Belevitch's theorem
Belevitch's theorem is a theorem in electrical network analysis due to the Russo-Belgian mathematician Vitold Belevitch (1921–1999). The theorem provides a test for a given S-matrix to determine whether or not it can be constructed as a lossless rational two-port network. Lossless implies that the network contains only inductances and capacitances – no resistances. Rational (meaning the driving point impedance Z(p) is a rational function of p) implies that the network consists solely of discrete elements (inductors and capacitors only – no distributed elements). The theorem
For a given S-matrix  of degree ;

where,
p is the complex frequency variable and may be replaced by  in the case of steady state sine wave signals, that is, where only a Fourier analysis is required
d will equate to the number of elements (inductors and capacitors) in the network, if such network exists. Belevitch's theorem states that,  represents a lossless rational network if and only if,

where,
,  and  are real polynomials
 is a strict Hurwitz polynomial of degree not exceeding 
 for all . References

Bibliography
Belevitch, Vitold Classical Network Theory, San Francisco: Holden-Day, 1968 . Rockmore, Daniel Nahum; Healy, Dennis M. Modern Signal Processing, Cambridge: Cambridge University Press, 2004 . Circuit theorems
Two-port networks