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Linear microwave circuit analysis by sparse-matrix techniques is discussed. Optimum equation ordering and pivoting are proposed to reduce execution time, storage requirement, and to improve accuracy. A direct first-order sensitivity method using sparse-matrix techniques is proposed and compared with the adjoint network method. Details on the implemented program and a numerical example are given.

The instrument described here is essentially a time-encoder, which directly gives a digital read-out of capacitance, inductance or resistance, by measuring the transient response of an RC or RL circuit to a step-voltage input. This simple device can easily achieve high accuracy, which mainly depends upon three resistance standards. Time-encoding permits fast measurement, and impressively wide range, covering several decades, substantially independent of the dissipation factors of capacitance or inductance. It can be used as a laboratory instrument or for batching operations in the mass manufacture of electronic components and sampling reactive transducers on board an instrumented space vehicle. High speed of measurement and availability of digital read-out make it fit ideally into computer interfaces. Problems peculiar to the device in sampling applications are discussed in detail.

Recent studies of SGEMP circuit hardening techniques indicate that the ferrite bead is an ideal component for these purposes. However, to many designers, its ability to introduce high-frequency losses into a circuit is still widely misunderstood. In this paper, the basic attenuation properties of ferrite shielding beads are discussed in detail, as well as other important parameters and environmental considerations which might affect their usefulness in a SGEMP reduction application. Analytical techniques to predict insertion loss ratios in circuitry with beads are developed, and the effects of gapping and dc bias on the effective impedance levels presented by ferrite beads are examined.

This paper shows the conditions affecting the magnitude and rate of rise of recovery voltage at the terminals of an oil circuit breaker upon interruption of a short circuit, and explains their effect in quantitative terms. Factors are presented whose numerical value takes into account the number of phases involved in the short circuit and the ground connections of short circuit and generator, the decrement of short-circuit current previous to interruption, and the effect of unequal reactances in the direct and quadrature axes of synchronous machines. It is also indicated how to take into account the effect of displacement and of initial load current, and the effect of saturation is discussed very briefly. Magnetic oscillograms are presented which verify the most important of the points brought out. The most common locations and a rough idea of the magnitude of the capacitances affecting the rate of rise of recovery voltage for various types of short circuit are indicated. Calculations of the recovery voltage curve for several representative cases, at both low and high voltages, are presented, and in some cases cathode ray oscillograms are presented for comparison with the calculated curves. While no systematic data appear to be available at present regarding the effect of the rate of recovery voltage rise upon circuit breaker operation, several tests showing a very pronounced effect, some of them made by the authors and some by others, are reported briefly.

A novel circuit arrangement that supplies a large current to a circuit breaker under test and then subjects the open terminals to a high recovery voltage has been used in testing the 2,500,000-kva 287.5-kv impulse oil circuit breakers built for the Boulder Dam-Los Angeles transmission line. A description of this arrangement, which makes available several times the apparent power of the testing apparatus, is given in this paper, together with oscillograms which show details of the arc extinction process not previously known, and the results of a study of voltage distribution.

The measuring accuracy and time required for the measurement of iron-free induction coils by the time-pulse method are almost entirely determined by the compensating method employed to allow for the error introduced by the active impedance of the coil under test. The method of compensation based on connecting a discretely variable resistance in series with the inductance not only enables the resistance r of the coil to be determined but also gives a more accurate measurement of the inductance. However, in this case the rapidity of action suffers, since the rate of changing the resistance Ry is limited by transient processes in the RL circuit. Compensation methods based on a change in the supply voltage E0 of the R0 circuit give greater rapidity. The time required to measure the inductance increases negligibly on using these methods, since noncontact switches may be used to vary the voltage E0. The greatest rapidity of action is achieved by using the voltage in the test coil itself as the corrective agent, since in this case the rather slow-acting circuits for determining the r/R0 ratio are unnecessary. However, with this method of compensation the accuracy of the measurements is some four times worse than in the case of a linear variation of the additional voltage.

This paper proposes an original booster of a newtype which is applied for almost all kinds of discharge lamps as the starter.The booster consists essentially of two closed circuits: the first closed circuit including an electric source, a linear inductor and a capacitor in series connection; and the second closed circuit including a capacitor common to the first closed circuit, a bi-directional diode thyristor and a nonlinear inductor. The nonlinear inductor of the second closed circuit is characterized by functions of inducing the backswing voltage due to its distributed effective capacitance on the unsaturated state and providing high saturable voltage against impressed voltage of high frequency.These two circuits act continuously and alternately to generate high-amplitude oscillating voltage across the capacitor, that is, the nonlinear inductor checks the thyristor's conduction for a given time at every cycle of oscillation by the induction of the backswing voltage and by the subsequent saturating characteristics thereof, while the capacitor is linearly charged by the electric source through the linear inductor giving a constant-current function.Consequently, an output voltage across the capacitor is boosted by about ten times the source voltage or the break-over voltage of the thyristor.It is also disclosed that such boosted output voltage can be controlled arbitrarily by adding a bias means for the nonlinear inductor.The particular significance of this newtype booster lies in its simplified construction.

A new dimension has been added to monolithic integrated circuit (IC) voltage regulators. A combination of circuit, device and processing innovations has led to the development of the ?A7800 series of 3-lead, 20-watt voltage regulators which feature output current capability in excess of 1A, low noise, and excellent regulation. They are available in fixed output voltage options covering the range of 5V to 30V using a built-in internal resistor matrix.

A discussion of a laboratory experiment involving a parallel LC circuit containing a real inductor (RL ≢ 0) is presented. By choosing component values to be confined to certain ranges, equations are presented for the (1) ratio of the output to input voltages, (2) Q of the circuit, and (3) phase of the output signal relative to the input. It is found that the phase goes to zero as the frequency decreases when a real inductor is used, rather than to π/2 as is the case for an ideal inductor (RL = 0). Experimental results are presented.

In a recent paper ``Similitude of Critical Conditions in Ferroresonant Circuits,''24 a generalized solution for the critical conditions of the series circuit was given. The same type of generalized treatment when applied to the parallel circuit yields a number of interesting conclusions to supplement those found for the series circuit.

In certain nonlinear systems, a form of frequency response has been observed in which the peak is bent over to the right or left depending on the type of nonlinearity. It will be shown that a similar response may be obtained in the RC phase-shift feedback circuit by inserting a nonlinear resistor, such as a thyrite, in the feedback loop. This circuit is discussed with emphasis on a graphical sinusoidal analysis of some general applicability which predicts its frequency response. An informative physical interpretation is also obtained from the analysis of the triple-valued region in the response and of the "jump" phenomena. The method is essentially a graphical superposition of the voltageresistance characteristic of the nonlinear resistor upon the voltage-resistance characteristics (with frequency as a parameter) of the circuit between the two points where the nonlinear resistor is intended to be placed. The points of intersection satisfy both sets of characteristics, and therefore yield the response of the circuit. The method is also applied to a series RLC circuit containing a nonlinear iron core inductor, for which current-inductance curves are super-imposed.

The following problem is investigated: given any polynomial N ( s ) of the form N(s)= ∏ l n (s+p i ) ∏ l m (s+s i ) what are the necessary and sufficient conditions that N ( s ) be formed in the following manner: N(s)=A 0 ∏(s+a i ) + B i ∏(s+b i ) A 0 , B 0 > O where the − a i and − b i alternate at most in pairs along the negative real axis. Such formation is necessary for the − p i and − s i to be the natural frequencies of a network consisting of RC and RL subnetworks joined at two terminals. It is shown that N ( s ) may be so formed if and only if (a) for n=0, Σ l m arg s i ≥ π 2 (b) for n > 0, p i > 0 and Σ l m arg s i π 2 Also, a simple method is presented for finding suitable a i and b i whenever formation is possible. The result is expected to have application in the synthesis of both passive and active networks.

The theory and line of reasoning used in developing this circuit are described. The circuit elements aside from the crystal are resistors and capacitances. The type 57 tube was found to fulfill to a large measure the requirements of a sufficiently high mutual conductance and a fairly high internal plate resistance in the oscillating state. A method of varying the frequency of oscillation is described. The stability using a seven-megacycle crystal was found to be within about one in twenty million for a ten per cent variation in either or both the filament and plate voltages.

An exact electrical analogue is given for the thermal system between the collector junction and the constant-temperature environment of a transistor. For this circuit analogue, the voltage response to an applied current is equivalent to the temperature response of the collector junction to an applied-power dissipation. The objective of this paper is (1) to prove that this thermal equivalent circuit is entirely consistent with the rigorous, academic approach to the problem, which is to solve a boundary-value problem for heat flow in the transistor system; (2) to present an experimental method for obtaining the circuit parameters in the thermal equivalent circuit; and (3) to demonstrate the utility of the thermal equivalent circuit for the circuit designer and the transistor designer.

The influence of saturation phenomena in series reactors on the circuit performance of load ratio control equipment is discussed. It is shown that unless care is exercised in the design of these reactors, gross distortion may be introduced into the circuit, resulting in obtaining across the reactor voltage peaks which on the one hand may endanger the insulation, and on the other hand greatly increase the rupturing duty on the circuit breaking devices. Formulas are developed which show what proportion of line voltage is absorbed by a series reactor subject to magnetic saturation. It is shown that this voltage can be expressed in terms of the reactive constants of which the circuit is composed, and that it is independent of the current or voltage wave form. Numerical solutions are given in the shape of curves, assuming that the magnetic circuit of the reactor is made up of typical transformer steel. The great influence of a small air gap in the magnetic circuit in reducing these voltages is shown.

An active RC realization scheme of a bilinear RL impedance is presented. The active device incorporated is a current-controlled current source. Discussions pertaining to p-factor maximization and sensitivity minimization are also appended.

One of the most useful small-signal equivalent circuit representations is based on a m-equivalent circuit representation of the transistor in a common-emitter connection. This m-equivalent circuit representation is more readily and commonly employed in circuit analysis or design in comparison with a ^'-equivalent circuit representation. The variation of equivalent circuit parameters at high frequencies in the π-equivalent circuit representation was determined by Giacoletto experimentally. Unfortunately, however, we have no example but the above, in spite of this problem being very common and important. The exact expression for π-equivalent circuit parameters is too complicated to be calculated. The result may be somewhat simplified by expanding the hyperbolic function into a Taylor series and retaining only the first few terms. Numerical values of these approximate expressions are calculated and then compared with values calculated from the corresponding exact expression. Furthermore, w-equivalen...

Some apparent anomalies in oscillograms obtained in the course of electrical impulse tests of a material used in the construction of lightning arresters have led to a fuller investigation of the behaviour of the test circuit as applied to the study of a material with a non-linear voltage-current characteristic.This investigation has been carried out by evaluation of solutions of the equations of a simplified form of the circuit numerically and by means of the differential analyser, and by further oscillograms taken under conditions suggested by the behaviour of these solutions.The apparent anomalies which originally gave rise to the investigation have been shown to be a real feature of the response of the circuit, and not a spurious effect due to the recording apparatus, and the study of the initial response of the circuit to the impulse leads to the interpretation of another feature of the oscillographic records which had been previously regarded as an instrumental error.

Chapter IV. The general method of designing any but the simplest of circuits is to draw a vector diagram and then calculate circuit constants that will give vectors of the proper lengths and directions. This method has been exemplified by designing a circuit in which the grid is tuned and contains the load. The plate circuit is magnetically coupled and is partially tuned to act as an harmonic by-pass. A numerical example of the method is given. Chapter V.-The criteria for double periodicity of two coupled circuits are first developed and it is shown that for a singly periodic circuit the secondary volt-amperes cannot exceed the primary. The maximum power which can be transferred to the secondary is limited by this requirement. A greater amount of energy can be transferred by a closer coupling, which results in making the circuit doubly periodic, and tuning the circuits individually to other than the desired frequency. High power will then be delivered on only one of the stable frequencies. The method of designing a circuit to deliver energy under such conditions is developed. Such a circuit always tends to oscillate at the frequency giving least load. It is shown that grid keying cannot be used without other modifications of the circuit.

The small-signal equivalent parallel capacity of forward-biased semiconductor junctions is strongly dependent on the current. At very low currents (less than 10 µa for a junction area of 1 mm2) the capacity appears to be chiefly due to space charge effects. For currents up to approximately 100 µa, the capacity complies with Shockley's predicted low-level theory. For larger currents, however, there is a definite deviation from the low-level diffusion predominance and capacity reaches a maximum after which it decreases through zero and then goes to large inductive values. The latter phenomena is explained, qualitatively, by considering an inductance in series with the diffusion capacity. The capacity increases linearly with current but the inductance (due to conductivity modulation) increases faster. The result is that a change from an equivalent RC circuit to an equivalent RL circuit is made at high enough currents (5 ma is a typical value for the 1 mm2junction area). Measurements were made on abrupt silicon junction diodes with junction areas of about 7 × 10-4, 10-2, 10-1cm2and on the emitter junction (about 5 × 10-5cm2) of a diffused base silicon transistor.

The short-circuit collector current of many silicon transistors is proportional to the exponential of the emitter-base voltage over 9 decades of collector current ( 10^{-11} a to 10^{-2} a ). Such a transistor may be connected as a three-terminal feedback network in an operational amplifier to obtain accurate logarithmic transfer response over a dynamic range of 9 decades.

Three principal categories have been known in electrical circuitry so far. They are the lumped-constant (0-dimensional) circuit, distributed-constant (1-dimensional) circuit, and waveguide (3-dimensional) circuit. The planar circuit to be discussed in general in this paper is a circuit category that should be positioned as a 2-dimensional circuit. It is defined as an "electrical circuit having dimensions comparable to the wavelength in two directions, but much less thickness in one direction." The main subject of this paper is the computer analysis of an arbitrarily shaped, triplate planar circuit. It is shown that a computer analysis based upon a contour-integral solution of the wave equation offers an accurate and efficient tool in the design of the planar circuit. Results of some computer calculations are described. It is also shown that the circuit parameters can be derived directly from Green's function of the wave equation when the shape of the circuit is relatively simple. Examples of this sort of analysis are also shown for comparison with the computer analysis.

Full voltage line to ground fault tests are performed on typical potential devices and the subsidence transient recorded. To show the worst case of residual voltage, faults are initiated while the primary voltage is passing through crest and zero.

The microwave circuit characteristics of bulk GaAs transit-time mode and limited space-charge accumulation (LSA) mode oscillators have been evaluated experimentally and theoretically. Experimental measurements were performed with a waveguide-coaxial microwave circuit having two experimental degrees of freedom in which the circuit radiation impedance at the device contacts was evaluated by a dyadic Green's function method. Experiments conducted in three rectangular waveguide circuits at fixed bias voltage have established that the LSA mode frequency tuning range is determined by the magnitude and variation of the circuit series inductive reactance X L relative to the device low-field resistance R 0 . At a bias voltage which is twice threshold the tuning range is given by 1/2.4\leq X_{L}/R_{0}\leq 2.4 . No fixed, linear equivalent circuit characterizes the LSA mode. Analysis and experimental results indicate that the device impedance of small-signal transit-time mode oscillators changes from a passive parallel RC impedance well below threshold to an impedance just above threshold which can be approximated by a series RLC circuit. The series L and C decrease linearly with transit-time mode harmonic order number.

The superposition integral is used to express the voltage produced in the inductance of a tuned circuit in response to a voltage impulse of exponential form. The expression is given in terms of the voltage and time constant of the impulse and the frequency and decrement of the oscillating circuit. This method is more direct and more easily manageable than the conventional method which expresses the relations in terms of the current produced in the secondary or oscillating circuit in terms of the voltage applied to this circuit by the primary or exciting source. The conventional equation, Ldi/dt+Ri+q/C=E may be quite troublesome with certain forms of voltage E. Comparisons are made between oscillograms of an experimental circuit and curves calculated from theory. A simple graphical method is given for determining the constants of an exponential impulse from the response curve and known constants of the oscillating circuit. General conclusions are drawn which are of interest relative to radio interference.

A circuit design method for linear circuits is needed which will adequately predict circuit per formance as a function of component tolerances. This paper describes a method which weights the probable component variation from its nominal value into one of three groups; the group assignment depends on how seriously the component variation affects over-all performance This technique, identified as the quantized probability design (QPD) method, is compared with the absolute worst case (AWC), the Taylor worst case (TWC), and the uniform probability (UP) methods. The QPD procedure is given, based on the circuit performance equation. Two linear circuit applications are presented and analyzed whic show the effect each component will have on circuit performance. A comparison of design methods shows that the quantized probability design predicts less amplifier gain variation. Actual experience has shown that a closer correlation exists with the quantized probability design method, and therefore its use for linear circuits is recommended.

An automatic voltage regulator for an alternator consists essentially of a voltage sensitive element which controls, through suitable apparatus, the excitation of an alternator. In the voltage regulator described herein, the voltage sensitive element is a nonlinear bridge circuit. Its output controls, through a phase shifting circuit, a grid-controlled mercury-vapor tube, the output of which is fed into the field circuit of the alternator. The phase shifting circuit employs a fixed condenser and a variable resistance, the latter being obtained from 2 3-electrode vacuum tubes whose grids are controlled by the nonlinear bridge circuit. The regulator is rugged in construction and at constant frequency provides close regulation without apparent hunting or voltage distortion.

The post-zero current that flows in power circuit breakers during the voltage recovery period is calculated from the restored voltage transient, knowing the equivalent circuit for the test circuit. A differential equation for the post-zero current is derived, and numerical methods for solving it by means of an electronic computer are discussed. Data from a typical circuit breaker test are used to illustrate the different numerical methods.

Series RL circuits having a power factor between 40 and 50 percent with a resistor shunting the inductor and drawing one percent of the power are presently used for evaluating breaking capacity of motor starters. Transient recovery voltages of these circuits show anomalies which indicate that test circuits in different laboratories may have widely different characteristics and produce different test results. It is shown that important differences in the transient recovery voltage may be caused by differences in the effective capacitance shunting the series inductor and parasitic inductance in the shunt resistor. Test circuit recovery voltages are compared with representative recovery voltages of induction motors.

An active HC circuit suitable for the realization of an inductor is presented. Adjustment or the passive parameters lead to the realization of a bilinear or a linear RL impedance in the circuit. An ideal inductor is also realizable in the circuit whose value can be abitrarily changed. The circuit is therefore conveniently used to form a sinewave generator whose frequency can be varied over a wide range. The theoretical findings are experimentally supported.

Static constant-current circuits have been constructed by connecting an iron-core reactor, with predetermined characteristics, in parallel with a capacitor of a specified size such that the resultant input current is independent of line voltage. This parallel circuit is connected in series with the element through which the current is to be regulated. The current will remain essentially constant for large variations in line voltage; large variations in load impedance; or a variation in both quantities simultaneously as long as the variation in voltage across the parallel circuit does not exceed certain limits. This type of circuit is useful for applications where a constant heating independent of line voltage is desired; for series lighting circuits; and vacuum-tube filament circuits.

An equivalent circuit for a cycloconverter is developed which is valid for both ac and dc outputs. A relatively simple and straightforward derivation is presented which results in a new insight into the real reactive voltage drops in cycloconverter power circuits. Applications of this equivalent circuit in the analysis of power systems are discussed and possible extensions of the equivalent circuit are suggested.

A simple transistorized pulse voltage dividing circuit based on a sampling technique is described. The circuit makes use of the fact that the voltage rise of a capacitor is a linear function of V 1 V 2 when it is charged with a constant current which is proportional to ane voltage input V1 during a time t which is inversely proportional to another voltage input V2. Input pulse voltages are required to be the flat topped positive input pulses of some 10 μs duration and 5–20 volt in amplitude. The linearity of the circuit for a constant value of V2 was better than 2%. The circuit was used for the measurement of the mass distribution of the fragments resulting from the thermal neutron induced fission of U235 with the aid of a back-to-back arrangement of Si surface barrier type solid detectors.

A synthesis procedure that can realize any RCrealizable rational transfer function as the open-circuit-voltage transfer ratio of a nonuniform, passive RC distributed circuit is presented. The resulting circuits have a simple, standardized topology and can be readily constructed by thin-film techniques. The synthesis procedure has been completely programmed on a digital computer. From the specification of the transfer function and the electrical properties of the construction materials, the computer produces the complete geometry for the construction of the distributed circuit.

An instability curve of series impedance versus voltage common to the parallel branch of the circuit as in figure 1 can be calculated approximately. If this curve contains maximum and minimum points the circuit will have two states of stability with an intermediate unstable range. Some practical use of this phenomenon has been suggested for circuit control and energy conversion. The circuit which produces reciprocating motion has not been completely analyzed, hence the optimum operating conditions cannot be stated until further knowledge is obtained.

A circuit for the electrical simulation of transient diffusion and flow of material between two volumes is described. It allows such processes to be simulated even when forward and reverse transfer rates between the two volumes are unequal. When the reverse rate is zero, the circuit functions as a very‐high‐input‐impedance integrator of wide dynamic range and high accuracy. The circuit will integrate the current through a given resistor, even when this resistor is time varying or nonlinear. For voltage integration, it can have a minimum input impedance approaching 109 ohms.

A NUMBER of bistable configurations are known which use vacuum tubes and transistors. Each of these requires two active elements and has two stable states. Binary coded decimal counters having ten stable states and using eight active elements, can be made with these devices. Point contact transistors, tetrodes and gas tubes (by virtue of internal positive feedback) exhibit bistability with a single active element. A scale of ten counters can be made with these devices with the use of four active elements. In general, either the speed of response of the reliability is inferior to that obtainable with counters using two active elements per trigger. This paper will consider a method of multistable operation which requires only two active elements, theoretically, for any number of statically stable states. These stable states are achieved by using two active elements in a conventional trigger arrangement. The feedback in the circuit is controlled by a nonlinear load which determines whether the net positive feedback makes the circuit stable or unstable. Thus it is possible to divide the operating range of the trigger into a number of alternately stable and unstable regions.

A relationship is obtained for the nonsingular T transformation that exists between two minimal realisations of the state equations and the Howitt transformation between the corresponding 2-element-kind networks. It is proved that the Howitt transformation can generate all the passive minimal RC or RL equivalent networks that can be generated by the nonsingular T transformation.

A circuit employing one operational amplifier and one analog multiplier is used to produce a voltage output proportional to the quantity t when the input voltage is related to t (e.g., temperature) by at + bt2, where a and b are constants. The determination of the resistor values, the useful operating voltage range, the accuracy of the linearizing process and the effects of changes in the ambient temperature are discussed. Extension of the circuit to higher order polynomial functions is also considered.

As a possible method of increasing the transient stability limits of a long transmission system the author discusses the effects of inserting series resistances into the generator circuits to load the machines during fault conditions and thus retard subsequent overswings.