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.
-
AA-1, B-4, C-3, D-2
-
BA-1, B-2, C-3, D-4
-
CA-2, B-3, C-1, D-4
-
DA-3, B-4, C-2, D-1
Answer
Correct Answer: A-1, B-4, C-3, D-2
Explanation
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:
A → (1): Reactance theorem ↔ Foster.B → (4): Driving-point impedance realizability ↔ PR function.C → (3): Continued-fraction expansion ↔ Cauer forms.D → (2): Bisection theorem ↔ Bartlett.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