About this previous year paper
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 |