(SEM IV) THEORY EXAMINATION 2021-22 NETWORKS ANALYSIS & SYNTHESIS

SECTION–A — Short but Conceptually Loaded Questions (20 Marks)

Section–A of this exam consists of ten short questions, each carrying two marks, but although they appear brief, each one touches on highly important fundamentals of network theory. The questions span graph theory, network theorems, transient analysis, two-port parameters, and classical filter theory. For example, the very first question asks about the properties of a complete incidence matrix, which requires understanding how nodes and branches of a network are mathematically represented. The next question moves deeper into graph theory concepts like tree, co-tree, twig, link, cut-set, and tie-set — definitions that form the heart of network topology.

The section then shifts toward network theorems, such as finding the resistance RRR that delivers maximum power to a 3-ohm load (illustrated clearly in the figure on page 1 of your PDF), and identifying the limitations of Millman’s theorem. It also tests transient concepts by asking what transient and steady-state responses are, and asks for the immediate current in a series LC circuit right after switching — which demands knowledge of initial conditions in reactive components.

Later questions involve determining Y-parameters of a two-port network (shown in the diagram on page 1), explaining the reciprocity theorem and stating reciprocity conditions for Z-parameters, describing Hurwitz polynomials along with their properties, and finally defining a low-pass filter along with its characteristics and diagram. Overall, Section–A checks whether the student has a strong foundational command of basic network concepts, topology, theorems, two-port modelling, and classical filter ideas.

SECTION–B — Long Descriptive Questions Requiring Analysis, Diagrams, and Derivations (30 Marks)

Section–B requires the student to attempt any three out of five questions, each worth 10 marks. These questions move beyond definitions and require deep analytical explanations, diagrams, and full mathematical handling. One question asks the student to draw the dual of a given network (shown on page 1, bottom figure), which demands understanding of duality principles such as exchanging series ↔ parallel, inductance ↔ capacitance, voltage ↔ current, and loop ↔ node relationships.

Another question asks for the Thevenin equivalent circuit at terminals x–yx–yx–y (diagram appears on page 2). This involves finding the open-circuit voltage, Thevenin resistance, and then constructing the final equivalent. A third question asks for the voltage and current response of a series RL circuit when suddenly excited by a DC source, which involves solving a first-order differential equation and explaining the exponential rise of current and the voltage distribution across resistor and inductor.

Another question requires deriving T-parameters (transmission parameters) in terms of hybrid parameters, which is a detailed symbolic derivation. The final question asks for the first Foster form of a complex impedance function

Z(s)=s(s2+2)(s2+1)(s2+3)Z(s) = \frac{s(s^2 + 2)}{(s^2 +1)(s^2 +3)}Z(s)=(s2+1)(s2+3)s(s2+2)​

This requires performing partial fraction expansion and synthesizing the impedance in Foster Form-I. Thus, Section–B tests mathematical maturity, conceptual clarity, and the ability to apply formulas to real networks.
 

SECTION–C — Technical, High-Weightage, Problem-Solving Questions (50 Marks Total)

Section–C consists of five groups (Q3 to Q7). From each group you must attempt one sub-question. Each carries 10 marks and demands rigorous application of network analysis techniques.

Group Q3 — Graph Theory Application

One option asks students to write the cut-set matrix and derive equilibrium equations on voltage basis, then compute branch voltages and currents. The alternate question requires drawing the oriented graph for a network (figure on page 2), forming the tie-set matrix, and using it to calculate branch current iii. These tasks test strong understanding of graph theory, KCL/KVL matrix formation, and systematic network solving.

Group Q4 — Network Theorems: Reciprocity & Norton’s Theorem

The first option asks you to verify the reciprocity theorem for a ladder network (shown on page 3). This involves applying a source at one port, measuring response at another, exchanging positions, and proving equality. The alternate option asks to find ibi_bib​ using the Norton equivalent of a circuit, assuming a given resistance of 667Ω667 \Omega667Ω. This tests the student’s practical grasp of circuit transformations.

Group Q5 — Transient Analysis in RLC Circuits

One question presents a circuit initially at steady state where the switch moves from position 1 to 2 at t=0t = 0t=0. The student must find the current after switching. The second option describes a scenario where a switch moves from S1S_1S1​ to S2S_2S2​ at t=0t = 0t=0, and asks for voltage across the capacitor for t>0t > 0t>0, as well as the exact time at which the capacitor voltage becomes zero. Both questions require solving first- or second-order differential equations and applying initial condition concepts.

Group Q6 — Two-Port Network Analysis

The first option directly asks for Y-parameters of the two-port network shown on page 4, which contains resistances of 12Ω\frac{1}{2}\Omega21​Ω, 1Ω1\Omega1Ω, and an independent dependent source of 2V12V_12V1​. You must apply open-circuit conditions and derive admittance equations. The alternate question asks for the equivalent parameters when two two-port networks are cascaded, requiring derivation of ABCD (or T) parameter relations.

Group Q7 — Network Synthesis: Cauer & Positive Real Functions

One option asks for Cauer-I and Cauer-II realizations of the driving-point impedance function

Z(s)=10s4+12s2+12s3+2sZ(s)=\frac{10s^{4}+12s^{2}+1}{2s^{3}+2s}Z(s)=2s3+2s10s4+12s2+1​

This requires continued fraction expansion and physical network synthesis. The alternate asks to check the positive realness of two rational functions — a critical concept in determining whether a function can be realized as a passive network.

FINAL SUMMARY (Complete, Descriptive Form)

This Networks Analysis & Synthesis exam paper is extremely well-structured and comprehensive. Section–A tests whether the student has mastered core fundamentals — graph theory terms, theorems, transient basics, two-port parameters, Hurwitz criteria, and filters. Section–B evaluates the ability to perform analytical derivations, compute equivalent circuits, develop Foster realizations, and solve transient RL responses. Section–C is the most application-heavy: it requires graph matrices, reciprocity verification, Norton analysis, modeling transient switching, two-port parameter derivations, and network synthesis through Cauer forms and positive-realness tests.

The paper ensures that students demonstrate both mathematical rigor and practical engineering insight, connecting theoretical knowledge with network modeling and real-world circuit behavior.