Pair Of Zeros Research Articles

High selective bandpass filter with mixed electromagnetic coupling and source–load coupling

High selective bandpass filters with a pair of transmission zeros using right-angled triangular stepped-impedance resonators are proposed and analyzed. The transmission zeros on both sides of passband are attributed to the mixed electromagnetic coupling and capacitive source–load coupling, respectively. The transmission zeros locations from the central frequency can be adjusted by controlling the mixed electromagnetic coupling and source–load coupling. The design is also suitable for dual-band bandpass filter with high frequency selectivity. Single band bandpass filters which center at 2.45GHz and 3.2GHz, respectively, and a dual-band bandpass filter which centers at 2.45GHz and 3.5GHz have been designed, fabricated and measured, the measurements have demonstrated the prediction. Experimental results show that each passband of the presented filters have a pair of transmission zeros as prediction, which improve the frequency selectivity greatly. The measured filters’ passband insertion losses are less than 2.74dB at central frequencies.

Tri-band filter with multiple transmission zeros and controllable bandwidths

This paper presents a compact microstrip tri-band bandpass filter (BPF) using two multimode stepped-impedance resonators (SIRs) with a 0° feed structure. The fundamental odd-mode and even-mode resonant frequencies and the third resonant frequency are utilized to determine the center frequencies of the tri-band filter. The mode-splitting technique is used by combining two SIRs with electrical coupling. Therefore, two modes generate one passband and the bandwidths can be controlled by the electrical coupling strength. The 0° feed network is applied to create one pair of transmission zeros at each side of all the triple passbands, resulting in high selectivity. Finally, a tri-band BPF with the central frequencies of 1.8, 2.4, and 5.8 GHz, and respective fractional bandwidths of 8.9, 12.5, and 5.3% are designed and fabricated. The simulated and measured results show a good agreement.

Compact Tri-Band Bandpass Filter Using Open Stub Loaded Tri-Section $\lambda /4$ Stepped Impedance Resonator

A modified tri-mode λ/4 stepped impedance resonator (SIR) is proposed, in which a shunt open stub is loaded in the conventional λ/4 tri-section SIR. The resonant frequencies and frequency ratios can be properly controlled by adjusting the loaded open stub. A compact second-order tri-band bandpass filter (BPF) based on two coupled proposed open stub loaded λ/4 tri-section SIR is presented. A pair of transmission zeros (TZs) are generated at the lower and upper stopband of each passband for high selectivity and excellent band-to-band isolation. A tri-band BPF with the central frequencies of 1.92, 3.50, 5.75 GHz, and respective fractional bandwidths of 5.4%, 4.0%, and 2.4% is designed and fabricated. Measured results show good agreement with simulations. Moreover, the circuit only occupies 0.09 λg ×0.10 λg.

CMOS Compatible Reconfigurable Silicon Photonic Lattice Filters Using Cascaded Unit Cells for RF-Photonic Processing

This paper presents an overview of a complementary metal-oxide-semiconductor-compatible, programmable, analog optical lattice filter based on silicon unit cells arrayed in large-scale photonic integrated circuits. The unit cell employs a combination of a ring resonator and a Mach-Zehnder interferometer with tunable phase elements in both of the paths. Each proposed unit cell contributes a separately controllable pole and zero pair. Under various configurations, we experimentally achieved >60-dB two-tone spurious-free dynamic range. For more sophisticated signal processing, we experimentally demonstrated an optical lattice filter with four cascaded unit cells capable of dynamically reconfiguring between a bandpass filter and a notch filter. The reconfiguration of the unit-cell and four-cell silicon lattice filter is based on a recursive algorithm, which brings new possibilities to RF photonic processing and a wide range of applications with design scalability to a large number of poles and zeros. The experimental results and the recursive algorithms show potentials for scaling to higher order filter designs.

LTCC Multilayered Substrate-Integrated Waveguide Filter With Enhanced Frequency Selectivity for System-in-Package Applications

This paper presents a cross-coupled bandpass filter with stacked substrate-integrated waveguide cavities on low-temperature cofired ceramic substrates. The proposed filter has a local multipoint distribution service band with a novel same-side-feed input/output structure. Conventionally, a cross-coupled structure generates only a single pair of transmission zeros. The proposed filter can generate two pairs of transmission zeros beside the passband, thereby providing an excellent cutoff rate in the stopband and improved frequency selectivity. The additional pair of transmission zeros is created by the same-side-feed structure, which constructs an additional source-load coupling path without increasing the circuit size. A multipath coupling diagram is used to illustrate the conformation of the second pair of transmission zeros and predict its behavior. The experimental filter exhibits responses centered at 27.95 GHz with an insertion loss of -2.8 dB, and a bandwidth of 9%. Two pairs of transmission zeros (at 26.3 and 29.6 GHz, and at 23.2 and 37 GHz) around the passband were obtained, achieving excellent selectivity and a wide stopband.

Design of a Wideband Bandpass Filter With Composite Short- and Open-Circuited Stubs

A new wideband bandpass filter (BPF) with composite short- and open-circuited stubs has been proposed in this letter. With the two kinds of stubs, two pairs of transmission zeros (TZs) can be produced on the two sides of the desired passband. The even-/odd-mode analysis method is used to derive the input admittances of its bisection circuits. After the Richard's transformation, these bisection circuits are in the same format of two LC circuits. By combining these two LC circuits, the equivalent circuit of the proposed filter is obtained. Through the analysis of the equivalent circuit, the open-circuited stubs introduce transmission poles in the complex frequencies and one pair of TZs in the real frequencies, and the short-circuited stubs generate one pair of TZs to block the dc component. A wideband BPF is designed and fabricated to verify the proposed design principle.

Fully canonical dual‐band bandpass filter with λ /4 stepped impedance resonators

A fourth-order fully canonical dual-band bandpass filter (DB-BPF) using λ/4 stepped impedance resonators (SIRs) is presented. In the mainline path, four dual-band λ/4 SIRs are serially coupled by alternative J and K inverters, and cross-couplings, K 14 and J SL, are analytically introduced to achieve two pairs of finite transmission zeros at both sides of each passband. To experimentally demonstrate this attractive fully canonical dual-passband filtering performance, a fourth-order microstrip DB-BPF centring at 1.8 and 5.8 GHz with two pairs of finite transmission zeros for each passband is synthesised and fabricated.

Novel Compact UWB Bandpass Filters Design With Cross-Coupling Between $\lambda / 4$ Short-Circuited Stubs

Two novel, compact, and highly frequency selective ultra-wideband (UWB) bandpass filters (BPFs) based on an improved model are presented in this letter. The improved model contains four short-circuited stubs connected by transmission lines. A cross-coupling between the first and last short-circuited stubs is introduced to obtain new pairs of transmission zeros on both sides of the passband. The relationship between the coupling factor and the position of the transmission zeros was analyzed and good agreement was obtained between the analysis and model simulation results. Based on the model, two UWB BPFs are designed with 51% (3.1 to 5.2) GHz and 108% (3 to 10) GHz relative bandwidth and small size of 15 mm × 15 mm and 19 mm × 14 mm, respectively. The insertion loss of the (3.1 to 5.2) GHz filter is less than 0.4 dB in passband and the other one is less than 3 dB. The simulation and measurement results agree well.

A Linear Phase Filter in Quadruplet Topology With Frequency-Dependent Couplings

This letter presents a design of a linear phase microwave bandpass filter. The filter is composed of four resonators arranged in the quadruplet topology. Making the cross and one direct coupling dispersive gives additional design flexibility. The first advantage of using frequency-dependent couplings is the possibility to chose an arbitrary location of a pair of complex transmission zeros (TZs) in the s-domain. The second one is the presence of an additional imaginary transmission zero that improves the filter selectivity. We provide a proof-of-concept design of a filter using substrate integrated waveguide (SIW) technology. The frequency-dependent couplings are implemented in SIW as a composition of both: an inductive part realized in a form of an H-plane iris and a capacitive part realized as a grounded coplanar waveguide (GCPW). The measured filter characteristics prove the validity of the model.

A NOVEL COMPACT WIDEBAND BANDPASS FILTER USING ROTATIONAL SYMMETRIC LOADED STRUCTURE

A novel compact wideband bandpass fllter using rotational symmetric loaded structure is proposed in this paper. A ‚/4 parallel coupled line is flrst introduced to form a passband with desired center frequency. The rotational symmetric structure with short/open circuit stubs is then introduced as a loading structure to improve the fllter's performance. The rotational symmetric loading structure is discussed in detail in this paper, and a pair of transmission zeros is obtained and located at two sides of the passband to improve the passband selectivity intensively. Moreover, three open circuit stubs are utilized to replace one single stub for obtaining a wide stopband. At last, the proposed fllter is fabricated and measured, and the results show a good agreement with each other.

Balanced Right/Left-Handed Coplanar Waveguide With Stub-Loaded Split-Ring Resonators

In this letter, a host coplanar waveguide (CPW) loaded with modified split-ring resonators (SRR) is presented. In recent publications, it has been demonstrated that the capacitive interaction between the host CPW line and the SRRs is the cause of a right-handed band, which degrades the selectivity of the response. Consequently, an open-ended microstrip stub connected to the rings is used to modify this interaction, and thus has an effective control of the rejection above the passband. Fortunately, these stubs only affect the frequency position of the right-handed band. As a result, it is quite straightforward to obtain balanced composite right/left-handed (CRLH) transmission lines with increased transmission bandwidth and improved rejection levels, which are the main drawbacks of traditional SRR-loaded CPW lines. Moreover, the response of the modified cell shows a pair of transmission zeros at both sides of the passband. Therefore, this new cell is a very interesting choice for designing balanced CRLH lines and is very attractive for filter applications.

Novel Multiplexer Topologies Based on All-Resonator Structures

This paper presents two novel multiplexer topologies based on all-resonator structures. Such all-resonator structures remove the need for conventional transmission-line-based splitting networks. The first topology is a diplexer with transmission zeros in the guard band, shared by both channels. These transmission zeros are generated by introducing a cross coupling in a quadruplet in resonators common to both channels. A twelfth-order diplexer with a pair of transmission zeros is presented here as an example. The second topology is a multiplexer with a bifurcate structure that limits the connections to any resonator to three or less, regardless of the number of output channels. A sixteenth-order four-channel multiplexer is presented as an example. Both topologies have been demonstrated at X-band using waveguide technology. Good agreements between measurements and simulations have been achieved.

Compact Varactor-Tuned Microstrip High-Pass Filter With a Quasi-Elliptic Function Response

This paper presents a novel circuit topology of a tunable high-pass filter with a quasi-elliptic function response. A detailed theoretical analysis for the performance operating mechanism is demonstrated. With the assistance of mutually inductive coupling introduced, a pair of tunable transmission zeros (TZs) is synthesized at the lower passband edges and significantly improves the filter selectivity. Experiments are carried out by using the liquid crystal polymer bonded multilayer printed circuit board technology to validate the design. It is found that the implemented filter achieves a wide continuous tuning range covering from 1030 to 2150 MHz with low insertion loss, and which indeed are limited by the Schottky diodes used. It is also illustrated that two measured TZs are properly controlled at each tuning stage, which not only offers a sharp cutoff frequency response with a rejection level greater than 22 dB, but also provides an approximately unchanged response shape. Good agreement between the measured and simulated results can finally be observed.

Heat capacity decomposition by partition function zeros for interacting self-avoiding walks

A novel method based on partition function zeros is developed to demonstrate the additional advantages by considering both loci of partition function zeros and thermodynamical functions associated with them. With this method, the first pair of complex conjugate zeros (first zeros) can be defined without ambiguity and the critical point of a small system can be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and two overlapping phase transitions can be well separated. This method is applied to the interacting self-avoiding walk (ISAW) of homopolymer with N monomers on the simple cubic lattice, which has a collapse transition at a higher temperature and a freezing transition at a low temperature. The exact partition functions ZN with N up to 27 are calculated and our approach gives a clear scenario for the collapse and the freezing transitions.

Compact Ultra-Wideband (UWB) Bandpass Filter Using Dual-Stub-Loaded Resonator (DSLR)

A compact ultra-wideband (UWB) bandpass filter using dual-stub-loaded resonators (DSLR) is presented. The DSLR is analyzed by using the odd- and even- mode method. Four resonant modes can be tuned by the DSLR in 3.1 GHz - 10.6 GHz, and a pair of transmission zeros can be generated at the lower and upper stopband when the DSLR is applied to a UWB filter. Therefore a UWB bandpass filter is realized with good skirt selectivity, harmonic suppression, as well as compact size. Finally the proposed filter is simulated and fabricated. The measured results are in good agreement with the predicted one, demonstrating this structure is feasible in practical use.

Quantitative Analysis of Transmission Zeros in Cross-Coupled Two-Port Power Systems

In this paper, we present a practical and quantitative method for theoretical determination of the complex transmission zero locations of lumped two-port power systems. We have derived several closed-forms of transmission zero characteristic equations in order to prove an important result – that the integer pairs of complex transmission zeros originate solely from the cross-coupled portion of the system.

A Simple Compact Microstrip Wideband Bandpass Filter

Two wideband bandpass filters with miniature size and wide stopband are proposed by using cascaded U-shaped resonators. The filters exhibit bandwidths of 31.1% and 28.8% at about 5.3GHz and 5.6GHz, respectively. Both designed filters have simple structures and compact sizes, wide passband, excellent out-band performance with wide lower and upper stopbands, and a pair of transmission zeros on both sides of passband. The new designs have evident circuit size reduction compared with relative reports. A wideband microstrip BPF is fabricated and measured, and the measurement exhibits good agreement with the prediction.

A compact HTS bandpass microstrip filter with novel coupling structure for on-chip integration

A compact low-complexity high-selectivity high-temperature superconducting (HTS) microstrip bandpass filter is presented in this paper, which consists of only three half-wavelength resonators. A novel coupling scheme is used to provide a pair of transmission zeros outside the passband, so that the selectivity of the filter is improved. The filter is fabricated on an MgO substrate with YBa2Cu3O7−x (YBCO) coating. Measurement result shows an in-band insertion loss at 0.5dB, a sharp slope, and a stopband rejection better than 20dB. The compactness and high-selectivity features make the filter suitable for on-chip integration of HTS receiver front-ends.

Compact Split-Type Dual-Band Bandpass Filter Based on $\lambda/4$ Resonators

This letter presents a compact split-type dual-band bandpass filter based on the λ/4 resonators, whereas the filter's dual-band frequency response is achieved by creating a stopband inside a virtual wide passband. Besides the uniform microstrip λ/4 resonators, dimensions of both required <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> inter-resonator inverters for the proposed coupling topology are analytically derived based on the synthesized coupling matrix. In parallel, the hook-type coupled line is designed not only to provide the desired external and cross I/O ports' couplings, but also to manipulate the associated finite transmission zero as demanded in getting an improved upper stopband. To justify our proposed idea, a split-type dual-band BPF with central frequencies at 1.8 and 2.45 GHz, and fractional bandwidths of both 5.0% are designed. These closely proximate dual passbands are primarily realized by properly allocating two finite transmission zeros between them at 2.13 and 2.29 GHz. Moreover, an extra pair of transmission zeros at 1.53 and 3.04 GHz, contributed by cross I/O ports' coupling, is produced at lower and higher sides of virtual wide passband, thus enhancing the out-of-band rejection ratios. The final measured and simulated results show good consistence with the theoretical counterparts.

Design of Microstrip Cross-Coupled Bandpass Filter With Multiple Independent Designable Transmission Zeros Using Branch-Line Resonators

This letter proposes a novel branch-line resonator to design a fourth-order cross-coupled bandpass filter (BPF). Theoretically, the proposed branch-line resonator plays two crucial roles. First, the arbitrary number transmission zeros can be designed in the stopband of a fourth-order cross-coupled BPF. Second, the required external quality factor can also be designed without an impedance transformer. This study examines a novel fourth-order cross-coupled BPF with a single pair of transmission zeros produced by a cross-coupled mechanism near the passband and five independent designable transmission zeros created by the proposed resonator in the stopband.