Restrictions on the natural frequencies of an RC-RL network

✍ Scribed by D.A. Calahan

• Publisher: Elsevier Science
• Year: 1961
• Tongue: English
• Weight: 751 KB
• Volume: 272
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(61)90737-2

✦ Synopsis

The following problem is investigated: given any polynomial N(s) of the form

1 1 what are the necessary and sufficient conditions that N(s) be formed in the following manner :

N(s) = AoII(s + aO + BoII(s + bO

Ao, Bo > 0

where the -ai and -bt alternate at most in pairs along the negative real axis. Such formation is necessary for the -Pt and -st to be the natural frequencies of a network consisting of RC and RL subnetworks joined at two terminals.

It is shown that N(s) may be so formed if and only if ra (a) for n = 0, ~ arg s¢ < ~r/2 1 m (b) for n > 0, p~ > 0 and Z arg st < ~r/2 1 Also, a simple method is presented for finding suitable a~ and bi whenever formation is possible.

The result is expected to have application in the synthesis of both passive and active networks.