Classical Network Synthesis Forms: Match Realization Form to Its Ladder/Branch Description List I (Form) A. Cauer I B. Cauer II C. Foster I D. Foster II List II (Network Description) L in series arm and C in shunt arm of a ladder C in series arm and L in shunt arm of a ladder Series connection of multiple branches, each branch being a parallel L || C Parallel connection of multiple branches, each branch being a series L – C

Introduction / Context:
For positive-real driving-point functions of passive LC networks, Foster and Cauer forms offer canonical realizations. Recognizing which description corresponds to each form helps when translating a target impedance or admittance into a practical ladder or branch network.

Given Data / Assumptions:

• Lossless synthesis context (L and C elements only).
• Driving-point realizations (one-port networks).
• Descriptions emphasize whether elements appear in series/shunt ladder arms, or as sums of resonant branches.

Concept / Approach:

Cauer forms arise from continued-fraction expansions, producing ladders that begin with series L (Cauer I) or series C (Cauer II). Foster forms arise from partial-fraction expansions: Foster I yields a series chain of parallel LC branches; Foster II yields a parallel network of series LC branches.

Step-by-Step Solution:

Verification / Alternative check:

Expanding an impedance via partial fractions produces summands resembling resonant terms realizable as either parallel or series LC branches, directly mapping to Foster I/II. Continued fractions cascade series/shunt elements, matching Cauer ladders.

Why Other Options Are Wrong:

Swapping Foster I and II reverses series/parallel roles; swapping Cauer I and II reverses which element appears in the series arm first.

Common Pitfalls:

Confusing impedance versus admittance realizations; one must stay consistent with the form derived from the chosen expansion.

Final Answer:

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