Modeling RF passive circuits using coupled lines and scalable models

Coupled line sections are critical structures in distributed RF and microwave passive circuits. Their applications have been well known in the design of filters, and couplers. However, they also constitute the building blocks for other passive structures such as spiral inductors, transformers and capacitors. This paper presents an approach to model passive structures, such as rectangular spiral inductors, with the aid of common multi-line parameters. The multiple coupled line approach uses a distributed model, which can relate voltages and currents at the start and end of a multiple coupled line section using impedance and admittance matrices. The discontinuities in the circuit, such as the bends in inductors, can be modeled using scalable models. The system response for the complete passive structure is obtained using the theory of segmentation.