Cascade synthesis of polylithic crystal filters containing double-resonator monolithic crystal filter (MCF) elements

Commutativity of first‐order discrete‐time linear time‐varying systems

“…The synthesis of a complete network in the form of cascade (chain) connected subsystems is an important subject in electrical network theory . Some orders of connections are dominant and have preferable performance considering parameter sensitivity, stability, robustness, and other effects such as noise and disturbance.…”

“…As the final simulation to validate Corollary 2, let the system A in Figure 2 be defined by Equation 38 with the forward and backward feedback gains α = 2, β = 0.5 which is a choice satisfying Equation 33. Hence, the system A and its feedback connected version B defined in Figure 2 are supposed to be commutative with nonzero initial conditions as well.…”

“…The synthesis of a complete network in the form of cascade (chain) connected subsystems is an important subject in electrical network theory. [38][39][40] Some orders of connections are dominant and have preferable performance considering parameter sensitivity, stability, robustness, and other effects such as noise and disturbance. In such cases, the order of connection of subsystems A and B in the form whether AB or BA to yield the same input output relation due to the commutativity gains importance practically.…”