Match the items correctly: (A) SSB (Single-Sideband) modulation, (B) ∇ · B = 0, (C) Modal dispersion — with (1) Transmission line, (2) Hilbert transform, (3) Faraday’s law, (4) Absence of magnetic monopoles, (5) Waveguides, (6) Phase-locked loop.

Introduction:
This matching problem connects three distinct concepts to their canonical associations in communications and electromagnetics: (A) SSB modulation in signal processing, (B) the divergence of magnetic flux density in Maxwell’s equations, and (C) modal dispersion in guided-wave structures. Correct matching relies on recognizing the theoretical tool or physical principle each item is best known for.

Given Data / Assumptions:

• A: Single-Sideband (SSB) is a bandwidth-efficient modulation.
• B: ∇ · B = 0 expresses a fundamental Maxwell relation.
• C: Modal dispersion occurs in multi-mode guided media.
• Available matches: (1) Transmission line, (2) Hilbert transform, (3) Faraday’s law, (4) Absence of magnetic monopoles, (5) Waveguides, (6) Phase-locked loop.

Concept / Approach:

SSB generation and analysis commonly use the Hilbert transform to create a 90-degree phase-shifted quadrature (analytic) signal, enabling sideband suppression. The equation ∇ · B = 0 states that magnetic flux lines have no beginning or end, capturing the absence of magnetic monopoles. Modal dispersion is inherent to waveguides (including multimode fiber), where different modes propagate with distinct velocities, spreading pulses.

Step-by-Step Solution:

Verification / Alternative check:

Alternative SSB realizations (filter method, phasing method) still hinge on quadrature generation; the phasing method specifically uses the Hilbert transform. Maxwell’s equations universally support ∇ · B = 0. Modal dispersion is not a property of a simple two-conductor transmission line (single TEM mode), but of multi-mode guiding structures.

Why Other Options Are Wrong:

(1) Transmission line for SSB is too generic and not the key enabling tool. (3) Faraday’s law pertains to time-varying flux and induced EMF, not ∇ · B. (6) PLLs relate to carrier/clock recovery, not SSB synthesis per se.

Common Pitfalls:

Confusing general RF blocks (PLLs, mixers) with the specific mathematical construct used in SSB; mixing Maxwell relations (curl vs divergence) for B-fields.

Final Answer:

A-2, B-4, C-5