Q5
(a) Explain the ratio error and phase angle error of current transformer. 10 marks (b) The two top rows of a Routh table of a characteristic polynomial is given in the table. Determine the roots of the characteristic equation which lie in the left half s-plane. Complete the remaining rows of the table. 10 marks (c) A pulse is applied to a piezo-electric transducer for a time T. Prove that in order to keep the undershoot of the response to a value within 5%, the value of time constant should be approximately 20T. 10 marks (d) A discrete memoryless source (DMS) has five symbols x₁, x₂, x₃, x₄ and x₅ with P(x₁) = 0·4, P(x₂) = 0·19, P(x₃) = 0·16, P(x₄) = 0·15 and P(x₅) = 0·1. (i) Construct a Shannon Fano code for the source and calculate the efficiency of the code. (ii) Repeat for Huffman code. Compare the results of (i) and (ii). 10 marks (e) List the functional classification of 8085 instruction set. Give one example for each class. 10 marks
हिंदी में प्रश्न पढ़ें
(a) विद्युत धारा परिणामित्र की अनुपातिक त्रुटि व कला कोण त्रुटि की व्याख्या करें । 10 (b) एक अभिलक्षण बहुपद (कैरेक्टरिस्टिक पॉलिनोमियल) की रूथ सारणी की सबसे ऊपर की दो पंक्तियाँ नीचे दर्शायी गई हैं । s-तल के अर्ध बाम में स्थित अभिलक्षण समीकरण के मूलों का निर्धारण करें व सारणी की शेष पंक्तियों को पूर्ण करें । 10 (c) एक दाब विद्युत पारातंत्र पर T समय के लिए एक स्पंदन अनुप्रयुक्त किया गया है । सिद्ध करें कि समय स्थिरांक का अनुमानित मान 20T होगा यदि प्रतिक्रिया का अधोचरम (अंडरशूट) मान 5% तक सीमित हो । 10 (d) एक असतत स्मृतिहीन स्रोत (DMS) पांच प्रतीक चिह्न x₁, x₂, x₃, x₄, x₅ हैं जहाँ कि; P(x₁) = 0·4, P(x₂) = 0·19, P(x₃) = 0·16, P(x₄) = 0·15, P(x₅) = 0·1 है । (i) इस स्रोत के लिए शैनन फैनो कूट (कोड) का निर्धारण करें व कूट (कोड) की दक्षता की गणना करें । (ii) इस स्रोत के लिए हफमैन कूट का भी निर्धारण करें व (i) व (ii) के परिणामों की तुलना करें । 10 (e) 8085 सूक्ष्म संसाधक के अनुदेश समुच्चय को कार्यात्मक वर्गीकरण के अनुसार सूचीबद्ध करें । प्रत्येक वर्ग का एक उदाहरण लिखें । 10
Directive word: Explain
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How this answer will be evaluated
Approach
Begin with a brief introduction acknowledging the diverse instrumentation, control systems, and digital electronics topics covered. For part (a), explain ratio and phase angle errors with phasor diagrams and reduction methods; for (b), complete the Routh table systematically and apply stability criteria to count left-half plane roots; for (c), derive the piezo-electric transducer response equation and solve for the time constant condition; for (d)(i)-(ii), construct Shannon-Fano and Huffman codes stepwise, computing efficiencies and comparing optimality; for (e), enumerate 8085 instruction classes with clear examples. Allocate approximately 15% time to (a), 20% to (b), 20% to (c), 30% to (d), and 15% to (e), ensuring all derivations and calculations are shown explicitly.
Key points expected
- Part (a): Define ratio error (KnIs - Ip)/Ip × 100% and phase angle error (δ) with phasor diagram showing excitation current I0, secondary current Is, and primary current Ip; mention reduction by using high permeability core, stranded conductors, and minimizing secondary burden
- Part (b): Complete Routh table using standard recurrence formula b1 = (a1a2 - a0a3)/a1 etc.; determine sign changes in first column to identify right-half plane roots; deduce left-half plane roots count from polynomial degree minus RHP roots
- Part (c): Derive piezo-electric transducer as second-order system with transfer function; apply rectangular pulse input of duration T; solve for undershoot condition at t=T+ and set ≤5% to obtain τ ≈ 20T
- Part (d)(i): Construct Shannon-Fano code by recursive probability bisection (0.4|0.19,0.16,0.15,0.1 then subdivide); calculate average code length L and entropy H; efficiency η = H/L × 100%
- Part (d)(ii): Construct Huffman code by iterative minimum probability combination; compare code lengths, efficiency, and note Huffman achieves optimal prefix code while Shannon-Fano may be suboptimal
- Part (e): List 8085 functional classes: Data transfer, Arithmetic, Logical, Branch, Stack I/O & Machine control; provide one specific example each (e.g., MOV A,B, ADD B, ANA B, JMP addr, PUSH B, HLT)
- Cross-cutting: Demonstrate awareness of practical CT applications in Indian power grid metering, 8085 relevance in legacy industrial controllers, and source coding in modern communication systems
Evaluation rubric
| Dimension | Weight | Max marks | Excellent | Average | Poor |
|---|---|---|---|---|---|
| Concept correctness | 20% | 10 | Precise definitions of CT errors with correct phasor relationships; accurate Routh-Hurwitz stability criterion application; correct piezo-electric model as electromechanical transducer; proper Shannon-Fano bisection and Huffman tree construction; exact 8085 instruction classification with valid examples | Generally correct concepts but minor errors in phasor orientation, Routh formula application, transducer model assumptions, coding algorithm steps, or instruction set categorization | Fundamental misconceptions about CT error definitions, incorrect stability criterion, wrong transducer physics, confused coding procedures, or major errors in 8085 classification |
| Numerical accuracy | 20% | 10 | Correct Routh table completion with accurate root counting; precise derivation yielding τ = 20T for 5% undershoot; exact entropy H = 2.066 bits/symbol, Shannon-Fano and Huffman code lengths calculated correctly with efficiencies ~96-98% | Minor arithmetic errors in Routh coefficients, approximate time constant derivation, or small calculation mistakes in entropy/code lengths leading to slightly off efficiency values | Major computational errors in Routh table, incorrect time constant relationship, wrong entropy calculation, or completely incorrect code construction and efficiency values |
| Diagram quality | 15% | 7.5 | Clear phasor diagram for CT with Ip, Is, I0, Im, Iw components labeled; neat Routh table with proper alignment; well-labeled piezo-electric equivalent circuit; clean Huffman tree diagram; 8085 instruction format diagram if relevant | Present but cluttered diagrams, missing some labels, or poorly organized tables that are still decipherable | Missing essential diagrams, incomprehensible sketches, or diagrams that contradict the textual explanation |
| Step-by-step derivation | 25% | 12.5 | Complete derivation of CT error equations from equivalent circuit; systematic Routh table construction with all intermediate steps shown; full differential equation solution for piezo transducer with boundary conditions; explicit step-by-step code construction for both algorithms; logical flow throughout | Some steps omitted or condensed, particularly in transducer differential equation solution or coding algorithm intermediate steps, but overall traceable logic | Missing derivations, jumps in logic, no working shown for Routh coefficients, unsupported claims about time constant, or purely final answers without process |
| Practical interpretation | 20% | 10 | Contextualizes CT errors in Indian grid protection (IS 2705 standards); relates Routh stability to practical control system design; connects piezo transducer to ultrasonic applications; discusses coding efficiency in data compression; notes 8085 legacy in Indian industrial training and embedded systems | Brief mention of practical relevance without specific standards or applications; generic statements about importance | No practical context provided; purely theoretical treatment without real-world connection or relevance to engineering practice |
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