Symmetrical two‐port networks: An eigenspace perspective

Abstract

SUMMARYIn this letter, it is shown how the canonical circuits for the synthesis of symmetrical two-port networks can be derived from the eigendecomposition of the impedance matrix. Extensions to reciprocal two-port networks are discussed.

Synthesis of low‐complexity mechanical networks with constrained element values

“…To show the equivalence, it is noted that the existence of a pair of parameters x and y satisfying (8) to (10), if and only if any of the intervals in (8) to (10) is nonempty, and the intersection between the interval in (10) and the range of |y|∕|x| implied from (8) and (9) is also nonempty. The former part is equivalent to (11) to (13), and the latter part is equivalent to (14) and (15).…”

“…Since the invention of a mechanical element named “inerter,” research interest in synthesis of passive networks has revived due to the control approach utilizing passive mechanisms . As an important branch of system theory, passive network synthesis experienced its “golden era” during the 1930s to the and after the 1970s, its research interest declined despite some new developments .…”

“…It is noted that the velocities related to an inertial system, which is denoted as the mechanical ground . Using the force‐current analogy, the capacitor can be completely analogous to the inerter, and the analogy between passive electrical and mechanical networks is completed . Therefore, passive network synthesis can be completely transplanted into passive mechanical network design.…”

“…Since the invention of a mechanical element named "inerter," 1 research interest in synthesis of passive networks has revived due to the control approach utilizing passive mechanisms. [2][3][4][5][6][7][8][9][10][11][12][13] As an important branch of system theory, passive network synthesis experienced its "golden era" during the 1930s to the [14][15][16][17][18][19][20][21][22][23] and after the 1970s, its research interest declined despite some new developments. [24][25][26][27][28][29][30] This field is to investigate the physical realization of passive systems as networks containing only passive components such as resistors, inductors, and capacitors and how to reduce the realization redundancy.…”

Realization of a transfer function as a passive two‐port RC ladder network with a specified gain

“…To date, minimal realizations of one‐port passive networks and transformerless realizations of multi‐port passive networks are still far from being solved. Passive network synthesis has experienced a ‘golden age’ from the 1930s to the 1970s , but its research interest had declined after the 1970s and yet has seen some developments recently.…”