Complex Quality Factor Research Articles

Coupling Matrix-Based Co-Design of Filter-Oscillators

This letter presents a methodology of designing integrated filter-oscillators using the coupling matrix technique. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N + 4$ </tex-math></inline-formula> coupling matrix is developed for the first time to describe the filter-oscillator topology. Accordingly, the corresponding group delay, loop gain, loop phase, and complex quality factor of the feedback filter can be calculated using the matrix. This helps rapidly predict oscillating frequencies at group delay or complex quality factor peak frequencies to achieve lower phase noise. Moreover, since the transistor and the transmission line (TL) entries are incorporated in the coupling matrix, the physical geometries can be directly determined, resulting in improved design efficiency. Two third-order filter-oscillators are implemented at 2.91 GHz (group delay peak) and 3.15 GHz (complex quality factor peak) frequencies, respectively. The developed filter-oscillators are measured with −121 and −145 dBc/Hz phase noise at 1-MHz offset frequency, validating this coupling matrix-based co-design approach.

Low Phase Noise Feedback Oscillators Utilizing High-Q SIW Filter with Dielectric Loading

Abstract High-Q substrate integrated waveguide (SIW) resonator and its application to low phase noise oscillators are focused in this paper. By drilling air holes in the substrate, SIW bandpass filters (BPFs) with high Q factor could be achieved. This SIW filter is embedded into the feedback loop to be treated as a frequency stabilization element in designing the oscillator. The complex quality factor (Qsc)-peak frequency of the filter is chosen as the final oscillation frequency to obtain low phase noise performance. Moreover, air boxes are utilized instead of the air holes in the substrate to design another oscillator with lower phase noise performance and good harmonic suppression. Two low phase noise oscillators based on fourth-order SIW BPFs with dielectric loading have been studied, demonstrated and fabricated to verify the design concept.

A new approach to the push–push oscillator based on a differential SIW bandpass filter

ABSTRACTA novel push–push oscillator based on a differential bandpass filter (BPF) using substrate integrated waveguide (SIW) technique is presented in this paper. For the first time, the differential SIW BPF is utilized as a frequency stabilization element to provide differential outputs in designing the push–push oscillator. The complex quality factor (Qsc)-peak frequency of the BPF is chosen for the design at approximately half the final output frequency to achieve low phase noise performance. Moreover, two transmission zeros (TZs) below the passband and two TZs above the passband which highly improve the out-of-band rejection are obtained by using both electromagnetic coupling and cross coupling. An SIW power combiner is also designed to obtain the desired signal. A push–push oscillator has been proposed and experimentally demonstrated at 27.8 GHz to verify the above design concept. The measured results show that the output power is −17.3 dBm with a phase noise of 128.6 dBc/Hz at 1-MHz offset.

Configuration for Realizing a Push-Push Parallel-Feedback Oscillator Through a Differential Bandpass Filter

A push–push parallel-feedback oscillator constructed through a differential bandpass filter (BPF) is investigated in this paper. For the first time, the differential filter has been utilized as the parallel-feedback element to provide differential outputs in designing the push–push oscillator. Low phase noise performance and easy design process can be obtained due to the parallel feedback circuits compared with series feedback ones. The complex quality factor ( $Q_{\textrm {sc}}$ )-peak frequency of the BPF is chosen as the half final output frequency to further improve the phase noise performance. Also, the improvement of the odd harmonic suppression and even harmonic enhancement can be easily obtained. Moreover, due to the existence of the common mode suppression, only 180° out-of-phase mode will be achieved which makes the oscillator run in a stable condition. To validate the design concept, a push–push oscillator based on a microstrip differential BPF has been achieved which is operating at 8.37 GHz. The measured results show that the output power is −5.4 dBm with a phase noise of −134.6 dBc/Hz at 1-MHz offset.

Design of Low Phase-Noise Microwave Oscillator and Wideband VCO Based on Microstrip Combline Bandpass Filters

This paper presents a new low phase-noise microwave oscillator and wideband voltage-controlled oscillator (VCO) based on microstrip combline bandpass filters. For this type of oscillator, the passband filter is embedded into the feedback loop to treat as a frequency stabilization element. Instead of designing the oscillator at the group-delay-peak frequency of the filter to achieve a good phase-noise performance, in this paper, the peak frequency of the complex quality factor Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> is adopted for oscillator design. To demonstrate the effectiveness of using Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> -peak frequency, two filter-based oscillators are implemented at the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> -peak and group-delay-peak frequencies, respectively. The oscillator designed at the Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> -peak frequency improves the phase-noise about 10 dB as compared with that realized at the group-delay-peak frequency. The developed oscillator with the three-pole combline filter is experimentally demonstrated at 2.05 GHz with -148.3-dBc/Hz phase noise at 1-MHz offset frequency. Moreover, by attaching a varactor on each resonator of the combline filter, the oscillator can be extended to a wideband VCO. The developed VCO has a frequency tuning range from 1.3 to 2.2813 GHz with a 54.8% bandwidth. Over this frequency range, all the phase noises measured at 1-MHz offset frequency are better than -117.19 dBc/Hz.