A unified theory for the characteristics of dual modes in a circular r
esonator is elucidated in simple analytical expressions. First, a circ
ular resonator is considered as a ring transmission line which allows
two oppositely traveling waves. The essential quantities that characte
rize a transmission line, i.e., the propagation constant and character
istic impedance are obtained theoretically and/or experimentally. Seco
ndly, any circular resonator is described by a ring resonator model wh
ich can be treated analytically, and the resonant frequencies are obta
ined when perturbations are added along the periphery of a circular re
sonator. A two stage BPF is created by adding I/O ports to the perturb
ed circular resonator. Its center frequency and bandwidth is calculate
d based on the ring resonator model. The circuit condition for obtaini
ng two attenuation poles at both sides of the passband is given togeth
er with the method for their control.