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

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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

No.	Question	Explanation
(a)	Define Two-Port Network	Electrical system with two pairs of terminals used to relate input and output quantities (voltage/current). Common parameters: Z, Y, h, T.
(b)	Network Synthesis	Process of designing a physical network (RLC) that realizes a given impedance or admittance function.
(c)	Transfer Function	Ratio of output response to input excitation in Laplace domain; H(s)=Vo(s)Vi(s)H(s) = \frac{V_o(s)}{V_i(s)}H(s)=Vi(s)Vo(s).
(d)	Twig and Link (Graph Theory)	Twig → branch in a chosen tree; Link → branch not in the tree forming a loop.
(e)	Convolution	Mathematical operation combining two signals to form a third: y(t)=x(t)∗h(t)=∫x(τ)h(t−τ)dτy(t) = x(t) * h(t) = \int x(\tau)h(t-\tau)d\tauy(t)=x(t)∗h(t)=∫x(τ)h(t−τ)dτ.
(f)	Network Stability	A network is stable if all poles of its transfer function lie in the left half of the s-plane (negative real part).
(g)	Filters	Circuits that pass signals of certain frequency range and attenuate others (e.g., low-pass, high-pass, band-pass, band-stop).
(h)	Superposition Theorem	In a linear network with multiple sources, the response (voltage/current) is the algebraic sum of individual responses when each source acts alone.
(i)	Loop Impedance Matrix Properties	Symmetric, diagonal elements = self-impedances, off-diagonal elements = mutual impedances, determinant non-zero for connected network.
(j)	Tree in Graph Theory	A connected subgraph that includes all nodes but contains no loops — forms the network backbone for topological analysis.

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}[V1V2]=[Z11Z21Z12Z22][I1I2]

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

Type	Frequency Range	Example Application
Low Pass	Passes < cutoff fcf_cfc	Audio processing
High Pass	Passes > cutoff fcf_cfc	Radio transmitters
Band Pass	Passes between f1f_1f1 and f2f_2f2	Communication receivers
Band Stop (Notch)	Rejects narrow band	Noise reduction
All Pass	Equal amplitude, phase correction	Phase compensation

(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}[I1I2]=[Y11Y21Y12Y22][V1V2]

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+ω02s2+ω02

Proof: Derived using standard RLC network where resonance frequency ω0=1LC\omega_0 = \frac{1}{\sqrt{LC}}ω0=LC1.

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=4RsV2

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=2πLC1=2π2×2×10−61≈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:

Topic Area	Core Concepts
Network Theory	Two-port networks, Z/Y parameters, network theorems
System Functions	Transfer functions, stability, convolution
Filters	Classification, design, frequency response
Graph Theory	Trees, twigs, links, cut-set/loop matrices
Network Synthesis	Foster & Cauer forms, LC network realization