04-BroadbandDelayFilter - EE 541, Fall 2009: Course Notes...

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EE 541, Fall 2009: Course Notes #4 Coupled Inductor, Constant Resistance, Broadband Delay Filter Dr. John Choma Professor of Electrical Engineering University of Southern California Ming Hsieh Department of Electrical Engineering University Park: Mail Code: 0271 Los Angeles, California 90089–0271 213–740–4692 [USC Office] 213–740–8677 [USC Fax] johnc@usc.edu ABSTRACT: This paper develops a three-terminal delay filter whose topology is an interconnection of only ideally lossless, coupled inductors and capacitors. In the absence of significant capacitive loading at the input and/or output ports, the proposed filter emulates an all- pass network whose low frequency delay is twice that afforded by the poles of the proposed circuit. Moreover, the driving point input and output impedances of the struc- ture are frequency invariant resistances whose values over the frequency spectra of inter- est are independent of the envelope delays achieved. These impedance characteristics allow for the convenient implementation of a cascade of match-terminated delay filter sections, thereby allowing for reasonably large envelope delays without incurring band- width penalties in either the magnitude or the delay responses. An example demonstrates the feasibility of designing a filter providing zero frequency delays in the mid-hundreds of picoseconds that remain nominally constant for signal frequencies extending through a few gigahertz. Correspondingly, the magnitude responses of these delay structures offer 3-dB bandwidths that can be significantly larger than the frequencies at which the ob- served envelope delays decay monotonically to a user-defined percentage of their respec- tive zero frequency values. Original: August 2006
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Course Notes #4 USC Viterbi School of Engineering J. Choma August 2006 - 121 - Coupled Inductor Delay 1.0. INTRODUCTION A recurring theme in the design of circuit cells indigenous to modern communication systems is the attainment of distortionless signal transmission from the input port to the output port of the circuit. “Distortionless” signal transmission is herewith taken to mean that the wave shape of an output response differs from the applied signal excitation by little more than a fre- quency invariant scale factor and a time delay that is likewise independent of the frequency con- tent of the input signal. For a linear, lowpass circuit, this requirement implies that if Y(s) denotes the Laplace transform of the time domain output response, y(t) , and if X(s) symbolizes the trans- form of the corresponding input signal, x(t) , the desired transfer function, H(s) , is d sT Y(s) H(s) H(0) , X(s) e == (1) where H(0) is the zero frequency transmission factor, or gain, of the circuit, and T d is the con- stant time delay implicit to signal transmission from the input port -to- the output port. While a circuit whose transfer function is defined by (1) is physically unrealizable, specific system applications allow for suitable emulations of the subject relationship. For example, constant I/O
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04-BroadbandDelayFilter - EE 541, Fall 2009: Course Notes...

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