SELF

38

S.B. Karavashkin, O.N. Karavashkina

Using the conventional regularities

(5)

where _n is the voltage at the nth node with respect to common wire, and presenting

(6)

we yield the sought modelling system of equations for a semi-finite homogeneous ladder filter:

(7)

Comparing (3) and (7), we yield the sought relationship between the electrical ladder filter and mechanical long line:

(8)

The relationship (8) essentially differs from the conventional system of electromechanical analogy shown in Table 1 [8, p. 32, 34], [12, p. 15], [13, p. 471]. Particularly, in (8) the elements mass and the mechanical line stiffness correspond not to the specific inductance or capacitance but to the longitudinal and transversal conductance of the electrical filter section relatively. Due to it, as an active electrical conductance as some complicated-form complex conductance as the input impedance of some ladder filter being the subsystem of a studied branched filter can correspond to them. While according to Table 1, only the active resistance of a mechanical elastic line can correspond to the active resistance of an electrical circuit. And relatively to the impedances it is also accepted that the change of the capacitive pattern of the analogue to that inductive (and vice versa) must be accompanied by change of the system of analogy (see, e.g., [8, pp. 33 – 34]). In the relationship (8) we need not such operation.

Electrical value

Mechanical value

1^st system

2^nd system

voltage (e.m.f.) U

force F

velocity v

current i

velocity v

force F

inductance L

mass m

pliability c_m

capacitance C

pliability c_m

mass m

active resistance r

active mechanical resistance r_m

active mechanical conduction 1/r_m