**ERIC Number:**EJ829056

**Record Type:**Journal

**Publication Date:**2007-Mar

**Pages:**11

**Abstractor:**As Provided

**Reference Count:**10

**ISBN:**N/A

**ISSN:**ISSN-0143-0807

Ladder-Type Circuits Revisited

Yoon, Sung Hyun

European Journal of Physics, v28 n2 p277-288 Mar 2007

Ladder-type circuits where a given unit is repeated infinitely many times are dealt with in many textbooks on electromagnetism as examples of filter circuits. Determining the impedance of such circuits seems to be regarded as simple, which may be due to the fact that the invariance of the infinite system under the operation of adding one more unit leads to a quadratic equation and to the implicit assumption that selecting the physical one between two roots of the resulting equation should be trivial. However, there are important cases where the choice of the right root is not obvious at all. There have been some numerical studies of related examples. In the present work ladder-type circuits are treated analytically based on the transfer matrix method. In particular, for infinite circuits a simple rule is given for selecting the right impedance. For that purpose we consider the propagation of current down the circuit when the system is driven by oscillatory voltage. It turns out that choosing the physical root amounts to requiring absence of unphysical part in the current wave. Also the question whether the impedance of the infinite ladder is the limit of those of finite systems which get ever longer is answered, and a related regularization property concerning the limit is given. (Contains 7 figures and 1 footnote.)

Descriptors: Textbooks, Magnets, Energy, Equations (Mathematics), Science Instruction, College Science, Undergraduate Study, Graduate Study, Electronics

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A