All‐pass dispersion synthesis using microwave C‐sections

Abstract

A closed-form iterative procedure for synthesizing quasi-arbitrary phase responses with cascaded microwave C-section all-pass phasers is presented. The synthesis consists in mapping the transmission poles of the cascaded C-section structure onto the transmission poles of the specified transfer function, where the latter poles are computed using a closed-form polynomial generation method. The real and complex transmission poles of the specified transfer function are realized using C-sections of different lengths and different couplings coefficients. The proposved synthesis is validated by both full-wave analysis and measured multilayer prototypes.

Hybrid‐cascade coupled‐line phasers for high‐resolution radio‐analog signal processing

“…3(a) shows that the specified delay response can be successfully achieved by using a 4-HC coupled-line phaser of different length and coupling coefficients. The previous approach consists in using a transversal cascade of C-sections of different lengths and couplings, as depicted in [8]. However, as seen from Fig.…”

A Geometric Approach to Group Delay Network Synthesis

“…Furthermore, the digitization process of future wideband channels (such as the International Telecommunication Union 71-76 and 81-86 GHz bands) requires sampling speeds of at least 10 GSPS, currently achievable at the cost of sacrificing resolution and dynamic range [2]. The fundamental building block of any analog signal processor is a delay structure [3][4][5] of prescribed response. This quasi-arbitrary group delay function can be synthesized by cascading all-pass sections to obtain a delay function approximating the required response to within a constant.…”

“…In an effort to address these limitations, analytical techniques for synthesizing the group delay of an electrical network have been developed [3], [4], [10], [13][14][15]. Of these, only one presents a rigorous theoretical treatment to finding minimal-order solutions to the synthesis problem [13].…”

“…This method is also limited to the low-pass case and provides poor convergence if the bandpass signal is treated as an extended low-pass spectrum [7], [8]. The approach presented in [3], [4] solves the approximation problem by generating a Hurwitz polynomial, with the desired phase response, at specified frequencies, which are chosen a priori. No rigorous method of choosing these frequency points, such that the resulting solution is minimal-order, is presented.…”

“…2) The resulting group delay function is an approximation of the required response to within any arbitrarily specified maximum delay variation across the passband, extending on methods in literature [3][4][5][6], [10], [13], [14] where the network's order is chosen and not, explicitly, the resulting maximum delay variation.…”