Two-port Parameters Research Articles

Solvable nonuniform distributed parameter Y-Z-KY networks

A solvable nonuniform distributed parameter (NUDP) Y-Z-KY structure of new shape may be obtained, if the pattern of variation of the per-unit-Iength (PUL) series impedance and that of PUL shunt admittance of a known solvable nonuniform Y-Z-KY structure are mutually interchanged. The two-port four-terminal matrix parameter functions (MPF's) for the new NUDP Y-Z-KY structure are formulated and their relationship with those of the known Y-Z-KY network are derived. A theorem embodying the above result is presented

On Nonuniform Distributed ParameterZ-Y-KZNetworks

The physical shape of nonuniform distributed parameter (NUDP) Z—Y—KZ structure may be changed, if the patterns of variation of the per-unit-length (PUL) parameters of a given NUDP Z—Y—KZ structure are mutually interchanged. Expressions for the two-port four-terminal matrix parameter functions (MPF's) for the new NUDP Z—Y—KZ structure are derived and their relationships with those of the known Z—Y—KZ network are evaluated. A theorem is formulated on the basis of the results yielded by the mutual interchange of the patterns of variation of the PUL parameters of the NUDP Z—Y—KZ structure.

Automated Network Analyzers for the 0.9- to 12.4-GHz Range

Two highly accurate automated network analyzers have been developed to cover the frequency ranges of 0.9 to 4.2 GHz and 3.7 to 12.4 GHz. In addition to the directly measured quantities of insertion loss and phase, the analyzers provide insertion delay, impedance, and two-port parameters as derived quantities. The functional architecture of the systems is described along with some of the novel techniques used to obtain the high signal-to-noise ratios and system stabilities needed for the precise measurements of loss, phase, and delay. General descriptions of these techniques are given along with some of the design considerations. Experimental results that demonstrate measurement accuracy are presented for one-port and two-port devices using both coaxial and waveguide connectors.

Two-port four-terminal matrix parameter functions of solvabel distributed parameter Y-Z-KY networks

The two-port four-terminal matrix parameter functions (MPF's) are obtained in terms of current solution and per-unit-length (PUL) parameters of any solvable four-terminal distributed parameter (DP) network made up of two dielectric films separated by a resistive film †. It is shown that any voltage-current two-port matrix parameter of such a DP network is always available as the ratio of two linear relationships of the two-port four terminal MPF's.

Cost function minimization in RC ladder networks

For a canonic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> ladder network realized from specified two-port parameters, a proper transformation is applied so as to generate a family of equivalent networks in which the total resistance, total capacitance, and the gain vary continuously with respect to a single variable. A straightforward method is subsequently developed for the minimization of the cost function which combines the above three components with weighting factors.

A Stability Test for a Class of Linear, Active Two-Ports with Uncertain Parameters

A new procedure is presented for testing the stability of lumped, linear, active, time-invariant two-ports. The mare advantage of this procedure is that it can consider conditional stability when the passive terminating impedances are limited to only a small subset of all passive impedances represented by the entire right half of the complex plane (RHP). The method can be easily computerized. It is especially useful when only the numerical values of the two-port parameters at various frequencies are known. One version of such a computer program is currently in use at Bell Laboratories for studying the stability properties of two-wire voice-frequency telephone circuits containing E6 type repeaters.

The effect of feedback on noise figure

Exact formulas for the effect of series and Shunt feedback on noise figure are derived. The resulting noise figure is expressed by the feedback impedance, the two-port parameters, and the noise parameters of the device without feedback. The formulas are useful when considering the effect of biasing network and package elements on noise figure.

Source Mismatch Effects on Measurements of Linear Two-Port Noise Temperatures

A noticeable source mismatch occurs in measurements of noise parameters of a linear two-port, since an admittance-transformer network between the source and the two-port must be inserted. A generalized analysis of the source mismatch effects on noise measurements, which considers the dependence of the noise performance of the two-port on the input admittance, is presented here. On this basis, two types of noise generators are considered and compared with each other.

Numerical Determination of Two-Port Parameters from Measured Unrestricted Data

A procedure is developed for fitting a large (>3) number of arbitrarily chosen experimental data points to a fractional linear transformation on a complex plane. The transformation coefficients as well as their standard deviations are computed directly from the set of measured impedances or reflection coefficients, without any resort to graphical procedures. The procedure can be applied to linear reciprocal two-ports.

On the Existence Range of the S Parameters of a Passive Two-Port Network (Short Papers)

The existence range of the S parameters of a passive two-port is analyzed and various limitations on their moduli are deduced. In particular, it is shown that when three moduli are given, the last, in general, may be upper and lower bounded by passivity conditions.

On the Calibration Process of Automatic Network Analyzer Systems (Short Papers)

Formulas are presented for the direct calculation of the scattering parameters of a linear two-port, when it is measured by an imperfect network analyzer. Depending on the hardware configuration of the test set, the measurement system is represented by one of two flowgraph models. In both models presented, leakage paths are included. The error parameters, i.e., the scattering parameters of the measuring system, are six respective ten complex numbers for each frequency of interest. A calibration procedure, where measurements are made on standards, will determine the error parameters. One of many possible calibration procedures is briefly described. By using explicit formulas instead of iterative methods, the computing time for the correction of the scattering parameters of the unknown two-port is significantly reduced. The addition of leakage paths will only have a minor effect on computational complexity while measurement accuracy will increase.

Author's reply to Comments on 'Two-Port Four-Terminal Matrix Parameter Functions of Solvable Distributed Parameter Z-Y-KZ Networks'

Author's reply to Comments on 'Two-Port Four-Terminal Matrix Parameter Functions of Solvable Distributed Parameter Z-Y-KZ Networks'

Computer-Aided Analysis of Estuarine Dynamics Simulated by a Distributed Parameter Model

A simulation model of water pollution dynamics for computer-aided analysis of water quality along an estuary is developed. The model is based on the analytical solution of the diffusion equation describing the pollution concentration when the vertical and lateral dynamics of the estuary are negligible. The estuary is simulated by a cascade connection of uniform distributed parameter networks which represent estuary segments. Each distributed parameter network is treated as a two-port device whose input-output characteristics in the frequency domain are given by its transmission matrix. An algorithm is given for approximating the two-port parameters to any prescribed accuracy so that the two-port dynamics can be synthesized as an active lumped-parameter electrical network. This network, when used with a computer-aided circuit analysis program, yields the pollution concentration profile along the estuary.

Single-transistor all-pass networks

A network configuration consisting of a resistive twoport bridged by a lossless one-port is considered. It is shown that in certain cases this configuration is capable of realizing a voltage transfer function equal to that of a constant-resistance passive lattice. As a special case, conditions are derived on the two-port parameters for the structure to be all pass. It is determined that a single transistor suffices to realize the two-port network, thus resulting in a very simple all-pass structure; only one coil, one capacitor, and one transistor are necessary to realize a second-degree all-pass voltage transfer function. Higher order transfer functions can be realized by adding an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</tex> branch per each additional second-order factor to the same transistor circuit. In the second-order case, losses in the coil can be compensated. In higher order realizations coil losses cannot be compensated, but a design technique which achieves an arbitrarily close approximation to the desired all-pass transfer-function is presented. Methods of cascading lower order sections are discussed and experimental results are given.

Solvable Non-uniform Distributed ParameterZ-Y-KZNetworks and Their Two-port Four-terminal Matrix Parameters

A systematic procedure for the evaluation of all the voltage-current network matrix parameters of any solvable four-terminal two-port distributed parameter (DP) network, consisting of two resistive films separated by a dielectric film, is outlined for the first time. Six algebraic expressions to be identified as the two-port four-terminal matrix parameter functions (MPF's) are derived in terms of voltage (or current) solution and per unit length (PUL) parameters of the four-terminal DP structure. It is established that any two-port matrix parameter of a four-terminal DP network may be obtained as the ratio of two linear expressions involving the two-port four-terminal MPF's.

Application of Topological Formulas to Distributed Parameter Networks

Topological formulas for lumped electrical networks are extended to distributed parameter networks, and explicit expressions are obtained for the two-port parameters of a non-uniform transmission line. The results agree with those derived earlier by Protonotarios and Wing following a different procedure.

Notes on the Conjugate Matched Two-Port As an UHF Amplifier (Short Papers)

Because of the relative simplicity of measurement of scattering parameters of active two-ports at frequencies up to the lower microwave region, investigations have been made into the application of these parameters to the design of UHF amplifiers. The theory of generalized scattering parameters has been developed by Kurokawa, applied to two-port power-flow analysis by Bodway, and used in the design of a single-stage UHF amplifier by Froehner. In this last paper, the bandwidth limitations imposed by the matching networks were not considered, nor was the capacitive matching arrangement to a purely resistive load fully developed. Both of these topics are the subject of this short paper, in which the relevant design expressions are also given.

Representation of Two-Port Networks by Chan-Mai Graphs

Representation of two-port networks by Chan-Mai graphs has been discussed. It is observed that the proposed model is superior to the signal flowgraph model, while retaining all its advantages. Elementary transformations of Chan-Mai graphs are described with special reference to their use in two-port parameter interconversions by inspection. A Chan-Mai cascade is defined and used for computing the overall chain matrix of n two-port networks in cascade.

Two-port four-terminal matrix parameter functions of solvable distributed parameter Z-Y-KZ networks

Six algebraic expressions identified as the two-port four-terminal matrix parameter functions (MPF's) are derived in terms of voltage-solution and per-unit-length (PUL) parameters of any solvable four-terminal distributed-parameter (DP) network consisting of two resistive films separated by a dielectric film. Any voltage-current two-port matrix parameter of the DP network is readily obtainable as the ratio of two linear expressions involving the two-port four-terminal MPF's.

Driving-point immittance functions of nonuniform lc, rcg, rlg and rlcg pseudo-distortionless transmission lines

The pole-zero distributions of the driving-point immittance functions of nonuniform lc, rcg, rlg and rlcg pseudo-distortionless transmission lines are examinedusing classical Sturn-Liouville theory. The results are applicable to any of the other two-port parameters and the conclusions parallel many of the powerful theorems concerning lumped, passive networks. The pseudo-distortionless line is a new class of line having interesting pole-zero characteristics.