A Caltech Library Service

Null Double Injection and the Extra Element Theorem

Middlebrook, R. D. (1989) Null Double Injection and the Extra Element Theorem. IEEE Transactions on Education, 32 (3). pp. 167-180. ISSN 0018-9359. doi:10.1109/13.34149.

[img] PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


The extra element theorem (EET) states that any transfer function of a linear system can be expressed in terms of its value when a given “extra” element is absent, and a correction factor involving the extra element and two driving point impedances seen by the element. One class of applications is when a system has already been analyzed and later an extra element is to be added to the model: the EET avoids the analysis having to be restarted from scratch. Another class of applications is when a system is to be analyzed for the first time: if one element is designated as “extra,” the analysis can be performed on the simpler model in the absence of the designated element, and the result modified by the EET correction factor upon restoration of the “extra” element. Although the EET itself is not new, its interpretation and application appear to be little known. In this paper, the EET is derived and applied to several examples in a manner that has been developed and refined in the classroom over a number of years. The concept of “null double injection” is introduced first, because it is the key to making easy the calculation of the two driving point impedances needed for the EET correction factor.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 1989 IEEE. Manuscript received October 20, 1988.
Issue or Number:3
Record Number:CaltechAUTHORS:20151224-110234507
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63233
Deposited On:24 Dec 2015 19:17
Last Modified:10 Nov 2021 23:13

Repository Staff Only: item control page