Analysis and design of lumped-element quadrature couplers with lossy passive elements

The analysis and design of lumped-element quadrature directional couplers is described for monolithic applications. The analysis is carried out using the fourfold symmetry of capacitively and inductively coupled hybrid circuits. S-parameter responses of these two types of couplers are compared when losses and other parasitic effects of typical on-chip passive elements are taken into account. The analysis provides analytical expressions that make it possible to determine the effects that each non-ideality has on overall circuit performance before circuit simulations are performed using a particular process design kit