Analysis and Design of Tri-Coupled-Line-Based Attenuator for Miniaturized Terahertz Integrated Systems

This article presents the analysis and design of a cell-based passive digital attenuator operating at the millimeter-wave (mmW) and terahertz (THz) regimes. Each attenuator cell comprises nonidentical tri-coupled-lines (TCLs) with associated attenuation switches, controlling the targeted attenuation levels. Unlike the traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula>- or T-type attenuators, the switches are turned off in the reference states, thus their ON-resistance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\text {ON}}$ </tex-math></inline-formula> hardly increases the insertion loss (IL) of the TCL-based attenuator, alleviating the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\text {ON}} \times C_{\text {OFF}}$ </tex-math></inline-formula> technology bottleneck in the attenuator implementation. Compared to dual-coupled lines, the TCL structure offers further miniaturized circuit area with an extended attenuation range. The complete circuit analysis is constructed using the six-port TCL model with embedded transistor switch models, which is adopted and validated through a 220 GHz 4-bit attenuator prototype designed in the 0.13-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>m SiGe BiCMOS technology. The fabricated chip features very small IL of 1.4–2.4 dB, 16 attenuation states with 1-dB amplitude step-size, minimal 0.3-dB/1.7°rms amplitude/phase errors at 200 to 230 GHz, and a compact core area of 0.0075 mm2 (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.00385\lambda _{0}^{2}$ </tex-math></inline-formula>). In addition, thanks to the intrinsic dc-isolated transistors at radio frequency (RF) ports in the TCL structures, the attenuator has >8 kV human body model (HBM) electrostatic discharge (ESD) protection at RF ports without using ESD protection circuits, which typically degrades the RF performance, especially at THz frequencies.