Impedance-Transforming Symmetric and Asymmetric DC Blocks

Abstract

Design formulas of symmetric and asymmetric dc blocks are presented for achieving Chebyshev and Butterworth frequency responses. They can also be used for impedance transformers. Design formulas of symmetric dc blocks are first derived and those of asymmetric dc blocks are also computed based on the symmetric ones. For easy derivation of design formulas of the symmetric dc blocks, coupling coefficient, being proportional to bandwidth, is defined. It is then clarified that symmetric Chebyshev dc blocks are not possible for the impedance transforming. For the symmetric Butterworth dc blocks, three design methods are exploited. To verify the symmetric Butterworth dc blocks, a microstrip dc block with 50- and 25-Ω termination impedances designed at a center frequency of 2 GHz was fabricated. The measured <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> are - 0.19 and - 57 dB around 2 GHz, showing quite good agreement with simulation results. Based on synthesized symmetric dc blocks, the coefficients of transfer function | <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sub> | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> are calculated and design formulas of the asymmetric dc blocks are derived based on the symmetric ones. Asymmetric Chebyshev dc blocks are verified by the measurements provided in a previously published paper and asymmetric Butterworth dc blocks by the symmetric Butterworth dc block measured in this paper.