Transfer functions interpolating an ideal amplitude with arbitrary phase and delay

A method is presented to generate polynomials with phase values and delay (first derivative) specified at given frequencies. Then a closed form solution is described for the scattering transfer function S₁₂(p) of a resistively terminated lossless reciprocal two-port network with ideal amplitude and arbitrary phase and delay.     

A chebyshev rational function with low Q-factors

The presented rational function is a modification of a recently published Chebyshev rational function defined by means of some orthogonal polynomials. the necessary conditions providing for the lowest pole Q-factors for a given ripple are found. the function is a ratio of two similar Chebyshev polynomial transfer functions with multiple poles. The selectivity of the function can be increased by using the Chebyshev rational characteristic function instead of the characteristic polynomials. the minimum number of active elements in the cascade connection is obtained with third-order elliptic characteristic functions. The function is compared with the Cauer (elliptic) and MCPER filters. the distinctive features of the presented function are small Q-factors of the poles, almost ideal dynamic range, simple design and poles with the same multiplicity m, where m designates the number of cascaded blocks.     

Computer-aided design of stable recursive digital filters from magnitude specifications

This paper presents a method of designing one- and two-dimensional recursive digital filters making use of the properties of bilinear transformation of strictly Hurwitz polynomials. The result is a stable digital filter in both one- and two-dimensional cases, which requires no further testing for stability. The well known unconstrained minimization technique of Fletcher—Powell is used, making use of a transformation of optimization parameters to satisfy the mild constraints of stability. This method is considered to be more efficient on an overall basis than the existing l_p design technique of Maria and Fahmy. Nor does it rely on Deczky's theorem to ensure a stable filter which may sometimes lead to unstable solutions in the two-dimensional case. An example is provided illustrating the method.     

Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems

The “new transformation polynomials for discretization of analogue systems” was recently introduced. The work proposes that the discretization of 1/s ⁿ should be done independently rather than by raising the discrete representation of 1/s to the power n. Several examples are given in to back this idea. In this paper it is shown that the “new transformation polynomials for discretization of analogue systems” is exactly the same as the parameterized Al-Alaoui operator. In the following sections, we will show that the same results could be obtained with the parameterized Al-Alaoui operator. This research was supported, in part, by the University Research Board of the American University of Beirut.     

New transformation polynomials for discretization of analogue systems

The novel transformation polynomials for discretization of analogue systems have been presented. A generalization of some of the existing transformation methods has also been done. A comparative analysis, through the corresponding examples involving several known discretization methods, has been carried out. It has been demonstrated that the application of these transformation polynomials allows the reduction of discretization error compared to other approximation methods. The response to an arbitrary excitation of the discrete system obtained by these transformations is approximately equal to that of the original analogue system. The transformations are rational since variable s ^{− n} ,n ∈ N, transforms to the quotient of two linear functions of variable z.     

Direct synthesis technique (DST) for complex general Chebyshev filters

Recently, we discussed the concept of direct synthesis technique (DST), in which real‐coefficient filtering polynomials containing all information of the filters to be synthesized are derived directly for realization, and they could find applications in the design of lumped‐element LC filters, active RC filters, and infinite impulse response digital filters. In this paper, another DST for complex general Chebyshev bandpass filters is discussed, which is based on a complex mapping relation and featured by complex‐coefficient filtering polynomials. It is called as complex DST in this paper. Compared with real‐coefficient filtering polynomials whose polarities are determined by the number of their zeros at zero frequency, the polarities of complex‐coefficient filtering polynomials can be easily changed by multiplying imaginary unit j . Such advantage might make their realization more flexible. The analysis shows that conventional coupling matrix could be considered as narrow‐band approximation of network matrix derived by complex DST in the normalized frequency domain. In order to demonstrate the validity of complex DST in this paper, it is applied in the design of classic parallel‐coupled microstrip bandpass filters. Compared with conventional synthesis techniques, complex DST could find out better dimensions and provide more choices for realization and synthesize both even‐order and odd‐order parallel‐coupled microstrip bandpass filters. Copyright © 2017 John Wiley & Sons, Ltd.     

Efficient estimation of adjoint‐variable S‐parameter sensitivities with time domain TLM

We present a novel algorithm for efficient estimation of S‐parameter sensitivities with the time‐domain transmission line modelling (TLM) method. The original electromagnetic structure is simulated using TLM to obtain the S‐parameters in the desired frequency band. For each port, an adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the S‐parameters in the desired frequency band are estimated using only the original and adjoint simulations. For a structure with N_p ports and n designable parameters, our approach requires only N_p additional simulations regardless of n. This can be easily contrasted with the 2nN_p additional simulations required by the central difference approximation. Our algorithm is illustrated through the estimation of S‐parameter sensitivities with respect to the dimensions of waveguide discontinuities. Very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Copyright © 2005 John Wiley & Sons, Ltd.     

Generalized linear phase polynomials—application in filter synthesis

In this paper, we give explicit expressions for the study of attenuation and phase characteristics of generalized linear phase polynomials (i.e. Jacobi and generalized Bessel polynomials for transmission line and lumped filters respectively). We present an exact method to find the digital transfer function which exhibits [n/2] to (n?1) simultaneous conditions on amplitude and delay.     

Application of direct synthesis techniques to customize filters with complex frequency response

Recently, direct synthesis techniques (DSTs) have been presented for filter synthesis. Unlike conventional synthesis techniques, DSTs derive the filtering polynomials of the filters to be synthesized directly in their own frequency domain. These filtering polynomials are real coefficient so that they might find applications in various fields. Furthermore, DSTs might be used to customize filters with a more complex frequency response, such as asymmetric frequency response or multi‐band frequency response. In this paper, DSTs are compared with some well‐known filter synthesis techniques. Then, the application of DSTs in the design of lumped‐element LC filters, distributed‐element filters, active RC filters, and infinite impulse response digital filters with complex frequency response is discussed. Some examples are presented for demonstration. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of n-port active rc networks with a minimum number of capacitors

A new and practical synthesis procedure is presented for the realization of an arbitrary n × n matrix of real rational functions of the complex frequency variable as the short-circuit admittance matrix of a transformerless active RC n-port network. The realization requires a theoretically minimum number of capacitors p, where p is the degree of the matrix, and no more than (n + p + 1) grounded finite-gain phase-inverting voltage-controlled voltage sources. All the capacitors and ports are grounded. The freedom implicit in the synthesis procedure allows the inclusion of constraints on the passive element values. Furthermore, in special cases the realization is achieved with a reduced number of conductances and voltage-controlled voltage sources. The synthesis procedure is simple to apply and can readily be implemented on a digital computer. Several examples are given.     

One-dimensional cylindrical diffusion of electromagnetic fields, Part II

Contents This paper continues a previous one [1]. It discusses a magnetic fieldB _z (r,t) diffusing into a homogeneous conducting cylinder (of radiusr ₀). The difference between the two papers is that different boundary conditions are applied. The boundary condition now is an integrated one, the magnetic flux within a coaxial hollow cylinder (of radiusR ₀>r ₀) being proportional tot ⁿ (actually a more general problem is discussed). As in the previous paper the solution can be simplified by the introduction of certain polynomials, which are very useful and which have interesting properties. They are generalisations of the polynomials defined in [1]. The corresponding plane problem is discussed again, too. The polynomials defined in this case are related to generalisations of Bernoulli- and Euler-polynomials.

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Eindimensionale zylindrische Diffusion elektromagnetischer Felder, Teil II

Übersicht Die Arbeit stellt die Weiterführung einer vorhergehenden Arbeit [1] dar. In ihr wird die Diffusion eines Magnetfeldes in einen homogenen leitfähigen Zylinder (Radiusr ₀) diskutiert. Der Unterschied zwischen beiden Arbeiten liegt in den Randbedingungen. Hier ist die Randbedingung eine integrale. Der magnetische Fluß innerhalb eines koaxialen Hohlzylinders (RadiusR ₀>r ₀) ist proportional zut ⁿ (tatsächlich wird ein allgemeineres Problem behandelt). Wie in [1] kann die Lösung durch die Einführung bestimmter Polynome vereinfacht werden, die bemerkenswerte Eigenschaften haben und sehr nützlich sind. Sie stellen Verallgemeinerungen der in [1] eingeführten Polynome dar. Wie früher wird auch hier das analoge ebene Problem behandelt. Die dabei auftretenden Polynome hängen mit Verallgemeinerungen von Bernoulli-und Euler-Polynomen zusammen.

     

Synthesis of complex lossless two-ports

A new synthesis algorithm is presented for the realization of a doubly terminated complex lossless two-port from a given canonic set of scattering polynomials. the synthesis algorithm is based entirely on polynomial evaluations and thus polynomial arithmetic and routines for zero finding are not needed. the accuracy problem due to coefficient sensitivity is avoided. In particular, explicit knowledge of the intermediate polynomials is not required. the simplicity and functionality of the algorithm are based on a new representation of elementary sections given by a set of canonic parameters, namely the transmission zero of the section, the reflectance evaluated at the transmission zero and, for reciprocal sections, the return group delay evaluated at the transmission zero. A great deal of freedom is available, since transmission zeros with any multiplicity and located anywhere in the complex plane are realized independently. Also, complex networks composed exclusively of either inductors or capacitors as the dynamic elements are possible. an example is given to illustrate the robustness of the algorithm.     

Tangential nevanlinna-pick interpolation problem for bounded real matrices—A network approach

This paper deals with the so-called tangential Nevanlinna—Pick interpolation problem for bounded real matrices. This problem can be formulated as follows: given a set of n pairs {(p_i, K _i)}, where p_i are distinct complex numbers with Re p_i > 0 and K _i stands for 2m × l_i constant matrices, assuming that for every pair (p_i, K _i) with p_i complex there exists a complex conjugate pair (p _i, K _i) and that for every pair (p_i, K _i) in which p_i is real K _i is also real, find an m × m bounded real matrix S(p) such that [ S (p_i) 1_m] K _i = 0 for i= 1,…,n. The solution of this problem is obtained in an inductive way through the construction at each step of a real lossless multiport section that realizes two complex conjugate pairs or one real pair. After each step the number of pairs (p_i, K _i) is reduced by two (if p_i is complex) or by one (if p_i is real). the procedure is continued until all pairs have been considered. After the last step the final section may be terminated with any bounded real load. the scattering matrix S (p) of the resulting cascade multiport network is bounded real and satisfies the desired interpolation conditions. In this way the tangential interpolation problem is reduced to classical network cascade synthesis by the use of real lossless multiport sections.     

One-dimensional cylindrical diffusion of electromagnetic fields,part I

Contents We discuss magnetic fieldsB _z (r, t) andB (r, t) diffusing into homogeneous conducting circular cylinders of radiusr ₀ with boundary conditionsB _z (r ₀,t) orB (r ₀,t) proportional tot ⁿ. Laplace-transforms are used. The main difficulty is their inversion for larger values ofn. The procedures can be strongly simplified by the introduction of certain polynomials. They have very remarkable properties. They are also helpful for many applications. If one wants to calculate the dissipated Joule-heat for instance, one needs certain infinite sums related to the eigenvalues of the problems. These infinite sums can easily be evaluated with the help of the polynomials mentioned. The corresponding plane problems are also considered in order to show that these polynomials are the cylindrical analogues of Bernoulli- and Euler-polynomials. The relations between our polynomials and Fourier-Bessel-expansions are the same as those between Bernoulli- and Euler-polynomials and Fourier-expansions. Finally hollow cylinders are discussed, too. The results are similar but more complicated than for full cylinders.

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Eindimensionale zylindrische Diffusion elektromagnetischer Felder, Teil I

Übersicht Wir behandeln magnetissche FelderB _z (r, t) undB (r, t), die in homogene leitfähige Kreiszylinder mit dem Radiusr ₀ diffundieren mit der Randbedingung, daß fürr=r ₀ die Felder proportionalt ⁿ sind. Dabei wird die Laplace-Transformation benutzt, wobei deren Inversion für größere Werten sehr umständlich ist. Durch die Einführung bestimmter Polynome kann das Vorgehen sehr erleichtert werden. Diese Polynome haben bemerkenswerte Eigenschaften und können für viele Anwendungen sehr nützlich sein. Will man z.B. die dissipierten Energien berechnen, so benötigt man dazu gewisse unendliche Summen der Eigenwerte der Probleme, die mit Hilfe der genannten Polynome leicht berechnet werden können. Die Behandlung der analogen ebenen Probleme zeigt, daß diese Polynome das zylindrische Analogon der Bernoulli-und Euler-Polynome sind. Die Beziehungen zwischen unseren Polynomen und Fourier-Bessel-Reihen sind dieselben wie die zwischen Bernoulli-und Euler-Polynomen und Fourier-Reihen. Abschließend werden auch Hohlzylinder behandelt. Die Ergebnisse sind ähnlich, jedoch erheblich komplizierter als für Vollzylinder.

     

Multistage multiphase switched‐capacitor DC–DC converter with variable‐phase and PWM control

A closed‐loop multistage multiphase switched‐capacitor converter (n‐stage p‐phase MPSC) is proposed with a variable‐phase control (VPC) and a pulse‐width‐modulation (PWM) technique for low‐power step‐up conversion and high‐efficiency regulation. In this n‐stage MPSC, n voltage doublers are connected in series for boosting the voltage gain up to 2ⁿ at most. Here, VPC is suggested to realize a variable multiphase operation by changing the phase number p and topological path for the more suitable level of voltage gain so as to improve the power efficiency, especially for the lower output voltage Besides, PWM is adopted not only to enhance output regulation for different desired outputs, but also to reinforce output robustness to source/loading variation. Further, some theoretical analyses and designs include: n‐stage p‐phase MPSC model, steady‐state analysis, conversion ratio, power efficiency, output ripple, stability, capacitance selection, and control design. Finally, the closed‐loop MPSC is simulated, and the hardware is implemented and tested. All the results are illustrated to show the efficacy of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of stable two-dimensional analogue and digital filters with applications in image processing

A method is proposed for the frequency domain design of linear two-dimensional analogue and digital filters with guaranteed stability. The technique used is based on the result that the numerator and the denominator of the input immittance of a two-variable network (which is passive and lossy) are strictly Hurwitz polynomials. One of these strictly Hurwitz polynomials is assigned to the denominator of a two-variable analogue transfer function and the network elements are then used as the variables of optimization thereby guaranteeing the stability of the analogue transfer function. The transfer function of the corresponding two-dimensional discrete (digital) filter is obtained from the analogue transfer function by the bilinear transformation. Examples illustrating the versatility of the technique in designing 2D digital filters of arbitrary order approximating a given magnitude and group delay response are presented. These filters are used to process a simple binary image. The results obtained demonstrate the importance of linear phase in image processing applications. The method presented here can be extended to the design of stable m-dimensional analogue and digital filters.     

Mixed norm regularized recursive total least squares for group sparse system identification

A mixed l_p,0‐regularized recursive total least squares (RTLS) algorithm is considered for group sparse system identification. Regularized recursive least squares (RLS) has been successfully applied to group sparse system identification; however, the estimation performance in regularized RLS‐based algorithms deteriorates when both input and output are contaminated by noise (the error‐in‐variables problem). We propose an l_p,0‐RTLS algorithm to handle group sparse system identification with errors‐in‐variables. The proposed algorithm is an RLS‐like solution that utilizes l_p,0‐regularization. The proposed algorithm provides excellent performance as well as reduces the required complexity by effective inversion matrix handling. Simulations demonstrate the superiority of the proposed l_p,0‐regularized RTLS for a group sparse system identification setting. Copyright © 2015 John Wiley & Sons, Ltd.