Short-circuit Impedance Research Articles

On the invariance of the ratio of open- and short-circuit impedances in linear networks

On the invariance of the ratio of open- and short-circuit impedances in linear networks

On the invariance of the ratio of open- and short-circuit impedances in linear networks

On the invariance of the ratio of open- and short-circuit impedances in linear networks

On the invariance of the ratio of open and short circuit impedances in linear networks

On the invariance of the ratio of open and short circuit impedances in linear networks

Open and short circuit impedances in linear networks

Open and short circuit impedances in linear networks

Active nonreciprocal realisation of the compact symmetrical network for transfer-function synthesis

The well known method of realising a prescribed short-circuit transfer admittance function or open-circuit transfer impedance function (having real- or imaginary-frequency poles with unspecified associated driving-point immittances) as a compact symmetrical lattice is applied to a nonreciprocal form with the advantage of avoiding the lattice-to-ladder conversion problem. An example is given of an open-circuit transfer impedance function having real-frequency poles, requiring LC elements, which (if ideal transformers are ruled out) needs a smaller total amount of L or C than its reciprocal equivalent. In the RC case, Ozaki presented a method of realising a compact symmetrical network in the form of two parallel passive RC networks without the need for the intermediate lattice form. Accordingly, comparison is made between the nonreciprocal and Ozaki's method; two examples are given—one minimum-phase, the other non-minimum-phase—for both of which the nonreciprocal method is found to require substantially fewer passive components.

Synthesis of a Variable-Parameter One-Port

It is shown that a positive real function containing a parameter n^2 \geq 0 in the form of a linear function can be realized as the input impedance of a nonbilateral passive two-port terminated in a loaded n: 1 ideal transformer. The same impedance can also be synthesized by a pair of bilateral two-ports, each of which is terminated in a loaded n: 1 or 1 : n ideal transformer. The method of synthesis for the case where n^2 is a complex variable is also given. It is found that any two positive real functions can be realized as the open-circuit and the short-circuit driving-point impedances of a nonbilateral two-port or, under additional conditions, of a bilateral two-port.

The Realizability of Multiport Structures Obtained by Imbedding a Tunnel Diode in a Lossless Reciprocal Network

Necessary and sufficient conditions are presented for the realization of the short-circuit admittance matrix or open-circuit impedance matrix of the most general n-port structures characterized by such matrices obtained by imbedding a tunnel diode, represented by a parallel combination of a capacitor and a negative resistor, in a finite lossless reciprocal network. Techniques for realizing prescribed immittance matrices are included.

An analysis of base resistance for alloy junction transistors

For the circular disk type of transistor geometry, as commonly used in alloy junction transistors, base resistance is determined by treating it as a boundary value problem. This treatment results from consideration of the over-all behavior of both minority and majority charge carriers in the base region and leads to an expression for base spreading resistance in terms of alpha, frequency, resistivity, and transistor dimensions. Further consideration of this over-all charge carrier behavior leads to a determination of the entire common-emitter short-circuit input impedance, which in general is complex. Comparison with measurement shows that this impedance, which includes the base resistance, can be calculated accurately over a wide frequency range in terms of physical constants, dimensions, frequency, dc emitter bias, and effective minority carrier lifetime in the base region for small-signal operation of low power alloy junction transistors. Application to other types, such as power transistors and diffused-base transistors, may require extension of the present analysis with a considerable increase in complexity. Limitations and extensions of the analysis in its present form are discussed.

Some Properties of Image Circles

Some properties of image circles for four-terminal networks are discussed. A procedure for correcting an image circle, obtained with a Iossy short, is presented. Indirect methods for determining the open and short circuit impedances of a symmetrical four-terminal network are discussed.

Synthesis of Three-Terminal RC Networks

Several methods are available for synthesizing three-terminal RC networks when only two of the three short-circuit admittances or two of the three open-circuit impedances are specified. This paper treats the synthesis problem in which all three functions are given; that is, in which terminal behavior of network is entirely prescribed. There is a discussion of necessary conditions which must be satisfied by a set of short-circuit admittances or open-circuit impedances in order that it correspond to a three-terminal RC network. A synthesis method is then developed by means of which networks can be found for a wide variety of specified functions. By means of well-known correspondences between networks of different kinds of elements, similar synthesis methods are easily derived for LC and RL. network, without mutual inductances.

A Bridge for Measuring Audio-Frequency Transistor Parameters

A bridge is described which measures the small-signal parameters of point contact and junction transistors at a frequency of 1 kc. The impedance parameters of point-contact transistors are measured for the grounded-base connection, while a set of parameters representing a compromise between the impedance parameters and the h parameters is measured for junction transistors operating in either the grounded-base or grounded-emitter connections. This set includes the short-circuit input impedance h11, the short circuit current amplification factor h2l, a paralleled resistance r22 and capacitance C22 representing the open-circuit output impedance, and two feedback resistances r12 and r12' which in the particular case of the grounded-base connection represent the "low-frequency" base resistance rb and the "high-frequency" base resistance rb' respectively. It is also shown that the α cut-off frequency of junction transistors can be calculated with good accuracy from the bridge measurements.

Frequency Variations of Junction-Transistor Parameters

A Theoretical solution for the frequency variation of the four small-signal parameters of a junction transistor has been obtained by extending Shockley's analysis and by taking account of space-charge-layer widening as suggested by J. M. Early. From the results of this solution, it has been possible to explain the experimentally observed frequency variation of open-circuit collector-base admittance of fused-junction p-n-p junction transistors that was reported earlier and is described here in more detail. The theoretical frequency variation of the current-amplification factor and of the other two small-signal parameters (open-circuit voltage-feedback factor h12 and short-circuit input impedance h11, for the grounded-base connection) also is discussed in some detail. Numerical results are included for each of the four parameters in the form of curves of normalized parameters versus relative frequency. Derivation of the voltage-current relations for the theoretical model is given separately in section II. The effect of base-spreading resistance is taken into account in the usual manner by addition of a lumped resistance to the base contact of the theoretical model.

Delay networks having maximally flat frequency characteristics

A lumped-constant equivalent of a transmission line can be obtained in general in the form of a symmetrical lattice, in which the series and lattice arms are inverse and approximate respectively to the short-circuit and open-circuit impedances of half the line. One such set of approximations can be derived from the infinite ladder networks (Cauer's canonical form) equivalent to these impedances. These approximations produce all-pass constant-impedance networks (dissipation being neglected) in which the delay is maximally flat in the sense that the first 2m ? 1 derivatives of the delay with respect to frequency are zero at the origin; m is an integer expressing the order of the approximation.

The Measurement of the Permeability of Low-conductivity Ferromagnetic Materials at Centimetre Wavelengths

A waveguide impedance method for the measurement of the permeability of low-conductivity ferromagnetic materials at centimetre wavelengths is described. The method avoids the difficulties and anomalies present in earlier measurements. The complex magnetic and dielectric properties of a specimen filling a section of waveguide are derived from standing-wave measurements of the short-circuit and open-circuit impedances of the section. The experimental apparatus and techniques which have been employed at wavelengths of 60-20 cm., 15-6 cm., 3 cm. and 1¼ cm. are described, and some typical results of measurements on γ-ferric oxide are given. It is shown that the observed magnetic dispersion is an inherent property of the material, and is not attributable to skin-effect.

Note on the Measurement of Transformer Turns-Ratio

This note shows that in many important cases the turns-ratio of iron-core transformers is given by the simple relation N 1 /N 2 = √X sc1 /X sc2 , in which X sc1 and X sc2 are the reactive components of the short-circuit primary and secondary impedance of the windings concerned. The measurements are conveniently made with an impedance or inductance bridge. This equation also gives the turns-ratio of certain air-core transformers.

Copper-Oxide Modulators in Carrier Telephone Systems

Copper-oxide modulators are widely used in telephone systems for translating either single speech channels or groups of speech channels to carrier-frequency locations on the lines. A number of simple circuit arrangements have been developed that enable suppression of certain undesired frequencies to a degree that is impractical in tube modulators. These modulators transmit equally well in either direction and the modulating elements are more nonlinear than in tube modulators. As a result numerous effects are found that ordinarily are not important in the tube arrangements. Analytical studies have been considerably simplified by the use of a small signal, and a large carrier controlling the impedance variation of the copper oxide. It is found in this case that the superposition and reciprocity theorems hold for all the circuits that it has been possible to analyze even though the modulator is made up of nonlinear elements. Open and short-circuit impedance measurements can be made use of as in four-terminal linear networks, and a generalized reflection theory developed. Performance data are given for an idealized modulator under a variety of operating conditions.

Copper-oxide modulators in carrier telephone systems

Copper-oxide modulators are widely used in telephone systems for translating either single speech channels or groups of speech channels to carrier-frequency locations on the lines. A number of simple circuit arrangements have been developed that enable suppression of certain undesired frequencies to a degree that is impractical in tube modulators. These modulators transmit equally well in either direction and the modulating elements are more nonlinear than in tube modulators. As a result numerous effects are found that ordinarily are not important in the tube arrangements. Analytical studies have been considerably simplified by the use of a small signal, and a large carrier controlling the impedance variation of the copper oxide. It is found in this case that the superposition and reciprocity theorems hold for all the circuits that it has been possible to analyze even though the modulator is made up of nonlinear elements. Open and short-circuit impedance measurements can be made use of as in four-terminal linear networks, and a generalized reflection theory developed. Performance data are given for an idealized modulator under a variety of operating conditions.

Copper Oxide Modulators in Carrier Telephone Systems*

Copper oxide modulators are widely used in telephone systems for translating either single speech channels or groups of speech channels to carrier frequency locations on the lines. A number of simple circuit arrangements have been developed that enable suppression of certain undesired frequencies to a degree that is impractical in tube modulators. These modulators transmit equally well in either direction and the modulating elements are more nonlinear than in tube modulators. As a result numerous effects are found that ordinarily are not important in the tube arrangements. Analytical studies have been considerably simplified by the use of a small signal, and a large carrier controlling the impedance variation of the copper oxide. It is found in this case that the superposition and reciprocity theorems hold for all the circuits that it has been possible to analyze even though the modulator is made up of nonlinear elements. Open and short-circuit impedance measurements can be made use of as in four-terminal linear networks, and a generalized reflection theory developed. Performance data are given for an idealized modulator under a variety of operating conditions.

Transmission Characteristics of Electric Wave-Filters

The transmission loss characteristic of a transmitting network as a function of frequency is an index of the network's steady-state selective properties. Methods of calculation heretofore employed to determine these characteristics for composite wave-filters are long and tedious. This paper gives a method for such determinations which greatly simplifies and shortens the calculations by the introduction of a system of charts. Account is taken of the effects of both wave-filter dissipation and terminal conditions. The method is based upon formulae containing new parameters, called “image parameters,” which are the natural ones to use with composite wave-filters. A detailed illustration of the use of this chart calculation method is given and the transmission losses so obtained are found to agree, except for differences which in practice are negligible, with those obtained by long direct computation. In the Appendix are derived two sets of corresponding formulae which are applicable to a linear transducer of the most general type, namely, an active, dissymmetrical one; the one set contains image parameters and the other set recurrent parameters. An impedance relation is found to exist between the four open-circuit and short-circuit impedances of a linear transducer even in the must general case. Reduction of these formulae to the more usual case of a passive linear transducer is also made, those containing the image parameters being especially applicable to the case of composite wave-filters.

Stray losses on transformers

The object of this paper is to obtain a convenient method of evaluating the actual losses in the copper of a transformer and in figuring the regulation. The effects of various factors on the copper loss of transformers are discussed. It is pointed out that they are, as a rule, negligible in well designed transformers. It is shown theoretically that the copper loss and regulation of a mutual inductance may be derived from its short circuit loss and impedance voltage. The transformer differs from the mutual inductance, due to the fact that the primary and secondary inductances are functions of the induction in the iron. It might be inferred therefore that the short circuit losses, as obtained in the ordinary way, might differ from the equivalent quantities obtained under full load condition. The equation derived in Section 2 furnishes a method of testing to obtain this equivalent short circuit loss under full load conditions. To ascertain if the values of short circuit loss and impedance, obtained in this way, differ from those obtained in the ordinary way, tests were made by both methods yielding results which, after proper corrections were made, checked very closely. Results of tests are tabulated. Practical formulas for figuring copper loss and regulation are given. Recommendations are made as to tests and formulas to be used for obtaining true copper loss and regulation.