Characteristic Impedance Of Transmission Line Research Articles

Generalized Complex-to-Complex Impedance Transformers Based on Conjugately Characteristic-Impedance Transmission Lines

The novel technique of generalizing complex-to-complex impedance transformers (CCITs) with miniaturization is introduced in this paper. The generalized CCITs are designed based on conjugately characteristic-impedance transmission lines (CCITLs) along with the Meta-Smith charts (MSCs), resulting in convenient design equations. For illustration, a prototype of generalized CCITs is designed, simulated, and implemented with an asymmetric compact microstrip resonant cell (ACMRC), which is one of the CCITLs. The measurement results confirm that the proposed technique offers approximately 28.5% shorter in physical length compared to the CCIT designed using standard transmission lines.

Extraction of the Complex Relative Permittivity from the Characteristic Impedance of Transmission Line by Resolving Discontinuities

This paper describes a material complex permittivity extraction technique based on four measurements of two identical coaxial (circular and rectangular) lines, distinguished by their lengths. The paper presents a combination of propagation parameters through mixing the eigenvalue principle and the lines’ characteristic impedance to improve the extraction techniques of intrinsic material parameters. However, the accuracy of some material parameters is insufficient, as the discontinuities at the feedline–ideal line interface are not adequately solved. In these cases, a new formulation of the complex effective permittivity is suggested, associating the propagation constant and the characteristic impedance for a homogeneous structure. Next, uncertain errors that can negatively impact the method are removed from the mathematical expression. Then, a characteristic impedance expression is developed in the second stage to improve the mathematical formulation. Finally, a correction coefficient in tune with reality and a polynomial function to amend the behavior of some of the curves are provided. The approach’s novelty lies in its ability to extract and correct the characteristic impedances despite discontinuity impedances at the ideal line–feedline interface. Several materials are tested with circular and/or rectangular coaxial fixtures to confirm the performance of the suggested method. The test cells are homogeneous, full, and long, at 80 mm and 100 mm (50 mm for the circular one). Determining the propagation constant from the eigenvalue of the wave cascading matrix (WCM) is a fundamental step in this method. Knowing the propagation constant helps to automatically compute a correction coefficient that depends on the fixture and the material being tested. Experimental validation is performed in the frequency range from some MHz to 10 GHz, 13.5 GHz, and 20 GHz, according to the tested material. Both test fixtures are filled with the sample material, with a vacuum considered as a reference parameter. The method’s accuracy is better than 5% on the relative permittivity parameter throughout the frequency range. All the tested samples are compared with the results using the filled two-transmission-line technique (FTTL), using only the eigenvalue determination principle. The trapper cells are coaxially circular and rectangular.

Design of Reactance-to-Reactance Impedance Transformers Based on Conjugately Characteristic-Impedance Transmission Lines (CCITLs) and Meta-Smith Charts (MSCs)

Design of Reactance-to-Reactance Impedance Transformers Based on Conjugately Characteristic-Impedance Transmission Lines (CCITLs) and Meta-Smith Charts (MSCs)

Transmission lines characteristic impedance versus Q-factor in CMOS technology

AbstractThis paper presents a systematic comparison of the relationship between transmission line characteristic impedance and Q-factor of CPW, slow-wave CPW, microstrip, and slow-wave microstrip in the same CMOS back-end-of-line process. It is found that the characteristic impedance for optimal Q-factor depends on the ground-to-ground spacing of the slow-wave transmission line. Although the media are shown to be similar from a mode of propagation point of view, the 60-GHz optimal Q-factor for slow-wave transmission lines is achieved when the characteristic impedance is ≈23 Ω for slow-wave CPWs and ≈43 Ω for slow-wave microstrip lines, with Q-factor increasing for wider ground plane gaps. Moreover, it is shown that slow-wave CPW is found to have a 12% higher optimal Q-factor than slow-wave microstrip for a similar chip area. The data presented here may be used in selecting Z0 values for S-MS and S-CPW passives in CMOS that maximize transmission line Q-factors.

Modeling and Analysis of Terahertz Graphene Switches for On-Wafer Coplanar Transmission Lines

We present an analysis of graphene-loaded transmission line switches for sub-millimeter wave and terahertz applications. As such, we propose equivalent circuit models for graphene-loaded coplanar waveguides and striplines and examine the switching performance under certain parameters. Specifically, we identify the optimum design of graphene switches based on transmission line characteristic impedance, scaling factor, graphene shape, and topology (series or shunt). These parameters are varied to obtain the insertion loss and ON/OFF ratio of each switch configuration. The extracted results act as the design roadmap toward an optimum switch topology and emphasize the limitations with respect to fabrication challenges, parasitic effects, and radiation losses that are especially pronounced in the millimeter wave/terahertz bands. This is the first time that such an in-depth analysis is carried out on graphene-loaded transmission line switches, enabling the development of efficient millimeter wave/terahertz tunable topologies in terms of insertion loss and ON/OFF ratio. Specifically, the optimized switches can be integrated with antennas or employed for the development of tunable phase shifters, leading to the implementation of efficient reconfigurable reflective surfaces (e.g., reflectarrays) or coded phased arrays either for imaging or wireless communication applications. In our models, we use measured graphene values (sheet impedance) instead of theoretical equations, to obtain the actual switching performance. Moreover, the proposed study can be easily expanded to other thin film materials that can be characterized by a sheet impedance including vanadium dioxide and molybdenum disulfide. Finally, the proposed equivalent models are crucial for this in-depth study; since we simulated more than 2,000,000 configurations, a computationally challenging task with the use of full-wave solvers.

프리프레그 가공을 통한 인쇄회로 기판의 유효 유전상수 하향 조정

As electronic devices become more compact, the thickness of the layer in printed circuit boards(PCBs) decreases, and the characteristic impedance of transmission lines with a minimum allowable trace width often becomes less than 50 Ω. Reducing the minimum trace width or switching to a dielectric with lower dielectric constant is prohibitive owing to increased manufacturing costs. We propose a new way of reducing the effective dielectric constant by drilling holes in prepreg. We perform measurements and simulations to verify the effectiveness of the proposed approach. Results demonstrate that using drilled prepreg enables the lowering of the effective dielectric constant by up to 7 %.

Dual-frequency Wilkinson power divider with ±45° phase shifts at the two bands

ABSTRACTA new Wilkinson power divider with ±45° phase shifts at two bands for dual-frequency operation is studied in this paper. Studies show that the phase shift can be controlled by the characteristic impedances of transmission lines of a π-shaped network, as compared with the conventional case. Moreover, by optimally determining the characteristic impedances, flat phase responses, thus widened bandwidths, can be achieved at the two bands. Analysis of the π-shaped network is performed and corresponding design considerations are given. Demonstration on a 2.4/5.2-GHz dual-band power divider with, respectively, +45° and – 45° phase shifts at the two bands verifies the analyses well.

Dual-Band Gysel Power Divider With Different Power Dividing Ratios

This letter presents a dual-band Gysel power divider (PD) with different power dividing ratios. Unlike traditional dual-band Gysel PDs, the power dividing ratios of proposed PD are determined by both electrical lengths and characteristic impedance of transmission lines. The proposed circuit is analyzed based on transmission line theory and design equations are derived. For illustration, a prototype operating at 1 and 2 GHz is designed and measured. The concept has been verified by the measured results.

Quasi-static Analysis Based on an Equivalent Circuit Model for a CMOS Terahertz Plasmon Detector in the Subthreshold Region.

An analytic method for a complementary metal-oxide-semiconductor (CMOS) terahertz plasmon detector operating in the subthreshold region is presented using the equivalent circuit model. With respect to design optimization of the detector, the signal transmission from the antenna port to the output of the detector is described by using the proposed circuit model, which does not include a complicated physical operating principle and mathematical expressions. Characteristics from the antenna port to the input gate node of the detector are analyzed through the superposition method by using the characteristic impedance of transmission lines. The superposition method shows that the effect of interconnection lines at the input is simplified with the optimum bias point. The characteristics of the plasmon detection are expressed by using small-signal analysis of the single transistor at the sub-threshold operation. The results of the small-signal analysis show that the unity gain preamplifier located between the detector core and the main amplifier can improve the detection performances such as the voltage responsivity and the noise equivalent power. The measurement results using the fabricated CMOS plasmon detector at 200 GHz suggest that the unity gain preamplifier improves the detector performances, which are the same results as we received from the proposed analytic method.

Compact arbitrary terminated power divider with bandwidth‐enhanced negative group delay characteristics

SummaryA novel compact arbitrary terminated power divider with bandwidth‐enhanced negative group delay (NGD) characteristics is proposed. The NGD characteristics are controlled by characteristic impedances of transmission lines and the coupled line between two output ports. Flat and wide NGD bandwidth is produced by using the combination of a series resistor and short‐circuited coupled‐line section. The complete closed‐form equations are presented. For experimental demonstration, a prototype is designed and fabricated at f0 of 2.14 GHz. The measured results indicate that the proposed power divider is able to realize wide NGD bandwidth and good NGD flatness.

Series-connected array of superconductor–insulator–superconductor junctions in the 100 GHz-band heterodyne mixer for FOREST on the Nobeyama 45 m telescope

Abstract We have designed and experimentally evaluated a series-connected array of superconductor–insulator–superconductor (SIS) junctions in the 100 GHz-band mixer for the multi-beam receiver FOREST on the Nobeyama 45 m millimeter-wave telescope. The construction of the junction chip comprised a waveguide probe antenna, impedance-matching circuit, SIS array junction, and choke filter, which were made from a superconducting niobium planar circuit on a quartz substrate. The multi-stage impedance-matching circuit between the feed point and the SIS junction was designed as a capacitively loaded transmission line, and it comprised two sections with high (∼90 Ω) and low (∼10 Ω) characteristic impedance transmission lines. The structure of this tuning line was simple and easy to fabricate, and the feed impedance matched with the SIS junction in a wide frequency range. The signal coupling efficiency was more than 92% and the expected receiver noise temperature was approximately twice the quantum limit for 75–125 GHz based on quantum theory. The array junction devices with three to six connected junctions were fabricated and we measured their performance in terms of the receiver noise temperature and gain compression in the laboratory. We successfully developed an array junction device with a receiver noise temperature of ∼15–30 K and confirmed that the improvement in the saturation power corresponded to the number of junctions. The newly developed array junction mixer was installed in the FOREST receiver and it successfully detected the 12CO(J = 1–0) molecular line toward IRC +10216 with the Nobeyama 45 m telescope.

Design and Implementation of a Three-Section Transmission Line Transformer

New formulations of fundamental load impedance circuit in the Z-plane are employed to study transformers. Transformer configuration consists of three-section serial lines. The design procedures employ prototypes of transfer function, parametric modeling techniques, and optimization methods; dual-band uncorrelated frequencies of transfer function at the normalizing frequency (π) are studied. This transformer was designed on a PCB FR4 substrate featuring a permittivity er = 4.4, a loss tangent tanδ = 0.0245, and a thickness of h = 1.6 mm. The results of simulation and measurement show that complex load impedance can be matched at two uncorrelated frequencies. The values of characteristic impedances of transmission lines synthesizing the transformers are adjusted according to the autoregressive process by optimization algorithms. The experimental results are in good agreement with theoretical values.

Arbitrary Prescribed Wideband Flat Group Delay Circuits Using Coupled Lines

This paper presents the analytical design of transmission-type arbitrary prescribed wideband flat group delay (GD) circuits (type-I and type-II) using $\lambda $ /4 coupled lines. The GD circuit type-I consists of two sections of coupled lines, whereas the GD circuit type-II consists of $\lambda $ /4 transmission lines (TLs) at input and output, in addition to coupled lines. The additional $\lambda $ /4 TLs at input–output ports in GD circuit type-II provide more freedom to obtain larger GD, as compared to type-I, without fabrication difficulties. The analytical analysis shows that the wideband flat GD response can be obtained by selecting the appropriate even- and odd-mode impedances of coupled lines and the characteristic impedance of TLs. To obtain the arbitrary prescribed wideband flat GD response, the closed-form analytical design equations are provided. For experimental validation of the proposed structures, prototypes of GD circuits (type-I and type-II) are designed and fabricated at the center frequency of 2 GHz. The measurement results agree well with the simulation and theoretical predicted results.

Moving Reference Planes of Unit Cells of Reciprocal Lossy Periodic Transmission-Line Structures

An analysis of moving reference planes of unit cells of reciprocal lossy periodic transmission-line (TL) structures (RLSPTLSs) by using the equivalent bi- characteristic-impedance transmission line (BCITL) model is presented. Applying the BCITL theory, only the equivalent BCITL parameters (characteristic impedances for wave propagating in forward and reverse directions and associated complex propagation constant) are of interest. In the analysis, an arbitrary infinite RLSPTLS is firstly considered by shifting a reference position of unit cells along TLs. Then, a semi-infinite terminated RLSPTLS is subsequently investigated in term of associated load reflection coefficients. It is found that the equivalent BCITL characteristic impedances of the original and shifted unit cells, as well as the associated load reflection coefficients of both unit cells, are mathematically related by the bilinear transformation. However, the equivalent BCITL complex propagation constant remains unchanged. Numerical results are provided to show the validity of the proposed technique.

Thru-Reflect-Line Calibration Technique: Error Analysis for Characteristic Impedance Variations in the Line Standards

In this paper, we analyze the impact of characteristic impedance variations among standards on the accuracy of the thru-reflect-line (TRL) calibration technique. The impedance transformer method is adopted to derive the expressions of the calibration coefficient errors due to the manufacturing tolerances. It is found that three factors can affect the magnitude of the errors in the calibration coefficients (c/a and b terms), which are crucial to get the final calibrated results. The first factor is related to the original parameters of the error networks (test fixtures): the larger the insertion losses, the smaller the error in b ; the error in c/a may see an opposite trend if the error network is lossy instead of lossless. The second factor is denoted as the phase contribution (one of the three multipliers of the derived error expression): the magnitude of this error contributing item is approximately equal to the ratio of two hyperbolic sine functions, the variables of which are the length of Line and the length difference between Line and Thru, respectively. The third factor comes from the impedance differences between Thru and Line: the smaller the impedance variation, the smaller the error. The error analysis, presented here, can help engineers evaluate the calibration accuracy by analyzing the error contributing items. It also can be further used to guide test fixture designs to maximize TRL's error immunity to the transmission line characteristic impedance variations.

A Novel Wideband Balanced-to-Unbalanced Power Divider Using Symmetrical Transmission Lines

A novel wideband balanced-to-unbalanced power divider using symmetrical transmission lines is proposed. Due to the symmetry of the power divider circuit, even/odd-mode analysis method is applied to derive the even/odd-mode values and transmission line characteristic impedance. A resistor in the middle of two single-ended output ports is used to realize high isolation for the power division ports. One prototype of the wideband balanced-to-unbalanced power divider operating at 2.2 GHz (1.24–3.20 GHz) is designed and measured to prove the proposed methods.

An efficient analysis of the far-field radiation of an electric/magnetic Hertzian dipole embedded in electromagnetic bandgap structures of periodic lossless multilayers using the equivalent CCITL model

In this paper, the far-field radiation of a Hertzian dipole embedded in electromagnetic bandgap structures of periodic lossless multilayers is studied analytically and numerically. To simplify the analysis of this radiation problem, the equivalent transmission line (TL) model based on conjugately characteristic-impedance TLs (CCITLs) is employed to efficiently compute the far-field radiation of the Hertzian dipole due to the periodic nature of the problem, where associated reflection coefficients, which are useful in computing far fields, can be determined effectively. It is found that numerical results based on the equivalent CCITL model are in very good agreement with those obtained from a commercial electromagnetic software.

A Generalized Lossy Transmission-Line Model for Tunable Graphene-Based Transmission Lines with Attenuation Phenomenon.

To investigate the frequency shift phenomenon by inserting graphene, a generalized lossy transmission-line model and the related electrical parameter-extraction theory are proposed in this paper. Three kinds of graphene-based transmission lines with attenuation phenomenon including microstrip line, double-side parallel strip line, and uniplanar coplanar waveguide are analyzed under the common conditions where different chemical potentials are loaded on graphene. The values of attenuation constant and phase constant, and the real and imaginary parts of the characteristic impedance of transmission lines are extracted to analyze in details. When the attenuation constant and the reactance part of the characteristic impedance are approximately equal to zero, this kind of transmission line has low or zero insertion loss. On the contrary, the transmission line is under the radiation mode with obvious insertion loss. The phase constant changes linearly under the transmission mode and can be varied with changing of chemical potentials which attributes to the property of frequency tunability. Furthermore, a bandwidth reconfigurable uniplanar coplanar waveguide power divider is simulated to demonstrate that this theory can be applied to the design of three-port devices. In summary, this work provides a strong potential approach and design theory to help design other kinds of terahertz and mid-infrared reconfigurable devices.

Design of Triple-Band Impedance Transformers Using Z-Transform Techniques

A new formulation of one section transmission-line and load impedance circuit in the $\boldsymbol{Z}$ - plane is employed to study transformers. The design procedures employ prototypes of transfer function, parametric modeling techniques, and optimization methods; a model describing transformer of multi-section transmission-line with load impedances is proposed. Triple-band of transfer function at the microwave frequencies is studied. This transformer was designed on a PCB FR4 substrate featuring a permittivity $\varepsilon\text{r} = 4.4$ , a loss tangent $\tan\delta = 0.0245$ , and a thickness of $\text{h} = 1.6 \text{mm}$ . The results of simulation and measurement show that a complex impedance can be matched at three frequency bands. The values of characteristic impedances of transmission lines synthesizing the transformers are adjusted according to the AR process by optimization algorithms. The experimental results are in good agreement with theoretical values.

A Numerical Study of Moving Reference Planes Associated with Unit Cells of Reciprocal Lossy Periodic Transmission-Line Structures by Using the Equivalent BCITL Model

A moving reference plane of unit cell of reciprocal lossy periodic transmission-line (TL) structures (RLSPTLSs) by using the equivalent bi- characteristic-impedance transmission line (BCITL) model is studied numerically in this paper. Applying the BCITL theory, only the equivalent BCITL parameters, characteristic impedances for wave propagating in forward and reverse directions and associated complex propagation constant, are of interest. In this study, a unit cell of an infinite RLSPTLSs is obtained by shifting a reference position of unit cells along TLs of interest. For illustration, an example of symmetrical RLSPTLSs is initially considered. Then, unsymmetrical structures are subsequently investigated by shifting a reference position of unit cells. It is found that the equivalent BCITL complex propagation constant remains unchanged as expected, while the equivalent BCITL characteristic impedances are generally different, depending on the reference position of unit cells. Numerical results will be provided and discussed in this paper.