Double semiconductor substrate in overlay shielded superconducting microstrip lines

The Transverse Transmission Line (TTL) is used in the theory of the overlay shielded microstrip lines considering the superconductor strip on two semiconductor regions. The superconductor effect is included with the boundary condition of the surface impedance, that is related to the complex conductivity of the material, calculated from the advanced two-fluid model. Applying the moment method the complex propagation constant of the structure, including the phase constant and the attenuation constant, is obtained. Results are presented for the complex propagation constant, versus the frequency and the temperature, of this overlay superconducting microstrip lines.     

High frequency loss and electromagnetic field distribution forstriplines and microstrips [MCM packages]

A new three-component measured equation of invariance (MEI) boundary condition is developed and applied to the hybrid edge/nodal vector finite element method. The electric field distribution on the cross section of various lossy transmission lines is calculated. The propagation constant of a lossy transmission line with coated conductor strip is also calculated. The three-component MEI boundary condition simulates the field distribution on the artificial boundary for electromagnetic field excited by the surface charge density and the three vector components of the electric current density. Numerical experiments are performed to test the method by comparing calculated transmission loss with the measured data     

Attenuation and propagation in various finline structures

The theory and numerical results of the asymmetric single and coupled bilateral and unilateral finlines and arbitrary antipodal finline considering the attenuation of the substrate are presented. Results are given to the complex propagation constant. The full wave analysis of the Transverse Transmission Line — TTL method is used in the FTD. Applying the moment method the complex propagation constant, including the attenuation constant and the phase constant, are obtained. The effective dielectric constant, ?_eff,, and the characteristic impedance are also calculated. The results are compared with the references, and news results are presented for these parameters.     

Field Solution, Polarization, and Eigenmodes of Shielded Microstrip Transmission Line

Application of the reciprocity theorem leads to a variational expression for the propagation constant of the fields inside shielded microstrip-like transmission lines. The resulting equation involves both the propagation constant and the tangential fields at the air-dielectric interface. Using the Rayleigh-Ritz optimization technique, both the propagation constant and the fields are completely determined. The calculated results of the propagation constant compare well with other available data. Moreover, the field solution obtained is presented in the form of a polarization ratio relating the axial to the transverse electric field. Results cover both low and high frequencies, and the technique proves valid at both frequency ranges. The method may be extended to other configurations of planar striplines by proper adjustment of the integration limits.     

Transmission theory of a parallel-two-wire-transmission-linecovered with three layer media

A parallel-two-wire-transmission-line covered by a three layer media has particular transmission characteristics. It is expected that this type of line might therefore be applied to new microwave circuits and antennas. Such lines have been analyzed by solving Laplace equations as a two dimensional boundary value problem. However, at higher frequencies, it is not appropriate to explain these particular properties using the quasi-TEM mode analysis. Transmission theory for these lines has to be solved using a rigorous three dimensional analysis. in this paper, we describe a new three dimensional analysis technique that is used to obtain more accurate propagation constants by considering the E_Z, H_Z components of the field. The assumed current distribution of the parallel-two-wire-line system is Fourier expanded over the angular coordinate &thetas;, and the boundary value problem is solved by the mode matching technique. It is found that mainly hybrid modes are transmitted via this type of transmission system and that the propagation constant varies discontinuously at frequencies where the dipole mode can exist on the three layer dielectric media itself. Numerical results are presented and compared with experimental data     

微波通信电路中传输线电磁特性与过渡结构夹角关系

微波通信电路中会广泛应用共面波导（CPW）-共面波导以及共面波导-微带（MS）过渡结构。实际应用时,为了布线的方便,通过过孔连接的2段传输线并非始终处于直线上,而可能是任意夹角。仿真分析了经由过孔连接的2段传输线在不同夹角情况下的传播特性。仿真结果表明过渡结构的散射参数受两线夹角影响显著,总体而言,2种过渡结构的|S11|随夹角增大而增大,而|S21|则随夹角增大而减小。散射参数的变化趋势在夹角大于和小于90°时存在差异,在夹角为180°时更明显。此外,还比较并分析了CPW-CPW和CPW-MS结构传播特性的区别。     

Analysis of Microstrip-Like Transmission Lines by Nonuniform Discretization of Integral Equations

The nonuniform discretization of the integral equation on the tangential electromagnetic (EM) field on the boundary surface is proposed as a numerically efficient method to analyze the microstrip-like transmission lines. The calculated results of the propagation constant of the microstrip line based on this method are compared with other published analytical results. Various types of planar striplines are treated by the same formulas. The dominant and higher order modes of shielded microstrip line are discussed and compared with the longitudinal-section electric (LSE) and linear synchronous motor (LSM) modes of a two-medium waveguide.     

Parameter extraction and correction for transmission lines anddiscontinuities using the finite-difference time-domain method

The finite-difference time-domain (FDTD) method is useful for performing broadband characterization of uniform transmission lines and discontinuities. Modeling a geometry often requires the implementation of an absorbing boundary condition (ABC). When this is the case, numerical reflections from the ABC's will add significant error to the calculated transmission line or scattering (S) parameters. This paper introduces a simple post-processing algorithm for extracting these parameters and correcting for numerical reflection error. Furthermore, this method is shown to have a unique relationship to Prony's method. Practical application and limitations of this technique are also discussed. Finally, the impedance and propagation constant of a microstrip line are calculated using this method     

Tutorial note on the general transmission line theory for a thinwire above the ground

Transmission along an overhead wire or cable conductor is considered. It is shown that the rigorous solution of the problem can be put in the context of classical transmission line theory that has been used by power engineers for many years. However, the effective line parameters are spatially dispersive in the sense that they depend on the actual propagation constant of the mode in question     

Hybrid-mode analysis of multilayered and multiconductortransmission lines

Hybrid-mode propagation properties of multilayered and multiconductor transmission lines are studied by using an efficient vector finite element method (FEM) with high-order hybrid edge/nodal triangular elements, which can give frequency-dependent propagation constants directly. Characteristic impedances are also calculated from the FEM field solutions employing a reciprocity-related definition and taking the modal orthogonality into account. The numerical results of a coupled microstrip line are compared with those of the boundary integral equation technique, and good agreement is obtained. Also, a dual-plane triple microstrip line is analyzed. The approach is found to be very general and able to simultaneously handle different thicknesses and widths of strip conductors. The flexibility of the approach is also shown by including anisotropy in the dielectric substrates of such lines     

Analysis of Slotted, Dielectrically Loaded, Ridged Waveguide

This paper considers a symmetrical double-ridged waveguide with an axial dielectric slab inserted into it. Series expansions are used to describe the waveguide fields. The method of moments is employed to provide a system of linear equations from which the propagation constant and the coefficients of the series expansions are obtained. from these quantities, the field distributions and power flow are determined and a characteristic impedance based on a power-voltage definition is computed. The calculated propagation constants are compared with measured values.     

Embedded microstrip interconnection lines for gigahertz digitalcircuits

Transmission line structures are needed for the high-performance interconnection lines of GHz integrated circuits (ICs) and multichip modules (MCMs), to minimize undesired electromagnetic wave phenomena and, therefore, to maximize the transmission bandwidth of the interconnection lines. In addition, correct and simple models of the interconnection lines are required for the efficient design and analysis of the circuits containing the interconnection lines. In this paper, we present electrical comparisons of three transmission line structures: conventional metal-insulator-semiconductor (MIS) and the embedded microstrip structures-embedded microstrip (EM) and inverted embedded microstrip (IEM). In addition, we propose closed-form expressions for the embedded microstrip structures EM and IEM and validate the expressions by comparing with empirical results based on S-parameter measurements and subsequent microwave network analysis. Test devices were fabricated using a 1-poly and 3-metal 0.6 μm Si process. The test devices contained the conventional MIS and the two embedded microstrip structures of different sizes. The embedded microstrip structures were shown to carry GHz digital signals with less loss and less dispersion than the conventional MIS line structures. S-parameter measurements of the test devices showed that the embedded microstrip structures could support the quasi-TEM mode propagation at frequencies above 2 GHz. On the other hand, the conventional MIS structure showed slow-wave mode propagation up to 20 GHz. More than 3-dB/mm difference of signal attenuation was observed between the embedded microstrip structures and the conventional MIS structure at 20 GHz. Finally, analytical RLCG transmission line models were developed and shown to agree well with the empirical models deduced from S-parameter measurements     

Transmission line models for lossy waveguide interconnections in VLSI

At high frequencies the waveguide nature of interconnections in VLSI circuits becomes important. Moreover, losses in interconnection are a major feature, not a perturbation. Here it is shown that even for such lossy waveguide structures an exactly equivalentRLGCtransmission line can be found. Equations are given determining these transmission line parameters in terms of the waveguide propagation constant and complex average power, and also in terms of integrals over the electric and magnetic field varibles. The resultingL,C, andGparameters differ from the usual static values when losses are important, and R is not restricted to the usual formula based upon a perturbation treatment of the skin effect. Consequently, semiconductor substrates can be treated. "Current" and "voltage" are found to have an abstract meaning in the equivalent transmission line. For a waveguide in a medium where conductivity and permittivity vary with position (such as a many-layered medium) an explicit formula relating "current" and "voltage" to weighted averages of transverse waveguide fields is given. A brief discussion of the reformulation of Thevenin equivalent circuit parameters in terms of reflection coefficients avoids terms such as "open circuit voltage" that are difficult to interpret for the equivalent transmission line. The framework presented allows construction of equivalent circuits for lossy waveguide interconnections, drivers, and terminations that provide correct spatial dependence in the direction of propagation and correct power relations despite the abstract nature of "current" and "voltage" in these lines.     

De-embedding and unterminating microwave fixtures with nonlinearleast squares

A general method of characterizing microwave test fixtures for the purpose of determining the parameters of devices embedded in the fixture is discussed. The technique was used to investigate deembedding under the assumptions that all measurement errors are random and normally distributed and that the standards are distributed uniformly around the Smith chart. It was shown that for any given number of standards, the greatest accuracy under these assumptions is achieved by utilizing a large set of known reflective loads. When the propagation constant and the reflection coefficients of the standards are not known, then equal numbers of thru lines and reflective loads give the highest accuracy, although not as high as when the propagation constant and reflection coefficients are known. The accuracy of the technique was studied and compared with that of the common open-short-load (OSL) and thru-reflect-line methods. The OSL technique was found to be considerably less accurate than using sets of offset reflective loads     

Higher Order Modes in RTHOCT

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High-Performance Slow-Wave Transmission Lines With Optimized Slot-Type Floating Shields

A novel slow-wave transmission line with optimized slot-type floating shields in advanced CMOS technology is presented. Periodical slot-type floating shields are inserted beneath the transmission line to provide substrate shielding and to shorten the electromagnetic (EM) propagation wavelength. This is the first study that demonstrates how the wavelength, attenuation loss, and characteristic impedance can be adjusted by changing the strip length (SL), strip spacing (SS), and metal layer position of the slot-type floating shields. Wavelength shortening needs to be achieved with a tradeoff between slow-wave effect and attenuation loss. The slot-type floating shields with different SLs, SSs and metal layer positions are analyzed. It is concluded that minimum SL provides the most optimal result. A design guideline can be established to enable circuit designers to reach the most appropriate slot-type floating shields for optimal circuit performance. Transmission line test structures were fabricated by using 45-nm CMOS process technology. Both measurement and EM waves simulation were performed up to 50 GHz. Transmission lines are frequently used at a length of half- or quarter-wavelength. With a shortened wavelength, a saving in silicon area of more than 67% can be achieved by using optimized slot-type floating shields. Experimental results demonstrated a higher effective relative permittivity value, which is improved by a factor of more than 9, and a better quality factor, which is improved by a factor of more than 6, as compared to conventional transmission lines.      

A Double-Ground-Plane Strip-Line System for Microwaves

The double-ground-plane strip line consists of two parallel conducting planes with a conducting strip imbedded in a homogeneous dielectric between them. Transmission characteristics for this system are calculated, and design formula are given. Practical viewpoints on design and application of strip lines are discussed. System can be used as an inexpensive base for microwave circuits and is well adapted to laboratory experiments and mass production.     

Propagation in layered biased semiconductor structures based ontransport analysis

A transport-field parallel-plate formulation and solution method to determine the small-signal propagation constant is given for wide microstrip lines over an inhomogeneously doped semiconductor substrate of small transverse dimensions. Included in the detailed transport model are two carrier species, recombination-generation mechanisms, DC and AC field-dependent mobilities and diffusion constants, and boundary condition contact effects. A transverse DC bias condition is applied. Structures numerically simulated are a voltage-variable GaAs distributed Schottky-barrier phase shifter and a transmission line over an Si bipolar junction. Numerical data based on a finite-difference technique are generated on carrier densities, electric potentials and fields, and current densities. Propagation constant calculations compared favorably to those calculated by both full-wave field analysis and moments-of-the-Boltzmann-equation analysis for some less general cases. Propagation constant results for the GaAs structure are compared with available experimental data, and good agreement is obtained     

Measurements of the characteristic impedance of coaxial air linestandards

A method for electrically measuring the characteristic impedance of coaxial air line standards is described. This method, called the gamma method, determines the characteristic impedance of a coaxial air line from measurements of its propagation constant and capacitance per unit length. The propagation constant is measured on a network analyzer, and the capacitance per unit length is measured on a capacitance bridge at 1 kHz. The measurements of characteristic impedance with the gamma method are independent of any dimensional measurements. Measurements of the characteristic impedance using the gamma method are compared to theoretical predictions from dimensional measurements. Test results are shown for 14 mm, 7 mm, and 3.5 mm coaxial air lines     

Clarke components for a system of busbars with pronounced proximity effect

The equations governing multiple straight transmission lines are applied to a configuration of three lines in the same plane. By a transformation with a matrix T, corresponding to the Clarke components, the propagation coefficients and modes can easily be found. A numerical example is given of three busbars showing pronounced proximity effect. The example is calculated by analogue simulation on a capacitor-resistor network.