Noncommensurate Transmission Lines Research Articles

Design of Dual-Mode Dual-Band Outphasing Power Amplifier Leveraging on Periodicity of Non-Commensurate Transmission Line Combiner

Design of Dual-Mode Dual-Band Outphasing Power Amplifier Leveraging on Periodicity of Non-Commensurate Transmission Line Combiner

A Dual-Band Outphasing Power Amplifier Based on Noncommensurate Transmission Line Concept

This article proposes a design methodology of dual-band outphasing power amplifier (OPA) based on two noncommensurate transmission lines (NCTLs). The devised NCTLs are used to replace the imperative reactance compensation and impedance matching networks in a conventional design. In virtue of this, the overall complexity of the combiner can be greatly reduced without sacrificing the load modulation effect. To support operations at two distinct frequencies, the conceptual NCTLs are further realized using two dual-band stub-loaded transmission lines. Comprehensive theoretical analysis is given to describe the proposed scheme and to illustrate how the electrical parameters of essential elements are determined. As a proof of concept, an OPA prototype operating at 2.6 and 3.5 GHz is fabricated. The implemented PA based on two 10-W GaN high electron mobility transistor (HEMTs) achieves 44.8 and 44.2-dBm maximum output power, and 74.5% and 62.1% peak drain efficiencies under continuous wave excitation at these two independent frequencies. At 6-dB output back-off points, the corresponding efficiencies reach 63.8% and 54.9%, respectively.

Application of Belevitch Theorem for Pole-Zero Analysis of Microwave Filters With Transmission Lines and Lumped Elements

This paper presents the application of Belevitch theorem for pole-zero analysis of microwave filters synthesized with transmission lines and lumped elements. The scattering ( $S$ ) matrix determinant ( $\Delta $ ) based on the Belevitch theorem, aptly called Belevitch determinant, comprises poles and zeros that are separated in different half-plane regions. Using the Belevitch determinant, the poles and zeros of filter transfer functions can be determined separately with certainty, e.g., by applying the contour integration method based on argument principle. Note that the contour integration can be evaluated numerically without requiring complicated overall analytical expressions. The proposed method is able to solve the poles and zeros for filters synthesized with noncommensurate transmission lines and lumped elements, where the transform method and the eigenvalue approach are inapplicable. Several applications are discussed to demonstrate the use of Belevitch theorem and the contour integration method to determine the poles and zeros of various microwave filters on the complex plane.

Group-Delay Engineered Noncommensurate Transmission Line All-Pass Network for Analog Signal Processing

A group-delay engineered noncommensurate transmission line two-port all-pass network for analog signal-processing applications is presented, analytically modeled, and experimentally demonstrated. This network consists of transversally cascaded C-sections, which are distributed implementations of the bridged-T equalizer lumped circuit. It is obtained by interconnecting the alternate ports of adjacent lines of a 2N -port coupled transmission line network with transmission line sections, and it is modeled using multiconductor transmission line theory with per-unit-length capacitance matrix C and inductance matrix L. By allowing the different C-sections of the network to exhibit different lengths, a generalized group-delay engineering procedure is proposed, where quasi-arbitrary group-delay responses are achieved by combining the group-delay responses of C-sections with different lengths. A computer design approach based on genetic algorithms is applied for synthesis, which consists of determining the structural parameters of the different C-section groups. Using this approach, noncommensurate networks are group-delay engineered in edge-coupled stripline technology, and Gaussian, linear and quadratic group-delay responses are realized. The theoretical results are validated by experiment. Finally, two application examples of analog signal processing-a tunable impulse delay line and a real-time frequency discriminator-using the proposed dispersive noncommensurate all-pass networks are presented.

Three-port hybrid power dividers terminated in complex frequency-dependent impedances

A new CAD algorithm for design of two- and four-section three-port hybrid power dividers terminated with complex frequency dependent impedances is described. The dividers under consideration are composed of lumped element resistors and noncommensurate transmission line sections whose characteristic impedances take extreme, practically realizable, values. These values are assumed freely at the beginning of a design process. The validity of the presented design algorithm has been confirmed by numerical modeling and experimentation.

A new set of realizability conditions for a class of multivariable functions

A new set of realizability conditions for the driving point impedance of a passive-lumped-terminated cascade of lossless two-ports separated by noncommensurate transmission lines is presented. The proposed set of realizability conditions eliminates the multivariable positive-reality requirement in favour of some simpler explicit conditions. Formulae for the chain matrices of the lumped lossless two-ports and the terminating impedance function are also given. Examples are provided to illustrate the main results.

Stability of multidimensional scalar and matrix polynomials

A comprehensive study of multidimensional stability and related problems of scalar and matrix polynomials is presented in this survey paper. In particular, applications of this study to stability of multidimensional recursive digital and continuous filters, to synthesis of network with commensurate and noncommensurate transmission lines, and to numerical stability of stiff differential equations are enumerated. A novel approach to the multidimensional stability study is the classification of various regions of analyticity. Various computational tests for checking these regions are presented. These include the classical ones based on inners and symmetric matrix approach, table form, local positivity, Lyapunov test, the impulse response tests, the cepstral method and the graphical ones based on Nyquist-like tests. A thorough discussion and comparison of the computational complexities which arise in the various tests are included. A critical view of the progress made during the last two decades on multidimensional stability is presented in the conclusions. The latter also includes some research topics for future investigations. An extensive list of references constitutes a major part of this survey.

Cascaded Noncommensurate Transmission-line Networks as Optimization Problems

Cascaded Noncommensurate Transmission-line Networks as Optimization Problems

Maximally flat approximation for noncommensurate cascaded transmission lines

The conditions for maximally flat attenuation are set up for a cascade connection of noncommensurate transmission lines. For structures with 2 and 3 lines, it is shown that arbitrary lengths cannot achieve a better maximally flat approximation than equal lengths.

Synthesis of a multivariable 2-port using parallel and series stubs

The necessary and sufficient conditions are established under which a multivariable transfer matrix can be realised as a cascade of noncommensurate transmission lines with parallel or series stubs, consisting of open-circuited or short-circuited single lines. A straightforward synthesis procedure is given.

Cascade synthesis of a multivariable transfer matrix

The necessary and sufficient conditions are established under which a multivariable transfer matrix can be synthetised as a cascade connection of lossless noncommensurate transmission lines. It is proved that, for this particular structure, the transmittance defines a unique reflectance.

Realizability of a Resistively Terminated Cascade of Lumped Two-Port Networks Separated by Noncommensurate Transmission Lines

The necessary and sufficient conditions are presented under which a multivariable impedance function may be realized by means of a cascade of passive, lumped, lossless, two-port networks connected by means of noncommensurate transmission lines and terminated in a positive resistor. Reference is also made to the particular case of a cascade of noncommensurate transmission lines with lumped, shunt capacitors at the junctions of adjacent lines.