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BELL SYSTEM TECHNICAL JOURNAL 



As an example of the phase characteristic of the circuit, fih from (4.26) 

 and (4.27) is plotted vs M for h/d = 0, 10, 100 in Fig. 4.6. The curve for 

 h/d = is of course the same as Fig. 4.2. 



If we integrate Poynting's vector from y = Q io y = d and for a distance 

 W in the x direction, and multiply by 2 to take the power flow in the other 

 half of the circuit into account, we obtain 



E'/^'P = (2//3oTF)(7/^)' 



sinh" 7^ 



sinh 'yd cosh 7^/ + yd 



Vix/e (4.30) 



/3h 



73oh 



Fig. 4.6 — The variation of /3 with frequency (proportional to 0oh) for the transverse 

 mode of the circuit of Fig. 4.3. Again, the curves are in error near the cutoff at /3^ = w. 



At very low frequencies, at which (4.28) and (4.29) hold, we have 

 £7/3' P = (y'/^o^'Kd/W) Vm76 

 E'/^'P = {h/df" (1 + d/hf" {d/W) V/IA 



(4.31) 



At high frequencies, for which yd is large, (4.30) approaches | of the value 

 given by (4.20). There is twice as much power because there are two halves 

 to the circuit. 



Let us now consider the case in which the field is symmetrical and E, does 

 not go to zero on the axis. In this case the appropriate field for y > is 



//. 



^j sinh y{d - y) -jp, 

 sinh yd 



(4.32) 



