Showing papers on "Equivalent circuit published in 1969"

Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model

Abstract: Immittance, transfer, and scattering characteristics are studied for acoustic surface wave transducers of the interdigital electrode form. Linear network models are used to represent the transducer as a chain of identical three-ports which are acoustically in cascade but electrically in parallel. Transducer operation at acoustic synchronism is described theoretically and compared to current experimental data for transducers operating at 100 MHz and fabricated on lithium niobate. Favorable lithium niobate configurations for efficient, broad-band transducer operation are given. Scattering characteristics as a function of electric load are discussed. Low values of acoustic reflection loss are predicted theoretically and observed experimentally when the electric load and transducer capacitance are in resonance. The frequency dependence of transducer radiation immittance is studied, and the response is found to be analogous to the response of an endfire antenna array.

Coupled Transmission Line Networks in an Inhomogeneous Dielectric Medium

Abstract: In this paper, two-port networks composed of two identical, coupled transmission lines embedded in an inhomogeneous dielectric (e.g., suspended substrate, microstrip) are investigated. The ABCD parameters of circuit configurations, considered by Jones and Bolljahn, are obtained for the case of inhomogeneous dielectilc. Equivalent circuits of these networks are also given. It is shown that the characteristics of such circuits differ markedly from those embedded in a homogeneous medium. In addition, experimental results are presented for three types of circuits which have been constructed and tested. There is excellent agreement between the experimental results and those predicted theoretically on the basis of the equivalent circuits.

Realisation of gyrators using operational amplifiers, and their use in RC-active-network synthesis

Abstract: The realisation of negative-impedance convertors (n.i.c.s) and invertors (n.i.i.s) using the bridge-type circuit is briefly surveyed. An equivalence relating the nullor to infinite-gain controlled sources is first proved, and is then used for the derivation of nullator-norator equivalent circuits for n.i.c.s and n.i.i.s. Some properties of networks containing singular elements, which are used in the realisation of gyrators, are investigated. Nullator-norator equivalent circuits for gyrators are derived by using the n.i.c.s and n.i.i.s. They are converted into physical networks by using the proved equivalence. Gyrator circuits are obtained by replacing nullors by operational amplifiers. A stability analysis of the gyrator circuits is produced and a relevant theorem concerning passivity is proved. The feasible Qfactors and the accuracy of the gyrator circuits are indicated by some experimental results. A generalised-impedance convertor (g.i.c.) is defined by generalising the n.i.c. theory, and it is shown that the gyrator circuits described can be used as g.i.c.s. The application of the gyrator and g.i.c. circuits in the synthesis of RC-active networks is considered. Finally, a highpass filter using gyrators and a bandpass filter using g.i.c.s are designed, and the experimental results are given.

Circuits for High Efficiency Avalanche Diode Oscillators

Abstract: This paper describes and analyzes the circuits which have been used successfully for TRAPATT oscillator studies. The results lead to a better understanding of the TRAPATT oscillator and yield a simple model of the oscillator which is useful for circuit design. The circuit characteristics of an experimental TRAPATT oscillator are determined from measurements on the circuits and from equivalent circuit model calculations. The following conclusions can be drawn from the analysis. First, the avalanche diode requires sufficient capacitance near the diode to sustain the high-current state required for TRAPATT operation. Secondly, at a distance from the diode corresponding to approximately one half-wavelength at the TRAPATT frequency the transmission line containing the diode should be terminated by a low-pass filter. The function of the filter is to pass the TRAPATT frequency and to provide a shorting plane for the harmonics of that frequency. Finally, on the load side of the filter, tuning for the TRAPATT frequency is required. The model of the circuit described above suggests a simple explanation of the diode-circuit interaction in a TRAPATT oscillator. Simplified waveforms suggested by the model have been used to calculate power out-put, efficiency, dc voltage change, and RF impedance for the oscillator. The results agree within a few percent with those obtained for an experimental oscillator. An important conclusion of the analysis is that the high-efficiency operation of avalanche diodes at frequencies in the UHF range can be explained by the TRAPATT theory, even though the trapped-plasma or low-voltage state may last only 1/20th of the oscillation period.

Design formulas for helix dispersion shaping

Abstract: A simple method of calculating effects of various boundaries around the helix on the dispersion relation and the interaction impedance is presented. The analytical technique is based on the use of equivalent circuit parameters derived from rigorous field analyses. The main advantage of this method is that effects of various perturbing objects (dielectrics, shields, etc.) can be calculated independently, regardless of the model of the unperturbed system. Equivalent circuit parameters are obtained for helices with several different forms of perturbing boundaries, including wedge-shaped dielectric rods, conducting boundaries, longitudinally conducting wires and fins, and combinations of these. The method of analysis is versatile so that the dispersion relation for any one particular form of the helix may be calculated from known characteristics of another using only three sets of universal curves.

Direct- and Quadrature-Axis Equivalent Circuits for Solid-Rotor Turbine Generators

Abstract: Direct- and quadrature-axis equivalent circuits are developed for solid-rotor turbine generators. The equivalent circuits model, in considerable detail, important current-carrying paths in the rotor in addition to the excitation winding. Impedance equations are formulated so that a valid representation can be obtained over a wide range of frequencies. Operational solution of the equivalent circuits provides a powerful means for accurate analytical description of generator performance during many types of transient conditions, such as faults and other system disturbances, excitation system forcing, and asynchronous operation. In addition to providing improved accuracy of representation of generator terminal characteristics, solution of the circuits provides a wealth of valuable generator design information.

Characterization of Piezoelectric Transducers Used in Ultrasonic Devices Operating Above 0.1 GHz

Abstract: Piezoelectric transducers for ultrasonic devices operating at frequencies above 100 MHz are presently being made either by thin‐film deposition techniques or by bonding thin plates to the substrate and lapping them to the required thickness. In either case the performance of the transducers cannot be evaluated separated from the device, and the evaluation is complicated by the presence of intermediate layers and spurious circuit elements. This paper uses Mason's equivalent circuit to critically appraise the validity of methods used to evaluate transducer performance from loss and admittance measurements made under these circumstances. Computed families of curves are presented, spanning the practically important range of mechanical impedances and coupling factors. Experimental data from a ZnO film and a LiNbO3 thin‐plate transducer on fused quartz substrates are presented to demonstrate the application of equivalent circuit descriptions to obtain the coupling factors.

The piezoelectric crystal unit—Definitions and methods of measurement

Abstract: The properties of a piezoelectric crystal unit as a circuit element are characterized and defined, in terms of a general equivalent circuit that is valid at any frequency up to and including the lower UHF ranges but reduces to the conventional equivalent circuit if the parameters are properly redefined. The characteristic values such as resonance frequency and resistance, parallel resonance frequency and resistance, etc., for a crystal unit with or without other reactive elements in series and/or parallel are tabulated and their significance is illustrated with the aid of the crystal impedance and admittance diagrams. These diagrams are also used in deriving and describing the methods to be followed when determining the crystal equivalent circuit parameters by impedance bridge measurements. Techniques are developed for use with various types of impedance and admittance bridges and the relations required to determine the resonance resistance R 1 , resonance frequency f s , and quality factor Q 0 of the motional arm, and the reactance X- 0 of the parallel capacitance from the measured quantitites are listed. The effects of transmission lines of various lengths between the plane of measurement in the bridge and the crystal unit are fully considered. The nature and magnitude of the sources of measurement errors, exclusive of errors in bridge calibration, are examined.

1.75‐GHz ACOUSTIC‐SURFACE‐WAVE TRANSDUCER FABRICATED BY AN ELECTRON BEAM

Abstract: Surface‐acoustic‐wave interdigital transducers operating at 1.75 GHz have been fabricated on y‐cut z‐oriented LiNbO3 and y‐cut x‐oriented quartz substrates by electron‐beam techniques. The transducers consist of 25 pairs of interleaved aluminum ``fingers'' 0.3 μ wide and 0.7 μ apart. Used as a surface acoustic wave delay line, the insertion loss has been measured to be as low as 25 dB with a bandwidth of 70 MHz for 2.2‐μsec delay. The parameters of the equivalent circuit of the transducer have been measured and agree with the theoretical calculation.

Exact analytical solution of high frequency lossless MOS capacitance-voltage characteristics and validity of charge analysis

Abstract: The small signal equivalent circuit model is employed to obtain the exact nonuniform transmission line for high frequency MOS capacitance calculations. The semiconductor capacitance, given by the open circuit input capacitance of the line, is described by a simplified Riccati equation which is valid for arbitrary impurity distribution in an extrinsic semiconductor. Numerical solutions are obtained using the fourth order Runge-Kutta method for the case of constant impurity concentration. The validity range (measured by the amount of surface band bending) and the accuracy of the various approximations of the capacitance calculations using charge analysis are established by comparing with the exact solution from the transmission line. It is shown that for doping greater than 1014/cm3, the complete minority carrier depletion model gives accuracy better than 10−6 C0 for carrier concentration ratio of (majority/minority) > 500 at the oxide-semiconductor interface, or UIS > 2UF−6. For stronger surface inversion, the high frequency charge analysis formula can be used with equal or better precision. It is noted that the exact transmission line model used here to verify the charge models is particularly valuable for substrates with spatially varying impurity concentration.

A Multiple-Diode High-Average-Power Avalanche-Diode Oscillator (Correspondence)

Abstract: This correspondence presents a simple circuit which allows direct combining of the power obtainable from several avalanche diodes. The circuit does not require extremely close matching of dc or RF diode characteristics, and no particular isolating networks such as hybrid combiners are necessary. CW power output exceeding 4 watts at 7 GHz and 3 watts at 9 GHz has been demonstrated in a device employing five diodes. The number of diodes which can be combined using this technique is limited by geometric and heat sink considerations. Descriptions of typical single-diode and multiple-diode oscillators are given along with equivalent circuits. The circuits employ resistors or resistor networks to suppress low-frequency oscillations and undesired resonances which occur when several oscillators are coupled together. Negligible insertion loss is incurred at the design output frequency. Measured performance is given on similar single- and multiple-diode oscillators. Data include frequency, power, AM noise, FM noise, temperature, and loaded Q.

Fundamentals of Network Analysis

Abstract: Equivalent circuits for electronic devices will be shown to consist of simple current or voltage generators, together with impedances or admittances. In Chapter 1, we found that such devices could only operate correctly if they were connected to suitable load and bias circuits consisting of impedances or admittances. In addition, any signal to be amplified was supplied from an a.c. current or voltage source together with its associated impedance or admittance.

High-frequency network properties of MOS transistors including the substrate resistivity effects

Abstract: The small-signal differential equations describing the intrinsic high-frequency characteristics of MOS transistors are derived under three basic modes of signal application: gate excitation, substrate excitation, and combined gate-substrate excitation. These equations are shown to be analogous to those of a double RC transmission line having a uniformly distributed common resistance but two separate capacitances distributed nonuniformly. High-frequency device admittances are calculated in terms of those of the analog RC transmission line using the method of "piecewise" uniformity for the capacitance distributions. Useful expressions are derived for the various Y-parameters which are explicitly related to the more readily measurable low-frequency input capacitance and transconductance parameters which, in turn, are related to the basic device physical parameters. The admittance expressions clearly indicate the influence of the substrate resistivity both on the forward transfer admittance magnitudes at low and high frequencies and on the input conductance at high frequencies. The intrinsic Y-parameters are combined with the associated extrinsic RC networks and presented in the form of equivalent circuits. Results of UHF admittance measurements on representative n-channel devices are given which support the overall validity of the proposed equivalent circuit models.

Stray losses of polyphase cage-induction motors with particular reference to the condition of imperfect rotor-barߝiron insulation

Abstract: The paper presents an analysis of stray losses in polyphase cage-induction motors, under linear and saturation magnetisation conditions, with particular attention being given to the effects of circumferential currents flowing in the rotor as a consequence of imperfect bar-iron insulation. Such effects are included in a modified equivalent circuit of the motor, and are expressed in terms of factors readily determined from a set of normalised curves, not previously available. For example, the consequent reduction in the effective skew of the rotor bars can be determined, and thus a more correct evaluation obtained for those factors and losses dependent upon the resultant skew. Also, a simple graphical method is given for determining the effective increase of the air gap due to main-flux saturation, which assists in demonstrating that favourable agreement between the predicted and experimental torque/slip characteristics can be obtained with some reduction of the empiricism employed hitherto.

Application of the distributed equilibrium equivalent circuit model to semiconductor junctions

Abstract: The small-signal equivalent circuits for a p-n junction at equilibrium and the MOS capacitor in the inversion range are derived from the general transmission line model. Detailed calculations are made to obtain the semiconductor admittance as a function of frequency for a gold-doped n-type silicon substrate. The transmission-line model provides the desired distributed time constant observed in experimental data of admittance versus frequency. A simple model is given to illustrate how the low-frequency junction capacitance depends on the position of the deep level recombination center in the band gap and the ratio of the hole and electron emission rates. Experimental results on gold-doped silicon junctions are analyzed in terms of the theoretical model, considering effects of this ratio, the effects of surface channels, and the effect of a nonuniform spatial variation of the gold impurity.

Eddy-current and hysteresis effects in rotating machines

Abstract: Hysteresis in the magnetic circuit of a rotating machine is represented by an approximate method which neglects harmonics and enables the hysteresis motor to be analysed by the equivalent Kron primitive machine. The method is extended to hysteresis and eddy-current effects in hysteresis, induction and synchronous machines; steady-state equivalent circuits are derived for the hysteresis motor and induction machine.

Computer-Aided Small-Signal Characterization of IMPATT Diodes

Abstract: This paper is a discussion of IMPATT wafer small-signal characteristics in the frequency range of 2.0-8.0 GHz. These characteristics have been obtained by computer conversion of reflection phase-gain data. The data handling technique which allows establishment of the desired reference plane and the reduction of the admittance data into the desired equivalent circuit is presented. A calibration procedure using reference impedances consistent with the diode geometry is discussed. The validity of the microwave measurement technique and the data handling process is demonstrated by comparison of the values of junction capacitance determined at microwave frequencies with junction capacitance measurements at 30 MHz. Representative plots are given for wafer conductance and susceptance as a function of frequency with current density as a parameter. In addition, typical values obtained for the circuit elements are presented. These data illustrate the capability of determining package inductance, series resistance as a function of bias voltage, and, with the diode in avalanche, the parallel G, L, and C of the wafer admittance. The diode equivalent circuit was studied as a function of current density to compare results with the existing analytical small-signal theories. This procedure permits the separation of the wafer elements from the parasitic elements of the package. Data obtained from these measurements are extremely useful for ascertaining wafer design parameters and assisting in circuit design.

The Finite Difference Solution of Microwave Circuit Problems

Abstract: Using finite difference methods this paper shows how solutions may be obtained with the aid of a digital machine to a wide range of microwave circuit problems These problems include the parameters of TEM-mode transrnission lines, the equivalent circuits of obstacles in these lines, the cutoff frequencies of the fundamental mode in a waveguide of very general cross section, and the equivalent circuits of obstacles in rectangular waveguide Methods for deriving the appropriate finite difference equations are presented and optimum methods for their solution set out; singularities are also included in the treatment The paper ends with a resume of some typical results to problems of practical interest which have been obtained by these methods

A New Simple Wide-Band Current-Measuring Device

Abstract: The current conveyor?a new circuit building block recently introduced?is applied to the design of a simple current-measuring probe. The monopolar version of this probe features high stability and accuracy (0.5 percent of nominal reading). A dc to 100-MHz frequency band is obtained from the bipolar version. Both versions minimize the disturbance to the measured circuit by presenting a very low impedance at the current-measuring terminals. The output voltage of the probe is directly proportional to the measured current with the transimpedance being chosen almost at will. The design makes use of a dual transistor and a commercially available integrated circuit.

Equivalent Circuits for Single-Phase Squirrel-Cage Induction Machines with both Odd and Even Order MMF Harmonics

Abstract: The special winding connections used in certain dual voltage or multiple-speed single-phase induction motors lead to large, even order MMF harmonics. The calculation procedures used to evaluate machines of this type must include proper representation of these harmonics. This paper develops the general describing equations for a two-phase machine with arbitrary MMF distributions. These equations are then specialized to yield harmonic equivalent circuits for steady-state operation. Proper interconnection of these harmonic circuits yields equivalent circuits representing actual machine windings. Examples are given, including circuits for representation of consequent pole windings. A numerical example of a machine operating with only its north poles excited is also included.

Small-signal, high-frequency equivalent circuit for the metalߝoxideߝsemiconductor field-effect transistor

Abstract: The differential equations describing the small-signal sinusoidal operation of the 'intrinsic' m.o.s.f.e.t. structure are solved using modified Bessel functions of the first kind. Expressions for the small-signal short-circuit admittance parameters are obtained in series form. By retaining appropriate terms in the series, the elements of a convenient equivalent circuit are computed for both the nonpinchoff and the pinchoff cases. Results are compared with those presented by other authors, to show that previous calculations for the nonpinchoff case are incorrect.

Equivalent electromechanical representation of trapped energy transducers

Abstract: Trapped energy resonators and transducers have attained a considerable importance in quartz crystal technology both as single-frequency resonators for the control of crystal oscillators and as drivers for the monolithic crystal filter which appears likely to have a wide use as a channel filter for the separation of voice frequency channels for long-distance carrier systems, microwave radio, and submarine cable systems. It is the purpose of this paper to derive the equations for trapped energy resonators of the thickness-shear and thickness-twist types and to calculate the ratios of capacitances for straight crested waves. It turns out that the ratios are lower (coupling higher) than are observed in practice. It appears that this difference is connected with the finite width of the plate which causes the motion at the edge of the plate to be somewhat smaller than the motion in the center of the plate. While no exact solution has been obtained for the finite plate, an approximation is made which is in good agreement with the experiment. The resonator on a plate is a symmetrical device, whereas a transducer for driving a monolithic filter is a dissymmetrical device since it is driving different impedances on its two boundaries. To represent this dissymmetry requires a distributed network representation which is somewhat similar to that found for a plane longitudinal or shear wave except that the propagation constant for a trapped wave replaces that of the plane wave. The representation also requires a transformer whose transformation ratio is a function of the frequency and two negative element terms. By transformations the negative elements can be made to disappear. These together produce an equivalent circuit whose values depend on the ratio of the electrode length to the crystal thickness.

Unbalanced Operations of Three-Phase Machines with Damper Circuits

Abstract: A study on unbalanced short circuits of three-phase machines with additional field circuits is discussed, and a detailed solution for the case of a double-line-to-ground short circuit of a salient-pole synchrenous machine is offered. By mathematical analysis, new and complete transient solutions for short-circuit currents, torque, and open-phase voltage are derived for ready uses.

Emitter controlled negative resistance in GaAs

Abstract: A triode which uses the negative differential mobility of GaAs is proposed for various microwave applications and is analyzed as an oscillator. With proper bias conditions, this device has a microwave equivalent circuit that is simply a capacitance in parallel with a negative resistance. The magnitude of the negative resistance is controlled by injected current. The major characteristics as an oscillator are: 1 < −Q < 10 for nL ⋍ 1011 cm−2 and 107 < fL < 108, maximum device efficiency between 15 and 20 per cent, power density approximately 110 that of LSA mode device, absence of noise associated with domain formation, and third terminal control of negative resistance. The maximum efficiency as an oscillator is available over a finite range of current density, which decreases as nL increases.

Analysis of the Hysteresis Machine - Part I

Abstract: A theoretical model has been developed for the hysteresis motor by solving Laplace's equation for the field in the air gap and the rotor ring subject to appropriate boundary conditions. The hysteresis phenomenon is accounted for through the use of an elliptical approximation for the hysteresis loop. The relation between the magnitude of the fundamental components of the B and H waves is assumed to be linear and the phase shift between them, due to hysteresis, is assumed to be constant. However, an iteration procedure is described to account for the nonlinearity in the actual machine. A similar approximation is used to represent the minor loops described by the harmonic components of the field, and the effect of MMF and slot harmonics on machine performance is thus estimated. Rigorous analysis predicts and evaluates the "gap leakage field," which constitutes a part of the main field without penetrating the rotor material. The inclusion of this field in the model is shown to eliminate the nonrealistic assumption that the B and H waves in the rotor material are in phase. The model is used to evaluate the output torque and the EMF and power factor of the stator windings. A simple equivalent circuit is developed, in which the three fields present inside the machine, two in the air gap and one in the rotor, are represented by individual elements. The nonlinearity of the rotor material is represented in the equivalent circuit by a nonlinear impedance whose characteristics are directly predictable from the shape of the B-H curve. A comprehensive model has been obtained which is flexible enough to handle the different nonlinearities. It has been rigorously derived from the field equations, and therefore is expected to be very useful in further investigations of the hysteresis machine.

Design, fabrication, and characterization of a germanium microwave transistor

Abstract: This paper summarizes the design, fabrication, and characterization of a p-n-p planar epitaxial germanium transistor for use as an amplifier in the 1-to 4-GHz frequency range and as a high-speed switch. The analytical basis for the geometry and impurity profile arrived at in the development of this transistor is presented in conjunction with experimental measurements. It is shown that good agreement between experiment and theory can be achieved even in the 1-to 6-GHz frequency region when sufficient attention is given to the formulation of an adequate equivalent circuit. For example, the calculated f T of this germanium microwave transistor is 5.7 GHz, which compares to a typical measured value of 5.6 GHz. The measured maximum available gain of the better transistors is 13.4 dB at 1.3 GHz (the corresponding calculated value is 13.9 dB) with a 2.7-dB noise figure at the same frequency.