FILTER-TYPE CIRCUITS 



209 



;4ap currents are in the same directions. In the representation of Fig. 4.23 

 the currents which will flow in the common inductances of Fig. 4.24 have 

 been drawn in opposite directions, and we see that the currents in the gap 

 capacitances flow alternately up and down. In other words, in Fig. 4.24, 

 every other gap appears inverted. This can be taken into account by adding 

 a phase angle — tt to ^ as computed from (4.48). 



Fig. 4.22 — The resonators of Fig. 4.11 coupled inductively. 



2L 2L 2L 2L 2L 2L 



KTKRP-KM^H i-^WU^-r-^M^5^ KOWH-O^M^ 



O 



O 



O 



O 



o 



o 



Fig. 4.23 — Another representation of the resonators of Fig. 4.11. 



2L 2L 2L 2L 2L 2L 



Fig. 4.24 — Figure 4.23 with inductive coupling added. 

 La La LMb 



I — 



I-- 



Lb 



— n 



Lb 



(a) ™ (b) ™ 



Fig. 4.25 — A r — TT transformation used in connection with the circuit of Fig. 4.24. 



Now, the T configuration of inductances in a of Fig. 4.25 can be replaced 

 by the TT configuration, b of Fig. 4.25. Imagiiae I and II to be connected 

 together and a voltage to be applied between them and III. We see that 



U= La+ 2LMa (4.52) 



Imagine a voltage to be applied between I and II. We see that 



l/La = l/U + 2/LMb (4.53) 



If LMa <3C La , then Lb will be nearly equal to La and LMb ^ Li . 



By means of such a, T — t transformation we can redraw the equivalent 

 circuit of Fig. 4.24 as shown in Fig. 4.26. The series susceptance Bi is now 



