Prescribed Transmission Zeros Research Articles

Synthesis of N-Foster-Section Filter With Maximum 2N Prescribed Transmission Zeros by Heuristic-Aided Graph Search

A graph-search-based optimization method to synthesize Foster-section-cascaded filters is introduced. A heuristic cost function that determines the direction of the graph search, is presented, and the optimization algorithm does not require the gradient calculation of the cost function. Auxiliary features of the optimization that can improve the heuristic efficiency and the quality of the result are explained. Several successful synthesis examples and designs of the synthesized filters are given.

Exact Synthesis of Inline Fully Canonical Dual-Band Filters Using Dual Extracted-Pole Sections

This letter provides a new mapping function which allows us to carry out the dual extracted-pole synthesis in inline fully canonical dual-band filters for the first time. To do this, it is a necessary condition that the reflection coefficient phase takes exactly the same value at the position of the two prescribed transmission zeros (TZs), one belonging to one band and the other to the second band, involved at simultaneous extraction. This is achieved by applying an antisymmetric or odd symmetry mapping function. Two different filters, one with asymmetric and the other with symmetric prescribed TZs at each of the passbands have been synthesized which validates the proposed approach.

Triple-Mode Microwave Filters With Arbitrary Prescribed Transmission Zeros

This article presents a new filter design for arbitrary placement of real frequency transmission zeros in triple-mode filters, allowing for either asymmetric or symmetric responses. Triple-mode filters can be viewed, in general, as a series combination of coupled resonators with non-adjacent couplings, allowing for the realisation of transmission zeros. The strength and phase of couplings dictate the transmission zeros locations. The arbitrary placement of transmission zeros requires controlling all amplitude and phase rations, i.e., the ability to realise both negative and positive couplings. In general, this necessitates the use of capacitive and inductive probe structures complicating the construction and hence increasing the filter cost. The method presented in this article enables arbitrary placement of transmission zeros using only inductive or only capacitive couplings structures. In addition, broadband filtering characteristics can be realised using triple-mode filters. Examples of several narrow and broadband bandpass filters are given indicating that this method is valid for most triple-mode structures.

Synthesis of multi‐band filters based on multi‐prototype transformation

In this article, a new synthesis method for generalized multi-band filters has been proposed. Different from the traditional frequency transformation method, which transforms a low-pass prototype into a multi-band filter, multiple low-pass prototypes have been transformed into a multi-band filter. This study introduces the idea of transforming more than two lowpass prototypes into a filter, called multi-prototype transformation. It divides the multi-band filter to be synthesized into different segments each of which corresponds to a low-pass prototype. After frequency transformation, these segments are combined together to get the final transfer function. The multi-band filter synthesized by this method can have different orders, bandwidths or return losses in different passbands. Prescribed transmission zeros can also be realized. The return loss adjustment, segment boundary estimation and equal-ripple realization of this method are further explained in theory. To verify this method, an asymmetric quad-band filter is synthesized as an example and a symmetric triple-band filter is synthesized, designed, fabricated and measured. The obtained results show good agreement with the simulation.

Synthesis of Multiband Filters by Linear Optimization

In this article, a new synthesis method for the generation of multiband generalized Chebyshev polynomials with prescribed transmission zeros is presented. The proposed linear optimization technique is applicable to symmetric and asymmetric filter responses. To demonstrate its general application, the technique has been applied to the direct synthesis of dual-and triple-bandpass filters. A 7th degree dual-band prototype and a 10th degree triple-band prototype, synthesized using the proposed technique, have been fabricated and tested to validate the practicality of the method.

Direct Synthesis of Complex Loaded Chebyshev Filters in a Complex Filtering Network

In this paper, a direct synthesis approach is proposed for designing a Chebyshev filter that matches the frequency variant complex loads at both the ports. The approach is based on the power wave renormalization theory and two practical assumptions: 1) the prescribed transmission zeros are stationary and 2) the reflection zeros are located along an imaginary axis. Three conditions are derived to stipulate the characteristic polynomials of the filter’s responses through the renormalization of reference load impedances. These conditions are sequentially applied to ensure that the filter is physically realizable and well matched to the complex loads. It has been shown that the optimally synthesized filtering network that consists of an ideal filter cascaded with a piece of transmission line of an optimal length at each port can match the complex loads over a given frequency band with the best effort. By incorporating with an adjustment of the junction parameters, the approach provides an analytical yet flexible way to synthesize advanced microwave circuits composed of multiple filters connected together through some generalized junctions. The effectiveness of the method is demonstrated through three synthesis examples.

Design of an Economical Compact Coaxial Cavity Combline Filter for 3G TD Base Station

The cross coupled microwave filter is widely used in the communication sub system .The synthesis of the cross coupled filter is from prescribed transmission zeros and return loss till the attainment of the coupling matrix of each cavity. A compact narrowband combline high rejection filter with cross coupled is presented. A configureiton using identical resonator post with capacitance-loading is introduced. Tested results show that with order-8 filter center frequency at 2017.5MHz, return loss lower than-25dB can be achieved over a relative bandwidth of 1.29%. A sample filter has been fabricated and tested result confirmed the theory result.

Direct Optimal Synthesis of a Microwave Bandpass Filter With General Loading Effect

This paper presents a direct approach to the synthesis of a general Chebyshev bandpass filter that matches to a frequency variant complex load. The approach is based on the power wave renormalization theory and two practical assumptions, which are: 1) the prescribed transmission zeros are stationary and 2) the reflection zeros are located along the imaginary axis. Three necessary conditions that stipulate the characteristic polynomials associated to the filter are derived through renormalization of the load reference impedances. It has been shown that these three conditions can only be satisfied by an ideal filter circuit model separated by a piece of interconnecting stub from the complex load. The length of the stub will be optimally designed in the sense that the designed filter will best match to the complex load over a given frequency range. The proposed method offers a deterministic, yet flexible way for optimally designing a diplexer or a multiplexer with a realistic loading effect. The effectiveness of the method is demonstrated by two design examples.

Microstrip Parallel-Coupled Filters With Cascade Trisection and Quadruplet Responses

Microstrip parallel-coupled filters with generalized Chebyshev responses are presented. The basic structure of the proposed filter is a conventional parallel-coupled filter of which the physical dimensions can be easily obtained by the well-known analytical method. With the aid of the equivalent circuit corresponding to a conventional parallel-coupled filter, the relative insertion phase from source or load to each open end of resonators can be easily obtained by observing the two-port admittance matrix. Applying the cross coupling from source or load to a proper nonadjacent resonator, a trisection or a quadruplet coupling scheme can be realized with prescribed transmission zeros. More importantly, the proposed trisection can be designed to have a transmission zero on the lower or upper stopband by just adjusting the length of the cross-coupling strip. Using the proposed structure, the conventional time-consuming adjusting procedure to obtain initial physical dimensions of filters is no longer required. In this paper, a fourth-order parallel-coupled filter is used as the basic structure to demonstrate various combinations of transmission zeros. Simulated and measured results are well matched.

Nonlinear model-state feedback control for nonminimum-phase processes

A general nonlinear controller design methodology for continuous-time nonminimum-phase systems is presented, which utilizes synthetic outputs that are statically equivalent to the original process outputs and make the system minimum-phase. A systematic procedure is proposed for the construction of statically equivalent outputs with prescribed transmission zeros. The calculated outputs are used to construct a model-state feedback controller. The proposed method is applied to a nonminimum-phase chemical reactor control problem where a series/parallel reaction is taking place.

Microstrip cascade trisection filter

A new configuration of odd-degree cascade trisection bandpass filter realized by combining a microstrip hairpin resonator and /spl lambda//2-line open-circuited resonator is proposed. The general asymmetric Chebyshev function is used to synthesize the cascade trisection prototype. A five-pole microstrip cascade trisection bandpass filter with two asymmetrically prescribed transmission zeros located on opposite of the passband is designed and fabricated. The experimental result matches well with the theory.

General coupling matrix synthesis methods for Chebyshev filtering functions

Methods are presented for the generation of the transfer polynomials, and then the direct synthesis of the corresponding canonical network coupling matrices for Chebyshev (i.e., prescribed-equiripple) filtering functions of the most general kind. A simple recursion technique is described for the generation of the polynomials for even- or odd-degree Chebyshev filtering functions with symmetrically or asymmetrically prescribed transmission zeros and/or group delay equalization zero pairs. The method for the synthesis of the coupling matrix for the corresponding single- or double-terminated network is then given. Finally, a novel direct technique, not involving optimization, for reconfiguring the matrix into a practical form suitable for realization with microwave resonator technology is introduced. These universal methods will be useful for the design of efficient high-performance microwave filters in a wide variety of technologies for application in space and terrestrial communication systems.

Realization of a loaded two-port with prescribed transmission zeros and driving point function†

In this paper it is shown that any arbitrary driving point function can always be realized as a two-port active network having prescribed transmission zeros in any one direction and terminated by a pre-fixed passive RC admittance.

Cascade Synthesis of Distributed RC Networks

The synthesis of simultaneously prescribed drivingpoint and transfer admittances for distributed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> networks without transformers is considered. Realizations with common ground connections are required. The realizations given, in general, involve an arbitrary multiplying constant for the transfer admittance and are valid except when the prescribed transmission zeros, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t = \tanh \sqrt{p} = \delta_{0} + j \omega_{0}</tex> are such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}^{2}</tex> < <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta_{0}^{2}</tex> < <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 + \omega_{0}^{2}</tex> . If only the short-circuit transfer admittance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y_{12}</tex> or the open-circuit voltage transfer ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{12}</tex> is specified, a realization using surplus factors is given valid for all transmission zeros other than real zeros less than unity, which can never be realized by an unbalanced commensurate distributed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> network, and that for such networks, zeros of transmission where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta_{0}^{2} &gt;\omega_{0}^{2} + (\delta_{0}^{2} + \omega_{0}^{2})^{2}</tex> always require the use of surplus factors. Examples of the various synthesis procedures are given.