Transfer Immittances Research Articles

Two-Port Characterization and Transfer Immittances of AC-DC Converters–Part II: Applications

This two-part paper presents a general method to model three-phase ac-dc converters as two-port networks for power system stability studies. Part I of the work has developed the two-port network models and identified two types of transfer characteristics that are unique to ac-dc converters and important for system stability. Part II presents the applications of the developed models in stability analysis of different power systems that use ac-dc converters, including grid integration of converter-based generation from wind, PV and other renewable sources, grid-connected dc microgrids and dc distributed power systems, high-voltage dc transmission, as well as hybrid ac-dc power systems. While impedance-based stability analysis has been studied for each of these systems, the new two-port models, especially the transfer immittance models, make it possible and easy to formulate more complete system models to include dynamics and coupling effects that have been ignored or impossible to consider in the past. The methods to study the stability of each type of systems are explained and illustrated by case studies that also highlight the effects of coupling modeled by the transfer immittances on system stability. Each case study also exemplifies a practical stability concern in converter-based power systems.

Two-Port Characterization and Transfer Immittances of AC-DC Converters—Part I: Modeling

This two-part paper presents a general method to model three-phase ac-dc converters in the frequency domain for power system stability studies. In the developed approach, an ac-dc converter is treated as a two-port network connecting an ac and a dc power system, and is characterized by a set of self and transfer immittances. The transfer immittances describe two types of small-signal coupling that are unique to three-phase ac-dc converters: The first type describes the coupling between the ac and dc port and involves a frequency shift by the fundamental; the second type models the coupling over frequency in the ac port current response and involves a frequency shift by twice the fundamental. Together with the self-immittances of each port, the developed models can be used as building blocks to support impedance-based stability analysis of various power systems that involve such converters, including ac, dc, and hybrid ac-dc power generation, transmission and distribution systems. Part I of the paper explains the two-port modeling approach and develops the associated models for a two-level voltage-source converter. Part II presents applications of the developed models for stability analysis of different systems.

FIRST PRINCIPLES CABLE BRAID ELECTROMAGNETIC PENETRATION MODEL

The model for penetration of a wire braid is rigorously formulated. Integral formulas are developed from energy principles for both self and transfer immittances in terms of potentials for the fields. The detailed boundary value problem for the wire braid is also set up in a very efficient manner; the braid wires act as sources for the potentials in the form of a sequence of line multi-poles with unknown coefficients that are determined by means of conditions arising from the wire surface boundary conditions. Approximations are introduced to relate the local properties of the braid wires to a simplified infinite periodic planar geometry. Furthermore, this is used to treat nonuniform coaxial geometries including eccentric interior coaxial arrangements and an exterior ground plane.

New methods of synthesizing transfer functions by applying CCIIs

Abstract Many methods of synthesizing voltage transfer ratios and current transfer ratios have been suggested, but few people have considered transfer immittances which are sometimes important. Simple methods are presented here to synthesize given transfer immittances and current transfer ratios using voltage transfer ratios. The functions used are rational. Similarly, simple methods are proposed to synthesize given voltage transfer ratios and the transfer immittances using current transfer ratios.

Synthesis of RC transfer immittance functions with a minimum number of capacitors

In this paper a method for the realization of RC transfer immittance functions with an unsymmetrical lattice is presented. The method yields minimal capacitor realizations for Z 12( s) with no pole at s = 0 and − y 12( s) having no pole at s = ∞. The number of resistors needed are only two more than the minimum needed.

Minimal realisation of 1st-order RC transfer immittances

Minimal realisations of 1st-order RC transfer immittances are derived. The proposed method of realisation works in the following two steps. First it realises an open-circuit RC voltage-transfer function obtained through the ratio of the specified transfer immittance and a suitably chosen RC driving-point immittance. Next it restores the location of the pole of the driving-point immittance chosen by scaling/adding a resistor in a suitable manner. It gives balanced realisation for nonminimum phase functions and unbalanced realisation for the remaining functions. In each case the realisation requires one, and only one, grounded capacitor except in one special case.

Asymmetrical lattice realisation of RC transfer immittances

Asymmetrical lattice realisation of RC transfer immittances

High-frequency measurement of integrated circuit components

A jig for extending a 50 Ω high frequency measuring system to the pads of a chip device is described. No permanent wire bonds are used and contact may be made with normal aluminium pads. The electrical characterization of the jig up to 1 GHz has been carried out using a General Radio transfer function and immittance bridge, and Y-parameter measurements on typical chip devices have been obtained. The results are applicable to the design of integrated circuits and to device modelling.

Bounds on the sum of element sensitivity magnitudes for network functions

Bounds on the sum of element sensitivity magnitudes for transfer immittances, transfer voltage, and current ratios are established for networks consisting of resistors, capacitors, inductors, and gyrators. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</tex> networks these bounds are given in terms of relevant driving-point functions and their frequency sensitivities. Further, for two-element-kind networks, bounds are given for the quadratic sensitivity index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> .

Active transmission lines driving-point and transfer immittance parameters

In this paper, the driving-point and transfer immittance parameters and gain functions of uniform active transmission lines are derived and examined. The poles and zeros of these functions are identified and used to determine the sinusoidal steady-state characteristics of rcg active lines. Various approximations are introduced to interpret the results.

Computer-Aided Circuit Design by Singular Imbedding

We give a new and powerful method for the direct solution of circuit design problems. The method begins with a prespecified topology and some or all elements undetermined in value. The designer imposes on the circuit any desired set of node-pair voltages, branch currents, or driving point and transfer immittances. Values of circuit elements that satisfy the constraints are directly calculated. This direct method of solution avoids the usual iterative analysis-optimization schemes, reducing computer times by up to three orders of magnitude. A linear set of design equations is formulated by choosing undetermined element currents and node voltages as the variables. Singular elements are introduced to impose the desired constraints. Inequality as well as equality constraints are permitted. Element values are determined from the solution of these equations. In this paper we emphasize our method of solution in relation to dc networks.

Distortion noise in frequency-dependent nonlinear networks

Formulas are derived for the computation of distortion-noise power in frequency-dependent nonlinear networks represented by a Volterra series. The integrals for the distortion-power spectrum contain higher-dimensional Laplace transforms of the corresponding kernels of the Volterra series. An analysis of the frequency-dependent nonlinearity is carried out for transistor feedback amplifiers and f.m. radio-relay amplifiers used in frequency-division-multiplex transmission systems. The nonlinearity of a given order for transistor feedback amplifiers is characterised by a distortion term, and its frequency characteristic, which can be computed or determined from certain intermodulation measurements. A linear f.m. amplifier is completely characterised by its transfer immittance W12 (jω).

Synthesis of 3-terminal RC networks

Transfer-function-synthesis techniques have been utilised to develop a systematic procedure for realising a transformerless general class of 3-terminal RC networks. The necessary and sufficient conditions for the applicability of this technique are stated. It is possible with this technique to realise both minimum-phase as well as nonminimum-phase transfer immittances. The technique can be extended to cover RC multiterminal and active networks as well.Illustrative examples of network realisations are given. This method has also been applied to the problem of synthesis of transfer functions with an operational amplifier.

Practical Realization of a Gyrator Circuit and RC-Gyrator Filters

A gyrator circuit containing only three transistors has been designed by providing an active feedback path such that the circuit behaves like a two-way feedback system with transfer immittance parameters that are equal in magnitude and opposite in phase. At the same time, very low input and output immittances are obtained by this arrangement so that the need for additional negative resistance circuits or negative impedance converters (NIC) to neutralize the residual input and output impedances is obviated. Experimental data exhibit evidence of the excellent performance of the circuit as a gyrator, impedance inverter, and isolator over wide ranges of load and, frequencies that are well below the microwave region. From a theoretical analysis of the circuit, design equations are derived and their application demonstrated by actual design of the gyrator circuit to realize specified open-circuit (o.c.) impedance parameters of the two-port network. These equations show how the network parameters can be individually varied; desired values of the gyration resistance are easily obtained by adjusting single passive elements. The gyrator is then cascaded in between two RC two-port networks to realize complex conjugate poles in such a way that the sensitivity of the poles due to variation in the gyration resistance is minimized. Experimental study of the frequency response of the filter and the sensitivity of the poles when the gyration resistance is varied gives very good results in agreement with theory.

Immittance synthesis in the non-reciprocal domain

Immittance synthesis may be carried out with greater freedom and generality in the non-reciprocal domain. The method described makes use of a non-reciprocal element called the unitor. A required realisation is first found as the driving-point immittance of a non-reciprocal network containing one or more unitors; then, if desired, each unitor element may be substituted by a passive reciprocal subnetwork without changing the value of the driving-point immittance. Otherwise, the immittance is left in non-reciprocal form and is readily realisable with an electronic representation of the unitor(s). The method may be extended in a straightforward manner to transfer immittance synthesis.

The Z-Matrix Parameters of Tapered Transmission Lines

This paper presents an improved method of computing the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -matrix parameters of 2-port tapered transmission lines. Linear second-order differential equations, in which the tapering information is contained in one variable coefficient, are derived for the transfer immittances; from the solutions of these the driving point impedances are found by differentiation and algebraic substitution techniques. As an example, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -matrix parameters for Jacobs' "generalized exponential" line are found.