S-Parameter Analysis and Compact Formulation of Two-Port 90° N-Path Circuits.

This brief introduces a compact S-parameter model of the two-port 90° N-Path circuit within the vicinity of the clock frequency. Transfer and reflection coefficients, which manifest the circuit filtering properties and the non-reciprocal phase shifting, are derived for a circuit that utilizes ideal switches and then extended to account for transistor parasitics. New simplified equations for parasitic phase and frequency shifts, which are of interest in the design of circuits such as electronic circulators, are proposed. Good agreement is demonstrated between the analytic coefficients and simulation results of behavioral 4-path as well as 65-nm NMOS 8-path circuits, both excited by a 1 GHz clock. The proposed expressions are utilized to compare an electronic circulator that includes an analytic 8-path model versus one that employs an NMOS switched circuit. Agreement of better than 0.2dB is demonstrated for insertion losses whereas isolation results differ by less than 2 dB over an 80 MHz bandwidth centered at 980 MHz.