Passive N-port Research Articles

Generalized Multimode Scattering Parameter and Antenna Far-Field Conversions

A general technique is presented to transform multimode and mixed-mode scattering parameters (S-parameters) between arbitrary sets of equivalent passive N-port networks, and transform antenna far-fields between N-port antennas with different sets of multimode or single-ended excitations. The technique makes use of simple transformation matrices, and makes provision for general multimode ports, coupled and uncoupled multiconductor transverse electromagnetic ports, and mixed-mode networks containing both differential ports and single-ended ports. A quadraxially fed multimodal antenna is analyzed as example.

Simple method for characterizing linear multi-port microstrip structures

A simple method for the full characterization of passive n-port microwave monolithic integrated circuit (MMIC) structures using standard two-port vector network analyzer (VNA) measurements is presented. Its main advantages are: it does not require to perform measurements from all the ports of the network, no special calibration procedure is needed, the auxiliary terminations required by the procedure can be integrated at the border of the structure under test with minimal area increase, and it can be easily implemented in commercial CAD software. The method was applied to a nine-port microstrip structure corresponding to the output power combiner and impedance matching network of an X-band MMIC high power amplifier (HPA). The full S-parameter matrix was derived from two-port measurements and compared to the circuit–as well as electromagnetic (EM)-based simulations of the structure.

Lumped- and distributed-element equivalent circuits for some symmetrical multiport signal-separation structures

This paper presents an extension to the synthesis of the symmetrical analysis methods for modeling passive n-port junctions. Two approaches are discussed: the electrical one, based on consideration of even- and odd-propagation modes, and the geometrical one, based on space symmetry operators. The convenience of using more complete models for both analysis and synthesis is manifest in the choice of the simplest topological circuits of some well-known signal-separation structures. An example of the synthesis of a lumped quadrature coupler is carried out via the geometrical approach and the results compared to those of a previously reported design performed via the electrical approach. Likewise, a distributed circuit for a ring-style five-port four-way equal-power divider simpler than others exhibiting the same power-division characteristics is presented.

Schwarz's Lemma for n-Ports

The scalar versions of Schwarz's Lemma have been extensively employed in the classical development of the synthesis of lumped RLC driving-point impedance function. A vector space generalization of Schwarz's Lemma, particularly suitable for application to linear passive n-port impedance functions, is derived in this paper. The concept of power dominant networks is introduced and a number of power inequalities derived.

A system operator theorem on positive real operators

A new theorem expands the domain of the scalar immittance functions Z(p) to the operator Z(T) where T(s) is an invertible linear passive n-port system. Elements R, L, C of Z(p) are replaced by operators RI, LT, and [CT] - 1. All frequency transformations may be considered contained in this theorem when T is a scalar.

A general theorem on the limitation of power consumption

The characteristic values of the open loop impedance (admittance) operator of a linear passive reciprocal n-port impose certain natural bounds on the effective total energy consumptions in the network. It is shown that the characteristic values of a linear system and the energy dissipated by it are interrelated via arithmetic and geometric inequalities. The link between the two concepts is the convexity of quadratic forms associated with nonnegative operators, and the minimax property of their eigenvalues. The energy limitation for passive system is best exhibited by a natural setting of the problem in a function space format; a format lacking thus far in the classical network theory approach. In this manner, the interplay between the quadratic energy forms and a set of standardized orthonormal input stimuli may be explicitly characterized by a doubly stochastic matrix. This, in turn, leads to a number of interesting and useful inequalities between energies and eigenvalues of the system.

Product of inductive and capacitive operators

The linear passive time-invariant systems are classified according to the reactive energy sign. Subsequently, overall inductive and capacitive systems and their ‘products’ are defined. A key theorem is presented, showing that the product of a pair of linear accretive inductive and capacitive operators corresponds to a linear passive system. The theorem has a broad range of applicability as the proposed proof encompasses lumped as well as distributed networks. In particular ‘the product’ of RL and RC n-port open-circuit impedance matrices represents a passive n-port. The same applies to ‘the product’ of arbitrary inductive and capacitive RLN n-ports open-circuit impedance or short-circuit admittance matrices.

The concept of the phase of a linear n-port and a general dynamical system

The paper outlines the concept of the energy of a linear passive n-port and of an accretive operator representing any linear Hilbert input-output system. Three definitions for phase angle are proposed, interrelated, and interpreted.

An extension of Hazony and Nain's synthesis procedure for n-ports

An extension of Hazony and Nain's passive reciprocal n-port network synthesis procedure to the case of passive nonreciprocal n-port networks is outlined. Generally, more than the minimum number of reactive elements is required for the realization, but the resulting network possesses a series-parallel type of structure which may be useful in certain applications. Transformers are in general required.

Network Synthesis Through Hybrid Matrices

Abstract : It is shown that the hybrid parameter matrix of a passive n-port network is a positive real matrix function. The hybrid, chain and immittance parameter matrices all have the same degree. The concept of combinatorial equivalence is extended from the linear programming field to network synthesis. An n-port extension of the Brune synthesis procedure is given. A novel concept of degree enumeration is given. (Author)