THEORY EXAMINATION (SEM–IV) 2016-17 NETWORK ANALYSIS AND SYNTHESIS

Course: B.Tech (Electronics & Communication Engineering)
Subject Code: EC404MTU
Subject Title: Network Analysis and Synthesis
Exam Type: Theory
Duration: 3 Hours
Maximum Marks: 100

SECTION – A (10 × 2 = 20 Marks)

Concept-based short questions to test definitions and basic principles

SECTION – B (5 × 10 = 50 Marks)

Medium-length analytical and derivation-based questions

(a) Z-Parameters (Impedance Parameters)

For a two-port network:

• [V1V2]=[Z11Z12Z21Z22][I1I2]\begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = \begin{bmatrix} Z_{11} & Z_{12} \\ Z_{21} & Z_{22} \end{bmatrix} \begin{bmatrix} I_1 \\ I_2 \end{bmatrix}[V1​V2​​]=[Z11​Z21​​Z12​Z22​​][I1​I2​​]

Z11Z_{11}Z11​: Input impedance with output open-circuited

Z22Z_{22}Z22​: Output impedance with input open-circuited

Z12,Z21Z_{12}, Z_{21}Z12​,Z21​: Transfer impedances

Used to analyze amplifier and filter interconnections.

(b) Classification of Filters

(c) Cut-Set Matrix

Represents relationship between branches and cut-sets in a connected network.
Derived from fundamental cut-sets (dual of loops) using tree-link relationships.

(d) Z-Parameters from a Circuit

Involves solving simultaneous equations for V1,V2,I1,I2V_1, V_2, I_1, I_2V1​,V2​,I1​,I2​ using KVL and KCL to extract the four impedance parameters.

(e) Superposition Theorem Application

For given circuit: suppress all sources except one and find output current ioi_oio​.

Total response = sum of individual contributions.

(f) Admittance Parameters (Y-Parameters)

[I1I2]=[Y11Y12Y21Y22][V1V2]\begin{bmatrix} I_1 \\ I_2 \end{bmatrix} = \begin{bmatrix} Y_{11} & Y_{12} \\ Y_{21} & Y_{22} \end{bmatrix} \begin{bmatrix} V_1 \\ V_2 \end{bmatrix}[I1​I2​​]=[Y11​Y21​​Y12​Y22​​][V1​V2​​]

Defines relationships under open/short circuit conditions — used in parallel networks and transistor modeling.

(g) Band Stop Filter

Purpose: Reject specific frequency band.

Transfer Function:

• H(s)=s2+ω02s2+(ω0/Q)s+ω02H(s) = \frac{s^2 + \omega_0^2}{s^2 + (\omega_0/Q)s + \omega_0^2}H(s)=s2+(ω0​/Q)s+ω02​s2+ω02​​

Proof: Derived using standard RLC network where resonance frequency ω0=1LC\omega_0 = \frac{1}{\sqrt{LC}}ω0​=LC​1​.

Used in audio equalizers and communication circuits.

(h) Maximum Power Transfer Theorem

States that maximum power is delivered to load when load resistance = source resistance (in magnitude).

Pmax=V24RsP_{max} = \frac{V^2}{4R_s}Pmax​=4Rs​V2​

Used in impedance matching for amplifiers and communication systems.

SECTION – C (2 × 15 = 30 Marks)

Long-form derivations and design-oriented synthesis problems

Q3. Foster Form Realization

Foster-I Form: Derived from partial fraction expansion of driving point impedance.

LC Network Example:

• Z(s)=(s2+4)(s2+16)s(s2+25)Z(s) = \frac{(s^2 + 4)(s^2 + 16)}{s(s^2 + 25)}Z(s)=s(s2+25)(s2+4)(s2+16)​

Decomposed into series/parallel LC branches — each term represents a resonant circuit.

Q4. Filter Design (Cutoff Frequency Calculation)

Given: R=2kΩ,L=2H,C=2μFR = 2k\Omega, L = 2H, C = 2\mu FR=2kΩ,L=2H,C=2μF

Corner frequency:

• fc=12πLC=12π2×2×10−6≈79.6 Hzf_c = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{2 \times 2 \times 10^{-6}}} \approx 79.6 \text{ Hz}fc​=2πLC​1​=2π2×2×10−6​1​≈79.6 Hz

Based on circuit topology (e.g., series → low-pass, parallel → high-pass).

Q5. Cauer Form Realization

Derived using continued fraction expansion of impedance function Z(s)Z(s)Z(s).

Each stage represents L or C in ladder form — offers more physical realizability and flexibility compared to Foster form.

Summary

This Network Analysis & Synthesis (EC404MTU) paper comprehensively tests: