904 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



7^201ogio(l + 2lro2re""0 



(10) 



1 - 



2 I ro2 Kl + cosh ap \ 



1 _ e-2"2^ + 2 I ro2 I'd + e-"')e-'"''l 



From this expression we deduce 



(a), / is strongly reduced when a^C » ro2. 

 ^ (b), Attenuation in line 1 is not an important factor until ail and 

 I ck:i — a2 1 ^ ^re of the order of 1 . In other words, for low attenuation in 

 both lines, aot assumes a major importance in the determination of I 

 because it influences the conditions of resonance. That the effect of ail 

 is small is shown in Fig. 3 (dotted line for the particular case ai = 0:2/4). 



In order to handle the general problem, (10) has been plotted in Fig. 

 3. We can enter with any two and obtain the third following quantities: 

 Zi , relative insertion loss in db; 10 logio e~^"^ , attenuation in db of the 

 spurious mode in the resonating environment; and 20 logio ro2 conversion 

 level at the junction, in db, of power in the spurious mode relative to 

 that in the first line. 



APPLICATION OF THESE RESULTS TO A TEqi TRANSMITTING SYSTEM 



The results of the preceding section have been checked experimentally 

 by measuring the relative insertion loss of different lengths of %" di- 

 ameter round waveguide tapered at both ends to round waveguides of 

 J4.6" diameter. This waveguide is shown in Fig. 4 with a schematic 

 diagram of the measuring set. In the round transmission line A-B, 

 section A will propagate only TEoi . Section B, which has been expanded 

 by means of the conical taper Ti , can support TE02 and TE03 in addition 

 to the principal TEoi mode. This section is a closed region to the spurious 

 modes ( TE02 , TE03) whose length can be adjusted to resonate each one 

 of these modes. A sliding piston provides a means for varying the 

 length, /, of section B. 



&^ 



T 



T 



X 



fl e- 



./^ 



1 

 2 



r~y 



TE 



01 



B 



TEo, 

 TE02 

 TE03 



1 



RECEIVER 



Fig. 4 — Circuit used to measure TEoi insertion loss due to resonance of the 

 TE02 and TE03 modes. 



