The TM0n multi-modal excitation of a coaxial line probe-to-circular waveguide is rigorously treated using the conservation of complex power technique. The overall scattering matrices of the coaxial line probe-circular wavguide are deduced

and computing results for the reflection coefficient of the coaxial line are then compared with the experimental results

both agree well. We also investigate the power distribution of various order modes excited in circular waveguide as a function of the probe length

and the analysis shows that the powper of the highest order mode excited in circular waxeguide is usually the largest.