Coupled Lines Research Articles

Nonlinearity in superconducting metamaterial structures, including spirally coupled lines

Superconducting devices can indicate nonlinear behaviors such as harmonic generation and intermodulation distortion (IMD) with regard to nonlinear Meissner effect even at low input powers. Firstly in this paper, a new method for nonlinear modelling of Superconducting Transmission Lines (SMTLs) with complex coupling is proposed. Then, based on the proposed new method, nonlinear equivalent circuit model for Superconducting Spirally Coupled Lines (SSCLs) is suggested. A numerical approach based on three-dimensional finite element method (3D-FEM) is used to compute the current distribution in SSCLs. Closed-form expressions for quadratic and modulus geometrical nonlinear factors (GNFs) of SSCLs are proposed. The proposed model can be analyzed nonlinearly by using of Harmonic Balance (HB) method to predict nonlinear behaviors. To validate the accuracy of the proposed nonlinear model, we modeled a superconducting metamaterial filter consisting of two SSCLs in this paper. Good agreement between calculated results and measured ones was found. Thereafter, based on the proposed model, effects of nonlinearity on main parameters of the superconducting metamaterial structure such as phase constant (β) and attenuation factor (α) are analyzed.

Compact Wideband Reflective/Absorptive Bandstop Filter With Multitransmission Zeros

Novel wideband reflective bandstop filters (RBSFs) and absorptive bandstop filters (ABSFs) with high stopband rejection (SR) and good frequency selectivity are proposed. Based on a coupled line (CL) with an open-circuited stub, a broad stopband response with three transmission zeros (TZs) is implemented in a compact circuit configuration. Two modified CL structures are loaded at the ports resulting in two additional TZs. In addition, a grounded resistor is introduced to absorb unwanted signals in the stopband. For demonstration, the five-zero RBSFs and three-zero ABSFs operating at 2 GHz are designed and built. The reflective filter shows a 35-dB SR with 79.5% relative bandwidth (RB). The absorptive filter with 69.5% RB of 24-dB SR achieves an all-passband 12.2-dB return loss. Good agreements between simulated and measured results are observed.

Exceptional Points of Degeneracy and Branch Points for Coupled Transmission Lines—Linear-Algebra and Bifurcation Theory Perspectives

We provide a new angle to investigate exceptional points of degeneracy (EPD) relating the current linear-algebra point of view to bifurcation theory. We apply these concepts to EPDs related to propagation in waveguides supporting two modes (in each direction), described as a coupled transmission line. We show that EPDs are singular points of the dispersion function associated with the fold bifurcation connecting multiple branches of dispersion spectra. This provides an important connection between various modal interaction phenomena known in guided-wave structures with recent interesting effects observed in quantum mechanics, photonics, and metamaterials systems described in terms of the algebraic EPD formalism. Since bifurcation theory involves only eigenvalues, we also establish the connection to the linear-algebra point of view by casting the system eigenvectors in terms of eigenvalues, analytically showing that the coalescence of two eigenvalues results automatically in the coalescence of the two respective eigenvectors. Therefore, for the studied two-coupled transmission-line problem, the eigenvalue degeneracy explicitly implies an EPD. Furthermore, we discuss in some detail the fact that EPDs define branch points in the complex frequency plane, we provide simple formulas for these points, and we show that parity-time (PT) symmetry leads to real-valued EPDs occurring on the real-frequency axis.

High-Selectivity Wideband Bandpass Filter Using Simple Coupled Lines With Multiple Transmission Poles and Zeros

A compact fifth-order wideband bandpass filter (BPF) using simple coupled lines with sharp rolloff skirts is proposed in this letter. Five transmission poles within the passband and eight deep transmission zeros from 0 to $2\!f_{0}$ ( $f_{0}$ denotes the center frequency of the passband) can be realized through input impedance calculations. For demonstration, a wideband BPF prototype centered at 2.05 GHz with high-stopband rejection is designed and fabricated, whose measured 3-dB fractional bandwidth is of 60% (1.44–2.66 GHz). Good agreement between the simulations and measurements validates the design idea.

Asymmetric coupled lines for common‐mode noise suppression in bent differential lines

In this Letter, novel asymmetric coupled lines are proposed to suppress common-mode (CM) noise in bent differential lines. Based on the concept of the relative permittivity of a single microstrip line, the width of the outer line is made smaller than that of the inner line in bent differential lines to reduce the time skew and the other design parameters are adjusted to account for the differential impedance. To verify the improvement afforded by the proposed method, the simulated and measured results of the proposed structure were compared with two different designs; the conventional bent differential lines and the compensated differential lines using a serpentine inner line. The results of the proposed method show better signal integrity than the other methods.

Crosstalk analysis of multi‐microstrip coupled lines using transmission line modeling

This article presents a new analytical method to predict crosstalk of a homogeneous terminated two microstrip coupled lines over a ground plane using transmission line theory. The derived formula is frequency and location dependent, which can be used to quickly estimate the crosstalk of a coupled line. Also, the effect of the geometrical parameters of the lines and load are included in the derived formula. Presented method can be used for the other types of coupled lines including lossy or lossless lines. To verify the accuracy of the introduced method, a few microstrip coupled line structures with different geometrical parameters are considered numerically and experimentally. The results of crosstalk based on the proposed analytical methods, simulation study using high frequency structure simulator and those obtained by measurements are reported and compared with each other. It is shown that our proposed method accurately estimates the amount of crosstalk for a two microstrip coupled lines.

Анализ и синтез несимметричных связанных линий в однородной диэлектрической среде

Анализ и синтез несимметричных связанных линий в однородной диэлектрической среде

Integrated Optimization of Mixed-Model Assembly Line Balancing and Buffer Allocation Based on Operation Time Complexity

This paper presents a new approach to coupling line balancing and buffer allocation for stochastic mixed-model assembly line. Three types of complexity are defined, that are time diversity complexity for single station, time diversity complexity for a whole line, and time stochastic fluctuations complexity. An integrated optimization model for line balancing and buffer allocation is established with the objectives of maximizing productivity, minimizing complexity and total buffer capacity. Then an improved genetic algorithm is applied to solve the model. Finally, the effectiveness of the method is verified by an example of a mixed-model assembly line.

Phase Reconfigurable Microwave Power Divider

A reconfigurable power divider (PD) that can operate either in an in-phase mode or out-of-phase mode is presented. To that end, the novel concept of using tunable phase shifter, which is a reflection-type loaded coupled lines, to emulate an effective variable length transmission line (TL) is utilized. The proposed PD uses a quarter-wavelength TL, a $100~{\Omega }$ isolation resistor and two tunable phase shifters. The presented theoretical analysis shows that by properly selecting the parameters of the phase shifter, it can be used to approximate the performance of variable length TL. To validate the design, a prototype of dimensions 50 mm ${\times }$ 25 mm is built, using Rogers RO3010 substrate, and tested. The results indicate that the device can operate as an in-phase and out-of-phase by using suitable biasing voltages. Across the band 0.9–1.1 GHz, the device has more than 12 dB return loss at all the ports and more than 15 dB isolation between the two output ports with less than 5° phase deviation for both of the in-phase and out-of-phase states.

Low-Loss Wide-Tuning-Range Three-Pole Frequency-Agile Bandpass Diplexer With Identical Constant Absolute Bandwidth

This paper presents a low-loss, high-isolation and wide-frequency-tuning-range (FTR) (45%) implementation of the three-pole frequency-agile bandpass diplexer (FA-BPD) with identical constant absolute bandwidth (IC.ABW). The FA-BPD includes two three-pole channels and each channel has three transmission zeros (TZs). To develop such a FA-BPD, first, two bandwidth (BW) -identical and -constant frequency-agile bandpass filters (FA-BPFs) with the FTRs of 1.35-2.25 GHz and 1.9-3 GHz are designed individually. Both two FA-BPFs simultaneously employ the cascaded triplet (CT) topology and source-load coupling to introduce three TZs. All couplings of two filters are arranged opposite in sign, thus two TZs of one channel are placed on the side of the other channel. Finally, two FA-BPFs are fed by a common coupling line, thus forming the three-pole 1.35-3-GHz FA-BPD. The design example is fabricated and measured. The experimental results show that the FTRs are 1.35-2.25 GHz (50%) and 1.9-3.0 GHz (44.9%). The ABW of the two channels keeps nearly a constant of 194±8 MHz. The insertion loss (IL) varies within the range of 2.1-3.3 dB. The measured isolation level keeps better than 38 dB.

Compact edge and end coupled wide band filter with notch at 5GHz

In this paper a compact Ultra Wide Band filter with notch at WLAN frequency is designed. The filter is a designed using coupled lines arranged in inter digital capacitor form. The filter is designed to allow microwave signals in the range of 2GHz to 7GHz with a notch at 5GHz. The measured results show the notch at 5GHz with transmission coefficient of -14dB. With uniform group delay in pass band and nonlinear group delay at notch frequency.

Development of Open stub loaded Square Resonator based Dual Band filter with a Notch band to reject 802.11a

This paper is about a dual band notch filter using inter-digital coupling line. A novel square resonator with inter-digital coupling at both sides plays a key role in this filter design. Design and EM Simulation of the dual band notch filter’s characteristics are discussed in this paper. The proposed dual band notch filter produces excellent bandwidth from 2 GHz to 5 GHz and from 5.3 GHz to 8 GHz. The filter rejects the band of frequency from 5 GHz to 5.3 GHz which is very narrow band in which the filter eliminates the effect of WLAN (IEEE 802.11a). Also the out band performance of the proposed dual band filter meets the requirement of FCC’s mask. The simulation analysis of the proposed filter is performed by electromagnetic solver. The return loss, insertion loss, group delay and phase of the filter are simulated and their performances are analyzed. The overall dimension of the filter is achieved to be 39mm×3.2mm×1.6mm on accounting the above features. The fractional bandwidth of the notch filter is calculated from the bandwidth and the center frequency and it is obtained about 115%. The S parameter results of the filter such as return loss (S11) in stop band is about -34 dB and insertion loss (S21) is about -37 dB is obtained.

Dual Band BPF Based on Parallel Coupled Lines Loaded by Open Stubs for Ku-Band Satellite Applications

This paper presents a dual band Band Pass Filter (BPF) operating at both the downlink and uplink frequency bands for Ku-band satellite applications. The commonly used frequency band in mobile communications satellites is the Ku-band. These mobile satellite systems help connect remote regions, vehicles, ships, people and aircraft to other parts of the world and/or other mobile or stationary communications units, in addition to serving as navigation systems. The structure of the proposed filter is based on parallel coupled microstrip lines and four sections are used. Tuning the two operational bands can be achieved using two open-circuited stubs at the first and last sections of the parallel coupled microstrip lines. The proposed filter is adjusted to operate at 12.54 GHz and 14.14 GHz for downlink and uplink bands, respectively. The proposed dual band BPF is fabricated, measured, and good agreement is obtained between simulated and measured results.

Design of a very compact and sharp bandpass diplexer with bended lines for GSM and LTE applications

In this paper a new miniaturized bandpass-bandpass diplexer with sharp pass-band is designed and fabricated. The proposed diplexer includes two bandpass filters with sharp pass-bands. Coupling lines and stepped impedance resonators are used to form each bandpass filter. In this paper, two filters are designed in the schematic circuit mode, and then they are combined to form the final diplexer layout. After combining these bandpass filters, the transmission lines are bended to reduce the overall size of the designed filter. The operating frequencies of the designed diplexer could be selected at the desired frequencies by changing the design parameters. Proposed diplexer shows good isolation which is better than 20 dB in entire operating frequency band. Also, insertion losses in the passbands are better than 0.7 dB in output ports. The final size of the fabricated diplexer is 19.8 mm × 51.3 mm or 0.08 λ g × 0.22 λ g which shows good reduction, compared to the recent designed diplexers. The designed diplexer operates at 900 MHz and 2.6 GHz, corresponding to GSM and LTE frequencies.

Mathematical Analysis of Microstrip Diplexer Design for WLAN System

Miniature microstrip diplexer at band frequencies of (1.45/1.95GHz and 2.5/3.5GHz) in two considered channels using the coupled stepped impedance resonators (SIRs) has been presented in this study with mathematical analysis. This diplexer has dual pairs of coupled SIRs with impedance ratio and the source-load coupling lines. As a result of the tuning of impedance ratio and length ratio of SIRs, the resonant modes are possibly determined to achieve 2nd order bandpass filter (BPF) with dualband frequency responses for the investigated diplexer. The investigated microstrip diplexer has a simple outline, compact dimensions, an in effect design technique and straightforward calculations of impedance, electrical lengths, fractional bandwidth, coupling factors and other electrical specifications.

Unconditionally Stable Multiple One-Dimensional ADI-FDTD Method for Coupled Transmission Lines

The unconditionally stable multiple one-dimensional alternating direction implicit finite-difference time-domain (M1-D ADI-FDTD) method for coupled transmission lines is presented. The differential equations for coupled transmission lines are formulated in compact matrix form. Proper $4 \times 4$ split matrices are introduced, which feature unconditional stability for the ADI procedures. These matrices also lead to update equations with the left-hand sides involving tridiagonal matrices that can be solved efficiently. The update equations of the M1-D ADI-FDTD method are given, which comprise one implicit and three explicit updates in each procedure. The analytical proof of unconditional stability is also provided based on the von Neumann method. The M1-D ADI-FDTD method allows quick simulation and visualization of electromagnetic fields everywhere along the coupled transmission lines. To demonstrate the usefulness of the M1-D ADI-FDTD method, various coupled line structures for filter and filtering antenna are analyzed using the method.

Multi-Band Balanced Couplers With Broadband Common-Mode Suppression

Three novel single-/multi-band balanced couplers with wide-band common-mode suppression are proposed. In these double-functionality balanced-coupler architectures, double-sided parallel-strip line 180° phase inverters are used to realize the broadband common-mode rejection. Furthermore, by loading quarter-wavelength open/short-ended coupled lines at all ports of the single-band differential-mode coupler, dual/triple-band balanced operation with high isolation for the differential-mode power-division bands can be realized into it. For practical verification, three balanced couplers with single-, dual-, and triple-band operation at 1 GHz, 0.72/1.24 GHz, and 0.66/1/1.36 GHz, respectively, are constructed in microstrip technology and tested.

A Compact Meandered Ring Antenna Loaded With Parasitic Patches and a Slotted Ground for Global Navigation Satellite Systems

A compact meandered ring patch antenna loaded with four parasitic-grounded patches and a slotted ground is proposed. It has two orthogonal T-shaped coupling line feeds with different lengths which produce circularly polarized radiation. The ground is developed with an inner square patch with four symmetric slant corner cuts and an outer ring that further reduces the overall size of the proposed antenna. The measured frequency band with $\vert S_{11}\vert dB, the axial ratio (AR) band with AR $0.169 \times 0.169\,\,\lambda _{\mathrm {g}}^{2}$ and the overall size of the proposed antenna is $0.285\,\,\lambda _{\mathrm {g}}\times 0.285\,\,\lambda _{\mathrm {g}}\times 0.035\,\,\lambda _{\mathrm {g}}$ ( $\lambda _{\mathrm {g}}$ denotes the guide wavelength at the center frequency). The proposed antenna is smaller than the existing antennas and can be an ideal compact antenna used for global navigation satellite system applications.

The Voltage Controlled Oscillator with Coupled Microstrip Lines Resonator

The Voltage Controlled Oscillator with Coupled Microstrip Lines Resonator

Broadband and compact complex ratio measuring unit

AbstractThis study designs and analyzes Complex Ratio Measuring Unit (CRMU) and a Six‐port Reflectometer (SPR) at a center frequency of 2.4 GHz. CRMU is designed using a compact size and wideband 3 dB‐branch line coupler (BLC) and 3 dB‐Wilkinson power divider with enhanced series‐diamond stubs. The usage of these compact components leads to a compact size and improves the operating bandwidth. The idea of designing SPR is based on integrating a CRMU with 2 directional couplers along with isolator rather than a single BLC; to get a signal balance that enhances the quality of the reflection coefficient measurement. From the measurement result, it is found that the bandwidth of the CRMU and SPR is 1.7 GHz and the dimension of the CRMU is 60 × 45 mm. The proposed CRMU is fabricated using RT/duroid 5880 substrate with thickness of 0.38 mm. The dimension of the CRMU is 13 × 6.5 mm. The simulation and measurement results for both CRMU and SPR show good agreement.