Trans-Impedance Filter Synthesis Based on Nodal Admittance Matrix Expansion
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Trans-Impedance Filter Synthesis Based on Nodal Admittance Matrix Expansion Lingling Tan · Yu Bai · Jianfu Teng · Kaihua Liu · Wenqing Meng
Received: 31 July 2012 / Revised: 17 October 2012 / Published online: 15 November 2012 © Springer Science+Business Media New York 2012
Abstract This paper demonstrates a method of synthesis of trans-impedance filters using the theory of nodal admittance matrix expansion. Two examples of the Bach Second-Order Lowpass trans-impedance filter and the Multiple Feedback (MFB) Second-Order Lowpass II trans-impedance filter are synthesized, which verifies the feasibility of the proposed method of circuit generation. Keywords Nodal admittance matrix (NAM) expansion · Nullor · Trans-impedance filter · Symbolic circuit design · Active network synthesis 1 Introduction Method of synthesizing active circuits from a given voltage or current transfer function has been illustrated in reference [6, 16], in which theory of nodal admittance matrix (NAM) expansion [5] has been proposed to implement on symbolic transfer function. Circuits of voltage mode and current mode have been synthesized using theory of NAM expansion [14, 15]. With the development of modern electronic technology, the transfer function of trans-impedance attracts more attention for its unique L. Tan · Y. Bai () · J. Teng · K. Liu · W. Meng The School of Electronic Information Engineering, Tianjin University, Tianjin 300072, P.R. China e-mail: [email protected] L. Tan e-mail: [email protected] J. Teng e-mail: [email protected] K. Liu e-mail: [email protected] W. Meng e-mail: [email protected]
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Circuits Syst Signal Process (2013) 32:1467–1476
characteristics [17]. Admittance matrix stamp for active block Operational Transresistance (Trans-impedance) Amplifiers (OTRAs) has been proposed and utilized in amplifier circuit synthesis [11], and the Nodal Analysis (NA) method has been applied to systematic analysis of OTRAs-based circuits [13]. However, how to synthesize an active trans-impedance filter has not been discussed yet. In this paper, where the input signal is current, and the output is voltage, bi-quadratic circuits of transimpedance such as Multiple Feedback (MFB) Second-Order and Bach Second-Order are taken as examples to demonstrate the method of synthesizing trans-impedance filters.
2 Theory of NAM Expansion 2.1 Method of Synthesis of Trans-impedance Circuits In active network synthesis, starting from the port matrix of VCVS, as shown in Table 1, circuits can be synthesized from a given voltage transfer function [3], which is the reverse process of the circuit analysis. For the VCVS, assuming that the initial conditions are zero (start “at rest”) and its transfer function is H (s) = V2 (s)/V1 (s), where V2 (s) and V1 (s) are the Laplace transforms of the output and input voltage, respectively. While for a two-port network where the input signal is a current source and the output is voltage signal, in this situation, the dimension of the transfer function H (s) = V2 (s)/I1 (s) is a trans-impedance, whi
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