Nevzat Yildirim

A revision of cascade synthesis theory covering cross-coupled filters

The classical zero-shifting technique is generalized to cover extraction of complex transmission zeros (TZs) in the form of fourth-order LC sections whereby the j/spl omega/- and /spl alpha/-axis TZs appear as special cases. Using this approach, bandpass filters can be synthesized in direct coupled resonator forms by pole placement instead of designing them through low-pass prototypes. By using circuit transformations, the resulting direct coupled resonator filter circuits can then be transformed into a variety of cross-coupled forms like a fully cross-coupled form or cascaded N-tuplet form. It is shown that one or more finite j/spl omega/-axis, /spl alpha/-axis, or complex TZs can be extracted as direct coupled resonator circuit blocks, which can be converted into cross-coupled triplets, quadruplets, or other N-tuplets of resonators. In particular, it is shown that a cascaded quadruplet section can be used to realize a complex TZ quadruplet S/sub i/ = /spl plusmn//spl sigma//sub i/ /spl plusmn/j/spl omega//sub i/, as well as two pairs of j/spl omega/-axis TZs, S/sub i/ = /spl plusmn/j/spl omega//sub i/, and S/sub k/ = /spl plusmn/j/spl omega//sub k/.

Synthesis of cascaded quadruplet filters involving complex transmission zeros

Cascade synthesis approach in transformed frequency domain (z-domain) is reformulated to cover the extraction of complex (s=/spl sigma/+j/spl omega/) and /spl sigma/-axis transmission zeros (TZs) in addition to the usual j/spl omega/-axis TZs. It is shown that complex conjugate quadruplets of TZs (s=/spl plusmn//spl sigma//spl plusmn/j/spl omega/) can be extracted as fourth order sections by applying zero shifting technique to the TZs at both s=0 and s=/spl infin/. The resulting fourth order sections are then transformed into cross-coupled forms with four coupled resonators, termed as linear phase cascade quadruplet (CQ) block. Such CQ blocks can be cascaded with the j/spl omega/-axis finite transmission zero (FTZ) CQ blocks or CT (cascaded triplet) blocks to realize linear phase filters with symmetric or asymmetric amplitude response.

Cascaded triplet filter design using cascade synthesis approach

A unified review of the design of Cascaded Triplet (CT) filters is presented. The cascade synthesis approach with pole placement is used to synthesize the filter and then Norton transformations are used to put the circuit into a standard form for conversion into CT form. Sections of the filter containing finite transmission zeros (FTZs) are then converted into bridge tees forming the CT sections. An example is given showing the development of equivalent alternative CT filter structures having all-inductive, all capacitive or mixed cross-couplings, depending on the location of FTZs with respect to the passband.

Synthesis of Bandstop Filters With Ultra Wide Upper Passbands

A new LP prototype-to-distributed bandstop mapping is defined to synthesize BSFs with controllable upper pass bandwidths. The synthesized filters involve resonators made up of commensurate OC and SC stubs coupled by inverters. It is shown that when inverters are approximated by several unit elements (UE) then their contribution to the response increases appreciably upon optimization. Thus, a novel approach is developed which can be used to synthesize BSFs with contributing UEs having ultra wide upper pass bands. Examples are presented with stopband centered at 1 GHz and having upper passband extending to 18 GHz.

Switched multiplexer design using Parallel Coupled Line three ports

It is shown that Parallel Coupled Line (PCL) three ports can be used to design switched multiplexers with wide or narrow channel bandwidths. Such three ports can be cascaded to form input and output manifolds for parallel or series connection of channel filters to form multiplexers. By incorporating switches into the filters it is possible to form switched multiplexers. The approach enables design of contiguous channels, thus avoiding the necessity of formation of even and odd numbered channels for preventing channel interactions in various switch combinations. As an example, a contiguous eight channel 2–18 GHz switched multiplexer is designed.

Waveguide filters with ridged and unequal width resonators

Analytical expressions are developed for characterization of ridged/finned waveguides for use in the design of direct coupled waveguide filters with ridged and/or unequal width resonators. The analytical expressions are used to control the harmonic passbands and higher order modes. A survey is made for comparison of responses of waveguide filters using unequal width resonators and unequal ridge resonators. It is found that ridged resonators are more effective in suppressing the spurious passbands in the upper stopband. A simple and accurate approach is developed for the design of the filters. It is based on impedance scaling of each resonator of the inverter coupled prototype filter so that it can be equated to the desired half wavelength waveguide resonator with selected cross-sectional dimensions. This approach is found to be more effective in controlling the band edge shifts seen in the classical susceptance slope parameter approach.

Synthesis of cascaded N-tuplet filters

In the theory of Darlington type filter synthesis extraction of transmission zero sections one by one, leading to a cascade of Darlington-A, B, C, D and Brune sections bears serious limitations like numerical accuracy problems, negative and/or extreme element values or impractical topologies for Darlington-C-D and Brune sections. In this paper all such problems are evaded/eased by extracting the transmission zeros as groups to form circuit sections which are readily convertible to multiple coupled resonator forms. In this approach, transmission zeros at s=0 and s= /spl infin/ are extracted as groups to form doublets of resonators, the j/spl omega/-axis and /spl sigma/-axis transmission zeros are extracted as groups to form triplets of resonators, pairs of j/spl omega/-axis and /spl sigma/-axis transmission zeros and complex transmission zeros are extracted as groups to form quadruplets of resonators, etc. The classical element extraction procedure in transformed frequency domain is revised to cover extraction of complex transmission zeros as forth order section by zero shifting from both s=0 and s= /spl infin/ leading to realisation as a quadruplet of resonators. Thus, the theory of cascade synthesis is generalised to include cascaded doublets, triplets, quadruplets and other N-tuplets of resonators as building blocks. It is found out that the limitations due to usual numerical accuracy problems are also reduced a lot and the resulting element value spreads can be controlled to avoid extreme values.

Cascaded triplet and quadruplet filter design using cascade synthesis approach

A unified review of the design of cascaded triplet (CT) and cascaded quadruplet (CQ) filters is presented. A cascade synthesis approach with pole placement is used to synthesize the filter and then Norton transformations are used to put the circuit into a standard form for conversion into CT or CQ form. Sections of the filter containing one finite transmission zero (FTZ) can be converted into bridge tee elements forming the CT sections and sections of filters containing two FTZs are converted into CQ sections. An example is given showing development of equivalent alternative CT and CQ filter structures having all-inductive, all-capacitive or mixed cross-couplings, depending on the location of FTZs with respect to the passband.

Comparison of efficient power combining techniques

Summary form only given. In microwave systems, the system scenario may require high output power. In this case, high-output power modules must be built to operate in microwave frequency range. In recent high power microwave systems, obtaining high power is commonly achieved by combining output powers of a bunch of transistor amplifier. In this approach, possible maximum efficiency is desired in order to reduce cost and thermal extraction.Regarding the power combining operation, apart from the operation frequency bandwidth, insertion loss of the combiner is a critical parameter. This loss is due to material losses, and generally increases with path length. In this study, by keeping the path lengths approximately the same, three power combining methods are investigated and implemented. The methods are compared by both efficiency properties and applicability to different microwave applications. Efficiency comparison is made at a single frequency, 17 GHz. The first method is combining by microstrip lines. An 8-way Wilkinson combiner is designed and implemented at 6-18 GHz band (Fig. 1 (a)). In order to have the possible shortest path lengths, inputs are placed at the edges of an octagon, where the output branch is also on the same plane. Loss per branch turned out to be 1.5 dB at 17 GHz. The second method is combining by suspended substrate striplines (SSS). A 4-way combiner consisting of branchline couplers is designed and implemented at 16.5-17.5 GHz band (Fig. 1 (b)). The average introduced loss per branch is observed to be 0.9 dB at 17 GHz. The last method is combining by microstrip probes in an air filled coaxial waveguide. An 8-way combiner is designed and implemented in 15-18 GHz band (Fig. 1 (c)). Insertion loss per branch is measured as 0.5 dB at 17 GHz. It is seen that the more the dielectric material is eliminated by one of the methods and the best efficiency is obtained by that method. In terms of efficiency, the best method turns out to be combining by microstrip probes in air medium, a relatively new technique. Moreover, the structure enables enough bandwidth for recent radar applications. Furthermore, the most efficient approach is to integrate low loss SSS technique (second method) to Wilkinson structure in an application having much wider frequency band of operation.

15 W power amplifier modules using coaxial waveguide combining by planar probes

Power combining in coaxial waveguide by printed planar probes is investigated. Combiners are designed and implemented at 8-12 GHz and 15-18 GHz. Average introduced insertion loss is measured as 0.5 dB per branch. Power amplifier modules are designed and implemented for both bands. ~20 W output power at 8-12 GHz and ~12 W output at 15-18 GHz are achieved by efficient power combining.