Electrical Engineering 2023 Paper II 50 marks Solve

Q2

(a) The block diagram of a feedback system is shown in the figure. (i) Sketch the complete root locus of the system. (ii) What is the value of K at s = 0? (iii) Find the range of K for closed-loop stability. (20 marks) (b) Draw the connection diagram of a Schering bridge to measure the capacitance and dissipation factor. Write the balance equations and derive the formulae for finding the capacitance and dissipation factor. (20 marks) (c) A linear delta modulator is designed to transmit speech signal bandlimited to 4 kHz. The specifications are— sampling rate = 10 times Nyquist rate; step size = 100 mV. The system is tested with 1 kHz sinusoidal signal. Determine the maximum amplitude of the test signal so that slope overload does not occur. Calculate the maximum power that can be transmitted without slope overload. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक पुनर्निवेश तंत्र का खंड आरेख चित्र में दर्शाया गया है। (i) तंत्र के पूर्ण मूल बिन्दुपथ (रूट लोकस) का रेखाचित्र बनाइए। (ii) s = 0 पर K का मान क्या है? (iii) बंद-लूप स्थायित्व के लिए K का परास बताइए। (20 अंक) (b) संधारिता एवं क्षय गुणक मापने के लिए एक शेरिंग सेतु का संयोजन आरेख बनाइए। संतुलन समीकरण लिखिए तथा संधारिता और क्षय गुणक ज्ञात करने के लिए सूत्र निकालिए। (20 अंक) (c) 4 kHz बैंड-बंधित स्पीच संकेत को संचारित करने के लिए एक रैखिक डेल्टा मॉडुलक डिजाइन किया गया है। इसके विनिर्देश इस प्रकार हैं— प्रतिचयन दर = नाइक्विस्ट दर से 10 गुनी; पद आमाप = 100 mV। तंत्र को 1 kHz के ज्यावक्रीय संकेत के साथ जाँचा गया। जाँच संकेत का अधिकतम आयाम निर्धारित कीजिए ताकि प्रवणता अधिभार न हो। अधिकतम शक्ति ज्ञात कीजिए, जो कि बिना प्रवणता अधिभार के संचारित की जा सके। (10 अंक)

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How this answer will be evaluated

Approach

Solve this multi-part problem by allocating approximately 40% time to part (a) root locus analysis, 40% to part (b) Schering bridge derivation, and 20% to part (c) delta modulation calculations. Begin with sketching the root locus using standard rules, then derive balance equations for the Schering bridge with clear circuit diagram, and conclude with slope overload calculations for the DM system. Ensure all numerical answers are boxed and diagrams are neatly labeled.

Key points expected

  • Part (a)(i): Correct identification of poles and zeros, asymptote angles and centroid, breakaway/break-in points, and complete root locus sketch with proper direction arrows
  • Part (a)(ii): Application of magnitude condition at s=0 to find K value using |G(s)H(s)|=1
  • Part (a)(iii): Use of Routh-Hurwitz criterion or jω-axis crossing method to determine stable range of K
  • Part (b): Accurate connection diagram of Schering bridge with four arms labeled, balance equations derived from Z1Z4=Z2Z3, and final expressions Cx=C3R1/R2 and tanδ=ωC4R4
  • Part (c): Calculation of maximum amplitude A_max = (Δ·fs)/(2πfm) for slope overload avoidance, and maximum power P_max = A_max²/2

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies root locus rules (angle/magnitude conditions), understands Schering bridge as comparison of series RC with parallel RC, and recognizes delta modulation slope overload condition as |dm/dt| ≤ Δ·fs; no conceptual confusion between DM and PCMIdentifies basic concepts but makes minor errors in applying root locus rules or confuses series/parallel RC configurations in bridge; understands slope overload vaguely but applies wrong formulaFundamental misconceptions such as treating root locus as Bode plot, incorrect bridge configuration, or confusing slope overload with granular noise
Numerical accuracy20%10Exact values: correct K at s=0, precise stability range, accurate Cx and tanδ expressions, and correct A_max = 0.159V with P_max = 12.66mW for part (c) using fs=80kHzCorrect method but arithmetic errors in centroid calculation, algebraic mistakes in bridge balance, or incorrect substitution of Nyquist rate (uses 8kHz instead of deriving fs=80kHz)Major calculation errors, wrong formulas applied, or missing units throughout; no verification of answers
Diagram quality20%10Neat, labeled root locus with real axis segments, asymptotes, and complex loci clearly shown; Schering bridge diagram with standard arm notation (R1C1 series, R2, R3C3 parallel, C4) and detector position; all components identifiedDiagrams present but poorly labeled, missing key features like arrow directions on root locus or ground connections in bridge; legible but incompleteMissing diagrams, unrecognizable sketches, or no labels; diagrams contradict written explanation
Step-by-step derivation20%10Systematic application of root locus construction rules (8 rules stated and applied); complete derivation from Z1Z4=Z2Z3 separating real and imaginary parts; clear derivation of slope overload condition from |dx/dt|max ≤ Δ·fsDerivations present but skips key steps, jumps to final formulas without showing intermediate algebra, or states rules without applying themNo derivations shown, only final answers stated, or mathematically incorrect steps that invalidate results
Practical interpretation20%10Interprets root locus stability range for controller design; explains Schering bridge application for high-voltage cable testing (e.g., Indian Railways/NTPC cable diagnostics); relates delta modulation step size to speech quality and mentions companding for Indian telecom standardsBrief mention of applications without elaboration; generic statements about bridge use for capacitance measurement without contextNo practical context provided, or irrelevant applications cited; fails to connect theory to engineering practice

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