General Chebyshev Bandpass Filters Research Articles

Low phase noise L‐band oscillators based on novel general Chebyshev bandpass filters

SUMMARYOscillators act as signal sources for wireless communication systems, radars, wireless charging, and other industrial applications, whose phase noises directly determine system performance. In this paper, two low‐phase noise microwave oscillators based on novel microstrip second‐order band‐pass filters are presented. These filters are characterized by good frequency selectivity owing to two transmission zeros near to the passbands. As a result, relatively high group delay can be achieved at center frequencies, which is vital to the phase noise performance of the oscillators to be designed. Simultaneously, the bandwidths can be made narrow enough so that actual oscillating frequency is very close to the designed one. In addition, the introduction of stepped impedance makes these filters capable of harmonic suppression, which efficiently suppresses the harmonics in the output such as the second harmonic. These filters are compact and also of easy design. Finally, two microwave oscillators at 2.0 GHz are designed on these microstrip filters. As the measured results show, their output frequencies are 2.002 GHz. The phase noises are −127.21 and −127.03 dBc/Hz@100 kHz, respectively. The second harmonic suppressions are as great as 30.45 and 39.21 dBc, respectively.

Direct synthesis technique (DST) for complex general Chebyshev filters

SummaryRecently, we discussed the concept of direct synthesis technique (DST), in which real‐coefficient filtering polynomials containing all information of the filters to be synthesized are derived directly for realization, and they could find applications in the design of lumped‐element LC filters, active RC filters, and infinite impulse response digital filters. In this paper, another DST for complex general Chebyshev bandpass filters is discussed, which is based on a complex mapping relation and featured by complex‐coefficient filtering polynomials. It is called as complex DST in this paper. Compared with real‐coefficient filtering polynomials whose polarities are determined by the number of their zeros at zero frequency, the polarities of complex‐coefficient filtering polynomials can be easily changed by multiplying imaginary unit j. Such advantage might make their realization more flexible. The analysis shows that conventional coupling matrix could be considered as narrow‐band approximation of network matrix derived by complex DST in the normalized frequency domain. In order to demonstrate the validity of complex DST in this paper, it is applied in the design of classic parallel‐coupled microstrip bandpass filters. Compared with conventional synthesis techniques, complex DST could find out better dimensions and provide more choices for realization and synthesize both even‐order and odd‐order parallel‐coupled microstrip bandpass filters. Copyright © 2017 John Wiley & Sons, Ltd.

Inverse general Chebyshev bandpass filters

SummaryIn this paper, the synthesis of inverse general Chebyshev bandpass filters is discussed. Unlike general Chebyshev filters that flexibly place transmission zeros to mainly control the performance of the filters in the stopband and keep constant ripple in the passband, inverse general Chebyshev filters are featured by flexible placement of reflection zeros in the passband and keep constant ripple in the stopband. Two approaches to directly derive filtering polynomials of inverse general Chebyshev bandpass filters in the bandpass domain are discussed in detail. By applying the zero‐extraction method, these filtering polynomials could be realized through appropriate networks. Finally, two examples are presented for demonstration.

A Reconfigurable Microwave Combline Filter

A general cascaded filter design technique is implemented to get a tunable narrow-band filter response based on the general Chebyshev bandpass filter. A cavity combline microwave filter is fabricated by cascading two asymmetrical filters without using an isolator between them. Tuning is provided by means of the screws on top of each resonator of the cavity combline filter. An optimization is applied to get the desired response. The designed example is presented together with the simulation and measurement results. The measured data are in good agreement with the simulation results.

Direct Synthesis of General Chebyshev Bandpass Filters in the Bandpass Domain

Conventional synthesis technique for general Chebyshev bandpass filters usually derives filtering polynomials from general Chebyshev filtering function. Then, lowpass prototypes or coupling matrices in the lowpass domain are derived and are transformed into the bandpass domain for practical application. Unfortunately, it has some disadvantages such as incapability to synthesize filters with asymmetric frequency response and narrow-band limitation. In this paper, two techniques to directly synthesize filters in the bandpass domain are discussed, i.e., the direct technique based on local mapping and the direct technique based on global mapping. The real-coefficient filtering polynomials constituting scattering parameters will be derived directly in the bandpass domain, and then used to constitute impedance or admittance parameters for network realization. In this paper, one approach to synthesize bandpass filters in terms of coupled resonators is discussed. Several examples are presented for demonstration. The direct techniques discussed in this paper are flexible so that general Chebyshev bandpass filters with arbitrarily placed transmission zeros might be synthesized.

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.

An Analytical Approach to Computer-Aided Diagnosis and Tuning of Lossy Microwave Coupled Resonator Filters

This paper presents a novel analytical approach to extracting of the coupling matrix of a narrow band general Chebyshev bandpass filter with losses. The approach is very useful for computer aided tuning of a microwave bandpass filter. The concept of phase loading is revealed for the first time in the community of computer aided tuning. The analytical approach consists of three elements: 1) a theoretic formula that leads to a practical scheme for determining the phase loading; 2) a theoretic formula for de-embedding the section of unknown transmission lines at the two ports of a filter; and 3) a theory for determining the unloaded Q of a filter if the loss for each resonator is nearly the same. To make the approach easy to use, some practical techniques for reconstructing rational functions of Y-parameters from a set of filter response are also provided in the paper. The proposed diagnosis approach is applicable to a general coupled resonator filter with losses and therefore can be effectively used in computer aided tuning of high order filters with cross couplings.

THE DESIGN TECHNIQUE FOR COAXIAL RESONATOR CAVITY DUPLEXER

A general design technique for the coaxial resonator cavity duplexer is proposed in this paper, based on the design method of the general Chebyshev band-pass filter. We can obtain the coupling matrixes of cross-coupled resonator duplexer by optimization technique, and complete the design of duplexer fast. The proposed duplexer is designed and fabricated with the 1.92–1.98 GHz downlink and 2.11–2.17 GHz uplink frequencies. Across the bandwidth, the measured insertion losses at the both bands are less than 1 dB, while the input and output return losses are well below 20 dB. More than 50 dB isolation performance is obtained from the duplexer. The measured results approximately meet all the conditions of the design targets.