Electrical Engineering 2022 Paper I 50 marks Solve

Q4

For the network shown in Figure 4(a)(i) and its excitation function shown in Figure 4(a)(ii), find the response v(t) using convolution by: (i) 's' domain approach. (ii) time domain analytical approach. (iii) graphical convolution approach. (b)(i) A 240 V, 50 Hz single phase supply is connected to a full controlled converter to control the speed of a 10 kW, 220 V separately excited dc motor. The rated current of motor at full load is 25 A, armature resistance is 0·4 ohm and machine constant is 0·3 V/rpm. Calculate the speed of motor when converter is operating at an angle α = 50°, assuming continuous armature current. (b)(ii) Describe the performance requirements of a chopper circuit that can perform the chopping functions in any modulation technique. (c) The amplifier shown in Figure 4(c) is biased to operate at I_D = 1 mA and g_m = 1 mA/V. Neglecting r_o, (i) determine the midband gain. (ii) determine the value of C_S that places f_L at 10 Hz.

हिंदी में प्रश्न पढ़ें

चित्र 4(a)(i) में दर्शाए गए संजाल और चित्र 4(a)(ii) में दर्शाए गए इसके उत्तेजक फलन के लिए संवलन का प्रयोग करते हुए, निम्नलिखित विधियों से अनुक्रिया v(t) ज्ञात कीजिए : (i) 's' क्षेत्र पद्धति (ii) काल क्षेत्र विश्लेषण पद्धति (iii) चित्रात्मक संवलन पद्धति (b)(i) एक 240 V, 50 Hz एकल कला आपूर्ति संयोजित एक पूर्ण नियंत्रित परिवर्तक द्वारा एक 10 kW, 220 V, अन्यतः उत्तेजित दिष धारा मोटर की चाल को नियंत्रित किया जाता है । मोटर की पूर्ण भार पर निर्धारित धारा 25 A, आर्मेचर का प्रतिरोध 0·4 Ω व मशीन स्थिरांक 0·3 V/rpm है । जब परिवर्तक का α = 50° कोण पर परिचालन किया जाता है तो मोटर की चाल की गणना, आर्मेचर में सतत धारा प्रवाह मानकर कीजिए । (b)(ii) एक अंतरायिक (चॉपर) परिपथ की कार्यकरण आवश्यकताओं का वर्णन कीजिए ताकि यह किसी मॉडुलन तकनीक में अंतरायि (चॉपिंग) कार्य कर सके । (c) चित्र 4(c) में दर्शाया गया प्रवर्धक, I_D = 1 mA और g_m = 1 mA/V पर कार्य करने हेतु अभिनति (बायस) है । r_o की उपेक्षा करते हुए (i) मध्य-बैंड लब्धि ज्ञात कीजिए । (ii) f_L को 10 Hz पर रखने हेतु C_S का मान ज्ञात कीजिए ।

Evaluate your answer to this question → See all 2022 Electrical Engineering questions

Directive word: Solve

This question asks you to solve. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Solve this multi-part problem by allocating approximately 35% time to part (a) covering all three convolution approaches, 30% to part (b) including both the numerical calculation and chopper description, and 35% to part (c) for amplifier analysis. Begin with a brief statement of the network parameters and circuit configurations, then present systematic derivations for each sub-part with clear sectional headings, and conclude with verification of results against physical constraints.

Key points expected

  • For 4(a): Derive impulse response h(t) from network in Figure 4(a)(i), then apply convolution integral v(t) = ∫e(τ)h(t-τ)dτ using s-domain (Laplace), direct time-domain integration, and graphical superposition methods
  • For 4(b)(i): Calculate average output voltage V_d = (2V_m/π)cosα, determine back EMF E_b = V_d - I_aR_a, and solve for motor speed N = E_b/Kφ using given 240V supply, α=50°, and motor parameters
  • For 4(b)(ii): Specify chopper requirements including fast switching capability, proper gate drive isolation, snubber circuits for dv/dt protection, current limiting, and EMI filtering for PWM/variable frequency operation
  • For 4(c)(i): Analyze CS amplifier midband gain A_M = -g_m(R_D||R_L) using given g_m = 1mA/V and appropriate load resistance from Figure 4(c)
  • For 4(c)(ii): Calculate source bypass capacitor C_S using f_L = 1/(2πR_S'C_S) where R_S' is equivalent resistance seen by C_S, targeting f_L = 10Hz

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%12Correctly identifies convolution as integral of excitation with impulse response for (a); applies proper full converter equations with continuous conduction assumption for (b)(i); states all four chopper performance requirements (switching speed, efficiency, control flexibility, protection) for (b)(ii); uses correct small-signal FET model for (c)Identifies basic convolution concept but confuses limits or variables; applies converter formula with minor errors in angle conversion; lists 2-3 chopper requirements without specificity; attempts small-signal analysis but misses body effect or proper loadConfuses convolution with correlation or multiplication; uses half-wave or discontinuous conduction formulas; omits chopper requirements entirely; uses BJT hybrid model or ignores g_m definition
Numerical accuracy20%12Precise calculation: V_m = 240√2 = 339.4V, V_d = 155.3V, E_b = 145.3V, speed N ≈ 484 rpm for (b)(i); C_S calculation yields exact value in μF range accounting for R_S||(1/g_m) for (c)(ii); all intermediate steps shown with proper unitsCorrect method but arithmetic errors in cos(50°) or rounding; speed calculation within ±10% of correct value; C_S order of magnitude correct but uses approximate resistanceOrder-of-magnitude errors in voltage or speed; ignores √2 factor for RMS conversion; C_S calculation completely wrong or missing; no unit tracking
Diagram quality20%12Clear sketches for 4(a)(i) network with labeled R,L,C elements; excitation waveform 4(a)(ii) with proper time axes; graphical convolution showing e(τ), h(t-τ), and product overlap regions for multiple t values; chopper circuit diagram with MOSFET/IGBT, freewheeling diode, and loadBasic network sketch with minor labeling issues; single graphical convolution example shown; chopper description without circuit or generic block diagramNo diagrams despite explicit 'graphical' requirement; misdrawn network topology; missing waveform annotations; no chopper illustration
Step-by-step derivation20%12For (a): systematic s-domain (H(s)→h(t)), time-domain integral setup with proper limits, and graphical flip-shift-multiply-integrate procedure; for (b): complete converter voltage derivation, motor equivalent circuit analysis; for (c): small-signal equivalent circuit, gain expression, and pole-zero analysis for C_SSome steps omitted or combined; correct final formulas but unclear limit transitions in convolution; motor speed found by shortcut; C_S formula stated without derivationNo derivation—only final answers; incorrect integral limits throughout; missing motor equivalent circuit; no small-signal model development
Practical interpretation20%12Interprets convolution result physically as system response buildup; notes 484 rpm < rated 220V speed confirms converter control; explains chopper modulation trade-offs (PWM vs frequency) for motor drives; discusses C_S impact on low-frequency response and bypass effectiveness; references Indian railway traction or industrial drive applicationsBrief physical interpretation of speed result; mentions chopper efficiency without modulation context; notes C_S affects low frequency without explaining source degenerationNo physical interpretation of any result; purely mathematical treatment; ignores practical significance of continuous conduction assumption

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Electrical Engineering 2022 Paper I