Miniature <inline-formula> <tex-math notation="LaTeX">$V$</tex-math> </inline-formula>-Band Rat-Race Coupler in CMOS Using Cascaded Bridged-T Coils

In this article, the design of a miniature <inline-formula> <tex-math notation="LaTeX">$V$</tex-math> </inline-formula>-band rat-race coupler in CMOS is presented. Through the employment of cascaded bridged-T coils in place of transmission line sections in conventional designs, a very compact circuit layout can be achieved through meandering the cascaded bridged-T coils. Also, in order to properly characterize the bridged-T coil design in CMOS, a new model extraction technique for lossy bridged-T coils is developed. The proposed model extraction technique is based on analytic equations only, and it can consider the frequency-dependent conductor and dielectric losses associated with a lossy bridged-T coil. With the aid of the proposed model extraction technique, a miniature <inline-formula> <tex-math notation="LaTeX">$V$</tex-math> </inline-formula>-band rat-race coupler is realized using a commercial 0.18-<inline-formula> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula>m CMOS process. It features a circuit size of only 312 <inline-formula> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula>m <inline-formula> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 234 <inline-formula> <tex-math notation="LaTeX">$\mu $</tex-math> </inline-formula>m, which corresponds to an electrical size of 0.062<inline-formula> <tex-math notation="LaTeX">$\lambda _{0} $</tex-math> </inline-formula> <inline-formula> <tex-math notation="LaTeX">$\times $</tex-math> </inline-formula> 0.047<inline-formula> <tex-math notation="LaTeX">$\lambda _{0}$</tex-math> </inline-formula> at 60 GHz. Good measured performance is obtained, and the measured bandwidth defined under an amplitude imbalance within 1.1 dB, a phase error within 5<inline-formula> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula>, a return loss better than 15 dB, and an isolation better than 20 dB is from 55.2 to 60.9 GHz or 9.82%.