Theory and implementation of T-coil network equivalent transmission line

This paper introduces a compact lumped element model for the replacement of an ideal lossless transmission line which is valid for electrical lengths up to π. Subsequently, a T-coil network is devised to emulate a quarter-wavelength transmission line of Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> = 70.7 Ω at f<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> = 10 GHz. The designed layout in a commercial 45RFE semiconductor process, excluding pads, demonstrates remarkable compactness, occupying a mere circuit size of 130 μm × 155 μm, equivalent to approximately 0.0043 λ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> × 0.0052 λ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> at f<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf>. Furthermore, it exhibits performance akin to an ideal transmission line with a simulated return loss better than 15 dB and an insertion loss under 0.8 dB across the frequency range from 5.7 GHz to 14.2 GHz.