New Classes of Multi-variable Positive Real Functions Part II Discussions on Upper-Half and Right-Half Plane Characteristics

Abstract

In Part I, formal definition of networks and their classification into six subclasses were presented and the corresponding sets of mpr-f's were defined according to the properties of their arguments. Here, in Part II, the upper-half and right-half plane characteristics of the six classes of functions are discussed. The properties presented in this Part II will be utilized in synthesis problems.

Indexing Terms:

• Positive Real Functions
• MPR-F
• Network Synthesis

Additional information

Notes on contributors

Hiroshi Ozaki

OZAKI, HIROSHI (Dr): (b. 1920, Osaka, Japan). After receiving his B.S. degree from Osaka University in 1942, he joined its Department of Communication Engineering, and later transferred to the Electronics Department. During this period, he was conscripted into the Japanese Navy as a temporary technical officer for three years.

In 1955, he received the PhD degree from Osaka University and at present is a Professor of Electronics.

His research interest is the field of circuit theory with emphasis on RC networks, distributed-constant networks and theories of mpr-f (multi-variable positive real function). The mpr-f, which he introduced in 1959, has since found application to the theories of mixed lumped- and distributed-constant networks. Further, he recently classified the mpr-f's into six subclasses.

The subclass of homogeneous positive real function is seen as playing an important role in the network synthesis theories. For his work in this field, he was awarded two prizes by the IECE. Professor Ozaki is a member of the IECE and a Fellow of the IEEE. Also, he is a member of the Information Processing Society of Japan.