition. An example with a nonlinearly loaded nonuniform transmission line shows the capability of the algorithm to determine the unknown optimum function with high precision.<<ETX>>

Optimierung von Schaltungen mit determinierten und statistischen Suchverfahren

Bei der Optimierung von integrierten Schaltungen entfallt der groste Teil der Rechenzeit auf die Schaltungsanalyse z.B. mit dem Programm SPICE. Gegenuber einem rein statistischen Verfahren kann die Anzahl der notwendigen Schaltungsanalysen um einen Faktor bis etwa 40 reduziert werden, falls eine Kombination von statistischen und determinierten Verfahren eingesetzt wird. Beim statistischen Teil geschieht dabei eine zeitsparende Austastung von geeignet gewahlten Teilraumen. Bei der Optimierung mit hoher Zahl von Parametern konnen lokale Optima z.B. durch Suche in Richtung des steilsten Anstiegs, wobei eine vorubergehende Verschlechterung in Kauf genommen wird, oder durch gleichzeitige Verfolgung mehrerer Richtungen oder mit Hilfe uberlagerter Gausverteilungen uberwunden werden. Schaltungseigenschaften konnen um den Faktor drei bis vier gegenuber dem ursprunglichen Entwurf verbessert werden.