Transmission Loss Due to Resonance 



of Loosely-Coupled Modes in a 



Multi-Mode System 



By A. P. KING and E. A. MARCATILI 



(Manuscript received Januarj' 17, 1956) 



In a multi-mode transmission system the presence of spurious modes 

 which reso7iafe in a closed environment can produce an appreciable loss to 

 the principal mode. The theory for the evaluation and control of this effect 

 under certain conditions has been derived and checked experimentally in 

 the particularly interesting case of a TEoi transmission system, where mode 

 conversion to TE02 , TE03 • • • is produced by tapered junctions between 

 two sizes of waveguide. 



INTRODUCTION 



In a transmission system, the presence of a region which supports 

 one or more spurious modes can introduce a large change in the trans- 

 mission loss of the principal mode when the region becomes resonant for 

 one of the spurious modes. This phenomenon can occur even when the 

 mode conversion is low and the waveguide increases in cross section 

 smoothly to a region which supports more than one mode. In general, 

 the conditions required to resonate the various spurious modes are not 

 fulfilled simultaneously and, in consequence, interaction takes place 

 between the principal mode and only one of the spurious modes for each 

 resonating frequency. Under these conditions the resonating environ- 

 ment can be visualized as made of only two coupled transmission lines, 

 one carrying the desirable mode and the other the spurious one. This 

 simplification makes it possible to calculate the transmission loss as a 

 function of (1) the coefficient of conversion between the two modes and 

 (2) the attenuation of the modes in the resonating en\-ironment. The 

 theory has shown good agreement with the measurement of transmission 

 loss of the TEoi mode in a pipe wherein a portion was tapered to a larger 

 diameter which can support the TE02 mode. 



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