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

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Course: B.Tech (Electrical Engineering)
Subject Code: NEE402
Subject Title: Network Analysis and Synthesis
Exam Type: Theory
Duration: 3 Hours
Maximum Marks: 100

SECTION – A (10 × 2 = 20 Marks)

Short conceptual questions testing basic theory and definitions

No.	Question	Concept Summary
(a)	Define a Two-Port Network	A circuit with two pairs of terminals — input and output — that allows linear relationships between voltages and currents (Z, Y, h, T parameters).
(b)	Network Synthesis	Designing a physical RLC network that realizes a given impedance/admittance function.
(c)	Transfer Function	Ratio of Laplace-transformed output to input: 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	Twig → branch part of the chosen tree; Link → remaining branch forming loops in a network graph.
(e)	Convolution Definition	Mathematical operation: y(t)=∫x(τ)h(t−τ)dτy(t) = \int x(\tau) h(t - \tau)d\tauy(t)=∫x(τ)h(t−τ)dτ, used for LTI systems.
(f)	Network Stability	All poles of transfer function lie in left half of s-plane (negative real part).
(g)	Filters	Circuits allowing certain frequency ranges while blocking others — used in signal processing.
(h)	Superposition Theorem	In a linear system, total response = sum of responses due to each independent source acting alone.
(i)	Loop Impedance Matrix Properties	Symmetric matrix, diagonal = self-impedances, off-diagonal = mutual impedances.
(j)	Tree (Graph Theory)	A connected subgraph with all nodes but no closed loops — forms the base for topological network analysis.

SECTION – B (5 × 10 = 50 Marks)

Descriptive and analytical questions on circuit parameters, theorems, and synthesis concepts

(a) Z (Impedance) Parameters

[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.

Z22Z_{22}Z22: Output impedance with input open.

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

Applications → amplifier and network analysis.

(b) Filter Classification

Type	Function	Frequency Response
Low Pass	Passes signals below cutoff fcf_cfc.	Attenuates high frequencies.
High Pass	Passes signals above fcf_cfc.	Blocks low frequencies.
Band Pass	Passes signals between f1,f2f_1, f_2f1,f2.	Used in communication circuits.
Band Stop	Rejects specific band.	Used in noise cancellation.
All Pass	Uniform gain, phase correction.	Used for equalization.

(c) Cut-Set Matrix

Derived using fundamental cut-sets of the network graph.
Relates branch currents and node voltages, dual to loop matrix representation.

(d) Z-Parameters from Circuit

Using KVL:

V1=Z11I1+Z12I2,V2=Z21I1+Z22I2V_1 = Z_{11}I_1 + Z_{12}I_2, \quad V_2 = Z_{21}I_1 + Z_{22}I_2V1=Z11I1+Z12I2,V2=Z21I1+Z22I2

Compute by applying open-circuit conditions sequentially.

(e) Superposition Theorem

Steps:

Retain one independent source; replace others by internal resistances.

Solve for required response (current/voltage).

Repeat for all sources and add algebraically.

Useful in analyzing multi-source linear networks.

(f) Y (Admittance) 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]

Used for parallel networks — reciprocal relation between impedance and admittance parameters.

(g) Band Stop Filter

Blocks a narrow range of frequencies (stopband).

Transfer Function:

H(s)=s2+ω02s2+ω0Qs+ω02H(s) = \frac{s^2 + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}H(s)=s2+Qω0s+ω02s2+ω02

Applications: audio circuits, communication receivers.

(h) Maximum Power Transfer Theorem

Maximum power delivered when RL=RSR_L = R_SRL=RS (for DC) or ZL=ZS∗Z_L = Z_S^*ZL=ZS∗ (for AC).

Pmax=V24RSP_{max} = \frac{V^2}{4R_S}Pmax=4RSV2

Used in amplifiers and impedance matching.

SECTION – C (2 × 15 = 30 Marks)

Comprehensive and synthesis-based problems

Q3. Foster Form Realization

Used to realize LC driving point impedance function.

First Foster Form: obtained by partial fraction expansion of impedance Z(s)Z(s)Z(s).

Each term corresponds to series LC resonant branch.

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)

realized as series combination of parallel LC circuits.

Q4. Filter Design Problem

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

Determine type of filter (e.g., low-pass or high-pass) from circuit configuration.

Q5. Cauer Form Realization

Based on continued fraction expansion of Z(s)Z(s)Z(s).

Ladder network realization alternates between series and shunt L/C elements.

More flexible for realizing practical frequency responses.

Summary

This Network Analysis and Synthesis (NEE402) paper thoroughly tests:

Unit	Focus Area	Topics
I	Network Theory	KCL, KVL, Theorems (Superposition, Thevenin, Norton)
II	Two-Port Networks	Z, Y, h, ABCD parameters
III	Filters & Frequency Response	Low-pass, high-pass, band-pass, band-stop
IV	Network Functions	Transfer function, poles, stability
V	Network Synthesis	Foster and Cauer forms, LC realization