Distortionless Transmission Line Research Articles

Hyperbolic-cosine waveguide tapers and oversize rectangular waveguide for reduced broadband insertion loss in W-band electron paramagnetic resonance spectroscopy. II. Broadband characterization.

Experimental results have been reported on an oversize rectangular waveguide assembly operating nominally at 94 GHz. It was formed using commercially available WR28 waveguide as well as a pair of specially designed tapers with a hyperbolic-cosine shape from WR28 to WR10 waveguide [R. R. Mett et al., Rev. Sci. Instrum. 82, 074704 (2011)]. The oversize section reduces broadband insertion loss for an Electron Paramagnetic Resonance (EPR) probe placed in a 3.36 T magnet. Hyperbolic-cosine tapers minimize reflection of the main mode and the excitation of unwanted propagating waveguide modes. Oversize waveguide is distinguished from corrugated waveguide, overmoded waveguide, or quasi-optic techniques by minimal coupling to higher-order modes. Only the TE10 mode of the parent WR10 waveguide is propagated. In the present work, a new oversize assembly with a gradual 90° twist was implemented. Microwave power measurements show that the twisted oversize waveguide assembly reduces the power loss in the observe and pump arms of a W-band bridge by an average of 2.35 dB and 2.41 dB, respectively, over a measured 1.25 GHz bandwidth relative to a straight length of WR10 waveguide. Network analyzer measurements confirm a decrease in insertion loss of 2.37 dB over a 4 GHz bandwidth and show minimal amplitude distortion of approximately 0.15 dB. Continuous wave EPR experiments confirm these results. The measured phase variations of the twisted oversize waveguide assembly, relative to an ideal distortionless transmission line, are reduced by a factor of two compared to a straight length of WR10 waveguide. Oversize waveguide with proper transitions is demonstrated as an effective way to increase incident power and the return signal for broadband EPR experiments. Detailed performance characteristics, including continuous wave experiment using 1 μM 2,2,6,6-tetramethylpiperidine-1-oxyl in aqueous solution, provided here serve as a benchmark for other broadband low-loss probes in millimeter-wave EPR bridges.

Transfer function-based modelling for voltage oscillation phenomena in PWM motor drives with long feeding cables

In this article, a transfer function-based modelling is proposed to investigate voltage oscillation phenomena, i.e. over-voltage at the motor terminal, associated with pulse-width modulation (PWM) inverter-fed motor drives with long feeding cables. As such, the long feeding cable is assumed to be a distortionless transmission line; then, a bounce diagram and time-harmonic method are utilised to derive a simple model with a minimum computational burden that is easy to realise using the Matlab/Simulink software package. Furthermore, the model takes account of the inverter output and the motor terminal filters, which are commonly used to suppress the motor terminal over-voltage. The model accuracy is verified by a comparison with the circuit-oriented software, OrCAD/PSpice, simulation results.

Analytical Eye-Diagram Model for On-Chip Distortionless Transmission Lines and Its Application to Design Space Exploration

This paper proposes a closed-form eye-diagram model for on-chip distortionless transmission lines with intentionally inserted shunt conductance. We derive expressions of eye-opening both in voltage and time, by assuming a piece-wise linear waveform model. The model is experimentally verified with various length, shunt conductance and resistive termination. We also apply the proposed model to design space exploration, and demonstrate that the proposed model helps estimate the optimal shunt conductance and resistive termination according to required signaling length and throughput.

Nonuniform distortionless transmission lines

Heavside's classical condition for distortionless signalling, g/c=r/l, is generalized to nonuniform transmission lines. The resulting class of nonuniform lines possesses several interesting properties, which are investigated in some detail. For instance, there exists a preferred direction for distortionless signalling, a phenomenon not observed with uniform lines. We also show that closed-form solutions to quite general wave propagation problems can be derived directly in the time domain.

Mechanism of the lightning M component

Analysis of simultaneous measurements of the channel‐base current and the vertical electric field 30 m from triggered lightning reveals that the fields associated with M components, although essentially electrostatic, appear to be proportional to the time derivatives of the associated M currents. Based on this finding, coupled with other observations and modeling, a mechanism for the lightning M component is proposed. According to this mechanism an M component involves a downward progressing incident wave (the analog of a leader) followed by an upward progressing reflected wave (the analog of a return stroke). However, as opposed to a leader‐return stroke sequence in which the latter removes the charge deposited by the former, both the upward and the downward processes contribute about equally to the total charge flowing from the bottom of the channel at any instant of time. Such a mode of charge transfer to ground, distinctly different from a leader‐return stroke sequence, is possible because of the presence of a path capable of supporting the propagation of a traveling wave (facilitated by a continuing current flowing to ground) and the fact that the ground is essentially a short circuit for the downward incident wave, so that the magnitude of the current reflection coefficient at ground is virtually equal to unity. We show that some observed properties of M components can be explained if the lightning channel traversed by an M‐current wave is represented as a linear R‐C transmission line. In this view, the preferential attenuation of the higher‐frequency components on an R‐C line is responsible for the lack of frequencies above several kilohertz in both the M‐current pulses measured at the channel base and the M‐light pulses observed in the bottom 1 km or so of the channel. Further, the relatively high characteristic impedance of the channel, of the order of tens to hundreds of kilohms for frequencies below some kilohertz, inferred from the linear R‐C line approximation, is consistent with the observation that even a relatively poor ground is sensed by an incident M wave as essentially a short circuit. However, on a linear R‐C transmission line the higher‐frequency components travel faster than lower‐frequency components (this velocity dispersion implying that the original pulse would spread while propagating along the line), whereas the shape of the M‐light pulses does not change much within the bottom 1 km or so, as if the channel were a distortionless transmission line. We speculate, on physical grounds, that the front of the traveling M‐current pulse heats the channel so that the pulse tail encounters a lowered resistance and, as a result, accelerates. By virtue of these two opposing effects, velocity dispersion and channel nonlinearity, an M pulse is formed whose more‐or‐less symmetrical shape is preserved over a relatively large distance, as in the case of a soliton.

Condition for distortionless transmission line with a nonuniform characteristic impedance

The well-known condition for distortionless signal propagation on a dissipative transmission line with constant impedance is generalized to the case of nonuniform impedance. The result is based on a time-domain wave-splitting formulation of the Telegraphist's equations. It is shown that an appropriate choice of the resistance and the conductance can eliminate the distortion caused by the varying characteristic impedance. A nonuniform transmission line that satisfies the given condition is distortionless in both directions, but reflectionless for signals propagating in one direction only.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Chaotic dynamics in an infinite-dimensional electromagnetic system

The paper deals with bifurcation and chaos phenomena theoretically observed in a simple electromagnetic system consisting of a linear, distortionless transmission line connected to an active linear resistor (R >

Eigenvalue assignment of an augmented hyperbolic system by linear feedback

A class of augmented linear hyperbolic systems subject to a boundary control is studied. It is shown that the eigenvalues of the closed loop system subject to a feedback control, can be assigned arbitrarily, apart from an asymptotic condition on the distribution of the eigenvalues. The feedback vector is constructed in an appropriate Hilbert space. The results are applied to an important example of the synthesis of a distortionless transmission line system by linear feedback.

A Microcomputer-Based Interactive Transmission Line Simulator

An interactive distortionless transmission line simulator, capable of providing dynamic oscilloscope displays of voltage and current waveforms along the line, has been implemented on an Intel 8086 based single-board microcomputer. The simulator helps the student grasp the fundamentals of transmission line behavior through the observation of transient and steady-state wave phenomena under various conditions. The user sets up a simulation by specifying the normalized line parameters, terminating resistors, and type of source. The simulator prompts the user with a mnemonic and defaul value for each parameter. A set of control commands provides a means offreezing the traveling waves, changing terminations, scaling the display, and single stepping the simulation. The simulator is easy to use, inexpensive, requires minimum hardware, and facilitates quantitative measurements on the oscilloscope. The numerical algorithm implemented on the 8036 provides a stable accurate simulation in almost all cases.

Hybrid Computer Simulation of Multiterminal DC Power Transmission Systems

Techniques are developed for the hybrid computer simulation of multiterminal dc power transmission systems with two- or three-conductor transmission lines. The switching of the static converters as well as the attenuation and transport delay of a distortionless transmission line are represented in detail. An example study is performed using a hybrid simulation of a singlepole three-terminal system, wherein the converter terminals are represented on the analog portion and the transmission line is represented on the digital portion of the hybrid computer. Results include waveforms for the transient behavior of the system during line faults on each of the three transmission branches.

Multiple Reflections on Pulse Signal Transmission Lines-Model for Computer Solution

A mathematical model for multiple reflections on lossless, distortionless signal transmission lines is developed for step changes in voltage or current at the source. The model is quite general and is valid for a source driving either one or two lines each loaded with an arbitrary number of discontinuities at arbitrary distances. It will give an exact solution for discontinuities and terminations which are purely resistive and allows for resistances of any size, none of which need be alike. Although an exact solution is valid only when the capacitances are negligible, a method is presented which will partially compensate for a capacitively distorted wave if the capacitive-characteristic resistance time constant is reasonably small compared to the transit time of the line. Considerations for digital computer simulation of the mathematical model are discussed and several examples including open backplane wiring comparing actual and computer results are given. The model and simulation are especially useful for lines which are not terminated in the characteristic impedance at the source or load end and also where modification of the model can be made to investigate reactive and nonlinear terminations.

The application of the differential analyser to transients on a distortionless transmission line

The behaviour of a transient on a finite distortionless line can be described in terms of two travelling-wave systems propagated in opposite directions along the line. The voltages in these two waves satisfy two ordinary differential equations depending on the terminal conditions, and involving a relation between the voltage at two times differing by the time of travel of a wave from one end of the line to the other and back. Equations of this type can be handled mechanically by means of the differential analyser, using a special form of input table, and the use of the differential analyser does not require that the terminal impedances should have linear characteristics.The application of the differential analyser to a line with a capacitance at one end and a non-linear resistance (lightning arrester) at the other is discussed in some detail as an example, and specimens of machine solutions, both with a linear and with a non-linear resistance at the far end, are given and discussed, and compared with oscillograms taken on an actual line.

Short Notices

THE title of this book, that of the series to which it belongs, and the first sentences of the preface, alike fail to convey a correct sense of the book's scope and aim. The preface says: “It is a book for engineers.”This is only a partial truth ; it is a textbook for engineering students (as indeed the preface goes on to explain), but it is not a handbook for working engineers and it is not a reference book. Much more is required before the author's hope that it “will help the student to attack any sort of transient problem with confidence” can be adequately realized. But as a text-book for students it is good; clear descriptions of the physical nature of transients take first prominence, the mathematical side being kept in its place as a necessary and important tool. Four introductory chapters are devoted to transients in simple series circuits of inductance, resistance and capacity. The next three deal with the indicial response of more complicated networks, the transient response to sinusoidal and non-sinusoidal voltages and transients in coupled resonant circuits. This last-named discussion is kept simple and illuminating by neglecting ohmic resistance. Then follows a chapter on solution of circuits with variable parameters by graphical and point-to-point methods. A clear exposition of travelling waves on non-dissipative and distortionless transmission lines leaves one to regret the serious omission of any discussion of standing-wave phenomena.

Sinusoidal Traveling Waves

The theory of transients arising from the sudden application of a sinusoidal potential is presented in this paper, for the distortionless transmission line. The solution is given in the form of a series of damped sinusoidal traveling waves, the reflections diminishing progressively until the steady state is reached. Oscillographic tests on an artificial line containing lumped parameters are shown to corroborate the theory, and graphical methods are described which permit a quick computation of the successive traveling waves.

Sinusoidal traveling waves

The theory of transients arising from the sudden application of a sinusoidal potential is presented in this paper, for the distortionless transmission line. The solution is given in the form of a series of damped sinusoidal traveling waves, the reflections diminishing progressively until the steady state is reached. Oscillographic tests on an artificial line containing lumped parameters are shown to corroborate the theory, and graphical methods are described which permit a quick computation of the successive traveling waves.