FILTER-TYPE CIRCUITS 



203 



where I is the current in By 



P ^\P\ Kt/2 



and hence 



vyp = 2/Bi^Kt 



VyP = -4{B,/B0(-Bo{B2 + 45i))-i/2 

 V'/P = -2(B2/B{)K. 



(4.40) 



(4.41) 

 (4.42) 



J lere the sign has been chosen so as to make V^/P positive in the pass band. 

 Let us now consider as an example the structure of Fig. 4.10. We see that 

 two sorts of resonance are possible. First, if all the slots are shorted, or if no 

 \oltage appears between them, we can have a resonance in which the field 

 between the top of the ridge R and the top of the waveguide is constant 



Fig. 4.13 — A ladder network broken up into tt sections. 



all along the length, and corresponds to the cutoff frequency of the ridged 

 waveguide. There are no longitudinal currents (or only small ones near the 

 slots S) and hence there is no voltage across the slots and their admittance 

 (the slot depth, for instance) does not affect the frequency of this resonance. 

 Looking at Fig. 4.12, we see that this corresponds to a condition in which 

 all shunt elements are open, or B^ = 0. We will call the frequency of this 

 resonance cct , the T standing for transverse. 



There is another simple resonance possible ; that in which the fields across 

 successive slots are equal and opposite. Looking at Fig. 4.12, we see that 

 this means that equal currents flow into each shunt element from the two 

 series elements which are connected to it. We could, in fact, divide the net- 

 work up into unconnected tt sections, associating with each series element of 

 susceptance Bi half of the susceptance of a shunt element, that is, Bo/2, 

 at each end, as shown in Fig. 4.13, without affecting the frequency of this 

 resonance. This resonance, then, occurs at the frequency co^ (L for longi- 

 tudinal) at which 



Bi + B2/A = 0. (4.43) 



We have seen that the transverse resonant frequency, cor , has a clear 

 meaning in connection with the structure of Fig. 4.10; it is (except for small 



