About this previous year paper
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 |