Match classic network synthesis concepts to their originators/definitions: (A) Reactance theorem, (B) Driving-point impedance, (C) Continued-fraction expansion, (D) Bisection theorem — with: (1) Foster, (2) Bartlett, (3) Cauer, (4) Positive-real function.

Introduction / Context:Classical network synthesis links mathematical properties of impedances/admittances to realizable passive networks. This question ties four famous results/names to their associated concepts.

Given Data / Assumptions:

• Reactance theorem
• Driving-point impedance
• Continued-fraction expansion
• Bisection theorem
• Names/definitions: Foster, Bartlett, Cauer, positive-real (PR) function

Concept / Approach:

Foster’s reactance theorem characterizes reactance vs frequency for lossless networks, underlying Foster canonical forms. A driving-point impedance function suitable for passive realization must be positive-real (PR). Cauer’s method uses continued-fraction expansion to realize networks (Cauer I/II forms). Bartlett’s bisection theorem aids in symmetrical network design by splitting networks while preserving properties.

Step-by-Step Solution:

Verification / Alternative check:

Any standard synthesis text (Foster/Cauer/Bartlett) confirms these pairings and the role of PR functions in passive realizations.

Why Other Options Are Wrong:

Mixing Cauer with bisection or mislabeling PR as a person breaks well-established attributions.

Common Pitfalls:

Confusing Foster and Cauer canonical forms; forgetting PR conditions (real part ≥ 0 on jω axis).

Final Answer:

A-1, B-4, C-3, D-2