SELF

42

S.B. Karavashkin and O.N. Karavashkina

Fig. 4. The schematic diagram of a finite mechanical elastic line with the mass M m at its end (a) and of corresponding ladder filter with the arbitrary load _load  (b)

Take as the mechanical analogue a finite elastic lumped line shown in Fig. 4a, whose last (n + 1)th element has the mass M different from the rest of elements. The exact analytical solutions for this model have the following form:

in the periodical vibration regime at <1

in the aperiodical vibration regime at >1

at the boundary vibration frequency at =1

where ; ; ; ; .

The electrical filter circuit corresponding to the Fig. 4a is shown in Fig. 4b. In accord with the relationships DEMA (8) and (23 – (25), the oscillations in this circuit will obey the following regularities:

at the filter pass band, <1