Calculation of gap impedance of TM₃₁₀ mode in coaxial output cavity with equivalent circuit theory

We have designed a single gap cylindrical coaxial cavity operating at transverse magnetic TM310-mode with low external quality factor for X-band klystron. Under the condition of the gap impedance imaginary part being zero at the working center frequency, the equivalent gap center of drift tubes at TM310 in the coaxial cavity is calculated with equivalent circuit theory, and then the equivalent length between the center and the transverse diaphragms in output waveguide is calculated. The equivalent gap impedance of the cylindrical coaxial cavity coupled with a waveguide filter containing a pair of transverse diaphragms is calculated with MATLAB and the result is coinciding with that of the cold test. This indicates that the equivalent length calculation method is correct. Thus the microwave equivalent circuit theory is not only applicable to analyzing TM010 mode in cylindrical cavity, but alsosuitable for studying the output circuit of high order transverse magnetic mode in single gap cylindrical coaxial cavity. Furthermore, its process is speedier compared with traditional cold test simulation and field analysis methods.