Abstract
All-pass networks with prescribed group delay are used for analog signal processing and equalization of transmission channels. The state-of-the-art methods for synthesizing quasi-arbitrary group delay functions using all-pass elements lack a theoretical synthesis procedure that guarantees minimum-order networks. We present an analytically-based solution to this problem that produces an all-pass network with a response approximating the required group delay to within an arbitrary minimax error. For the first time, this method is shown to work for any physical realization of second-order all-pass elements, is guaranteed to converge to a global optimum solution without any choice of seed values as an input, and allows synthesis of pre-defined networks described both analytically and numerically. The proposed method is also demonstrated by reducing the delay variation of a practical system by any desired amount, and compared to state-ofthe-art methods in comparison examples.
Highlights
The ever-increasing performance requirements of modern high-speed communication systems favor analog solutions for real-time signal processing applications
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
The sixth-order equalizing all-pass network is synthesized in only 10 iterations due to the natural reduction in group delay variation experienced in practical filters because of finite resonator Q-factors
Summary
The ever-increasing performance requirements of modern high-speed communication systems favor analog solutions for real-time signal processing applications. Only one presents a rigorous theoretical treatment to finding minimal-order solutions to the synthesis problem [13] This is done by approximating the original system’s group delay characteristic, to within a specified error, using the real Fourier series with an optimal number of all-pass sections. No rigorous method of choosing these frequency points, such that the resulting solution is minimal-order, is presented Due to these problems with state-of-the-art analytical synthesis methods, numerical approaches relying on optimization algorithms have been widely sought in the modern group-delay synthesis literature [1], [5], [6], [14,15,16,17]. We present a new numerical synthesis procedure of minimum-order series-cascaded all-pass networks having a quasi-arbitrary group delay response, making the following contributions to the state-of-the-art: 1) Our method does not require an initial value set. National Instruments AWR Microwave Office 10 is used as the circuit simulator
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