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A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this article. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary reactive frequency-variant coupling (AFVC) networks is proposed. The engineered formulation is more general than prior-art ones--with the only restriction that the coupling network is a reactive-type two-port circuit--and can be treated as an extension of previous synthesis models since constant or linear couplings are special cases of arbitrary frequency dependence. The suggested model is fully general, which allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded nonresonating nodes (NRNs), frequency-dependent source-load coupling, multiple frequency-variant cross couplings, and/or multiple dispersive couplings for connecting the source and load to the filter network. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. Finally, the third- and fifth-order examples of bandpass filter topologies involving AFVCs are shown, and the experimental validation of the proposed theory is presented through the manufacturing and characterization of a microstrip filter prototype with transmission zeros (TZs).

The azimuthally rippled cavity for a large-orbit, coharmonic gyro-multiplier, designed to operate at the second and fourth harmonics, at frequencies of 37.5 and 75 GHz, respectively, has been numerically and experimentally confirmed to be insensitive to the polarization of quadrupole, ${\text{TE}}_{2,n}$ -like modes, including the second-harmonic operating mode of the multiplier, a cylindrical TE2,2-like waveguide mode. To test the cavity with this mode required the design, construction, and measurement of ripple wall mode converters, converting the cylindrical TE2,1 mode into the TE2,2 mode. These were designed to operate at a central frequency of ~37.9 GHz, with predicted mode purity of better than 85%, and 3-dB bandwidth of 161 MHz. The constructed converter had a central operating frequency of 37.7 GHz, with $S$ -parameter measurements used to infer suitable mode purity and an operational 3-dB bandwidth of 50 MHz. This has allowed far-field phase measurements of the corrugated cavity to be conducted, where the orientation of the geometry to the polarization of both the TE2,1 and TE2,2 modes was shown to have no effect on the dispersion.

This article offers a novel approach to realize dual-polarized diplexers (DPDIPs), which can duplex horizontally and vertically polarized signals separately. The proposed device is composed of a turnstile junction (TJ) and four-channel filters. Compared with conventional orthomode transducer (OMT) and two diplexers scheme, it has an ultracompact size and comparable performance. A new arrangement for the TJ that is suitable for the DPDIP is analyzed and simulated accordingly. A Ka -band DPDIP is designed and fabricated as a verification example. Simulated and measured results have verified the accuracy and efficiency of the proposed method.

In this article, a novel design approach for designing $4\times 4$ and $8\times 8$ filtering Butler matrices is proposed. The matrices, composed of combined 90° couplers and 180° filtering couplers as well as phase shifters, provide incremental phase shifts and a bandpass filter performance. The detailed design process and synthesis method for the Butler matrices are presented. A three-layer symmetrical stripline structure is used to realize the Butler matrix, allowing a fully planar structure without interlayer connections. For experimental verification, two prototype $4\times 4$ and $8\times 8$ filtering Butler matrices, operating at the center frequency of 2.4 GHz with a bandpass response, are devised, manufactured, and tested. The test results match well with the simulation ones. Based on the measurements, array factors have been calculated, which further indicate the acceptance of the measured results.

This article presents a method to increase the isolation and control the operating frequency of a circulator. The internal signal flow of a circulator is analyzed, and the through-port reflection to cancel out the leakage signal is investigated. A reflection coefficient controller (RCC) is designed to ensure that such reflection occurs at the operating frequency. In addition, the operating frequency can be tuned by using two varactor diodes of the RCC for an arbitrary value of the antenna impedance. The experimental results from the proposed method show isolation of 70 dB and an insertion loss of −1.4 dB at the operating frequency. Moreover, the operating frequency can be changed from 2.2 to 2.8 GHz with high isolation for an arbitrary antenna impedance.

In this article, a broadband $W$ -band $\mathrm{TE}^{\square }_{10}$ – $\mathrm{TE}^{\bigcirc }_{02}$ mode converter is proposed and verified. To improve the output performance of the $\mathrm{TE}^{\square }_{10}$ – $\mathrm{TE}^{\bigcirc }_{02}$ mode converter, a $\mathrm{TE}^{\square }_{10}$ -to- $\mathrm{TE}^{\square }_{40}$ intermediate mode conversion section with a Y-type power divider structure and a $\mathrm{TE}^{\times }_{44}$ -like-to- $\mathrm{TE}^{\bigcirc }_{02}$ intermediate mode conversion section with a novel cross-sector-shaped transition structure are adopted in the design (the superscript symbol $^{\square }$ represents the rectangular waveguide, $^{\bigcirc }$ represents the circular waveguide, $^{\times }$ represents the cross waveguide). The simulation results show that the transmission coefficient (S21 parameter) of the designed $\mathrm{TE}^{\bigcirc }_{02}$ mode converter is better than −0.18 dB in the whole $W$ -band (75–110 GHz), and the corresponding mode conversion efficiency is larger than 96%. Cold test results show that the transmission coefficient is higher than −1.9 dB and the reflection coefficient (S11 parameter) is less than −15 dB in the frequency range of 75–110 GHz.

In this article, a novel configurable microwave passive component is presented, which can be programmed into multiple functions according to the design requirement. The proposed configurable microwave passive component is realized with a 2-D bridged-T coil array, which can be programmed through different wire-bonding configurations to achieve the desired functions. As a design example, a compact configurable microwave passive component implemented using the integrated passive device process is demonstrated. It can be configured into seven different functions, including filters, directional couplers, and power dividers with center frequencies of 2 or 4 GHz, while the circuit size is only 8.7 mm $\times8.1$ mm. The possible extension of the proposed configurable microwave passive component to a reconfigurable one using advanced RF switch technologies is also discussed.

Sensitivity analysis is important for electromagnetic (EM)-based design. The existing adjoint EM sensitivity analysis methods have to solve large systems of EM equations repetitively for different frequencies. This article addresses this situation and proposes to speed up the EM sensitivity analysis over a frequency range by solving EM equations at only a single frequency. A new adjoint EM sensitivity analysis algorithm for the fast frequency sweep using the matrix Pade via Lanczos (MPVL) technique based on the finite-element method (FEM) is proposed in this article. MPVL is incorporated to relate the information of one frequency to the information of multiple frequencies. A large system of EM equations is then solved at a single frequency to predict the sensitivity information for the entire frequency band. Adjoint formulations are further derived to avoid the effect of the number of design variables. The adjoint EM sensitivity analysis using the proposed technique can obtain the same accuracy as the existing techniques while taking less time by avoiding repetitively solving large systems of EM equations for different frequencies and different design variables. The proposed technique is demonstrated by three EM examples of microwave components.

In this work, we present a comprehensive analysis of port impedance effects on a signal coupled across two-port networks, derive an equation to evaluate the impedances for a specified coupling, and demonstrate two beam-shaping active array antenna prototypes to validate the theory. In this context, the generalized S-parameters are theoretically studied and verified through an example. Subsequently, a closed-form equation is derived to accurately evaluate the port impedances that enable the achievement of a desired magnitude and phase of the signal coupling across the two-port network. The meaningfulness of all the potential results and the additional capabilities of derived equations are then discussed. With this understanding, a general modeling procedure is formulated to achieve the simultaneous amplification and phase shifting only through the active devices, without resorting to any additional passive circuitry. As a proof of concept, two $1 \times 5$ active array antenna prototypes are developed and fabricated at 5 GHz: one for broadside radiation with a sidelobe level of less than −20 dB requirement, and the other for flat-top radiation beam between −10° and 30°. They are integrated with a $1 \times 5$ Wilkinson power divider that is designed for radiation pattern measurements, and the corresponding results agree reasonably well with the simulated counterparts and theory, thereby proving the developed concept. Such solutions demonstrate the inherent advantages of being low-loss, compact, and efficient, which are essential for the next generation of wireless systems.

Stroke identification by means of microwave tomography requires a very accurate reconstruction of the dielectric properties inside patient’s head. This is possible when a precise measurement system is combined with a full nonlinear inversion method. In this article, the inversion of S-parameter data collected in a metallic chamber is performed with a nonlinear inversion strategy in Lebesgue spaces with nonconstant exponents. This is the first time that this kind of nonlinear S-parameter electromagnetic formulation has been applied to this problem. The inverse-scattering method incorporates a 2-D electromagnetic model of the imaging chamber based on a finite-element formulation, which has led to a complete redefinition of the solving procedure with respect to previous works. This allows a suitable description of the multistatic S-parameters due to the interactions between the incident radiation and the structure under test. The developed inversion procedure is first assessed by means of numerical simulations. The experimental results, obtained with a clinical microwave system prototype containing a liquid-filled 3-D SAM phantom with an inhomogeneity mimicking a hemorrhagic stroke, further prove the effectiveness of the proposed approach.

We report the development of a simple interferometer-based microwave sensing system for multiple frequency characterization and differentiation of in-flow yeast cells. The interferometer uses a simple microstrip line, integrated with a microfluidic channel, for single-cell measurement. An algorithm was developed and verified with high-frequency structure simulator (HFSS) for complex permittivity, $\varepsilon ^{\ast }(f) = \varepsilon '(f)- j\varepsilon ''(f)$ , extraction from measured scattering parameters. The sensing system and the algorithm were evaluated by measuring polystyrene particles of different diameters and at different interferometer operating frequencies. Viable and nonviable Saccharomyces cerevisiae and Saccharomyces pastorianus cells were measured at those frequencies. The results showed frequency-dependent permittivity values for each species of yeast and viability as well as frequency-dependent permittivity differences between different yeast types. The differences at some frequency points are significant and enable the differentiation of cells in mixed suspension, which is also demonstrated with a prediction model developed in this work.

The matrix form of the reciprocity relationship for the ABCD matrix of a general distributed microwave circuit featuring multiple ports is revisited. The correct reciprocity relationship is used to identify mistakes previously made in the derivation of key relations in the vector-short-open-calibration (VSOC) deembedding methodology, which is commonly used for removing the effect of port discontinuities in the Method-of-Moments-based electronic design automation (EDA) models of microwave circuits, digital interconnects, and other structures. Numerical results demonstrating the impact of the incorrect reciprocity relation on the accuracy of VSOC deembedding are provided.

Magnetodielectric materials have been recently attracting great attention owing to their significant advantages for miniaturization and wide bandwidth of antennas. A precise measurement of broadband permeability and permittivity is crucial to develop and evaluate advanced magnetodielectric materials. The Nicolson–Ross–Weir (NRW) method is widely used to extract electromagnetic constitutive parameters from measured scattering parameters. One of the drawbacks of this method is requiring direct measurement of the actual sample position in the measurement fixture, which leads to uncertainties in the measured permeability and permittivity. In this article, we improve the standard NRW method by removing the need for prior knowledge of sample position. For any isotropic material, the sample position in the measurement fixture can be precisely determined by matching the phasor angles of the reflection coefficients at the sample surfaces. Due to eliminating the error from the direct measurement of sample position, the improved NRW method effectively reduces the uncertainties in the calculated permeability and permittivity. Based on the results from two kinds of magnetodielectric materials measured in two sets of test fixtures of different geometries, this straightforward, explicit, and noniterative method is theoretically and experimentally proven to have a high and position-independent accuracy over a wide frequency range.

We present a general model of noisy scattering-parameter (S-parameter) measurements performed by a vector network analyzer (VNA). The residual error of the S-parameter due to the noise is examined to appear like a complex Gaussian quotient. The statistical analysis of the residual error is given, and relevant statistical quantities are derived and discussed. Experiments were conducted on a two-port VNA to validate the noise-influenced S-parameter model. We show that the uncertainty due to the noise is often critical in S-parameter measurements, in particular for S-parameters of a small magnitude.

A scalable multiple-probe near-field sensing technique using coupled resonators is presented. The technique captures perturbation information about metal scatterers near each probe and exactly distinguishes the contribution of each probe to the variations of the scattering parameters. The multiple-probe structure can be utilized to save scanning time compared with single-probe designs. A systematic extraction approach based on a coupling matrix theory and a vector fitting algorithm is employed. A design principle that provides stable structures utilizing the concept of condition number is also presented so that better calculation stability can be achieved under noisy conditions. The proposed technique is illustrated by an inline three-probe implementation with three numerical examples and two experimental validations, in which both single and multiple metal scatterers are used. The agreement between the predicted results and the extraction results validates the proposed technique.

This article presents a new decoupling and matching network (DMN) design for symmetric, single- and dual-band two-element antenna arrays. The DMNs use parallel-line-based coupling elements. The decoupling between the output ports of the proposed DMN and the reflection coefficients at these ports is obtained using the scattering parameters of the coupled antenna array and those of the DMN. These are clearly expressed as functions of the DMN's design parameters. These design parameters are determined using a simple numerical method to provide high inter-element isolation and good impedance matching for the array. To verify the proposed synthesis procedure, three DMN example designs are considered. These include one for a single-band array and two for dual-band arrays having different frequency ratios. Prototypes of these antennas along with their DMNs were designed, fabricated, and experimentally characterized. In each case, a good agreement between the measured and theoretical results is achieved. Simulation and measurement results show that the proposed DMN design and its associated synthesis procedure can be employed to significantly improve the interelement isolation of single- and dual-band, two-element arrays in various scenarios.

In this article, we present a two-port on-wafer scattering parameter measurement method to tackle the issue of crosstalk between probes. The proposed method treats the crosstalk separately during the system calibration and the device measurement stages because the crosstalk during these stages is often different due to changes in the measurement conditions after the probes have been calibrated. For example, device under test (DUT) and calibration standards are often situated on different substrates, or the distance between probes during calibration is different from that during DUT measurement. Based on this concept, we develop a new error model in which the crosstalk is treated as a standalone two-port error network in parallel with the two-port calibration standards or DUTs. The two-port crosstalk error generated during probing, $E_{{\text {CT}}}$ , is removed in the system calibration and corrected during the measurement of the DUT by using a dummy pair of open-circuit standards that are fabricated on the same substrate as the DUT. Since the crosstalk is corrected while measuring the DUT, rather than during system calibration, we call this method “calibration on the fly” (COF). The method is demonstrated using measurements of a 10-dB attenuator between 140 and 220 GHz.

Gradient-based optimization algorithms are popularly used in electromagnetic (EM)-based design optimizations. Among the gradient-based optimization algorithms, Newton’s method is not practically applicable to EM optimization because it is very time consuming to obtain the Hessian matrix containing the second-order derivatives of the EM responses with respect to the geometrical variables. This article addresses this situation and proposes an efficient gradient-based EM optimization technique using the combined Lagrangian method with Newton’s method. EM optimizations can be reformulated into constrained optimizations when the finite element method (FEM) is applied to perform EM simulations. In this article, we propose to elevate the Lagrangian method (i.e., a popular constrained optimization method) to EM optimization. By using the Lagrangian method to perform the EM optimization, the Hessian matrix can be obtained efficiently without the time-consuming evaluations of second-order derivatives of the EM responses with respect to the geometrical variables. With the efficiently calculated the Hessian matrix, Newton’s method can be applied. We derive new formulations of Newton’s method specifically for the EM optimization with the Lagrangian method. The proposed EM optimization using the combined Lagrangian method with Newton’s method can converge faster than direct EM optimizations with other gradient-based optimization methods. The proposed technique is demonstrated by two EM optimization examples of microwave components.

International audience; This article presents the small-signal and noise characterization of different technologies based on chemical vapor deposition (CVD) and silicon-carbide (SiC) graphene field-effect transistors (GFETs). The noise model, built on noise figure measurements under 50 Ω using the F 50 method, was verified by additional source-pull measurements, with special care for the GFET stability. The four noise parameters were then extracted by using the validated F 50 model up to 18 GHz, and the correlations between noise and small-signal parameters were shown for two different configurations: top-gated and back-gated GFETs.

In this article, the design and realization of low-loss 3-D printed waveguide filters in the X-band are discussed. Multiple transmission zeros (TZs) are introduced by using symmetrical TE301/TE102 dual-mode cavities. The design flexibility is enlarged by adding classical triplet and quadruplet sections that are combined with the dual-mode blocks. The coupling matrices of all topologies are derived, and the fundamental limitations are presented. All proposed filter setups are symmetrical and can, therefore, be cut in the $E$ -plane. This allows the application of low-cost fused deposition modeling (commonly known as FDM) additive manufacturing techniques. The galvanization process to achieve a high conductivity surface will be discussed as well. The measurements show good agreement with the simulation, while $Q$ -factors of up to 2000 can be achieved.

This article presents a method for analyzing the coupling between two adjacent substrate-integrated waveguides (SIWs) sharing a common row of metallic cylinders, which is based on the concept of equivalent circuit and wavenumber calculation. When the specific sizes of two adjacent SIWs are known, the scattering parameters of the shared common row of metallic cylinders can be derived, and the equivalent transmission line model of the SIW coupling structure is extracted. The even-and odd-mode wavenumbers in both transverse and propagating directions are calculated for this equivalent circuit. For an ideal forward-wave directional coupler, the transmission and coupling coefficient are then derived directly from the wavenumber and the length of the structure. Based on the proposed method, three SIW directional couplers with different coupling levels are designed and fabricated for verification. Good agreements between the calculated and simulated coupling parameters are observed. The proposed method provides a simple and accurate approach to estimate the coupling between two closely spaced SIWs sharing one common row of metallic cylinders and is expected to use for the design of millimeter-wave SIW-based circuits and systems.

A technique for the characterization of a class of coaxial-line-to-waveguide adaptors, which is based on the eigenvalues and eigenvectors of their scattering matrix, is presented. The adaptor comprises a number of coaxial-line ports symmetrically distributed on the surface of the waveguide. This allows for the independent excitation and measurement of different propagating modes in a multimodal operation. The latter is required for, e.g., the simultaneous determination of both constitutive parameters in microwave, millimeter-wave, and terahertz material characterization. It is shown that the junction is fully characterized in terms of the eigenvalues of its generalized scattering matrix. The measurement of these eigenvalues through a calibration procedure enables a complete characterization of the adaptor. A four-port coaxial-line adaptor was designed and fabricated. A modified calibration technique together with both measurements and electromagnetic simulations has been used for the determination of its scattering parameters.

In this article, we propose an effective mixed extracting method for anisotropic constitutive parameters of periodically loaded substrate integrated waveguide (SIW). This method takes the advantage of both scattering parameters retrieval theory and the equivalent homogeneous medium dispersion analysis, which could accurately and effectively extract the equivalent constitutive parameters of the periodically loaded SIW. With this method, the corresponding constitutive parameters of the six typical patterns of periodically loaded SIW schemes are accurately extracted, verified, explained, and compared for their performance. It can be used to quantitatively predict the miniaturization potential of each unit cell and sequentially evaluate the performance as an integrated component. In addition, in terms of application, with the aid of equivalent parameters extracted by the proposed method, a slow-wave SIW evanescent mode filter centered at 12.64 GHz with a frequency bandwidth of 300 MHz is synthesized, fabricated, and measured. In the meanwhile, the theory of slow-wave evanescent mode filter is further consummated, by introducing the dual factors of enhanced permittivity and permeability, as well as analyzing respective advantages in filter synthesis. Measurements and simulation results show good agreement, which embodies the role of the method in guiding the design of actual microwave devices.

A measurement technique to reduce the error of measured frequency-domain reflection and transmission coefficients, in particular, scattering parameters (S-parameters) measured with a vector network analyzer (VNA), and load reflection coefficients measured in wideband active load–pull system, is proposed. The technique models either the incident or reflected wave as the output of a finite impulse response (FIR) filter, and subsequently apply least-squares estimation (LSE) to estimate the reflection or transmission coefficients which minimize the error of said wave. When compared against the existing technique, the proposed technique offers precision improvement to the estimated reflection and transmission coefficients. Faster VNA measurements using up to 15-MHz intermediate frequency (IF) bandwidth are experimentally shown to be significantly improved to give good correspondence with slower measurements using 100-Hz IF bandwidth as reference. Error improvement across the measurement bandwidth of more than 17 dB is experimentally observed. Furthermore, the improvement is applicable to both the frequency regions with higher and lower signal to noise ratios of the reflected waves. On the other hand, applying the proposed technique in a wideband active load–pull system to estimate the load reflection coefficients, results in significant error improvement over the existing technique. The error improvement is also experimentally observed both in the in-band 3-dB bandwidth frequency region of the wideband modulated test signal and the out-of-band intermodulation frequency regions, where error improvement of 36 dB is observed.

In this article, a new experimental characterization technique for coupled transmission lines is presented. Three specific experimental test patterns (E-, F-, and G-type structures) that can individually characterize the electromagnetic coupling of two coupled lines are developed and fabricated on the same wafer using a 0.18- $\mu \text{m}$ CMOS process. Since the devised test patterns are two-port networks, well-established two-port network characterization techniques can be exploited. Transmission line model parameters (i.e., propagation constants and characteristic impedances) associated with the three two-port test patterns can be directly determined from the measured S-parameters, followed by circuit model parameters ( $R$ , $L$ , $C$ , and $G$ ) for two coupled lines. Without rigorous equipment calibration and deembedding parasitic effects, experimental characterizations for two coupled lines using four-port network S-parameter measurements may yield physically ambiguous data above 10 GHz due to the parasitic resonances, whereas the proposed technique can determine stable and accurate network parameters over a broad frequency band. To further support the validity of the proposed technique, they are compared with data using 3-D numerical calculations and low-frequency capacitance measurements.

A combination of the body-of-revolution and finite element methods is adopted for full-wave analysis of waveguides and waveguide discontinuities involving angular field variation. Such an approach is highly efficient and much more flexible than analytical techniques. The method is performed in two different cases: utilizing a generalized impedance matrix to determine the scattering parameters of a single waveguide section and utilizing periodic boundary conditions without sources. In order to confirm the validity and efficiency of both approaches, a few examples of axially symmetrical structures have been analyzed. The obtained results are compared to those obtained from commercial software and available in the literature.

Reflective metasurfaces are utilized as a bridge linking propagating waves and surface waves. However, the effective constitutive parameters (permittivity and permeability) cannot be retrieved by conventional theory without transmission coefficients. In this paper, an innovative method based on a quasi-one-port network model is proposed to robustly retrieve the effective electromagnetic parameters ( $\varepsilon _{\mathrm {eff}}$ , $\mu _{\mathrm {eff}}$ , $n_{\mathrm {eff}}$ , and $z_{\mathrm {eff}}$ ) for reflective metasurfaces with isotropic unit cells. The validity of the method is demonstrated by imping TE-polarized terahertz waves normally and obliquely (10°) on the multiple-layer unit cells. The effective boundary of the multiple-layer cells is determined by minimizing the deviation of the effective refractive indices from 0.1018 to 0.0260 using a genetic algorithm, which increases the consistency of the retrieval results. The sensitivity of the effective constitutive parameters to the accuracy of reflection coefficients and nonzero incident angle $\theta _{i}$ is also discussed. This method is beneficial for the design of reflective metasurfaces or multichannel reflectors, the coupling of spoof space plasmon polaritons, and other applications of anomalous reflection.

In this paper, we present a comparative study of S-parameter measurements of electronic components on planar substrates performed with a waveguide module and in a conventional on-wafer probing environment. Measurements were conducted at three well-established measurement laboratories for the investigation of reproducibility at frequencies from 110 to 170 GHz. For the comparison, we fabricated waveguide modules for six passive structures, including devices under test (DUTs). Four of these structures are related to using a second tier calibration to achieve the same reference planes for the waveguide module measurements as used for the on-wafer probing measurements. Additionally, we processed three complete on-wafer calibration sets, including DUTs, equipped with different probe-to-pad interfaces. In this comparison, the DUT measurement from the waveguide module acts as a reference standard, with reduced crosstalk behavior in comparison to the on-wafer measurement. With the waveguide reference, we are able to assess the ability of two techniques to compensate for crosstalk and higher order modes influencing the on-wafer S-parameter measurements. On the one hand, we use a shielded probe-to-pad transition and on the other hand, we use an algorithm-based crosstalk correction scheme. To the best of our knowledge, this is the first time that such a comparison has been undertaken, comparing well-established waveguide calibrations with an equivalent on-wafer calibration.

Vanadium dioxide (VO2) has been identified as a material capable of transitioning from an insulator to a metal close to room temperature. Previous works have demonstrated potential applications of this material in various microwave components or devices. However, the complex permittivity and permeability characterization of the VO2 over X-band has not been previously reported. Knowledge of these properties is essential for accurate modeling of the components and devices utilizing VO2. This paper characterizes a VO2 film deposited on a quartz substrate in a WR90 waveguide using a vector network analyzer. The S-parameters, conductivity, relative complex permittivity, and permeability of the VO2 film are determined across the transition temperature.

This paper presents a method for the measurement of liquid permittivity without using liquid reference materials or calibration standards. The method uses a single transmission line and a single microfluidic channel which intercept the line twice. As a result, two transmission line segments are formed with channel sections to measure liquid samples. In single-connection measurements, the scattering parameters of three transmission line states can be obtained. The three states are both segments filled with air, one segment filled with a liquid sample while the other with air, and both segments filled with liquid. By choosing a 2:1 ratio for the two line segment lengths, closed-form formulas are provided to calculate line propagation constants directly from measured S-parameters. Then, sample permittivity values are obtained. A coplanar waveguide is built and tested with deionized water, methanol, ethanol, and 2-propanol from 0.1 to 9 GHz. The obtained line performance agrees with the simulation results. The obtained sample permittivity values agree with commonly accepted values.

This contribution establishes the relationship between the complementary condition and the singly terminated (ST) networks. The general theory is first presented in the form of bandpass/bandstop complementary diplexers. Furthermore, the well-known limitation of a complementary diplexer, i.e., using maximally flat prototypes, is overcome. From the first principle, it is rigorously proven that predefined complementary features can be obtained by connecting two channel filters in an ST prototype of the same filter function but exchanging the transfer and reflection part. This paper leads to a general design procedure for bandpass and bandstop complementary diplexers using arbitrary functions. A complementary diplexer design example with full electromagnetic simulated results and measured results verified the accuracy of the proposed theory. Finally, the theory is further extended to N-ports networks. A new “partially-complementary” condition is proposed. The new theory leads to an extremely simple and “direct approach” to estimate the performance of contiguous multiplexers without any optimization.

A branch-line hybrid (BH) topology is suggested, consisting of four equal lengths of transmission-line sections (TLs) with two different characteristic impedances and four identical L-sections with each a TL and an open stub. The topology can provide three distinct properties; lower characteristic impedances of TLs, longer electrical paths for the scattering parameters, and additional transmission zeros, enabling high performance of harmonic suppressions from $2f_{0}$ , where $f_{0}$ is a design frequency, wideband and selective harmonic suppressions. A compact equivalent circuit of a TL is suggested for harmonic suppression BH which can be applied for all possible power-division ratios. As a proof-of-concept demonstration, two prototypes for the power-division ratios of 0 and 6 dB are tested and measured. The measured frequency responses are in a good agreement with the predicted ones, given fabrication errors.

This paper presents a novel quarter-mode packaged bandpass filter with four transmission zeros (TZs) in substrate-integrated waveguide (SIW) technology. The filter has an insertion loss of 2.85 dB at 30 GHz and fractional bandwidth of 20%. The design methodology of the TZs was first demonstrated to increase the attenuations of the filter stopband. The quarter-mode SIW resonators were analyzed with high-mode suppression by properly setting their feed points. The packaged filter was consistent between the simulation and measurement results and offers the advantages of compact configuration and easy integration with other devices. Mode suppressions of up to 110 GHz were also provided. The proposed concept is attractive for designing miniaturized and high-performance-packaged filters for 3-D millimeter-wave transceiver systems.

For the first time, a planar crossover with balanced and single-ended (SE) paths composed of double rings is presented. The parameters’ constraint is extracted, and rigorous derivations are provided. In addition, the relationships between the parameter values and the bandwidths are thoroughly analyzed. Finally, a prototype is designed and fabricated, which achieved 36.9% and 37.7% 1-dB insertion-loss bandwidths for the balanced and SE paths. Meanwhile, the 15-dB path-isolation bandwidth is 32.4%, and a 40.6% bandwidth of 15-dB common-mode suppressions is realized.

This paper proposes a new algorithm, very efficient numerically, used for locating zeros and poles of complex function and its exemplary applications in microwave technique problems. The algorithm starts its run from two arbitrary regions on the complex plane, where the searched function yields values with different signs for either or both real and imaginary parts. The algorithm runs along the path created by the chain of equilateral triangles, at whose vertices the function is evaluated. When analyzing the signs of the function, the tracking directions are chosen along the borders of complex regions, where zeros/poles are further expected. Calculations of complex propagation coefficients for a slab dielectric waveguide, complex dispersion coefficients of graphene transmission lines, and a zero/pole analysis of microwave filters are given to show some of the possible applications of the proposed algorithm. A comparison to other methods is also included.

We present precision scattering-parameter measurements of chip-to-chip connections in heterogeneous integrated circuits: indium phosphide or gallium nitride “chiplets” mounted on Silicon Complementary Metal-Oxide-Semiconductor carrier chips. We demonstrate methodology, experimental results, and modeling results of these chip-scale interconnections from dc to 110 GHz. We used thru-reflect-line on-wafer calibration to establish reference planes inside heterogeneous integrated circuits, and then, we translated those reference planes to the proximity of the chip-to-chip transitions to isolate their contribution to the scattering parameters.

In this paper, a novel approach is presented for determining the electromagnetic (EM) parameters of the lossy and dispersive inhomogeneous material loaded in the waveguide. The state-space approach is used for the parameter retrieval in the waveguide structure. In order to enhance the accuracy of reconstructing the inhomogeneity profile, a novel technique is suggested based on the hybrid of lateral dimension diversity and the Fourier series expansion. The validity of the proposed approach is verified for some applicable and practical types of the inhomogeneous material. The approach leads to a stable and unique converged solution due to the system of linear equations, which can be easily solved. Unlike the previous investigation based on the state space, the presented approach can determine the EM parameters of the lossy and dispersive inhomogeneous material in the wide microwave frequency range. The measurement setup is fabricated based on the presented approach in order to characterize the two-layered sample. From the practical point of view, the proposed waveguide characterization approach eliminates the common drawbacks in the free space system such as large sample size, fault in the calibration, and the common error due to the imperfectness of the anechoic chamber and environmental noise.

For the first time, the impedance spectrum of a live Jurkat T-lymphocytes human cell was characterized in a single sweep, spanning six decades of frequency from 9 kHz to 9 GHz. The ultra-wide bandwidth bridged the traditional impedance spectroscopy at kilohertz–megahertz frequencies with the recently developed microwave dielectric spectroscopy, which can probe the cell interior without being hindered by the cell membrane. Based on the measured scattering parameters and a simple cell model, an equivalent circuit of four nondispersive elements, including membrane resistance, membrane capacitance, cytoplasm resistance, and cytoplasm capacitance, was extracted and found sufficient to explain the so-called $\beta $ relaxation over the frequencies measured. These extracted cell parameters are in general agreement with the literature but are believed to be more accurate, giving the relatively small standard deviations, the configuration with a cell in intimate contact with the measurement electrodes, and the ultra-wide bandwidth of the measurement.

An ultra-wideband inline coaxial-to-single ridge waveguide transition is designed to feed the ridge gap waveguide (RGW). The transition covers the frequency band of 11.5 to 33 GHz. This bandwidth cannot be covered by a single RGW. Therefore, two RGWs are manufactured covering two different bands to be used as devices under test. Simulations and measurements of back-to-back transitions have achieved better than 15 dB return loss. In addition, a tuning capability in the transition is simulated using two different commercial simulators showing that the transition may cover up to 40 GHz with over 90% bandwidth to cover the entire Ku , ${K}$ , and Ka -bands.

A measurement technique to emulate coupling between power amplifiers (PAs) such as that in an antenna array is presented. The case that the technique aims to emulate is referred to as the target array. The technique provides emulation of the distorted output signal for each PA under the coupling effect without the requirement for constructing the target physical coupling network or antenna array. Furthermore, given that the target array contains identical elements or PAs, transmitting either identical or different signals, the technique merely requires one PA as the device-under-test (DUT) to produce all output signals. The technique has direct connection to active load–pull, and aims to present the output of the DUT with corresponding time-varying impedances of each transmission path in the target array. The emulated output signals can then be analyzed, for example, in terms of adjacent channel power ratio, error vector magnitude, and normalized mean square error. Such measurement technique provides insight into the distortion and the impairment generated in the target array without the requirement to realize an actual array, and can be used, as an example, during the design stage of an array. The technique is theoretically motivated. The procedure is thoroughly described. The technique is experimentally demonstrated and verified under various usage cases and scenarios. Subsequent comparison to conventional active load–pull is provided.

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.

For the first time, the 6-port quadrature and rat-race couplers with balanced-unbalanced-hybrid ports are proposed. The corresponding design methodology is presented, which is capable of designing the proposed couplers with arbitrary power divisions and terminated resistances. In this paper, four types including quadrature and rat-race couplers are fully analyzed, covering all the application configurations of the balanced/unbalanced ports. Besides, the design equations are rigorously derived, with the final design procedures presented. Eventually, prototypes of the four coupler types are fabricated and experimentally measured. The final results sufficiently validate the proposed methodology.

This paper presents a rigorous analysis to determine the noise parameters of linear noisy microwave networks with any number of ports. The analysis expands a well-established approach for the determination of the noise parameters of a linear two-port network to any linear $N$ -port networks and enhances the understanding of its measurement procedure as a particular case of this analysis. A thorough discussion of the results of this analysis identifies constraints and highlights practical requirements for a successful noise characterization setup of any $N$ -port networks. The analysis is then applied to the measurement of four-port networks. The determination of passive network’s noise parameters allows the experimental validation of the theory, while the determination of an active four-port network’s noise parameters is of particular interest, because its differential noise figure can be determined directly from its noise parameters without the use of external baluns.

In this paper, a novel planar compact coupled-line circuit is proposed to design a single-ended-to-balanced power divider (PD) that can be used in numerous balanced circuits and systems. By using the matrix transformation between the mixed-mode (MM) scattering parameters and the single-ended scattering parameters, the constraint rules are deduced to realize the performance of equal power division with in-phase, good input (output) port matching, high isolation between two balanced outputs, high suppression of the common-mode (CM) noise, as well as the mode-conversion suppression between differential-mode signals and CM noise. Then, the closed-form design equations are derived using the even- and odd-mode analysis. Finally, a microstrip PD, which works at 1 GHz, is designed and fabricated. The measured (simulated) operating relative bandwidth is 37% (38%) from 0.76 (0.83 GHz) to 1.13 GHz (1.21 GHz). The consistency between the simulated and measured MM scattering parameters verifies the correctness of the design theory.

This paper presents an efficient time-domain approach to evaluate the effect of the metallic shield on enclosed multilayered structures. In the proposed method, using the surface equivalence theorem, the multilayered structure is divided into separate layers, which are coupled together by the assumed unknown magnetic currents on the nonmetallic interfaces (apertures) between the layers. As a result, the problem is converted to a cascade of coupled rectangular cavities whose Green’s functions in time-domain are available. To eliminate the late time instabilities, the marching-on-in-degree method is used to solve the produced integral equations. Then, the impressed current source model is utilized to extract the scattering parameters at the ports of the multilayered structure. In addition, a new accelerating algorithm that is based on the separation of time and space variables in the Green’s function of the rectangular box is applied to the presented method. The proposed acceleration technique reduces the order of computational process and memory usage as $O(MN_{s}N_{{{\text {mod}}}})$ and $O(N_{{{\text {mod}}}}(M+N_{s}))$ , respectively, where $M$ , $N_{s}$ , and $N_{{\text {mod}}}$ denote the maximum temporal degree, the number of spatial unknowns and the total number of the Green’s function modes. It is shown that the presented technique is more efficient than the commercial software, CST-MWS, for the considered problem.

This paper presents a frequency-sweep technique based on model-order reduction and finite elements, for the broadband analysis of structures fed by waveguides (WGs) possessing frequency-dependent modal field patterns. Standard order reduction requires the matrices and right-hand sides (RHSs) to exhibit affine frequency parameterization. This precondition is violated when the transverse fields of the WG modes vary with frequency. The proposed solution involves two steps. First, a reduced-order model (ROM) for the WG is constructed. It enables the accurate yet inexpensive computation of propagation characteristics. Second, order reduction is applied to the driven problem, wherein the reduced WG model is utilized to construct affine approximations to the matrices and RHSs. Since this process requires operations on reduced-order matrices only, it is computationally cheap and enables offline/online decomposition. Both impedance and scattering formulations are considered. For the latter, an alternative to the transfinite element method is proposed, which does not employ modal field patterns as shape functions. It avoids interior resonances and computes scattering parameters more efficiently when only a limited set of excitations is of interest. The resulting algebraic system is of somewhat larger dimension but easier to assemble. Its simple structure greatly facilitates the construction of the ROM.

Lately, there has been a growing interest in the ridge gap waveguide (RGW) technology as a guiding structure for high-frequency applications. Low loss and low dispersion are two major advantages of the RGW. On the other hand, the major disadvantage of this technology is the difficulty in fabrication as it requires fabrication with high precision, in particular for high-frequency applications. The operating bandwidth of the RGW is controlled by the stopband of the texture surrounding the ridge. A study to enhance the bandwidth is introduced for possible utilization of the full band achievable by the unit cell in the presence of the ridge. Modifications of the cell filling shape and the ridge structure are carried out to enhance the RGW bandwidth. We have introduced a new RGW based on mixed fabrication technology. The proposed architecture introduces adaptive and straightforward structure with improved bandwidth while keeping the characteristic impedance at the same value. The proposed structure is fabricated and measured. The measured scattering parameters are in excellent agreement with the simulated ones.

This paper presents an addressable measurement method for ${S}$ -parameters characterization. To achieve this concept, compact transmit/receive (T/R) switches with radio frequency (RF)-oriented layout pattern are implemented to construct addressable signal paths. A customized deembedding method is performed to extract ${S}$ -parameters with acceptable accuracy. Thanks to the addressable structure which significantly eliminates unnecessary contact pads in RF device characterization, much less silicon area is required. Several prototypes, including nonaddressable and addressable test structures with different devices-under-test, have been fabricated using a commercial 0.13- $\mu \text{m}$ CMOS technology. Measurement results suggest that the proposed addressable test structure is able to provide accurate ${S}$ -parameters measurements at gigahertz range consuming about 50% less silicon area.

In this paper, we present a new effective methodology to build stochastic macromodels for the time-domain analysis of generic linear multiport systems. The proposed technique allows one to calculate a stable and passive polynomial chaos (PC)-based macromodel of a system under stochastic variations. The Galerkin projections method and a PC-based model of the system scattering parameters are used along with the Vector Fitting algorithm, leading to an accurate and efficient description of the system variability features. The proposed technique results to be very versatile and, thus, is well suited to be applied to many different and complex modern electrical systems (e.g., interconnections and filters). The accuracy and computational efficiency of the proposed technique are verified through comparison with the standard Monte Carlo analysis for two pertinent numerical examples, showing a maximum simulation speedup of 765 times.