Length Of Transmission Line Research Articles

Small Wideband Coupled-Line Ring Hybrids With No Restriction on Coupling Power

To realize any coupled-line ring hybrid without any restriction on coupling power, a set of coupled-line sections with two shorts was synthesized using one- and two-port equivalent circuits, and design equations were derived to yield perfect matching regardless of the coupling power. Based on the design equations, a new modified Pi-type transmission-line equivalent circuit is suggested. It consists mainly of a set of coupled-line sections and can be used to reduce a transmission-line section, especially when the electrical length is greater than 180deg. Therefore, the 270deg transmission-line section of a conventional ring hybrid can be reduced to less than 90deg. To verify the performance of the modified one, two kinds of simulations were performed: in the first, the electrical length of the coupled-line sections was held constant, in the second, the coupling coefficient was held constant. Simulated bandwidths of the resulting small transmission lines depended strongly on coupling power. Using modified and conventional Pi-type transmission-line equivalent circuits, a small wideband coupled-line ring hybrid (SWCLRH) was designed. Compared to the conventional ring hybrid, the SWCLRH has much wider bandwidth, but is less than one-third as large. To test the method, a microstrip SWCLRH with a total transmission-line length of 220deg was fabricated and tested. Measured S 21, S 41, S 23, and S 43 were -2.78, -3.34, -2.8, and -3.2 dB, respectively, at a design center frequency of 2 GHz. Matching and isolation with less than -20 dB were achieved in more than 20% fractional bandwidth.

Design and Analysis of Millimeter-Wave Marchand Balun with Interconnected Transmission Line

This paper presents the design and analysis of general baluns of Marchand-type with a transmission line connected between two sections. A series of new expressions of S-parameters are derived for such type of Marchand balun. The relations between the length of interconnected transmission line and the imbalance of Marchand balun are discussed. By using analytical method, a millimeter-wave Marchand balun was designed and simulated by the full-wave electromagnetic software HFSS, and fabricated in 0.15 µm pHEMT GaAs process. The measurement results show that the balun achieves low insertion loss and good balance in the band of 24–40 GHz. The results are in good agreement with the simulated ones. The theoretical analysis is verified.

Fast Methodology for Determining Eye Diagram Characteristics of Lossy Transmission Lines

As the speed of signal through an interconnection increases toward the multigigabit ranges, the effects of lossy transmission lines on the signal quality of printed circuit boards becomes a critical issue. To evaluate the eye diagram and thus the signal integrity in the modern digital systems, this paper proposes a fast methodology that employs only two anti-polarity one-bit data patterns instead of the pseudo-random bit sequence as input sources to simulate the worst-case eye diagram. Analytic expressions are derived for the impulse response of the lossy transmission lines due to the skin-effect loss, while the Kramers-Kronig relations are employed to deal with the noncausal problem related to the dielectric loss. Two design graphs that can be used to rapidly predict the eye diagram characteristics versus the conductive and dielectric losses are then constructed and based on which, the maximally usable length of transmission lines under a certain signal specification can be easily acquired. At last, the time-domain simulations and experiments are implemented to verify the exactitude of proposed concept.

Construction and applications of the Dirichlet-to-Neumann operator in transmission line modeling

The Dirichlet-to-Neumann (DtN) operator is a useful tool in the characterization of interconnect structures. In combination with the Method of Moments, it can be used for the calculation of the per-unit length transmission line parameters of multi-conductor interconnections, or to directly determine the internal impedance of conductors. This paper presents a new and fast calculation method for the DtN boundary operator in the important case of rectangular structures, based on the superposition of parallel-plate waveguide modes. Especially for its non-differential form, some numerical issues need to be addressed. It is further explained how the DtN operator can be determined for composite geometries. The theory is illustrated with some numerical examples.

Broadband Equalizer Design with Commensurate Transmission Lines via Reflectance Modeling

In this paper, an alternative approach is presented, to design equalizers (or matching networks) with commensurate (or equal length) transmission lines. The new method automatically yields the matching network topology with characteristic impedances of the commensurate lines. In the implementation process of the new technique first, the driving point impedance data of the matching network is generated by tracing a pre-selected transducer power gain shape, without optimization. Then, it is modelled as a realizable bounded-real input reflection coefficient in Richard domain, which in turn yields the desired equalizer topology with line characteristic impedances. This process results in an excellent initial design for the commercially available computer aided design (CAD) packages to generate final circuit layout for fabrication. An example is given to illustrate the utilization of the new method. It is expected that the proposed design technique is employed as a front-end, to commercially available computer aided design (CAD) packages which generate the actual equalizer circuit layout with physical dimensions for mass production.

Single-Length Method Used to Determine the Dielectric Constant of Polydimethylsiloxane

A new transmission-line method has been developed which is used to determine the propagation constant of a novel microwave material. Rather than requiring two or more transmission-line lengths to determine the propagation constant of a material, our method relies on a single fixture of known length and the use of a dielectric material of known properties to set a baseline measurement. By using a single fixture to make the measurements, we avoid introducing additional parasitic elements that would produce errors. We applied this approach to find the dielectric constant of the polymer polydimethylsiloxane over a frequency range of 0.1-40.0 GHz.

Preparation of distilled and purified continuous-variable entangled states

Two independent experiments demonstrate that quantum entanglement that has been lost in decoherence processes can be recovered. For the first time such ’entanglement distillation’ has been achieved for states of light that are entangled in continuous variables, which should help to increase the distance over which quantum information can be distributed. The distribution of entangled states of light over long distances is a major challenge in the field of quantum information. Optical losses, phase diffusion and mixing with thermal states lead to decoherence and destroy the non-classical states after some finite transmission-line length. Quantum repeater protocols1,2, which combine quantum memory3, entanglement distillation4,5 and entanglement swapping6, were proposed to overcome this problem. Here we report on the experimental demonstration of entanglement distillation in the continuous-variable regime7,8,9. Entangled states were first disturbed by random phase fluctuations and then distilled and purified using interference on beam splitters and homodyne detection. Measurements of covariance matrices clearly indicate a regained strength of entanglement and purity of the distilled states. In contrast to previous demonstrations of entanglement distillation in the complementary discrete-variable regime10,11, our scheme achieved the actual preparation of the distilled states, which might therefore be used to improve the quality of downstream applications such as quantum teleportation12.

Passive Intermodulation in Finite Lengths of Printed Microstrip Lines

This paper addresses the theoretical aspects of passive intermodulation (PIM) generation in printed transmission lines. In order to elucidate the mechanisms of PIM generation, a new model of the transmission line length with distributed nonlinearity is proposed. The developed model has been validated by the near-field measurements of PIM product distributions along the microstrip lines. The contributions of nonlinear mixing, power dissipation, and load matching to PIM products have been analyzed in detail. The obtained results reveal the fundamental properties of PIM generation in finite lengths of printed lines with distributed nonlinearity and identify possible means for PIM mitigation. It was shown for the first time that the reverse PIM products in a matched transmission line with distributed nonlinearity are generated due to nonlinear scattering.

Coupled Line으로 구성된 작고 넓은 대역폭을 가지는 3-dB Ring Hybrids

In this paper, two types of wideband 3-㏈ ring hybrids are compared and discussed to show the ring hybrid with a set of coupled-line sections better. However, the better one still has a realization problem that perfect matching can be achieved only with －3 ㏈ coupling power. To solve the problem, a set of coupled-line sections with two shorts is synthesized using one- and two-port equivalent circuits and design equations are derived to have perfect matching, regardless of the coupling power. Based on the design equations, a modified Π-type of transmission-line equivalent circuit is newly suggested. It consists of coupled-line sections with two shorts and two open stubs and can be used to reduce a transmission-line section, especially when its electrical length is greater than π. Therefore, the 3λ/4 transmission-line section of a conventional ring hybrid can be reduced to less than π/2. To verify the modified Π-type of transmission- line equivalent circuit, two kinds of simulations are carried out; one is fixing the electrical length of the coupled-line sections and the other fixing its coupling coefficient. The simulation results show that the bandwidths of resulting small transmission lines are strongly dependent on the coupling power. Using modified and conventional Π-types of transmission-line equivalent circuits, a small ring hybrid is built and named a compact wideband coupled-line ring hybrid, due to the fact that a set of coupled-line sections is included. One of compact ring hybrids is compared with a conventional ring hybrid and the compared results demonstrate that the bandwidth of a proposed compact ring hybrid is much wider, in spite of being more than three times smaller in size. To test the compact ring hybrids, a microstrip compact ring hybrid, whose total transmission-line length is 220°, is fabricated and measured. The measured power divisions(S₂₁, S₄₁, S₂₃ and S₄₃) are －2.78 ㏈, －3.34 ㏈, －2.8 ㏈ and －3.2 ㏈, respectively at a design center frequency of 2 ㎓, matching and isolation less than －20 ㏈ in more than 20 % fractional bandwidth.

최적 전송 선로를 이용한 고효율 분산형 증폭기의 설계

본 논문에서는 전송 선로 이론을 기반으로 분산형 증폭기의 역방향 전류 성분을 수식적으로 분석하고, 역방향 전류 성분을 상쇄시켜 최소화하기 위한 최적의 전송 선로의 길이를 구하는 방법을 제시하였다. 기존의 설계방법에서는 역방향 전류 성분을 종단 부하를 통해 단순히 소모시키는 형태이므로 게이트와 드레인 전송 선로의 길이 결정 기준이 설계상에서 뚜렷하게 주어져 있지 않았지만, 제안하는 방법에서는 역방향 전류 성분들이 서로 상쇄가 일어나도록 하는 전송 선로의 길이를 결정하는 이론적 바탕을 제시함으로써 좀 더 체계적인 설계 방법을 제시하고 있다. 제안하는 이론의 검증을 위하여 회로 시뮬레이션을 수행하였고, pHEMT 트랜지스터를 이용하여 차단 주파수가 3.6 GHz인 최적 전송 선로를 이용한 분산형 증폭기를 제작하였다. 측정을 통해 얻은 결과로서 동작 주파수 범위 내에서 최대 이득은 14.5 dB, 최소 이득은 12.8 dB로 측정되었다. 또한, 제안하는 분산형 증폭기의 측정된 효율은 3 GHz에서 25.6 %로 기존의 일반적인 분산형 증폭기에 비해 약 7.6 % 개선되었다. 출력 전력은 일반적인 분산형 증폭기에 비해 약 1.7dB 개선된 10.9 dBm을 얻었다. 이러한 성능 개선은 역방향 전류의 상쇄로 인한 것으로 분석된다. In this paper, we propose a numerical analysis on reversed current of distributed amplifier based on transmission line theory and proposed a theory to obtain optimum transmission line length to minimize the reversed currents by cancelling those components. The reversed current is analyzed as being simply absorbed into the terminal resistance in the conventional analysis. In the proposed analysis, however, they are designed to be cancelled by each other with opposite phase by the optimal length of the transmission lint Circuit simulation and implementation using pHEMT transistor were performed to validate the proposed theory with the cutoff frequency of 3.6 GHz. From the measurement, maximum gain of 14.5dB and minimum gain of 12.3dB were achieved In the operation band. Moreover, measured efficiency of the proposed distributed amplifier is 25.6% at 3 GHz, which is 7.6%, higher than the conventional distributed amplifier. Measured output power Is about 10.9dBm, achieving 1.7dB higher output power than the conventional one. Those improvement is thought to be based on the cancellation of refersed current.

Temporal skew and mode conversion management in differential pairs to 15 GHz

When used with emerging data-rates of 10 GHz and above, some standard transmission line length matching methods are shown to make mode conversion worse than without length matching. A new methodology for temporal skew management to preserve signal integrity in differential microstrip pairs to 15 GHz is proposed and validated through simulation.

Design Aspects of Printed Monopole Antennas for Ultra‐Wide Band Applications

This paper presents the design equations for lower band‐edge frequency for all the regular shapes of printed monopole antennas with various feed positions. The length of the feed transmission line is a critical design parameter of these monopole antennas. Design curves for the length of the feed transmission line for various lower band‐edge frequencies for all these regular shaped monopoles have been generated. A systematic study has been presented to explain the ultra‐wide bandwidth obtained from these antennas with an example of elliptical monopole antenna.

On the Efficacy of Using Ground Return in the Broadband Power-Line Communications—A Transmission-Line Analysis

The power-line infrastructure has been identified as an efficient system suitable for broadband power-line communication (BPLC) to connect and control various end users. However, the network is affected by stochastic attenuations due to the number of interconnected branches, their line lengths, associated terminal loads, etc. There is yet another parameter that could influence the above stated attenuations or distortions depending on the way the signals are allowed to return to the transmitting end. In this paper, we investigate whether a finitely conducting ground return could be used for BPLC and to investigate its performance over the conventional methods where one of the adjacent power-line conductors is used as signal return. This study could be helpful to those who are proposing the use of ground as a return conductor in BPLC systems. It will be shown that the use of ground return for the BPLC system is effective or better only when the ground conductivity is high (>50 mS/m). When ground conditions are poorer, attenuations increase with frequency, making them unsuitable for BPLC. There are situations where poor ground conditions can still be used but only the transmission-line lengths are shorter. The analysis presented here is based on transmission-line solutions both under lossless (without ground return) and lossy (with ground return) conditions and are applied to typical low-voltage and medium-voltage channels. Comparisons are also made based on the power spectral densities and channel capacities.

NONUNIFORM TRANSMISSION LINES AS COMPACT UNIFORM TRANSMISSION LINES

In this paper, we propose a new way to compact the transmission lines, which has a general application to miniaturization of RF and microwave circuits. In this way, we use Nonuniform Transmission Lines (NTLs) instead of Uniform Transmission Lines (UTLs). To synthesize the desired Compact Length Transmission Lines (CLTLs), the characteristic impedance function of the NTLs is expanded in a truncated Fourier series. Then, the optimum values of the coefficients of the series are obtained through an optimization approach. The usefulness of the proposed structures is verified using some examples.

Measurement of the Mutual Coherence Function of an Incoherent Infrared Field with a Gold Nano-wire Dipole Antenna Array

The first direct measurement of the mutual coherence function of a spatially incoherent infrared beam was performed at 10.6 μm using a pair of infrared dipole nano-wire antennas that were connected to a common bolometer in the center of the pair by short lengths of coplanar strip transmission line. A spatially incoherent source was constructed by dithering a BaF2 diffuser near the focus of a CO2 laser beam. The distance from the diffuser to the nano-wire antenna pair was held constant while the distance from the focus of the laser beam to the diffuser was varied to control the effective diameter of the source. The measured bolometer signal was proportional to the magnitude of the mutual coherence function at the plane of the antennas. The experimental results were found to match the predicted performance closely. If this technology can be extended to large arrays, a form of synthetic aperture optical imaging based on the Van Cittert-Zernike theorem is possible, similar to that performed at microwave frequencies now by astronomers. This has the potential to greatly increase the angular resolution attainable with optical instruments.

High-Impedance Coaxial Autoaccelerator

Experimentation of a single-stage, 100 coaxial autoaccelerator was carried out on a 3 MeV, 9 kA, and solid (non-annular) electron beam and achieved a maximum energy gain of about 900 keV. This method provides an alternative to multiple-stage, lower-impedance cavity designs in achieving higher energy gain. Upper and lower bounds for the transmission line length exists which depend on the total pulse width and the rise time of the pulse if one were to maximize the cavity voltage. Experimental measurements of the highest energy electrons included aluminum foil transmission, bremsstrahlung photon absorbed dose using a PIN diode dosimeter, depth-dose profiles in aluminum, and direct cavity voltage measurements using a capacitive voltage probe. Simulations were also performed using a particle-in-cell (PIC) plasma code to model coupling of the beam to the cavity to calculate voltages. Calculation results of the experimental structure suggested that the autoaccelerator gap is magnetically insulated against breakdown while the beam is passing the gap due to the combined effect of the applied axial magnetic field and the azimuthal magnetic field of the electron beam.

Microstrip multiplexer with compact in‐line feed structure

AbstractA microstrip multiplexer circuit using a compact in‐line feed structure is presented and experimentally demonstrated. The multiplexer consists of four edge‐coupled microstrip bandpass filters that are independently designed using any filter synthesis technique. The bandpass filters are interconnected in a sequential manner using specific lengths of transmission line that isolate the filters from one another at the center frequency of their passbands. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3128–3130, 2007; Published online in Wiley Inter‐Science (www.interscience.wiley.com). DOI 10.1002/mop.22945

Coherent quantum state storage and transfer between two phase qubits via a resonant cavity

As with classical information processing, a quantum information processor requires bits (qubits) that can be independently addressed and read out, long-term memory elements to store arbitrary quantum states, and the ability to transfer quantum information through a coherent communication bus accessible to a large number of qubits. Superconducting qubits made with scalable microfabrication techniques are a promising candidate for the realization of a large-scale quantum information processor. Although these systems have successfully passed tests of coherent coupling for up to four qubits, communication of individual quantum states between superconducting qubits via a quantum bus has not yet been realized. Here, we perform an experiment demonstrating the ability to coherently transfer quantum states between two superconducting Josephson phase qubits through a quantum bus. This quantum bus is a resonant cavity formed by an open-ended superconducting transmission line of length 7 mm. After preparing an initial quantum state with the first qubit, this quantum information is transferred and stored as a nonclassical photon state of the resonant cavity, then retrieved later by the second qubit connected to the opposite end of the cavity. Beyond simple state transfer, these results suggest that a high-quality-factor superconducting cavity could also function as a useful short-term memory element. The basic architecture presented here can be expanded, offering the possibility for the coherent interaction of a large number of superconducting qubits.

A Pulsed Power Supply Based on Power Semiconductor Switches and Transmission Line Transformer

Transmission line transformers (TLT's) as pulse transformers have received increasingly more attention due to their excellent frequency response characteristics over conventional wound transformers. This transformer basically consists of equal lengths of transmission line (normally coaxial cables are used) connected in parallel at the input side of the transformer, and in series at the output side so that the output voltage can be boosted in proportion. Because the reactance of the outer conductor increases with the rise of the frequency of the input voltage, the output voltage of each transmission line can be isolated mutually when the frequency is high enough. Then, the output voltage will be amplified through the voltage superposition. To minimize the substantial loss of voltage gain and obtain a low pulse droop rate, one stage transformer is entwined together as a unit, the number of stages of the transformer can increase easily by piling units one by one. This spiral construction makes the transmission line transformers much more compact. On the other hand, with the development of modern semiconductor technology, high voltage, fast rise time power semiconductor devices have been produced, the collector emitter breakdown voltage of one IGBT is to 1.7 kV and the rise time is 100 ns. This paper describes a kind of compact pulse power supply constructed by combining transmission line transformer and modern power semiconductor devices-IGBTs. High voltage IGBTs (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CES</sub> =1.7 kV) have been used as charge switches, short pulses can be obtained at the input port of the transformer, then the output pulse amplitude is 10 kV through a 10-stage transmission line transformer. Finally, the output voltage pulse waveforms are given in the paper.

Practical electromagnetics: from biomedical sciences to wireless communication

Preface. 1. INTRODUCTION. 1.1 Electrical sources and fundamental quantities. 1.2 Static and dynamic fields. 1.3 Working with complex numbers and functions. 2. VECTORS AND FIELDS. 2.1 Working with vectors. 2.2 Coordinate systems. 2.3 Differentiation and integration of vectors. 2.4 Gradient of the scalar field and its applications. 2.5 Divergence of the vector field and its applications. 2.6 Curl of the vector field and its applications. 2.7 The divergence theorem. 2.8 Stokes' theorem. DELTA. 2.9 Other operations involving 2.10 Helmholtz theorem. 3. BASIC LAWS OF ELECTROMAGNETICS. 3.1 Maxwell's equations in large scale/integral form. 3.2 Maxwell's equations in point/differential form. 3.3 Constitutive relations. 3.4 Boundary conditions. 3.5 Lorentz force equation. 3.6 Poynting vector and power flow. 4. UNIFORM PLANE WAVES. 4.1 The wave equation and uniform plane wave solutions. 4.2 Plane electromagnetic waves in Lossy media. 4.3 Uniform plane wave incident normally on an interface. 4.4 Uniform plane wave incident obliquely on an interface. 5. TRANSMISSION LINES. 5.1 Transmission line equations. 5.2 Finite length transmission line. 5.3 Smith chart. 5.4 Transients on transmission lines. 6. MODIFIED MAXWELL'S EQUATIONS AND POTENTIAL FUNCTIONS. 6.1 Magnetic charge and current. 6.2 Magnetic vector and electric scalar potentials. 6.3 Electric vector and magnetic scalar potentials. 6.4 Construction of solution in rectangular coordinates. 6.5 Construction of solution in cylindrical coordinates. 6.6 Construction of solution in spherical coordinates. 7. SOURCE IN INFINITE SPACE. 7.1 Fields of an infinitesimal source. 7.2 Antenna parameters. 7.3 Linear antennas. 7.4 Antenna arrays. 7.5 Friis transmission formula and the radar range equation. 8. ELECTROSTATIC FIELDS. 8.1 Laws of electrostatic fields. 8.2 Gauss' law. 8.3 Poisson's and Laplace's equations. 8.4 Capacitors and energy storage. 8.5 Further applications of Poisson's and Laplace's equations. 9. MAGNETOSTATIC FIELDS. 9.1 Laws of magnetostatic fields. 9.2 Inductors and energy storage. 9.3 Magnetic materials. 9.4 Magnetic Circuits. 10. WAVEGUIDES AND CAVITY RESONATORS. 10. 1 Metallic rectangular waveguide. 10. 2 Metallic circular cylindrical waveguide. 10.3 Rectangular cavity resonators. 10.4 Circular cylindrical cavity resonators. 11. NUMERICAL TECHNIQUES. 11.1 Finite difference methods. 11.2 The method of moments. 11.3 Scattering of plane EM waves from an infinitely long cylinder. Appendix A. Mathematical formulas. Appendix B. Delta function and evaluation of fields in unbounded media. Appendix C. Bessel functions. Appendix D. Legendre functions. Appendix E. Characteristics of selected materials. Appendix F. Physical constants. Appendix G. Decibels and Neper. Appendix H. Nomenclature and characteristics of standard rectangular waveguides. SELECTED REFERENCE BOOKS . Index.