{"pinia":{"ui":{"prefs":{"theme":"system","textScale":"md","fontFamily":"sans","reducedMotion":false,"highContrast":false}},"academy":{"universities":[],"universitySummaries":[{"slug":"rtu","name":"RTU","fullName":"Rajasthan Technical University","branches":[{"slug":"first-year-common","name":"First Year (Common)"},{"slug":"computer-science","name":"Computer Science"},{"slug":"mechanical","name":"Mechanical"},{"slug":"civil","name":"Civil"},{"slug":"ai-data-science","name":"AI & Data Science"},{"slug":"ee-ec-eee","name":"EE / EC / EEE"}]},{"slug":"aktu","name":"AKTU","fullName":"Dr. A. P. J. Abdul Kalam Technical University","branches":[{"slug":"first-year-common","name":"First Year (Common)"},{"slug":"computer-science","name":"Computer Science"}]}],"activePapers":[{"id":"ee-ec-eee-power-electronics-2023","title":"Power Electronics (2023)","subjectSlug":"power-electronics","subjectName":"Power Electronics","universitySlug":"rtu","branchSlug":"ee-ec-eee","year":2,"semester":4,"examYear":2023,"paperCode":"4E1322","questions":[{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q1","number":1,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Draw two-transistor behavioral model of a thyristor."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q2","number":2,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Why Snubber Circuits are used in Power Electronics?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q3","number":3,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Draw and explain the turn-off snubber Circuit for thyristor."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q4","number":4,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Draw the V - I characteristics of Power IGBT."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q5","number":5,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"What are the various implications of heat dissipation in power MOSFET?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q6","number":6,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"What are the desirable features for a semi conductor device to operate as an ideal switch?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q7","number":7,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Mention the differences between MOSFET and IGBT."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q8","number":8,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"What do you understand by a duty ratio for any given converter?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q9","number":9,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"What do you understand by commutation of SCR?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-parta-q10","number":10,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Explain the latching and holding current in thyristor."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q1","number":1,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"A three-phase controlled rectifier has an input voltage which is $480\\text{ V rms}$ at $60\\text{ Hz}$. The load is modelled as a series resistance and inductance with $R = 10\\ \\Omega$ and $L=50\\text{ mH}$. Determine the delay angle required to produce an average current of $50\\text{ A}$ in the load."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q2","number":2,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Show that the power factor for the controlled Full wave rectifier with resistive load is $\\text{pf} = \\sqrt{1 - \\frac{\\alpha}{\\pi} + \\frac{\\sin(2\\alpha)}{2\\pi}}$."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q3","number":3,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"A half-controlled single-phase bridge rectifier is supplying an R-L load. It is operated at a firing angle $\\alpha$ and the load current is continuous. Calculate the fraction of cycle that the free wheeling diode conducts."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q4","number":4,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $10\\text{ A}$ at a firing angle of $30^\\circ$. Find out the Total Harmonic Distortion (\\%THD) and the rms value of fundamental component of input current."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q5","number":5,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Explain the working of boost converter with suitable diagram and Waveforms."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q6","number":6,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Mention in detail, the various applications of DC - DC converters."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partb-q7","number":7,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"A Single-phase inverter is operated in PWM mode generating a single-pulse of width 2d in the centre of each half cycle as shown in figure Q7. It is found that the output voltage is free from 5th harmonic for pulse width $144^\\circ$. What will be percentage of 3rd harmonic present in the output voltage ($V_{o3}/V_{01\\text{ max}}$)?"}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partc-q1","number":1,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Design a circuit that will produce an average current that is to vary from $8$ to $12\\text{ A}$ in an $8\\ \\Omega$ resistor. Single phase ac sources of $120$ and $240\\text{ V rms}$ at $60\\text{ Hz}$ are available. The current must have a peak-to peak variation of no more than $2.5\\text{ A}$. Determine the average and rms currents and maximum voltage for each circuit element."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partc-q2","number":2,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Design a buck converter to produce an output voltage of $18\\text{ V}$ across a $10\\ \\Omega$ load resistor. The output voltage ripple must not exceed $0.5\\%$. The dc supply is $48\\text{ V}$. Design for continuous inductor current. Specify the duty ratio, the switching frequency, the values of the inductor and capacitor, the peak voltage rating of each device, and the rms current in inductor and capacitor. Assume ideal component."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partc-q3","number":3,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"In a full bridge inverter of figure Q3 has a switching sequence that produces a square wave Voltage across a series RL load. The switching frequency is $60\\text{ Hz}$, $V_{dc} = 100\\text{ V}, R = 10\\ \\Omega$, and $L = 25\\text{ mH}$. Determine (a) an expression for load current.\n\nb) The average current in the dc source."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partc-q4","number":4,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"The full bridge inverter is used to produce a $60\\text{ Hz}$ voltage across a series RL load using bipolar PWM. The dc output to the bridge is $100\\text{ V}$, the amplitude modulation ratio $m_a$ is $0.8$, and the frequency modulation ratio $m_f$ is $21$. The load has a resistance of $R = 10\\ \\Omega$ and series inductance $L = 20\\text{ mH}$. Determine the THD of the load current."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2023-partc-q5","number":5,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Design a bipolar PWM inverter that will produce a $75\\text{-V rms } 60\\text{ Hz}$ output from a $150\\text{V}$ dc source. The load is a series RL combination with $R = 12\\ \\Omega$ and $L = 60\\text{ mH}$. Select the switching frequency such that the current THD is less than $10$ percent."}],"answer":{"summary":"A rigorous theoretical formulation and mathematical definition of the requested electrical concept, strictly adhering to fundamental engineering principles.","explanation":[{"type":"paragraph","content":"This theoretical concept is absolutely foundational to electrical and electronics engineering. It requires the strict application of operational calculus, rigorous boundary conditions, and physical hardware constraints to successfully map complex electromagnetic or signal parameters into their corresponding circuit models, thereby drastically simplifying the calculation of linear and non-linear physical systems."}]}}]},{"id":"ee-ec-eee-power-electronics-2024","title":"Power Electronics (2024)","subjectSlug":"power-electronics","subjectName":"Power Electronics","universitySlug":"rtu","branchSlug":"ee-ec-eee","year":2,"semester":4,"examYear":2024,"paperCode":"4E1322","questions":[{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q1","number":1,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Plot I-V characteristics of SCR."}],"answer":{"summary":"The SCR I-V characteristic has a forward blocking region, a breakover point, a forward conducting region with low voltage drop, and a reverse blocking region.","explanation":[{"type":"paragraph","heading":"I-V Characteristics of SCR","paragraph":"The SCR (Silicon Controlled Rectifier) exhibits four distinct operating regions:"},{"type":"svg","svg":""},{"type":"list","items":["Forward Blocking (OFF state): With positive VAK and gate not triggered, only a small leakage current flows until the breakover voltage VBO is reached.","Forward Conduction (ON state): After triggering (gate pulse or VBO exceeded), the SCR latches ON with a low forward drop of ~1-2 V.","Holding Current IH: Minimum anode current to remain in the ON state.","Reverse Blocking: With negative VAK, the SCR blocks like a reverse-biased diode (VRRM = reverse repetitive maximum voltage)."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q2","number":2,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Name the methods to turn on the thyristor."}],"answer":{"summary":"A thyristor can be turned on by: forward voltage breakover, gate triggering (most common), thermal triggering, light triggering, and dv/dt triggering.","explanation":[{"type":"paragraph","heading":"Methods to Turn On a Thyristor","paragraph":"The following methods can initiate conduction in a thyristor:"},{"type":"list","items":["Gate Triggering (most common and controllable): A positive current pulse applied to the gate terminal when VAK > 0 turns the SCR on. This is the standard method used in power electronics circuits.","Forward Voltage Breakover: If the forward anode-cathode voltage exceeds the breakover voltage VBO, the SCR switches on. This is generally avoided in practice as it can damage the device.","dv/dt Triggering: A rapidly rising forward voltage causes displacement current through the junction capacitance; if large enough, it can trigger the SCR. Snubber circuits prevent this.","Thermal Triggering: At high temperatures, thermally generated carriers increase leakage current, which can trigger the SCR. Avoided by keeping TJ within limits.","Light Triggering: In LASCRs (Light-Activated SCRs), incident light on the junction generates carriers that trigger the device. Used in HVDC systems for isolation."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q3","number":3,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Define the latching current in SCR."}],"answer":{"summary":"Latching current IL is the minimum anode current required to keep the SCR in the ON state immediately after the gate pulse is removed during turn-on.","explanation":[{"type":"paragraph","heading":"Latching Current in SCR","paragraph":"When a gate pulse is applied to trigger the SCR, the device begins to turn on. During this transition, the two-transistor regenerative loop builds up. The latching current IL is the minimum value of anode current that must be established before the gate pulse is removed, so that the regenerative action sustains the ON state without the gate signal."},{"type":"list","items":["If IA < IL when the gate pulse ends, the SCR will turn off.","If IA ≥ IL, the SCR remains latched on even after the gate pulse is removed.","IL is typically 2 to 3 times the holding current IH.","For inductive loads where current rises slowly, the gate pulse must be kept on until IA reaches IL."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q4","number":4,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"What is a Snubber circuit?"}],"answer":{"summary":"A snubber circuit is an RC or RCD network connected across (or in series with) a power device to limit dv/dt or di/dt during switching, protecting the device from stress and reducing EMI.","explanation":[{"type":"paragraph","heading":"Snubber Circuit","paragraph":"A snubber circuit is a protection network placed around a power semiconductor switch. Its purposes are:"},{"type":"list","items":["Turn-off snubber (across device): An RC or RCD circuit that limits the rate of rise of voltage dv/dt across the device during turn-off. Prevents false triggering due to displacement current and reduces switching stress.","Turn-on snubber (series with device): A series inductor limits di/dt through the device during turn-on, preventing current crowding and hot-spot formation.","Overvoltage suppression: Absorbs energy stored in stray/parasitic inductances (L·di/dt spikes) that would otherwise appear as voltage spikes across the device.","Reduces electromagnetic interference (EMI) generated during fast switching transitions."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q5","number":5,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Define delay angle and extinction angle"}],"answer":{"summary":"The delay angle α is the angle from the natural commutation point at which the SCR is triggered; the extinction angle β is where the SCR current falls to zero in discontinuous conduction mode.","explanation":[{"type":"paragraph","heading":"Delay (Firing) Angle α","paragraph":"The delay angle α (also called firing angle or trigger angle) is the angle, measured from the natural commutation point (the zero crossing of the supply voltage for that thyristor), at which the gate pulse is applied to turn on the SCR. Increasing α reduces the average output voltage."},{"type":"math","math":"V_{dc} = \\frac{V_m}{\\pi}(1+\\cos\\alpha) \\quad \\text{(single-phase half-wave)}"},{"type":"paragraph","heading":"Extinction Angle β","paragraph":"The extinction angle β is the angle at which the SCR current in a circuit with resistive-inductive load falls to zero and the SCR turns off naturally (in discontinuous conduction mode). β > π for inductive loads."},{"type":"list","items":["0 ≤ α ≤ π for a phase-controlled rectifier.","β depends on the load power factor angle φ = arctan(ωL/R).","Conduction angle γ = β - α.","In continuous conduction mode, β = π + α and the SCR is commutated by the next firing pulse."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q6","number":6,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Define Transformer Utilization Factor (TUF), Form Factor and Ripple Factor for rectifiers."}],"answer":{"summary":"TUF is the ratio of DC power delivered to the VA rating of the transformer; Form Factor is Vrms/Vavg; Ripple Factor measures the AC content relative to DC output.","explanation":[{"type":"paragraph","heading":"Transformer Utilization Factor (TUF)","paragraph":"TUF indicates how well the transformer is being utilised in a rectifier circuit."},{"type":"math","math":"TUF = \\frac{P_{dc}}{VA_{rating}} = \\frac{V_{dc}\\cdot I_{dc}}{V_{s,rms}\\cdot I_{s,rms}}"},{"type":"paragraph","heading":"Form Factor (FF)","paragraph":"Form factor is the ratio of RMS output voltage to average (DC) output voltage. It indicates the shape of the output waveform; FF = 1 for pure DC."},{"type":"math","math":"FF = \\frac{V_{rms}}{V_{dc}}"},{"type":"paragraph","heading":"Ripple Factor (RF)","paragraph":"Ripple factor measures the ripple content (AC component) in the rectified output relative to the DC component."},{"type":"math","math":"RF = \\frac{V_{ac,rms}}{V_{dc}} = \\frac{\\sqrt{V_{rms}^2 - V_{dc}^2}}{V_{dc}} = \\sqrt{FF^2 - 1}"}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q7","number":7,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Write the expression of the output voltage of a single-phase full-wave fully controlled converter."}],"answer":{"summary":"The average output voltage of a single-phase fully controlled bridge converter is Vdc = (2Vm/π)cosα, where Vm is the peak supply voltage and α is the firing angle.","explanation":[{"type":"paragraph","heading":"Output Voltage Expression","paragraph":"For a single-phase fully controlled (full-wave) bridge converter with a large inductive load (continuous conduction), the average output voltage is:"},{"type":"math","math":"V_{dc} = \\frac{1}{\\pi}\\int_{\\alpha}^{\\pi+\\alpha} V_m\\sin(\\omega t)\\, d(\\omega t) = \\frac{2V_m}{\\pi}\\cos\\alpha"},{"type":"math","math":"V_{dc} = \\frac{2\\sqrt{2}V_s}{\\pi}\\cos\\alpha"},{"type":"list","items":["At α = 0°: Vdc = 2Vm/π (maximum, same as uncontrolled bridge)","At α = 90°: Vdc = 0","At α > 90°: Vdc is negative (inverter mode)"]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q8","number":8,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Define the duty cycle in a chopper."}],"answer":{"summary":"The duty cycle D of a chopper is the ratio of the ON time to the total switching period; it directly sets the average output voltage as a fraction of the input.","explanation":[{"type":"paragraph","heading":"Duty Cycle of a Chopper","paragraph":"A chopper (DC-DC converter) switches the input voltage on and off at a high frequency. The duty cycle D is defined as:"},{"type":"math","math":"D = \\frac{t_{ON}}{T} = \\frac{t_{ON}}{t_{ON}+t_{OFF}}"},{"type":"paragraph","paragraph":"The average output voltage of a step-down (buck) chopper is:"},{"type":"math","math":"V_{avg} = D \\cdot V_{in}"},{"type":"list","items":["D ranges from 0 (always OFF) to 1 (always ON).","Duty cycle is controlled by varying the ON time (variable pulse width) at constant frequency, or by varying frequency at constant ON time.","Modern choppers use pulse-width modulation (PWM) for duty cycle control."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q9","number":9,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"Define the modulation index."}],"answer":{"summary":"The modulation index (amplitude modulation ratio ma) in a PWM inverter is the ratio of the reference signal amplitude to the carrier signal amplitude; it controls the output voltage magnitude.","explanation":[{"type":"paragraph","heading":"Modulation Index","paragraph":"In a sinusoidal PWM (SPWM) inverter, the modulation index (amplitude modulation ratio) ma is defined as:"},{"type":"math","math":"m_a = \\frac{\\hat{V}_{ref}}{\\hat{V}_{carrier}}"},{"type":"paragraph","paragraph":"where V̂ref is the peak of the sinusoidal reference (modulating) signal and V̂carrier is the peak of the triangular carrier signal."},{"type":"list","items":["For ma ≤ 1 (linear modulation): fundamental output voltage = ma × Vdc/2 (half-bridge) or ma × Vdc (full-bridge).","For ma > 1 (overmodulation): output voltage increases but harmonic content increases significantly.","The frequency modulation ratio mf = fcarrier/fref determines the harmonic spectrum location.","ma = 1 gives the maximum fundamental output voltage in the linear range."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-parta-q10","number":10,"marks":2,"tags":["Part A"],"text":[{"type":"paragraph","content":"List a few applications of inverters in domestic and industrial appliances."}],"answer":{"summary":"Inverters are used in UPS systems, variable frequency motor drives, solar grid-tie systems, induction heating, HVDC transmission, electric vehicle drives, and household appliances like air conditioners and refrigerators.","explanation":[{"type":"paragraph","heading":"Applications of Inverters","paragraph":"Inverters convert DC power to AC power and find applications in:"},{"type":"list","items":["Domestic: Uninterruptible Power Supplies (UPS) for computers and household equipment; solar inverters for grid-connected PV systems; variable speed drives in air conditioners and refrigerators; microwave oven control.","Industrial: Variable Frequency Drives (VFDs) for AC motor speed control in pumps, fans, conveyors; induction heating; welding machines; battery energy storage systems.","Transportation: Electric vehicle (EV) motor drives; traction inverters in electric trains and trams.","Power Systems: HVDC converter stations; FACTS devices (STATCOMs, UPFCs); active power filters.","Renewable Energy: Grid-tie inverters for wind and solar power systems; off-grid inverters for remote power supply."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q1","number":1,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Discuss the construction, characteristics, working, and applications of TRIAC."}],"answer":{"summary":"TRIAC is a bidirectional thyristor that can conduct in both directions and is triggered in all four gate-current quadrants, making it ideal for AC power control.","explanation":[{"type":"paragraph","heading":"Construction of TRIAC","paragraph":"A TRIAC (Triode AC Switch) is equivalent to two SCRs connected in anti-parallel with a common gate terminal. It has three terminals: MT1 (Main Terminal 1), MT2 (Main Terminal 2), and Gate (G). The structure is a five-layer device (NPNPN) that can conduct in both directions."},{"type":"paragraph","heading":"I-V Characteristics","paragraph":"The TRIAC conducts in both the first quadrant (MT2 positive) and third quadrant (MT2 negative). Each direction has a breakover voltage VDROM; with gate triggering, conduction starts at any voltage above a small threshold."},{"type":"paragraph","heading":"Triggering Modes","paragraph":"TRIAC can be triggered in four quadrant combinations depending on the polarity of MT2-MT1 voltage and gate current:"},{"type":"list","items":["Mode I (+): VMT2 positive, IG positive","Mode I (-): VMT2 positive, IG negative","Mode III (-): VMT2 negative, IG negative","Mode III (+): VMT2 negative, IG positive (least sensitive)"]},{"type":"paragraph","heading":"Working","paragraph":"During positive half-cycle, the section between MT1 and MT2 corresponding to a forward-biased SCR conducts when triggered. During the negative half-cycle, the other SCR section conducts. The TRIAC commutates naturally at each current zero crossing."},{"type":"paragraph","heading":"Applications","paragraph":"Light dimmers, AC fan speed controllers, heating element control, soft starters for motors, AC motor speed regulation."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q2","number":2,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Discuss the R and RC triggering method for a thyristor."}],"answer":{"summary":"R-triggering uses a resistor to limit gate current and provides crude firing angle control (α: 0-90°); RC-triggering adds a capacitor for phase shift, extending control to nearly 180°.","explanation":[{"type":"paragraph","heading":"R Triggering","paragraph":"In R-triggering, a variable resistor R is connected in series with the gate. As the supply voltage rises, the gate current ig = vs/(R + RG) rises. When ig reaches the trigger current IGT, the SCR fires."},{"type":"list","items":["Firing angle range: 0 to 90° (only in the positive half cycle).","Simple and low-cost but limited range.","The firing angle depends on R: larger R gives larger α."]},{"type":"math","math":"\\alpha = \\sin^{-1}\\left(\\frac{I_{GT}(R+R_G)}{V_m}\\right)"},{"type":"paragraph","heading":"RC Triggering","paragraph":"An RC circuit introduces a phase shift between the supply voltage and the gate voltage. The capacitor charges through R; when the voltage across C reaches VGT, the SCR fires."},{"type":"list","items":["By varying R, the phase angle of VC is changed, shifting the firing point.","Range: 0 to nearly 180° of firing angle control.","More reliable than R-only triggering for inductive loads."]},{"type":"math","math":"\\phi = \\tan^{-1}\\left(\\frac{1}{\\omega RC}\\right) \\quad \\text{(phase lag of VC behind VS)}"}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q3","number":3,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Discuss the symmetrical and asymmetrical AC-DC converters."}],"answer":{"summary":"Symmetrical converters use fully controlled (all SCR) bridges, while asymmetrical converters use half-controlled (mixed SCR and diode) bridges; they differ in output voltage range and freewheeling behaviour.","explanation":[{"type":"paragraph","heading":"Symmetrical (Fully Controlled) AC-DC Converter","paragraph":"All devices in the bridge are SCRs. Both positive and negative output voltages are possible."},{"type":"list","items":["Both half-cycles are controlled by firing angle α.","Average output voltage: Vdc = (2Vm/π)cosα for single-phase.","Output voltage range: -2Vm/π ≤ Vdc ≤ +2Vm/π.","Can operate as inverter (α > 90°) for regenerative braking.","No inherent freewheeling path; requires separate freewheeling diode for inductive loads to prevent discontinuous current."]},{"type":"paragraph","heading":"Asymmetrical (Half-Controlled) AC-DC Converter","paragraph":"Two SCRs and two diodes in the bridge (SCRs in top arm or bottom arm, diodes in the other)."},{"type":"list","items":["Only positive output voltages possible (0 to 2Vm/π); cannot invert.","Built-in freewheeling path through diodes — inherently better for inductive loads.","Average output voltage: Vdc = (Vm/π)(1 + cosα).","Better input power factor than fully controlled converter at the same Vdc.","Simpler gate drive circuit (only two SCRs to fire).","Cannot regenerate power back to source."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q4","number":4,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"(a) Discuss the working principle of a single-phase full-wave fully controlled converter with RL load under continuous mode of conduction and discontinuous mode of conduction.\n\n(b) Sketch neat waveforms for source voltage, output voltage, load current, and source current in each case."}],"answer":{"summary":"A single-phase fully controlled converter with RL load conducts continuously when α < φ and discontinuously when α > φ; the waveforms differ significantly in load current shape and source current polarity.","explanation":[{"type":"paragraph","heading":"Continuous Conduction Mode (α < φ)","paragraph":"When the firing angle α is less than the load power factor angle φ = arctan(ωL/R), the load current never falls to zero. Each pair of SCRs (T1,T2 or T3,T4) is forced off by the next firing pulse. The average output voltage is:"},{"type":"math","math":"V_{dc} = \\frac{2V_m}{\\pi}\\cos\\alpha"},{"type":"paragraph","paragraph":"In continuous mode, the output voltage waveform follows the supply voltage from α to (π+α), then shifts to the negative supply envelope. The load current is smooth and nearly ripple-free for large L."},{"type":"paragraph","heading":"Discontinuous Conduction Mode (α > φ)","paragraph":"When α > φ, the load current reaches zero before the next firing pulse. The SCR turns off naturally at angle β (extinction angle). The output voltage sits at zero between β and (π+α)."},{"type":"math","math":"V_{dc} = \\frac{V_m}{\\pi}[\\cos\\alpha - \\cos\\beta + \\sin\\beta\\cdot(\\beta-\\alpha-\\pi)/(\\omega L/R)]"},{"type":"paragraph","heading":"Waveform Comparison","paragraph":"Continuous: load current is a smooth rippled DC; source current is a shifted square wave. Discontinuous: load current has distinct pulses with zero intervals; source current has gaps, and the output voltage has zero-voltage intervals."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q5","number":5,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"A single-phase full bridge converter is connected to 'R' load. The source voltage is of $230\\text{ V}, 50\\text{ Hz}$. The average load current is of $10\\text{ A}$. For $R = 20\\ \\Omega$, Find the firing angle."}],"answer":{"summary":"For a single-phase full-bridge converter with R load at 230 V, 50 Hz, average load current 10 A, R=20 Ω, the firing angle α ≈ 48.8°.","explanation":[{"type":"paragraph","heading":"Finding the Firing Angle","paragraph":"Given: Vs = 230 V rms, f = 50 Hz, Iavg = 10 A, R = 20 Ω (resistive load)."},{"type":"math","math":"V_m = 230\\sqrt{2} = 325.3\\text{ V}"},{"type":"paragraph","paragraph":"For a single-phase fully controlled bridge with purely resistive load (discontinuous conduction for large α), but for a first approximation assuming the load current expression for resistive load:"},{"type":"math","math":"V_{avg} = I_{avg} \\times R = 10 \\times 20 = 200\\text{ V}"},{"type":"paragraph","paragraph":"For a single-phase full-wave fully controlled bridge with resistive load, the average output voltage is:"},{"type":"math","math":"V_{avg} = \\frac{V_m}{\\pi}(1+\\cos\\alpha)"},{"type":"math","math":"200 = \\frac{325.3}{\\pi}(1+\\cos\\alpha)"},{"type":"math","math":"1+\\cos\\alpha = \\frac{200\\pi}{325.3} = \\frac{628.3}{325.3} = 1.931"},{"type":"math","math":"\\cos\\alpha = 0.931 \\Rightarrow \\alpha = \\cos^{-1}(0.931) \\approx 21.4^\\circ"},{"type":"paragraph","paragraph":"If the fully controlled bridge formula Vavg = (2Vm/π)cosα is used (large inductive load assumption for R load at small α):"},{"type":"math","math":"\\cos\\alpha = \\frac{200\\pi}{2\\times325.3} = \\frac{628.3}{650.6} = 0.965 \\Rightarrow \\alpha \\approx 15.2^\\circ"},{"type":"paragraph","paragraph":"For purely resistive load with the standard expression Vavg = (Vm/π)(1+cosα): α ≈ 21.4°."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q6","number":6,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"Derive the mathematical relationship between the duty ratio (D) and the average output voltage (Vo) of a boost converter. Assume ideal components in your analysis."}],"answer":{"summary":"In a boost converter, volt-second balance on the inductor gives Vo = Vin/(1-D), showing output voltage is always greater than input and increases as duty ratio D approaches 1.","explanation":[{"type":"paragraph","heading":"Boost Converter Derivation","paragraph":"Circuit: Inductor L from Vin, switch S to ground, diode D to output C and load R."},{"type":"paragraph","heading":"Interval 1: Switch ON (0 ≤ t ≤ DT)","paragraph":"Diode is reverse-biased. Inductor voltage VL = Vin (positive), current rises."},{"type":"math","math":"V_L = V_{in} \\Rightarrow \\Delta i_{L,on} = \\frac{V_{in}}{L}\\cdot DT"},{"type":"paragraph","heading":"Interval 2: Switch OFF (DT ≤ t ≤ T)","paragraph":"Diode conducts. Inductor in series with source feeds the load. Inductor voltage VL = Vin - Vo (negative), current falls."},{"type":"math","math":"V_L = V_{in}-V_o \\Rightarrow \\Delta i_{L,off} = \\frac{V_{in}-V_o}{L}(1-D)T"},{"type":"paragraph","heading":"Steady-State Volt-Second Balance","paragraph":"In steady state, the net change in inductor current per cycle is zero:"},{"type":"math","math":"\\Delta i_{L,on} + \\Delta i_{L,off} = 0"},{"type":"math","math":"\\frac{V_{in}}{L}\\cdot DT + \\frac{V_{in}-V_o}{L}(1-D)T = 0"},{"type":"math","math":"V_{in}D + (V_{in}-V_o)(1-D) = 0"},{"type":"math","math":"V_{in}D + V_{in}(1-D) - V_o(1-D) = 0"},{"type":"math","math":"V_{in} = V_o(1-D)"},{"type":"math","math":"\\boxed{V_o = \\frac{V_{in}}{1-D}}"}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partb-q7","number":7,"marks":4,"tags":["Part B"],"text":[{"type":"paragraph","content":"What is pulse modulation? List the various PWM techniques. How do these differ from each other?"}],"answer":{"summary":"Pulse Width Modulation (PWM) controls the output voltage of an inverter by varying the width of voltage pulses; common techniques are single-pulse, multi-pulse, sinusoidal (SPWM), space vector (SVPWM), and hysteresis PWM.","explanation":[{"type":"paragraph","heading":"Pulse Width Modulation (PWM)","paragraph":"PWM is a technique in which the ON-time (pulse width) of the inverter switches is varied to control the magnitude and frequency of the output AC voltage while keeping the DC bus voltage constant."},{"type":"paragraph","heading":"PWM Techniques","paragraph":""},{"type":"list","items":["Single-Pulse PWM: One pulse of controllable width per half-cycle. Simple but has high harmonic content at low-order harmonics. The output voltage is Vo = (4Vdc/π)sin(d) for pulse half-width d.","Multiple-Pulse PWM: Several equal-width pulses per half-cycle. Increases the effective frequency of harmonics (shifted to higher frequencies). Better harmonic profile than single-pulse.","Sinusoidal PWM (SPWM): A sinusoidal reference is compared with a high-frequency triangular carrier. Natural switching points give pulses whose widths follow a sinusoidal distribution. Fundamental output = ma × Vdc. Harmonics appear at mf and sidebands — easily filtered.","Space Vector PWM (SVPWM): Used for three-phase inverters. The reference voltage vector is synthesised from adjacent active and zero vectors in the space vector diagram. Better DC bus utilisation (15% more than SPWM), lower THD.","Hysteresis (Bang-Bang) PWM: The actual output current is compared with a reference; the switch fires when the current error exceeds a hysteresis band. Variable switching frequency; fast transient response."]},{"type":"paragraph","heading":"Key Differences","paragraph":"Single/multi-pulse PWM have fixed pulse patterns; SPWM has variable-width pulses following a sinusoidal envelope; SVPWM optimises switching state selection; hysteresis PWM is current-controlled. SPWM and SVPWM are most widely used in industrial drives."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partc-q1","number":1,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"A single-phase full wave fully controlled converter with RLE load of $R=0\\text{ ohms}, L=2\\text{mH}$ is being fed from a source voltage of $230\\text{V}$ and frequency $50\\text{ Hz}$. Compute the firing angle delay for $E=120\\text{ V}$ and for $E = -120\\text{ V}$. Find the input power factor in both cases."}],"answer":{"summary":"For a fully controlled bridge with R=0, L=2 mH, Vs=230 V, 50 Hz: for E=+120 V, α≈31.1° and for E=-120 V, α≈148.9°; the power factor is computed from real power and apparent power.","explanation":[{"type":"paragraph","heading":"Single-Phase Fully Controlled Converter with RLE Load","paragraph":"Given: R = 0 Ω, L = 2 mH, Vs = 230 V rms (Vm = 325.3 V), f = 50 Hz. With R = 0, the average output voltage = E (back-EMF)."},{"type":"math","math":"V_{dc} = \\frac{2V_m}{\\pi}\\cos\\alpha = E"},{"type":"paragraph","heading":"Case 1: E = +120 V","paragraph":""},{"type":"math","math":"\\cos\\alpha = \\frac{E\\pi}{2V_m} = \\frac{120\\pi}{2\\times325.3} = \\frac{376.99}{650.6} = 0.5795"},{"type":"math","math":"\\alpha = \\cos^{-1}(0.5795) = 54.6^\\circ"},{"type":"paragraph","paragraph":"With R = 0 (ideal), the power delivered to load is purely to the back-EMF. Average current = 0 in ideal case (R = 0), but the problem implies continuous conduction with the inductor smoothing current. The real average current is limited by the small resistance; for calculation purposes with ideal components and continuous current:"},{"type":"math","math":"P = E \\cdot I_{avg}, \\quad pf = \\frac{P}{V_s I_{s,rms}} = \\frac{2\\cos\\alpha}{\\pi} \\cdot \\sqrt{2} \\approx 0.9\\cos\\alpha"},{"type":"math","math":"pf_1 = \\frac{2\\sqrt{2}}{\\pi}\\cos(54.6^\\circ) = 0.9\\times0.5795 = 0.521 \\text{ lagging}"},{"type":"paragraph","heading":"Case 2: E = -120 V","paragraph":"For regenerative operation (E negative, inverter mode):"},{"type":"math","math":"\\cos\\alpha = \\frac{-120\\pi}{2\\times325.3} = -0.5795"},{"type":"math","math":"\\alpha = \\cos^{-1}(-0.5795) = 125.4^\\circ"},{"type":"math","math":"pf_2 = \\frac{2\\sqrt{2}}{\\pi}|\\cos(125.4^\\circ)| = 0.9\\times0.5795 = 0.521 \\text{ (power flows from load to source)}"}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partc-q2","number":2,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Discuss the three-phase 6-pulse AC-DC converter with RL load. Sketch the input voltage, current and output voltage, current waveforms for delay angles of 45 degrees and 90 degrees."}],"answer":{"summary":"A three-phase 6-pulse fully controlled bridge converter produces an average output of (3√6/π)Vph·cosα; for α=45° partial inversion begins; for α=90° average output is zero.","explanation":[{"type":"paragraph","heading":"Three-Phase 6-Pulse Converter Operation","paragraph":"The three-phase fully controlled bridge has six SCRs (T1-T6), two per phase (one in upper group, one in lower group). SCRs fire at 60° intervals in the sequence T1, T2, T3, T4, T5, T6. At any instant, two SCRs conduct."},{"type":"paragraph","heading":"Average Output Voltage","paragraph":""},{"type":"math","math":"V_{dc} = \\frac{3\\sqrt{6}}{\\pi}V_{ph}\\cos\\alpha = \\frac{3\\sqrt{2}}{\\pi}V_{LL}\\cos\\alpha"},{"type":"paragraph","heading":"Waveforms at α = 45°","paragraph":"Each SCR fires 45° after its natural commutation point. The output voltage waveform consists of segments of line voltages, each 60° wide, with the active segment shifted by 45°. The average output is (3√2/π)VLL·cos45° = 0.675VLL. The output has noticeable ripple at 6× supply frequency."},{"type":"paragraph","heading":"Waveforms at α = 90°","paragraph":"Each SCR fires 90° after its natural commutation point. Vdc = 0 (equal positive and negative areas). The output voltage waveform has equal positive and negative excursions. The current remains positive (flows through the inductive load). The source current waveform is displaced by 90° relative to voltage, giving zero displacement power factor."},{"type":"list","items":["At α = 45°: Vdc = 0.675 VLL, ripple frequency = 6f, source current lags voltage by 45°.","At α = 90°: Vdc = 0, pf = 0 (purely reactive), still continuous current for highly inductive load.","For α > 90°: Vdc becomes negative (inverter operation, energy flows back to source).","Input current is a quasi-square wave with fundamental displaced by α from the corresponding phase voltage."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partc-q3","number":3,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Explain the construction, operation, and output waveforms of both boost and buck converters."}],"answer":{"summary":"Buck converter steps voltage down (Vo = D·Vin); boost converter steps it up (Vo = Vin/(1-D)). Both use an inductor to store and transfer energy controlled by a switching transistor.","explanation":[{"type":"paragraph","heading":"Buck Converter","paragraph":"Construction: Switch S (MOSFET), freewheeling diode D, inductor L, output capacitor C, load R. The input is higher than the output."},{"type":"paragraph","heading":"Buck Operation","paragraph":"Switch ON: Current flows through L to load; inductor stores energy; iL rises. Switch OFF: Inductor maintains current through freewheeling diode; iL falls."},{"type":"math","math":"V_o = D \\cdot V_{in}"},{"type":"paragraph","heading":"Buck Waveforms (Output Voltage Ripple)","paragraph":"The inductor current is a triangle wave between Imin and Imax. Output voltage ripple is ΔVo = ΔiL/(8fsC)."},{"type":"paragraph","heading":"Boost Converter","paragraph":"Construction: Inductor L in series with input, switch S from inductor node to ground, diode D forward to output, capacitor C and load R in parallel."},{"type":"paragraph","heading":"Boost Operation","paragraph":"Switch ON: Inductor charges from Vin; diode is reverse-biased; capacitor supplies load alone; iL rises. Switch OFF: Inductor + Vin combined forward-biases diode; energy transferred to output; iL falls."},{"type":"math","math":"V_o = \\frac{V_{in}}{1-D}"},{"type":"list","items":["Buck: Vo < Vin; D controls step-down ratio.","Boost: Vo > Vin; Vo → ∞ as D → 1 (limited by losses in practice).","Both achieve high efficiency (>90%) through reactive energy storage (no resistive loss).","Inductor current ripple: ΔiL = (Vin - Vo)·D/(fsL) for buck; ΔiL = Vin·D/(fsL) for boost."]}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partc-q4","number":4,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"A buck converter as shown in Figure (a) is working in steady state. The output voltage and the Inductor current can be assumed ripple-free. Figure (b) shows the inductor voltage VL during a complete switching interval. Assuming all devices are ideal, calculate the duty cycle of the buck converter."}],"answer":{"summary":"For a buck converter with a given inductor voltage waveform VL, the duty cycle D is determined from the volt-second balance condition: the positive and negative volt-second areas must be equal in steady state.","explanation":[{"type":"paragraph","heading":"Duty Cycle from Inductor Voltage Waveform","paragraph":"From the given Figure (b), the inductor voltage VL has two levels during the switching period T:"},{"type":"list","items":["During the ON interval (duration = DT): VL = Vin - Vo (positive)","During the OFF interval (duration = (1-D)T): VL = -Vo (negative)"]},{"type":"paragraph","heading":"Volt-Second Balance","paragraph":"In steady state, the net flux change in the inductor is zero, so the volt-second product must balance:"},{"type":"math","math":"(V_{in} - V_o)\\cdot DT + (-V_o)\\cdot(1-D)T = 0"},{"type":"math","math":"V_{in}\\cdot D - V_o\\cdot D - V_o + V_o\\cdot D = 0"},{"type":"math","math":"V_{in}\\cdot D = V_o"},{"type":"math","math":"D = \\frac{V_o}{V_{in}}"},{"type":"paragraph","paragraph":"From the voltage waveform in Figure (b), if the positive level is A volts for time t1 and negative level is -B volts for time t2 (where t1 + t2 = T), then: A·t1 = B·t2, giving D = t1/T = B/(A+B)."}]}},{"id":"rtu-ee-ec-eee-s4-power-electronics-2024-partc-q5","number":5,"marks":10,"tags":["Part C"],"text":[{"type":"paragraph","content":"Discuss the principle of working of a three-phase bridge inverter with an appropriate circuit diagram. Draw phase and line voltage waveform on the assumption that each thyristor conducts for 180 degrees and the resistive load is star-connected. The sequence of firing of various SCRs should also be indicated in the diagram."}],"answer":{"summary":"A three-phase bridge inverter has six SCRs firing every 60°; with 180° conduction and star-connected resistive load, the phase voltages are six-stepped waveforms and line voltages are 12-stepped waveforms.","explanation":[{"type":"paragraph","heading":"Three-Phase Bridge Inverter Circuit","paragraph":"Six SCRs (T1-T6) are arranged in a full bridge: T1, T3, T5 in the upper group (positive group) connected to +Vdc, and T4, T6, T2 in the lower group connected to 0. The DC supply is Vdc."},{"type":"paragraph","heading":"Firing Sequence","paragraph":"SCRs fire in the order T1→T2→T3→T4→T5→T6, each 60° apart. With 180° conduction, each SCR conducts for half the period. At any instant, three SCRs conduct."},{"type":"paragraph","heading":"Phase Voltage Waveform","paragraph":"With star-connected resistive load, the phase voltage (e.g., VAN) takes three levels: +2Vdc/3, +Vdc/3, 0, -Vdc/3, -2Vdc/3. This creates a six-step staircase waveform with period T."},{"type":"svg","svg":""},{"type":"paragraph","heading":"Line Voltage Waveform","paragraph":"The line voltage (e.g., VAB = VAN - VBN) is a 12-step approximation to a sine wave, taking values ±Vdc and ±Vdc/3. The RMS fundamental line voltage is:"},{"type":"math","math":"V_{line,1,rms} = \\frac{\\sqrt{6}}{\\pi}V_{dc}"},{"type":"list","items":["Firing sequence: T1(0°), T2(60°), T3(120°), T4(180°), T5(240°), T6(300°)","Upper group: T1 → phase A high, T3 → phase B high, T5 → phase C high","Lower group: T4 → phase A low, T6 → phase B low, T2 → phase C low","Lowest order harmonics are 5th and 7th (triplen harmonics absent in line voltages)"]}]}}]}],"loading":false,"error":null}}}

Q2Power Electronics

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Answer