(SEM III) THEORY EXAMINATION 2023-24 NETWORK ANALYSIS AND SYNTHESIS

This examination evaluates a student’s understanding of electrical networks, circuit theorems, Laplace transform methods, two-port parameters, network functions, and resonance/filters.
The paper is structured to test analytical capability, theoretical clarity, mathematical rigor, and practical circuit-solving skills.

The question paper is divided into three sections, focusing on fundamentals, analytical problem solving, and long-form network derivations.

SECTION A — Short Answer / Basic Concepts (14 Marks)

(Seven questions × 2 marks each)

This section tests the core concepts required for deeper network analysis.

1. Node Analysis vs. Mesh Analysis

Definition of nodal method and how it differs from mesh method in terms of KCL/KVL usage and applicability.

2. Significance of Reactance in Network Analysis

How inductive/reactive components influence phase, impedance, and AC circuit behavior.

3. Superposition Theorem

Statement of how multiple independent sources contribute individually to linear circuit response.

4. Reciprocity Theorem

Definition of input-output interchange property in linear, bilateral networks.

5. Singularity Functions

Definition of unit step, unit impulse, ramp functions used to model discontinuities in signals.

6. Poles and Zeros in Network Functions

Concept of transfer function poles & zeros and their effect on system stability and frequency response.

7. Characteristics of Band-Reject (Notch) Filters

Behavior of filters that attenuate a narrow range and pass low/high frequencies.

Section A ensures foundational clarity before moving into advanced problem-solving.

SECTION B — Analytical & Application-Based Problems (21 Marks)

(Any three questions × 7 marks each)

This section tests numerical solving skills, theorem application, and dynamic response analysis.

1. Nodal Analysis

Write node equations → solve for required node voltage.

2. Superposition Theorem Application

Calculate current III by activating one source at a time and summing contributions.

3. Step Response of a Series RC Circuit

Derive voltage/current transient response → exponential charging → time constant impact.

4. Symmetry in Two-Port Networks

Explain how symmetry influences Z/Y/ABCD parameters → simplified network modeling.

5. Convolution Theorem (Statement + Proof)

Proof using Laplace transform properties and explanation of time-domain convolution.

Section B evaluates understanding of real-life network behaviors and mathematical tools.

SECTION C — Long Analytical Questions (35 Marks)

(One question from each part)

PART 3 — Circuit Equations & Network Graphs

Option A — Mesh Current Equations

Write loop equations using KVL and solve for mesh currents.

Option B — Duality of Network Graphs

Explain dual networks → nodes ↔ meshes, voltage ↔ current, impedance ↔ admittance → utilities in simplifying circuit analysis and their limitations.

PART 4 — Network Theorems

Option A — Reciprocity Theorem in AC Networks

Statement, conditions (linearity, passive, bilateral), and demonstration using AC circuit elements.

Option B — Norton Equivalent

Find Norton current, Norton resistance, and draw the Norton circuit at given terminals.

PART 5 — Laplace Transform & Time-Domain Analysis

Option A — Laplace Transforms of Basic Functions

Unit impulse, step, ramp, and parabolic signals.

Option B — Inverse Laplace Transform

Compute inverse Laplace of
L−1(e−5sU(s))\mathcal{L}^{-1}(e^{-5s} U(s))L−1(e−5sU(s))
using shifting theorem.

PART 6 — Two-Port Network Parameters

Option A — Cascading Two-Port Networks

Concept of ABCD parameters → how cascade allows multiplication → limitations (e.g., dependent on defined port currents).

Option B — Determination of Y & Z Parameters

Define, measure, and derive open/short circuit conditions to compute Y (admittance) and Z (impedance) matrices.

PART 7 — Network Synthesis & Filters

Option A — Quality Factor (Q-Factor)

Definition → Q = ω₀L/R or 1/(ω₀RC)
Relationship between Q, bandwidth, and resonant frequency.

Option B — Parallel Resonance

Derivation of resonant frequency → impedance peak → high Q behavior → practical characteristics.

Purpose of This Examination

This exam is designed to ensure students can:

Analyze electrical circuits using systematic methods (nodal/mesh)
Apply network theorems to simplify complex circuits
Use Laplace transforms to solve dynamic circuits
Understand and derive two-port network parameters
Analyze resonance, filters, and frequency response
Use mathematical tools like convolution, poles, and zeros
Apply network synthesis principles to real-world engineering systems

It reflects the analytical skillset expected from an engineering student specializing in Electronics, Electrical Engineering, Instrumentation, or Communication Systems.