Total Reactance Research Articles

SATURATION EFFECTS IN THREE-PHASE INDUCTION MOTORS

Abstract An analytical method for the calculation of the effect of magnetic saturation on the leakage reactance of three-phase induction motors is developed and confirmed by experiment. The method is based on assuming an equivalent magnetic circuit and representing the true magnetising characteristic of the iron forming the magnetic circuit, by an analytical function. Since the saturation of the leakage flux paths is related to the geometry of the tooth-tips and to the form of the slot openings, all three types of slot openings, i.e. open, semi-closed and closed, are considered in detail. Using the assumed equivalent magnetic circuit and the true magnetising characteristic together with the design details, the total leakage flux passing through the selected saturable areas is calculated and resolved into its various components. i.e. zig-zag, skew, slot leakage fluxes. From these the associated leakage reactance components are evaluated and the total leakage reactance is formed. The method has been applied...

Effect of rib cage and abdominal restriction on total respiratory resistance and reactance.

In 14 healthy male subjects we studied the effects of rib cage and abdominal strapping on lung volumes, airway resistance (Raw), and total respiratory resistance (Rrs) and reactance (Xrs). Rib cage, as well as abdominal, strapping caused a significant decrease in vital capacity (respectively, -36 and -34%), total lung capacity (TLC) (-31 and -27%), functional residual capacity (FRC) (-28 and -28%), and expiratory reserve volume (-40 and -48%) and an increase in specific airway conductance (+24 and +30%) and in maximal expiratory flow at 50% of control TLC (+47 and +42%). The decrease of residual volume (RV) was significant (-12%) with rib cage strapping only. Abdominal strapping resulted in a minor overall increase in Rrs, whereas rib cage strapping produced a more marked increase at low frequencies; thus a frequency dependence of Rrs was induced. A similar pattern, but with lower absolute values, of Rrs was obtained by thoracic strapping when the subject was breathing at control FRC. Xrs was decreased, especially at low frequencies, with abdominal strapping and even more with thoracic strapping; thus the resonant frequency of the respiratory system was shifted toward higher frequencies. Partitioning Rrs and Xrs into resistance and reactance of lungs and chest wall demonstrated that the different effects of chest wall and abdominal strapping on Rrs and Xrs reflect changes mainly of chest wall mechanics.

The forced oscillation technique in children with respiratory disease.

The single-frequency forced oscillation technique was used to estimate the total respiratory impedance, resistance, and reactance at 2, 4, and 12 Hz of children who had cricoid stenosis (CS; n = 11), provoked bronchoconstriction (PB; n = 6), or cystic fibrosis (CF; n = 13). The selection criteria for patients who had CS and CF were abnormal forced expiratory volume in 1 sec (FEV!) and/or maximal expiratory flow at 50% vital capacity (Vmax 50%). Sixteen of the 17 patients who had CS or PB were found to have resistance (Rrs) values outside the normal range at 4 Hz; at 2 Hz, 14 were found to have abnormal values and, at 12 Hz, only 9. The reactance in the CS and PB groups was somewhat less discriminative than Rrs at all frequencies. Of the 13 patients who had CF, only 4 had abnormal Rrs values; in this clinical condition, the reactance at 2 Hz was the most discriminative variable, being abnormal in 6 of the 13 patients. Irrespective of the clinical group, the Rrs was, in absolute terms, highest at 2 Hz, and it decreased with increasing frequency. This pattern of negative frequency dependence was, however, not obviously specific for any of the tested clinical conditions and offered no information in addition to a single low-frequency determination.

Total Resistance and Reactance in Patients with Respiratory Complaints with and without Airways Obstruction

A comparison was made of the frequency dependence of total respiratory resistance, (Rrs), and reactance (Xrs), determined by a forced oscillation technique in 442 healthy subjects and in 126 patients with respiratory complaints, with or without slight airways obstruction. The comparison was performed by means of a discriminant analysis. The latter demonstrated that the Rrs and Xrs data, measured between 8 and 24 Hz, of patients differ from those of healthy subjects primarily by a decrease of Rrs with frequency associated with more negative Xrs (and thus with an increase in resonant frequency). This probably also applies to patients with more advanced airways obstruction. The addition of the FEV1 values to the analysis provides only a small amount of independent information. The forced oscillation technique thus appears to be a sensitive tool to separate healthy subjects (smokers and nonsmokers) from patients with respiratory complaints associated or not with a reduced FEV1.

Normal Values of Total Respiratory Resistance and Reactance Determined by Forced Oscillations: Influence of Smoking

In 407 healthy male subjects, smokers and nonsmokers, the resistance and reactance of the respiratory system were determined between 4 and 24 Hz, using a forced oscillation technique. The values are significantly correlated with age, weight, height, FEV1, and vital capacity. After standardization of the data for the latter variables, there are no differences between smokers and nonsmokers. The technique thus lacks sensitivity for the detection of the effects of smoking.

Frequency dependence and partitioning of respiratory impedance in dogs.

Total pulmonary resistance (Rt) and reactance (Xt) from 1 to 30 Hz were determined by time series analysis in open-chest vagotomized dogs. Rt and Xt were partitioned by retrograde catheter into central airway resistance (Rc) and reactance (Xc) and peripheral resistance (Rp) and reactance (Xp). Rt, Rc, or Rp did not change with transpulmonary pressure (Pst) from 5 to 15 cmH2O, although Rc tended to decrease and Rp to increase. Vagal stimulation (Vs) and intravenous histamine (H) increased all resistances (R) at all lung volumes (V) and produced an inverse relationship between R and V. The increases in Rt produced by H and Vs were not significantly different at any volume, but H predominantly increased Rp and Vs predominantly increased Rc. In the control (vagotomized) dogs at Pst of 5 cmH2O, Rp/Rt was 0.41 +/- 0.03 (SE). Rp/Rt was significantly increased by H but not by Vs. Control Rt decreased slightly from 5 to 10 Hz and increased from 15 to 30 Hz. The increase of Rt at higher frequencies caused by the frequency dependence of Rc was not changed by H but was augmented by Vs. The slope of Xt and Xc vs. frequency was increased by Vs but not by H. The frequency dependence of Rt and Xt above 10 Hz appears to be caused by inertial losses proximal to the 2-mm airways. Thus central and peripheral bronchoconstriction caused by Vs and H, respectively, could be differentiated by increased frequency dependence of Rt and Xt above 15 Hz.

The longitudinal stability of intense nonrelativistic particle bunches in resistive structures

The longitudinal stability of intense particle bunches is investigated theoretically in the limit of small wall resistivity compared to total reactance. It is shown that both in the absence of resistivity and to lowest order in the resistance that an intense bunch is stable against longitudinal collective modes. An expression is derived for the lowest order instability rate. Application of these results are made to drivers for heavy ion inertial fusion.

DESIGN OF AUXILIARY PHASE WINDINGS FOR SINGLE-PHASE CAPACITOR FRACTIONAL-HORSEPOWER INDUCTION MOTORS

Abstract A method is described for the calculation of the auxiliary-winding parameters of single-phase capacitor motors. The design technique is an extension of that successfully applied to resistance-start motors(1) and is aimed toward assisting the practical design engineer to choose an auxiliary winding which uses the minimum amount of copper while simultaneously satisfying all specifications The equations developed do not use the turns ratio as the main design variable but a new design variable, the ratio of total auxiliary-phase resistance to total auxiliary-phase reactance. The method is equally well suited to computer or non-computer evaluation techniques.

Errors in the measurement of total respiratory resistance and reactance by forced oscillations

The total respiratory resistance determined by means of the forced oscillation technique during spontaneous breathing demonstates a variability which may be due (1) to variations of the resistance itself, (2) to the superposition of rapid oscillatory and slow respiratory signals, (3) to the presence in the breathing signals of harmonics the frequency of which is the same as that of the oscillations. In the present study, we investigate the importance of the third cause of variability, in a mechanical system in which causes 1 and 2 have been excluded. It is shown that the presence of high frequency components in breathing is an important source of error in the measurement of instantaneous resistance and reactance. The error is larger at higher frequency and amplitude of breathing, lower frequency and amplitude of forced oscillations, and in the presence of a high respiratory impedance. The error is likely to be negligible when the frequency of the forced oscillations is high ( e.g. 30 Hz). At lower frequencies, the influence of harmonics in breathing can be corrected by calculating average resistance or reactance values over one or more respiratory cycles.

Active RC Synthesis for Significant Reduction in Magnitudes of Reactive Elements

Low impedance levels and/or large system time constants lead to network realizations with large total reactance values in ordinary passive and active RC synthesis. It is shown how active RC networks may, instead, be designed, in which one may freely a priori specify the total capacitance and the input and output resistances. The basic design philosophy is to assign relatively faroff poles to the passive part of the system. Feedback is used to obtain the desired close-in (large time constant) system poles. In one method, employing a single negative-impedance-converter, any number of system poles may be simultaneously realized. However, the output is very sensitive to variations in active and passive parameter values. Also, the negative-impedance-converter must act as such over the bandwidth of the passive part of the network, which part is much larger than that of the system as a whole. A second approach is far more practical. It employs a cascade of isolated canonic second-order structures, each of which realizes a pair of system poles. The resulting design is much less sensitive to active and passive parameter variations, and is much easier to tune. The structure used is especially suitable for narrow-band filtering. Also, the active element bandwidth need only be of the same order of magnitude as that of the system poles. Design relations are developed and optimized with respect to a figure of merit ASA, being the product of amplifier gain required and system sansitivity to amplifier gain variations.

Active RC Synthesis for Significant Reduction in Magnitudes of Reactive Elements

Active elements may be used to significantly reduce the total reactance required in a network. This paper presents two active RC synthesis techniques for this purpose. One method employs a negative-impedance-converter to realize any number of system poles and reduces the total required capacitance to any desired extent. The resulting design is, however, very sensitive to active and passive parameter values. The second method also permits any prescribed total capacitance but employs a cascade of isolated second-degree sections. Two such sections are presented and optimized with respect to a figure of merit <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{t}AS_{A}</tex> , being the product of total capacitance, required active element gain and system sensitivity to the latter. System transmission zeros may be accommodated to a certain extent.

Capacitance Reduction in Active RC Synthesis†

ABSTRACT Low impedance levels in a network and/or small values of significant time constants lead to large total reactance values in passive RLC realization and in the presently available active RC realization techniques. This paper presents active RC techniques for significant capacitance reduction in such problems. One method is suitable for basically ‘all-pole’ transfer functions, in which any number of left half-plane poles may be simultaneously realized with one low-gain amplifier and a passive RC L-type network. The transfer function is, however, quite sensitive to variations in active and passive network parameters, In another technique, the transfer function is synthesized by means of a cascade of second-degree canonic sections, isolated from each other. Two types of canonic sections are presented and optimized with respect to a figure of merit (R i+ R o) C t, ASA T consisting of the product of the sum of source and load resistors, total capacitance, required gain and system sensitivity to gain va...

Transformer Design for Zero Phase Shift

A design method for obtaining minimum phase shift between output and input of a transformer is described. The method is applicable to precision reference transformers employed in analog computers and servo loops where minimum quadrature voltages are mandatory. A rigorous analysis of the equivalent circuit of the transformer demonstrates that the transformer can be treated as a combination lead and lag network to yield zero phase shift. This is done by making the ratio of primary resistance to primary shunt reactance equal to the quotient of total leakage reactance and load resistance. The procedure consists of l) designing for theoretical zero phase.

The Field of a Dipole with a Tuned Parasite at Constant Power

Theoretical curves are shown of the electric field in the forward direction and in the backward direction for a center-driven half-wave dipole in the presence of a parallel center-tuned parasite of the same length and radius. The ratio of the electric field of the two-antenna array to the field of the driven unit alone at constant power is given as a function of the distance b between the antennas in the range from b = 0 to b = λ 0 , for both the forward direction (the parasite is a reflector) and the backward direction (the parasite is a director). The total reactance of the parasitic antenna is used as a parameter in the form X 22 = X s2 + X 2 where X s2 = X s1 , is the self-reactance of the parasite in the presence of the identical, driven dipole and X 2 is the tuning reactance at the center of the parasite. Values for which curves are shown are X 22 = 20, 10, 0, -10, -20 ohms and X 22 = X s2 or X 2 = 0. Reactances and resistances used are those of the first-order King-Middleton-Tai theory.

The influence of various factors upon the leakage reactance of transformers

This paper investigates the leakage reactance of transformers by means of Roth&apos;s potential-vector method of analysis. The potential vector is divided into three components. The first component gives rise to the normal reactance as calculated by Kapp&apos;s equation; this is termed the “axial reactance.” The second, which is responsible for additional leakage reactance, is termed the “radial component”. The third, which does not lend itself to easy mathematical treatment, is shown to modify the axial term, giving a closer degree of approximation by its inclusion.In order to enable the total leakage reactance of various winding arrangements to be calculated, three Tables are provided. Thus it is possible to allow for the effects of cooling ducts, tappings, and end-turn reinforcement. In Appendix I a comparison is made between the calculated and tested values of the leakage reactance of two commercial transformers having non-uniform distribution of ampereturns.

Interaction Impedance of a System of Circular Pistons

Curves have been calculated for the total radiation resistance and reactance of a single circular piston as a function of frequency when another circular piston is vibrating in the same infinite plane, the distance of separation of the two pistons being a parameter. The curves shown are for equal velocity amplitudes and for phase differences of 0° and 180°. These results enable one to calculate the impedance of a piston when there are present an arbitrary number of pistons in arbitrary phases.

Abridgment of iron losses in turbine generators

In large turbine generators, there is no convenient method for determining the iron losses under load. It is the purpose of this paper to show, analytically, the factors influencing the change in iron loss with load; that on the basis of the flux distributions, the machines can be most conveniently divided into end zones, which present three dimensional problems, and a large central zone, which presents only two dimensional problems. The losses in each part are discussed qualitatively, and the losses in the central zone are obtained quantitatively for an ideal machine in which only the foundamentals of the flux waves are present. Contrary to the usual view, these losses do not vary as the square of the generated voltage, but are predominantly affected by the ratio of the slot to total leakage reactance. The results are given in curves. The complications in the problem introduced by the usual commercial designs by non-sinusoidal field forms, phase bands, etc., are discussed qualitatively.

Abridgment of the reactances of synchronous machines

Until somewhat recently, synchronous machine theory has been satisfied with a relatively few characteristic constants, or reactances, in terms of which the behavior of machines has been calculated. Present theory, however, requires many more coefficients. There are now generally recognized two values each of leakage, synchronous, and transient reactance, which correspond to the two symmetrical axes of magnetization of the armature current and which refer to balanced operation. Negative and zero phase-sequence reactances are also employed to determine operation under unbalanced conditions, and it is possible and desirable to distinguish other reactances. In view of the increasing complexity of the subject it is felt that a critical survey of it is in order and the object of the paper has been to provide that survey. The paper has been divided into two parts. Part I describes and treats of the subject with regard to those factors which are important to application or operating engineers, and to designers. In particular, the major types of reactances which include the synchronous, transient, and phase-sequence reactances, are discussed. These quantities are defined and their methods of test outlined. It appears necessary to consider a second type of transient reactance; namely sub-transient reactance. Both reactances may be determined from short-circuit oscillograms as illustrated in the paper. A table is included which gives the numerical range of reactances for the various types of synchronous machines. Part II discusses the theoretical considerations, with a view to broadening and classifying existing conceptions of reactance. It includes the effect of external reactance on negative phase-sequence reactance and the variation in this latter quantity, depending upon whether current or voltage is impressed on the machine. An important aspect of the division of synchronous reactance into armature reaction and leakage reactance is discussed. Transient reactance is shown to be the difference between synchronous reactance and the ratio of the mutual reactance between armature and field and the total field reactance. Calculations are included to show that the short-circuit and open-circuit time constants are related to each other in a simple manner. The appendixes cover the following subjects: a. Application of the Principle of Superposition to Synchronous Machine Analysis. b. Replacing the Effect of Induced Field Currents by Employing Transient Instead of Synchronous Reactances. c. Significant Rotor Circuits in Addition to the Main Field Winding (which effect transient reactances). d. The Negative Phase-Sequence Reactance of a Synchronous Machine with Negative Phase-Sequence Voltage Impressed. e. Construction of Equivalent Circuits: Concept of Field Leakage Reactance. f. Calculation of Total Field Reactance. g. Relation of the Mutual Reactance Between Armature and Field to the No-Load Excitation Current. h. Relation Between Three-Phase and Single-Phase Reactances. i. Discussion of the System of Notation Used in the Paper. j. Per-Unit Representation of Quantities.

Starting Characteristics and Control of Polyphase Squirrel-Cage Induction Motors

In the application of squirrel-cage induction motors to such severe service as frequent start-and-stop or frequent plugging operation, it is desirable to know how much loss the motor will be required to dissipate, plugging being understood as changing the motor from any speed in one direction to any speed in the opposite direction, by reversing the rotation of the field only. The subject of starting loss is also of interest from the control standpoint-such as the application of auto-transformers for starting purposes, or where an external resistance is inserted in the primary as is done in the control of elevator motors. Consideration is given to the part that the primary and secondary resistance and the total reactance play in the determination and the manipulation of the starting losses; and, as it is true that in many applications the time spent in accelerating the rotor from. rest is useless from the production standpoint, consideration is given to the value of secondary resistance that will give minimum starting time for a given field strength. This involves a method for the determination of the time taken to attain a given speed in general. There are many cases where a motor has already been designed and tested, and is about to be applied on a given job where the cycle of operation is known and includes either starting and stopping or plugging.

Resonance Phenomena in the Low Frequency Circuit of Radio Transmitters

For determining the resonance characteristics of the audio frequency circuits of a radio transmitter, either the primary ampere method or the secondary voltage method may be used. These methods are described. The method of calculation of the total circuit reactance is given, and the important bearing of this quantity on the resonance effects is discussed. Percentage reactance of any portion of the circuit is defined. The extent of detuning the transformer circuit from the generator frequency in quenched spark work, namely about 15 per cent., is given and explained. The transformer circuit of the Marconi trans-Atlantic station at New Brunswick, N. J., is described. Curves giving the results of measurements by the above methods are shown. The advantages of low resistance in primary and secondary of transformers for quenched spark work, and the superiority of the closed core transformer are considered.