Frequency-dependent Complex Loads Research Articles

A Novel Concurrent Dual Band Matching Network for Complex to Real Impedance Matching for RF Applications

A novel and simple technique to match Frequency Dependent Complex Loads (FDCLs) to real source impedance at any two arbitrary frequencies is presented. The proposed structure consists of stubs and two 50 Ohms series transmission lines, making it easy to fabricate. This arrangement allows concurrent operability. It has the versatility to transform all types of complex loads at any frequency ratio, which may not be possible with other conventional techniques. In this brief, the limitations of single section transmission line to transform FDCLs to two complex conjugate loads (CCLs) at two frequencies is thoroughly studied. In the proposed scheme, an L-section is used to match the complex load to source impedance at one frequency; and another section consisting of a transmission line and a combination of open-short stub is used to match the load at other frequency. Three prototype matching networks for frequency ratios 6.5, 2.3 and 1.583 are designed and implemented on ROGERS RO4003 substrate having dielectric constant of 3.38 and substrate height of 20 mils. The simulated and the measured results are in a good accordance.

Dual‐band impedance transformer with single shunt stub for complex impedance loads

AbstractThis letter presents a novel impedance transformer that can transform two unequal frequency‐dependent complex loads (FDCLs) to a resistive load at two diverse bands. The proposed transformer contains four sections of transmission lines and one shunt stub. The design parameters of the transformer are obtained from the analytical formulas. The feasibility analysis of the transformer is discussed and an example based on microstrip technology is implemented and measured for verification. The good agreement between the simulated results and measured results proves the validity of the proposed configuration and design method. Compared with the reported works, the transformer not only features single shunt stub and shorter total electrical length at transmission direction, but also provides simpler analytic design equations and less likely to use the very high‐ or low‐impedance transmission lines.

IPD-Based Miniaturized Wideband Bandpass Filter With Frequency-Dependent Complex Source and Load

In this article, an ultraminiaturized bandpass-filtering matching network based on GaAs substrate integrated passive device (IPD) technology is proposed, which is suitable for frequency-dependent complex source and load. The presented bandpass filter (BPF) is derived from an equal-ripple Chebyshev low-pass filter prototype through frequency transformation and impedance scaling. The susceptance required by the source and load is extracted from the adjacent susceptance blocks, and the final reactance/susceptance block is equivalent to a series/parallel LC circuit at the two edge frequencies. Therefore, the proposed design has both bandpass high-selectivity and impedance matching functions, and simultaneously, the bandwidth can be flexibly controlled. Finally, a wideband BPF example with the center frequency of 3.5 GHz was simulated and fabricated with the IPD process, showing satisfactory performances.

A Design Approach for Compact Wideband Transformer With Frequency-Dependent Complex Loads and Its Application to Wilkinson Power Divider

In this article, a new design approach for the wideband transformer with frequency-dependent complex loads is proposed, which is based on the least-square method and the generalized modified small reflection theory (MSRT) with proper electrical parameters. Compared with the wideband transformers based on other approaches such as the generalized MSRT and transmission line theory, the proposed ones feature easy design, compact size, and wide bandwidth. For validation, several wideband transformers with frequency-dependent complex loads are designed, simulated, and measured. The measured results are consistent with the calculated and simulated results, and a wideband transformer with a fractional bandwidth of 68.5% (defined by 15-dB return loss) and an overall size of $0.025\lambda _{g}^{2}$ is achieved. In addition, when applied to the design of wideband Wilkinson power divider, a fractional bandwidth of 110% (defined by 25-dB isolation) and an overall size of $0.069\lambda _{g}^{2}$ are attained.

Development and Thorough Investigation of Dual-Band Wilkinson Power Divider for Arbitrary Impedance Environment

In the design and development of front-end communication systems, the arbitrary impedance environments are encountered frequently. In this article, a three-port dual-band equal power divider is proposed which also transforms all types of impedance environments at its ports inherently. The power divider is suitable for a wide range of arbitrary frequency ratios and impedance terminations at each of the input and output ports. A systematic design procedure with a design flow graph is provided. The closed-form design equations make the design process simple and quick for prototyping purposes. The proposed design approach enhances the design flexibility significantly with the presence of multiple independent variables. Design examples with distinct design specifications are provided to demonstrate the effectiveness and flexibility of the architecture. A prototype working at 1/2.6 GHz and with frequency-dependent complex load (FDCL) terminations at the input and output ports is fabricated and measured to validate the proposed architecture and design methodology. The proposed dual-band impedance transforming power divider exhibits controllable bandwidths, planar structure without any reactive element, compact size, and the ability to provide port matching for any real, complex, and frequency-dependent complex impedance terminations.

A microstrip switched-band impedance transformer for frequency-dependent complex load

AbstractThis study presents a simple switched-band impedance transformer using microstrip lines. The proposed circuit is suitable for loads with frequency-dependent complex impedances at two arbitrary operating frequencies. The transformer comprises two cascaded microstrip lines and two detachable shunt stepped-impedance stubs, which are separately connected to the main line via switching diodes such that provide good matching at one of the two operating frequencies and suppress unwanted signal at the other frequencies. The structure contains several user-set parameters such that designers can create a smaller circuit. The circuit parameters, except the user-set ones, are obtained using the derived design formula. The numerical simulations and experimental results agree well such that validate the proposed structure and the design formula.

Reply to Comments on “A Three-Section Dual-Band Transformer for Frequency-Dependent Complex Load Impedance”

The author thanks Dr. R. Sinha very much for providing detailed design equations for the proposed dual-band impedance transformer in <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> . Note that the analytical solutions for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> are very necessary, which are developed in <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , in closed form. In fact, the generalized and closed-form solutions for this kind of impedance transformers have been published in <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> . It is very interesting that all results in <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> can be degenerated to the simple solutions in both <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> and the presented results in the comments by Dr. R. Sinha, when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In</sub> = 0 is considered in <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[2]</xref> .

Comments on “A Three-Section Dual-Band Transformer for Frequency-Dependent Complex Load Impedance”

In the above paper, Liu et al . proposed the dual-band impedance transformer based on three sections of the transmission line. However, there is some incorrectness in the design equations and inconsistencies in the derivations. Here, we have provided the corrected design equations.

A Generalized Approach for Multifrequency Transmission Line Transformer With Frequency-Dependent Complex Source and Load

In this paper, a generalized approach to design a multifrequency transformer with frequency-dependent complex source and load is proposed. By introducing an equivalent transformation between the perfectly matched complex-to-complex (a complex source impedance transformed to another complex load impedance) and unmatched real-to-real transformers (a real source impedance transformed to another real load impedance), the modified small reflection theory once limited to the design of the real-to-real transformer is further extended to that of the complex-to-complex transformer with more than two operating bands. Moreover, it is very useful to the design of multifrequency cascaded power amplifiers or low-noise amplifiers with compact size since its forward-stage output can be directly matched to the next-stage input. To validate the presented method, several multifrequency transformers are designed, simulated, and measured. Good agreement among the calculated, simulated, and measured results is achieved.

Synthesis Techniques on Multiband Impedance Matching Networks for Frequency-Dependent Complex Loads

In this paper, broad multiband impedance matching networks (MBIMNs) are synthesized for frequency-dependent complex loads. The MBIMNs are derived from a multiband bandpass topology that is obtained by conducting multiple low-pass-bandpass transformations and by sharing one topology for all matching bands. The concept of a frequency-dependent voltage transformer is then used for generating a frequency-dependent load conductance, while the load susceptance is borrowed from the nearest susceptance unit of the topology. The resulted MBIMN contains several multimode resonators that are practically realized by parallel connections of series LCs and series connections of parallel LCs, and iterative methods are used for extracting the circuit parameters. Three dual-band examples and one triband example are designed and simulated, and two of them are fabricated and measured, with compared results sufficiently demonstrating the feasibility of the topologies and theories. Broad bandwidths referring to low reflection coefficients are observed. The topologies and methods can also be expected to realize more than three matching bands provided with enough convenience in circuit implementation. Multiband bandpass filtering is another important function of the matching networks.

A New Design Methodology of a Triband Pi-Network Based on Multiresonant Networks

In a large number of multiband/multistandard applications, it is necessary to design matching networks that are capable of concurrently synthesizing impedances at different frequencies. In order to obtain this functionality, this paper presents a method based on multiresonant networks that is capable of providing impedance matching for frequency-dependent complex loads to the reference impedance \(Z_o\), normally 50 \(\Omega \). The capacity of multiresonant networks to generate an open circuit and a short circuit condition is used to respectively remove and insert inductors/capacitors in the network, and change the impedance generated by the matching network. To evaluate the potential of this proposal, triband matching networks operating at 915 MHz, 1.8 and 2.4 GHz were designed and evaluated from post-layout simulation results. According to the results, the target impedances were generated with reflection coefficients smaller than 0.2 and insertion losses less than 1 dB, which is acceptable in most RF applications. These results corroborate the potential of the proposal for the design of triband networks.

Improving Load Range of Dual-Band Impedance Matching Networks Using Load-Healing Concept

A novel and very simple scheme to mend conventional dual-band impedance matching networks is presented. It involves the employment of a load-modifying element (load-healer) so as to extend the range of frequency-dependent complex load that could be matched. Two simple load-healers incorporated in the conventional T-network are used to illustrate the concept. The proposed scheme can be successfully applied in many situations where conventional matching networks are severely limited. Two prototypes operating concurrently at 1 and 2 GHz are designed corresponding to the two types of load-healer. They are implemented on FR4 substrate having a dielectric constant of 4.6, a substrate height of 1.5 mm, and a 35-μm copper cladding. The prototypes exhibit good agreement between their EM simulated and measured results.

Generalised MIT in a tri‐band LNA

In this study, the authors propose a generalised multiband impedance transformer (MIT), which can transform the frequency-dependent complex loads at multiple arbitrary bands simultaneously. The proposed transformer has two parts: the multiple frequency-selection sections consisted of the series–parallel branches and the π-shape impedance transformer is composed of the multiple series transmission lines. Analytical equations are derived for the closed-form solutions and the rules of electrical parameters. Numerical examples are examined to verify the validity. On the basis of printed circuit board, a single-stage tri-band low-noise amplifier (LNA) with the proposed MIT is designed, simulated, and measured for practical application. The measured LNA maintains the tri-band performance and the 3 dB bandwidths are 400, 250, and 50 MHz with the 15, 12, and 7 dB minimum gain, respectively. The minimum input return losses are −24, −13, and −11 dB corresponding to the three bands, and the output return loss is lower than −10 dB from 1.5 to 2.6 GHz. The minimum input third-order intercept points are 4.1, 6.2, and 14.7 dBm, respectively. Besides, the noise figures (NFs) are 1.9, 2.6, and 5.0 dB separately at the centre frequencies of 1.8, 2.23, and 2.47 GHz.

Integration Design of Filtering Antenna With Load-Insensitive Multilayer Balun Filter

Integration design of a filtering antenna fed by a load-insensitive multimode balun bandpass filter is proposed in this paper. The balun filter is designed and realized using multilayer structure for miniaturization. To be directly integrated into the antenna, both amplitude and phase performances of the balun filter are investigated with different complex load impedances. With insensitive responses against the load, this balun filter is utilized to design a filtering antenna as the feeding of a quasi-Yagi antenna, which is considered as a frequency-dependent differential complex load. The radiation characteristics are improved by applying a metallic shield as the package for the proposed design. To verify the design concept, an experimental filtering antenna is designed, fabricated, and measured with almost the same passband as that of the balun filter benefiting from the load-insensitive property of the latter. The simulated and measured results are presented, showing good agreement.

Synthesis of lumped dual-frequency impedance transformers for complex loads using inverters

Novel lumped dual-frequency impedance transformers (DFITs) for arbitrary frequency dependent complex loads (FDCLs) are synthesized using the concepts of capacitive and inductive inverters. Such a dual-frequency impedance transformer is constructed with one Pi-shaped lumped inverter and two shunt susceptance blocks at two sides, and get simplified after susceptance merging. The shunt susceptance blocks have specified susceptance values at two frequencies and are realized with lumped circuits of certain topologies. Design formulas of the DFITs are derived and are validated by two examples. Compared with a former technique, this method uses less lumped elements and provides one design freedom, so largest matching bandwidths can be achieved by comparing a series of possible designs.

A DUAL-FREQUENCY MATCHING NETWORK FOR FDCLS USING DUAL-BAND λ/4-LINES

A new approach to design a dual-band matching network using a dual-band quarter-wave line is presented. The proposed matching network is capable of simultaneously matching frequency- dependent complex loads (FDCLs) having different values at two arbitrary frequencies to a real source impedance, Z0. A very simple step-wise design procedure is discussed for the transformer along with closed-form design equations which are very simple in nature. For experimental verification, two PCB prototypes have been fabricated using FR-4 material, operating at 1 GHz and 2.42 GHz. The measurements results matches well with that obtained from simulation, exhibiting good performance.

A T-SECTION DUAL-BAND MATCHING NETWORK FOR FREQUENCY-DEPENDENT COMPLEX LOADS INCORPORATING COUPLED LINE WITH DC-BLOCK PROPERTY SUITABLE FOR DUAL-BAND TRANSISTOR AMPLIFIERS

This paper reports design of a new dual-band T-type impedance transformer also exhibiting DC-blocking feature. The design aims at achieving matching for frequency-dependent complex loads having distinct values at two arbitrary frequencies to Zs (here, 50›). A step-wise analysis on the developed dual-band impedance transformer provides simple closed-form design equations. The design is verifled by simulation in Agilent ADS. For experimental veriflcation a PCB prototype is fabricated using FR-4 material, operating at 1.45GHz and 2.61GHz. A good result is obtained conflrming the theory and simulation.

Multi-Frequency Impedance Transformers for Frequency-Dependent Complex Loads

In this paper, a general synthesis method is proposed for the design of multi-frequency impedance transformers (MFITs) for arbitrary frequency-dependent complex loads (FDCLs) by adopting the concept of multi-frequency inverters (MFIs). An MFI, which is placed between two susceptance blocks, is constructed with a transmission line and two-side multi-frequency susceptances (MFSs), whose values at multiple frequencies are independently specified. By merging neighboring susceptances, we get a very simple Pi-shaped topology of MFITs, which in theory has no limitation on the number of matching frequencies. The MFS blocks are realized with one or more parallel shunt stubs, providing needed susceptance values at several specified frequencies. A genetic algorithm is used in extracting the circuit parameters of the parallel stubs. Several dual-, triple-, and quad-frequency impedance transformers for FDCLs are designed for illustrating the design methods. Experiment and simulation results are compared with good agreement, validating the feasibility of the theory. The designed impedance transformers are concise in circuit and compact in dimensions.

A NOVEL COMPACT DUAL-FREQUENCY COUPLED-LINE TRANSFORMER WITH SIMPLE ANALYTICAL DESIGN EQUATIONS FOR FREQUENCY-DEPENDENT COMPLEX LOAD IMPEDANCE

In order to perfectly match arbitrary frequency-dependent complex load impedances at two uncorrelated frequencies, a novel coupled-line impedance transformer without transmission-line stubs is proposed in this paper. This transformer mainly features small size, wide bandwidth, simple analytical design method, and easy planar implementation. The transformer simply consists of a coupled- line section and an additional transmission-line section. Due to the usage of a coupled-line section, the theoretical synthesis of the proposed transformer becomes very simple when compared with previous transformers and the total size of the planar circuit without deterioration of operating bandwidth becomes small. Furthermore, several numerical examples are presented to demonstrate the ∞exible dual-frequency matching performance. Finally, the proflle of matching frequency-dependent complex load impedance at two arbitrary frequencies has been examined by simulation and measurement of two microstrip generalized T-junction power dividers. Good agreement between the calculated results and measured ones justifles this proposed transformer and the design theory.

A DUAL-BAND IMPEDANCE TRANSFORMING TECHNIQUE WITH LUMPED ELEMENTS FOR FREQUENCY-DEPENDENT COMPLEX LOADS

In this paper, a new technique to realize lumped dual-band impedance transformers for arbitrary frequency-dependent complex loads is proposed. For the complex impedance transforming, closed- form design equations are presented for a series-shunt and a shunt- series type and a concept of combination is also presented. They use the proposed equation of input impedance. This equation can easily and exactly obtain the input impedance of any two-port network using the ABCD matrix. Then in order to realize dual- band operation, four topologies comprising two types and a design method are presented. This technique is numerically demonstrated by various examples with excellent results and it has advantages of simplicity, intuitiveness and versatility because it is a general solution for complex impedance transforming. The proposed dual- band impedance transforming technique can be utilized for practical matching problems such as microwave ampliflers and other devices.