Q: Three-phase dual converter structure A three-phase dual converter (for four-quadrant DC drive operation) is built using which pair of rectifier modules?

Introduction / Context: Dual converters provide reversible DC voltage and current for four-quadrant motor drives. They achieve this by pairing two controlled rectifier bridges so that the DC polarity can be reversed without reversing motor leads. Given Data / Assumptions: Need for both rectification and inversion in both current directions. Each bridge should be fully controlled to allow voltage reversal via firing angle control. Concept / Approach: Two fully controlled six-pulse bridges connected in antiparallel across the DC terminals allow the system to develop positive or negative average DC voltage with controlled current direction. Interbridge reactors or circulating-current control manage power flow between bridges. Step-by-Step Solution: Choose full converters → enable positive and negative V_dc by varying α.Connect antiparallel on the DC side → one bridge feeds in one polarity, the other in the opposite.Implement circulating-current or non-circulating control for safe operation. Verification / Alternative check: Drive textbooks depict dual converters explicitly as back-to-back fully controlled bridges (not semiconverters) to ensure full four-quadrant capability. Why Other Options Are Wrong: Semi-converters: Half-controlled bridges cannot provide symmetric bidirectional voltage control. Parallel connection: Does not reverse DC polarity and risks cross-conduction. Common Pitfalls: Confusing antiparallel (DC opposition) with paralleling on the AC side; the key is DC opposition for polarity reversal. Final Answer: two 3-phase full converters connected in antiparallel

Q: Understanding SCR surge current rating What does the surge current rating of an SCR specify?

Introduction / Context: SCR datasheets include a surge (overcurrent) rating that reflects the device’s ability to survive a single, short-duration current spike, such as during inrush at power-up or a transient fault, without permanent damage. Given Data / Assumptions: Surge is a short, high-magnitude, non-steady current event. Thermal capacity of the junction allows brief overloads if the integral of I^2 * dt stays within limits. Concept / Approach: The surge rating is defined for a non-repetitive event (often a half-sine current pulse of specified duration). Repetition would cause cumulative thermal stress and exceed safe junction temperature, so it is not a repetitive capability. Step-by-Step Solution: Identify surge waveform (e.g., half-sine for 10 ms).Consult I_TSM (non-repetitive surge current) rating in datasheet.Conclude: rating applies to single events, not cyclical occurrence. Verification / Alternative check: Manufacturers explicitly label I_TSM as non-repetitive and provide derating with case temperature and pulse width. Why Other Options Are Wrong: Repetitive: Not allowed; thermal accumulation would exceed limits. Both repetitive/non-repetitive: Overbroad and unsafe. With steady current together: Not the standard definition and can be misleading. Common Pitfalls: Using surge rating in design as if it were continuous or frequent—this leads to premature failure. Use RMS/average current ratings for steady operation. Final Answer: the maximum non-repetitive surge current in which the SCR can withstand

Q: What is a surge voltage? Choose the best description of a surge (impulse) voltage encountered in power and electronics systems.

Introduction / Context: Surge (or impulse) voltages arise from lightning, switching transients, or electrostatic discharge. Correctly characterizing their polarity and time scale is critical for selecting surge protective devices and insulation coordination. Given Data / Assumptions: Surges are brief events, typically microseconds to milliseconds. Amplitude can far exceed nominal system voltage. Both polarities are possible depending on source and coupling. Concept / Approach: Standards (e.g., 1.2/50 μs lightning impulse) define short rise time, short duration, and either polarity. Therefore, the most complete description must mention high magnitude, short duration, and bipolar possibility. Step-by-Step Solution: Assess duration → clearly very small relative to steady operation.Assess magnitude → significantly higher than normal line levels.Assess polarity → can be positive or negative based on event. Verification / Alternative check: Surge test waveforms used in EMC and insulation testing are generated with both positive and negative polarities to check equipment immunity. Why Other Options Are Wrong: Very long duration: Would describe an overvoltage swell, not a surge. Only positive: Incomplete; negative surges are common. Common Pitfalls: Confusing ‘‘surge’’ with long-duration overvoltage or undervoltage events; surge protection must address both polarities and fast edges. Final Answer: has very high magnitude and very small duration and can be positive or negative

Question 1

Forward conduction drop of a power diode When a silicon power diode conducts in the forward direction, what is the typical voltage drop across it?

Accepted Answer

Introduction / Context: Forward conduction voltage determines conduction loss and thermal load in rectifiers and power converters. Given Data / Assumptions: Silicon power diode operating at rated forward current (order of amperes to tens of amperes). Room to moderate junction temperatures. Concept / Approach: Silicon diodes exhibit a forward drop typically around 0.7–1.2 V depending on current and temperature. Power diodes at operating currents often show approximately 0.9–1.1 V forward drop. Values like 5 V, 20 V, or 50 V are characteristic of multiple series devices or totally different components. Step-by-Step Solution: Identify technology (silicon) and typical IF → choose about 1 V. Verification / Alternative check: Data sheets for power rectifiers list VF at rated IF in the 0.8–1.2 V range. Why Other Options Are Wrong: 5 V, 20 V, and 50 V are far above typical silicon junction forward drops and would imply multiple junctions or fault conditions. Common Pitfalls: Confusing VF of a single silicon diode with that of thyristors, IGBTs, or entire converter stages. Final Answer: 1 V

Question 2

RMS output voltage of a single-phase full-wave converter (M-2 connection) with R–L load For a single-phase full-wave controlled rectifier (M-2 connection) supplied by v(t) = Vm sin(ωt) and operating with continuous current into an R–L load, what is …

Accepted Answer

Introduction / Context: The RMS output voltage of a phase-controlled full-wave rectifier is needed for thermal ratings and ripple calculations. Unlike the average output, the RMS value depends on the square of the instantaneous waveform over its conduction intervals. Given Data / Assumptions: Input: v(t) = Vm sin(ωt). Full-wave, single-phase controlled rectifier (M-2 connection, two SCRs, center-tapped secondary equivalent). R–L load with continuous conduction; overlap neglected. Firing angle α (0 ≤ α ≤ π). Concept / Approach: With continuous current, the output follows the source magnitude during conduction windows: from α to π on the positive half and from π+α to 2π on the negative half (polarity corrected by rectification). RMS is computed from the square of the waveform over one full period, averaged, and square-rooted. Step-by-Step Solution: V_rms^2 = (1/2π) * [∫α^π (Vm^2 sin^2 θ) dθ + ∫{π+α}^{2π} (Vm^2 sin^2 θ) dθ].Because sin^2 is periodic, this equals (Vm^2/π) * ∫_α^π sin^2 θ dθ.Use sin^2 θ = (1 − cos 2θ)/2 → ∫_α^π sin^2 θ dθ = (π − α)/2 + (sin 2α)/4.Hence V_rms^2 = Vm^2 * [ (π − α)/(2π) + (sin 2α)/(4π) ].Therefore V_rms = Vm * sqrt( (π − α)/(2π) + (sin 2α)/(4π) ). Verification / Alternative check: For α = 0, V_rms = Vm/√2 (as expected for a full-wave rectified sine). For α → π, RMS tends to 0, consistent with vanishing conduction interval. Why Other Options Are Wrong: (b) and (c) are average or fundamental component relations, not true RMS of the chopped waveform; (d) omits the sin 2α term and overestimates RMS for intermediate α. Common Pitfalls: Mixing average and RMS expressions; forgetting to account for both conduction intervals in a full period. Final Answer: V_rms = Vm * sqrt( (π − α)/(2π) + (sin 2α)/(4π) )

Question 3

Thermal Ohm’s law analogy in power electronics In thermal analysis of electronic devices, the so-called ‘‘thermal Ohm’s law’’ is written as ΔT = P * R_th, where ΔT is the temperature rise, P is the power loss, and R_th is thermal resistance. In this…

Accepted Answer

Introduction / Context: Thermal modeling of electronics often borrows the language of electrical circuits. The relationship ΔT = P * R_th mirrors the familiar V = I * R, letting engineers use intuitive circuit methods to estimate heat flow and temperature rise in heat sinks, packages, and PCBs. Given Data / Assumptions: Thermal Ohm’s law: ΔT = P * R_th. Electrical Ohm’s law: V = I * R. R_th represents thermal resistance between two nodes (e.g., junction to ambient). Concept / Approach: Map each thermal quantity to an electrical counterpart so the forms of both laws coincide. The temperature difference plays the role of potential difference, power dissipation plays the role of current, and thermal resistance parallels electrical resistance. Step-by-Step Solution: Start from ΔT = P * R_th.Compare with V = I * R.Therefore, ΔT ↔ V, P ↔ I, and R_th ↔ R.So, temperature corresponds to voltage, and power loss corresponds to current. Verification / Alternative check: Heat flow rate Q_dot (watts) is analogous to electric current I (amperes). A larger power dissipation drives a larger ‘‘flow’’ of heat through a fixed thermal resistance, creating a larger temperature drop, just as higher current through a resistor creates a larger voltage drop. Why Other Options Are Wrong: Option B: Swaps the mapping and breaks the form of the law. Option C/D: Misassigns thermal resistance or mixes quantities inconsistently with ΔT = P * R_th. Common Pitfalls: Confusing absolute temperature with temperature rise; the analogy applies to differences (ΔT vs V), not absolute values. Also, thermal capacitance analogies are separate (for transients) and do not change the basic static mapping. Final Answer: V and I respectively of ohm's law

Question 4

Instantaneous negative output in a 3-phase full converter For a three-phase fully controlled bridge converter, under what condition can the instantaneous DC output voltage become negative (ignoring overlap), even though average output may be positiv…

Accepted Answer

Introduction / Context: Three-phase fully controlled converters select the highest instantaneous line-to-line source voltage pairs to appear across the DC terminals. While the average output voltage depends on the firing angle α, the instantaneous output can dip below zero for certain α, a key point when assessing commutation and freewheeling needs. Given Data / Assumptions: Six-pulse three-phase bridge, ideal supply, no overlap. Firing angle α referenced to natural commutation instants. Examining instantaneous v_o(t), not only the average V_dc. Concept / Approach: As α increases, the conduction shifts later in each 60° interval. Beyond α ≈ 60°, the selected line-to-line segment applied to the DC side can become negative for a portion of the cycle, creating negative instantaneous output voltage even when the average remains positive if α is below 90°. Step-by-Step Solution: For α ≤ 60°, each 60° segment applied is largely positive with respect to the DC polarity.For α > 60°, some applied line-to-line segments straddle zero crossings, producing intervals where v_o(t) < 0.Thus, the instantaneous output can be negative when α exceeds 60°. Verification / Alternative check: Standard converter waveforms show negative notches appearing in v_o(t) when α > 60°, while the average V_dc remains proportional to cos α and stays positive until α reaches 90°. Why Other Options Are Wrong: Less than 60°: Instantaneous negative portions are absent in the idealized no-overlap case. Less than 90° or more than 90°: These statements do not pinpoint the correct onset; negative instantaneous values begin just beyond 60°. Common Pitfalls: Confusing average negativity (α > 90°) with instantaneous negativity (α > 60°). These are distinct phenomena. Final Answer: firing angle is more than 60°

Question 5

Inverter topologies using coupled inductors Among common commutation-assisted inverter circuits, which uses magnetically coupled inductors for commutation energy transfer?

Accepted Answer

Introduction / Context: Classic thyristor inverters often require auxiliary commutation networks. The McMurray and McMurray–Bedford families are landmark designs that use inductors and capacitors to transfer energy for turn-off, sometimes employing coupled inductors to improve commutation and reduce device stress. Given Data / Assumptions: Considering historical thyristor inverter topologies. Focus on whether the circuit explicitly uses coupled (magnetically linked) inductors. Concept / Approach: The McMurray–Bedford variants introduced magnetically coupled commutation inductors to achieve efficient energy recovery and reliable device turn-off. The modified McMurray–Bedford half-bridge retains this coupled inductor concept with refinements. Step-by-Step Solution: Identify circuits known for coupled inductors → McMurray–Bedford half-bridge.Check modified variant → still employs coupled inductors for improved commutation.Therefore, both (b) and (c) use coupled inductors. Verification / Alternative check: Typical schematics show tightly coupled commutation chokes feeding capacitors to reverse-bias conducting thyristors and recover energy. Why Other Options Are Wrong: Option (a): The modified McMurray full bridge generally emphasizes capacitor-assisted commutation without the same hallmark coupled choke arrangement of the McMurray–Bedford variants. Common Pitfalls: Assuming all McMurray-type circuits use the same commutation parts. Details differ; coupled inductors are a signature of McMurray–Bedford implementations. Final Answer: Both (b) and (c)

Question 6

Definition of a series inverter In a basic series inverter used with thyristors, how are the commutating components positioned with respect to the load?

Accepted Answer

Introduction / Context: Series inverters employ a series RLC path driven alternately by SCRs so that resonant current reversals assist commutation. Understanding the placement of L and C relative to the load is essential for predicting current waveform and device stress. Given Data / Assumptions: Classic series inverter topology with two SCRs, one commutating capacitor, and an inductor. Idealized components and continuous resonant operation assumptions for explanation. Concept / Approach: In a series inverter, the load shares the same current as the commutation components because L and C are in the same series path. Resonance between L and C shapes a quasi-sinusoidal current that flows through the load during each half-cycle. Step-by-Step Solution: Identify the RLC loop → R (load), L, and C in series.Trigger SCR1 → current flows through the entire series path.Energy exchange between L and C reverses current to help turn off the conducting SCR. Verification / Alternative check: Time-domain analysis shows identical current through L, C, and the load, which is only possible if these elements are in series. Why Other Options Are Wrong: Parallel placement: Describes parallel or complementary inverters, not the series inverter class. Common Pitfalls: Confusing series inverter with parallel (or half-bridge) commutation topologies in which the capacitor can be across the load. Final Answer: the commutating elements L and C are in series with load

Question 7

Waveform quality vs. operating frequency in a series inverter In a thyristorized series inverter, what happens to the distortion of the output voltage waveform when the operating frequency is lower than the natural (damped) resonant frequency of the…

Accepted Answer

Introduction / Context: Series inverters exploit resonance to shape current and, via the load impedance, the output voltage. Matching or exceeding the natural frequency improves sinusoidality; driving well below resonance alters the charge/discharge intervals and increases distortion. Given Data / Assumptions: Series RLC branch sets a damped resonant frequency f_d. Inverter switches at an operating frequency f_o. Comparing cases where f_o < f_d. Concept / Approach: When f_o is less than f_d, the resonant current fully decays before the next switching event. The resulting piecewise waveform has pronounced dead intervals and sharp transitions, increasing harmonic content and thus distortion of the load voltage. Step-by-Step Solution: At f_o ≈ f_d, current waveforms are close to sinusoidal.Decrease f_o below f_d → extended decay and gaps between pulses.Voltage across the load reflects these discontinuities → higher THD and visible distortion. Verification / Alternative check: Fourier analysis of the pulsed, nonuniform conduction intervals shows stronger low-order harmonics when the inverter is driven significantly below resonance. Why Other Options Are Wrong: Low distortion claim: Opposite to behavior below resonance. ‘‘May be high or low’’: While load affects exact THD, the general tendency below resonance is increased distortion compared to near-resonant operation. Common Pitfalls: Assuming lower frequency automatically eases filtering; in resonant inverters, operation away from resonance can deteriorate waveform quality. Final Answer: the distortion of output voltage waveform is high

Question 8

Three-phase dual converter structure A three-phase dual converter (for four-quadrant DC drive operation) is built using which pair of rectifier modules?

Accepted Answer

Introduction / Context: Dual converters provide reversible DC voltage and current for four-quadrant motor drives. They achieve this by pairing two controlled rectifier bridges so that the DC polarity can be reversed without reversing motor leads. Given Data / Assumptions: Need for both rectification and inversion in both current directions. Each bridge should be fully controlled to allow voltage reversal via firing angle control. Concept / Approach: Two fully controlled six-pulse bridges connected in antiparallel across the DC terminals allow the system to develop positive or negative average DC voltage with controlled current direction. Interbridge reactors or circulating-current control manage power flow between bridges. Step-by-Step Solution: Choose full converters → enable positive and negative V_dc by varying α.Connect antiparallel on the DC side → one bridge feeds in one polarity, the other in the opposite.Implement circulating-current or non-circulating control for safe operation. Verification / Alternative check: Drive textbooks depict dual converters explicitly as back-to-back fully controlled bridges (not semiconverters) to ensure full four-quadrant capability. Why Other Options Are Wrong: Semi-converters: Half-controlled bridges cannot provide symmetric bidirectional voltage control. Parallel connection: Does not reverse DC polarity and risks cross-conduction. Common Pitfalls: Confusing antiparallel (DC opposition) with paralleling on the AC side; the key is DC opposition for polarity reversal. Final Answer: two 3-phase full converters connected in antiparallel

Question 9

Understanding SCR surge current rating What does the surge current rating of an SCR specify?

Accepted Answer

Introduction / Context: SCR datasheets include a surge (overcurrent) rating that reflects the device’s ability to survive a single, short-duration current spike, such as during inrush at power-up or a transient fault, without permanent damage. Given Data / Assumptions: Surge is a short, high-magnitude, non-steady current event. Thermal capacity of the junction allows brief overloads if the integral of I^2 * dt stays within limits. Concept / Approach: The surge rating is defined for a non-repetitive event (often a half-sine current pulse of specified duration). Repetition would cause cumulative thermal stress and exceed safe junction temperature, so it is not a repetitive capability. Step-by-Step Solution: Identify surge waveform (e.g., half-sine for 10 ms).Consult I_TSM (non-repetitive surge current) rating in datasheet.Conclude: rating applies to single events, not cyclical occurrence. Verification / Alternative check: Manufacturers explicitly label I_TSM as non-repetitive and provide derating with case temperature and pulse width. Why Other Options Are Wrong: Repetitive: Not allowed; thermal accumulation would exceed limits. Both repetitive/non-repetitive: Overbroad and unsafe. With steady current together: Not the standard definition and can be misleading. Common Pitfalls: Using surge rating in design as if it were continuous or frequent—this leads to premature failure. Use RMS/average current ratings for steady operation. Final Answer: the maximum non-repetitive surge current in which the SCR can withstand

Question 10

What is a surge voltage? Choose the best description of a surge (impulse) voltage encountered in power and electronics systems.

Accepted Answer

Introduction / Context: Surge (or impulse) voltages arise from lightning, switching transients, or electrostatic discharge. Correctly characterizing their polarity and time scale is critical for selecting surge protective devices and insulation coordination. Given Data / Assumptions: Surges are brief events, typically microseconds to milliseconds. Amplitude can far exceed nominal system voltage. Both polarities are possible depending on source and coupling. Concept / Approach: Standards (e.g., 1.2/50 μs lightning impulse) define short rise time, short duration, and either polarity. Therefore, the most complete description must mention high magnitude, short duration, and bipolar possibility. Step-by-Step Solution: Assess duration → clearly very small relative to steady operation.Assess magnitude → significantly higher than normal line levels.Assess polarity → can be positive or negative based on event. Verification / Alternative check: Surge test waveforms used in EMC and insulation testing are generated with both positive and negative polarities to check equipment immunity. Why Other Options Are Wrong: Very long duration: Would describe an overvoltage swell, not a surge. Only positive: Incomplete; negative surges are common. Common Pitfalls: Confusing ‘‘surge’’ with long-duration overvoltage or undervoltage events; surge protection must address both polarities and fast edges. Final Answer: has very high magnitude and very small duration and can be positive or negative

Question 11

Cycloconverter frequency reduction concept A bridge-type single-phase cycloconverter reduces the input frequency from f to f/3. During one half-cycle of the output (that is, one half-wave at f/3), how many half-waves of the input waveform are spanne…

Accepted Answer

Introduction / Context: Cycloconverters directly convert AC at one frequency to AC at a lower frequency without an intermediate DC link. Understanding the timing relationship between the input frequency and the synthesized output frequency is crucial for timing, gating logic, and harmonic analysis. Given Data / Assumptions: Single-phase bridge cycloconverter. Input frequency = f. Output frequency = f/3 (one-third of input). We consider one output half-cycle (one half-wave) at f/3. Concept / Approach: The period T of a waveform is the reciprocal of frequency. If the output frequency is f/3, then T_out = 1/(f/3) = 3 * (1/f) = 3 * T_in. An output half-cycle lasts T_out/2 = 3 * T_in / 2. Each input half-wave lasts T_in/2. Therefore, counting how many input half-waves fit inside one output half-cycle becomes a simple ratio problem. Step-by-Step Solution: Let T_in = 1/f and T_out = 3 * T_in.Duration of one output half-wave = T_out / 2 = 3 * T_in / 2.Duration of one input half-wave = T_in / 2.Number of input half-waves in one output half-wave = (3 * T_in / 2) / (T_in / 2) = 3.Thus, one output half-wave at f/3 spans three input half-waves. Verification / Alternative check: Another way: since the output frequency is one-third of input, every output cycle lasts three input cycles. A half-cycle of output is therefore one and a half input cycles, which equals three input half-cycles. Why Other Options Are Wrong: 3 full waves of input: that would be a full output cycle, not a half-cycle. 6 full waves or 6 half waves: overcounts the input segments for a single output half-cycle. 2 half waves: undercounts the required span. Common Pitfalls: Confusing cycles with half-cycles while converting frequencies. Forgetting that a bridge cycloconverter stitches selected input half-waves to synthesize the lower-frequency output. Final Answer: 3 half waves of input

Question 12

Turn-on energy loss of a power transistor with linear switching In the shown linear turn-on, voltage falls linearly from V to 0 while current rises linearly from 0 to I over time T. What is the switching energy lost during this interval?

Accepted Answer

Introduction / Context: Switching losses in power electronic devices occur during finite transition times when a device simultaneously supports nonzero voltage and current. Estimating these losses is key to heat-sinking, efficiency calculations, and safe operating area selection. A common textbook approximation assumes linear voltage and current transitions for quick, closed-form estimates. Given Data / Assumptions: Turn-on interval = T. Voltage across device v(t) decreases linearly from V to 0. Current through device i(t) increases linearly from 0 to I. Parasitics and nonidealities neglected beyond the linear approximation. Concept / Approach: Instantaneous switching power is p(t) = v(t) * i(t). With linear ramps, we can write simple expressions for v(t) and i(t), multiply them, and integrate over the transition time to obtain the turn-on energy. Step-by-Step Solution: Let v(t) = V * (1 − t/T), for 0 ≤ t ≤ T.Let i(t) = I * (t/T), for 0 ≤ t ≤ T.Instantaneous power: p(t) = v(t) * i(t) = V * I * (t/T) * (1 − t/T).Energy during turn-on: E_on = ∫_0^T p(t) dt = V * I * ∫_0^T (t/T − t^2/T^2) dt.Compute integrals: ∫_0^T t/T dt = (T/2), and ∫_0^T t^2/T^2 dt = (T/3).Therefore, E_on = V * I * (T/2 − T/3) = V * I * (T/6). Verification / Alternative check: Geometric method: the p(t) curve is a parabola peaking mid-interval. The average power over T equals the integral divided by T = (V * I)/6, giving the same energy E_on = (V * I)/6 * T. Why Other Options Are Wrong: V * I * T: ignores overlap shape; far too large. (1/2) VIT or (1/3) VIT: overestimates compared to the correct parabolic overlap. (1/12) VIT: underestimates by a factor of two. Common Pitfalls: Using a rectangular or triangular approximation without matching the specified linear rise/fall on both waveforms. Confusing turn-on and turn-off; formulas differ if the ramps differ. Final Answer: (1/6) * V * I * T

Question 13

Permissible dv/dt of an SCR (qualitative range) Typical values of the permissible rate of rise of anode–cathode voltage (dv/dt) for a standard silicon controlled rectifier are in which range (V/µs)?

Accepted Answer

Introduction / Context: SCRs can unintentionally turn on if the anode–cathode voltage rises too rapidly. This effect, known as dv/dt triggering, arises from the device’s junction capacitances. Manufacturers specify a maximum permissible dv/dt to ensure reliable blocking in off-state conditions. Given Data / Assumptions: “Typical values” refers to standard power SCRs (not special high-speed or snubberless variants). Ambient and junction temperatures are moderate; device is within datasheet operating limits. Concept / Approach: In off-state, capacitances across junctions translate a fast dv/dt into displacement current through the gate junction, which can mimic a gate trigger. The dv/dt rating represents how quickly the applied voltage may rise without causing spurious turn-on. Step-by-Step Solution: Identify the order of magnitude for common SCRs: a few tens to a few hundred V/µs.Associate options with known datasheet ranges: 25–500 V/µs is widely cited for general devices.Select the closest qualitative range: 25 to 500 V/µs. Verification / Alternative check: Check typical datasheets for industrial SCRs; standard dv/dt ratings commonly lie within tens to hundreds of V/µs unless special snubberless or high-performance devices are used. Why Other Options Are Wrong: 0.1–1 or 1–10 V/µs: far too conservative for most standard SCRs. 1000–2000 V/µs or higher: characteristic of special devices, not typical SCRs. Common Pitfalls: Ignoring temperature and gate-cathode conditions; dv/dt susceptibility increases with temperature and floating gates. Omitting snubbers where needed; RC snubbers are often used to limit dv/dt. Final Answer: 25 to 500

Question 14

Ripple in inductor current of a DC chopper feeding an R–L–E load For a step-down chopper with duty ratio a (0 < a < 1) supplying an R–L–E load, at which value of a is the steady-state inductor current ripple maximized?

Accepted Answer

Introduction / Context: In chopper (DC–DC) converters, inductor current ripple is a key design parameter influencing current stress, output voltage ripple (through R drop), and EMI. For a fixed switching period and input voltage, current ripple varies with the duty ratio a. Given Data / Assumptions: Ideal step-down (buck) chopper behavior for ripple estimation. Switching period T_s fixed; inductor L constant. R–L–E load; effect of E and R on average current is not needed for locating the ripple maximum. Concept / Approach: Over one switching period, the inductor voltage is approximately: during ON, v_L(on) ≈ V_in − V_o; during OFF, v_L(off) ≈ −V_o (neglect device drops). For a buck, V_o ≈ a * V_in in steady state. The triangular ripple amplitude ΔI is proportional to the area under v_L/L in each subinterval. Step-by-Step Solution: Let ΔI_up = (V_in − V_o) * (a * T_s) / L = (V_in − aV_in) * aT_s / L = V_in * a(1 − a) * T_s / L.Let ΔI_down = |v_L(off)| * ((1 − a) T_s) / L = V_o * (1 − a) T_s / L = V_in * a(1 − a) * T_s / L.Net peak-to-peak ripple ΔI = ΔI_up = ΔI_down = V_in * a(1 − a) * T_s / L.The factor a(1 − a) is maximized at a = 0.5, giving maximum ripple. Verification / Alternative check: The parabola a(1 − a) has its vertex at a = 0.5 with value 0.25, confirming the maximum ripple occurs at 50% duty. Why Other Options Are Wrong: a = 1 or a → 0: ripple tends to zero as the inductor sees nearly constant voltage or zero output. a = 0.8 or a < 0.5: ripple is non-maximal except at exactly 0.5. Common Pitfalls: Confusing current ripple with output voltage ripple; though related, their maxima can differ with nonidealities. Forgetting that device drops slightly skew the symmetry; however, the maximum remains near a ≈ 0.5. Final Answer: a = 0.5

Question 15

Assertion–Reason on DIAC structure and conduction Assertion (A): A DIAC has four semiconductor layers but only two external terminals. Reason (R): A DIAC conducts in both directions (it is a bilateral trigger device).

Accepted Answer

Introduction / Context: DIACs (diode for alternating current) are two-terminal trigger devices used to symmetrize TRIAC firing and to generate consistent breakover behavior in either polarity. Their internal structure explains both their two-terminal nature and their bidirectional conduction. Given Data / Assumptions: DIAC: four-layer, two-terminal device (often PNPN symmetrical). Breakover occurs at approximately the same magnitude in either polarity. No gate terminal exists; conduction is controlled by applied voltage magnitude. Concept / Approach: The DIAC’s symmetrical four-layer construction produces similar breakover characteristics for positive and negative voltages. Because it is bilateral, it uses only two terminals, and its behavior does not depend on polarity (apart from small asymmetries). This bilateral conduction is the essential reason that only two terminals are needed despite four layers. Step-by-Step Solution: Assess A: “Four layers but two terminals” is a factual description of DIAC construction—true.Assess R: “Conducts in both directions” is also true.Does R explain A? Yes; bilateral conduction arises from a symmetrical multilayer structure that does not require separate anode/cathode designation, hence only two terminals. Verification / Alternative check: Component datasheets and application notes show DIACs as two-terminal symmetrical PNPN devices with essentially equal positive/negative breakover voltages. Why Other Options Are Wrong: B: Splits the truths but denies the explanatory link; however, symmetry and bilateral action are exactly why the device is two-terminal. C/D/E: contradict established device structure and operation. Common Pitfalls: Confusing DIAC (no gate) with TRIAC (three terminals, bidirectional controlled device). Assuming four layers always imply three terminals like SCRs; symmetry changes terminal count. Final Answer: Both A and R are correct and R is correct explanation of A

Question 16

Basic capability of a step-up (boost) chopper What output–input voltage relationship does an ideal step-up (boost) DC chopper provide in steady state?

Accepted Answer

Introduction / Context: DC–DC choppers change the average DC voltage level. The step-up (boost) converter is widely used in regulated power supplies, electric vehicles, and renewable interfaces when the required output DC voltage must exceed the available input. Given Data / Assumptions: Ideal components for conceptual understanding. Continuous conduction mode behavior. Neglecting device drops and losses. Concept / Approach: In a boost converter, during the ON interval the inductor stores energy from the source. During the OFF interval, the inductor releases energy to the load through the diode, adding to the source voltage. This stacking effect produces an output average greater than the input average. Step-by-Step Solution: Boost steady-state relation: V_out = V_in / (1 − D), where D is the duty ratio (0 < D < 1).Since 1 − D < 1, division by a number < 1 gives V_out > V_in.Therefore, the output is higher than the input for any nonzero duty ratio. Verification / Alternative check: Example: D = 0.5 → V_out = V_in / 0.5 = 2 * V_in, clearly higher than the input. Why Other Options Are Wrong: Lower or equal output corresponds to buck or unity-gain behavior, not boost. “Both higher and lower” or “all of the above” would fit buck-boost or SEPIC, not a pure boost topology. Common Pitfalls: Mixing boost with buck-boost, which can invert and change magnitude in both directions. Ignoring the effect of losses; in practice V_out is slightly less than the ideal expression due to drops. Final Answer: higher than input voltage

Question 17

Symmetry of firing angles in a single-phase full-wave AC regulator In a single-phase full-wave AC voltage controller (regulator), are the firing angles in the positive and negative half-cycles kept equal for normal operation?

Accepted Answer

Introduction / Context: AC regulators control the RMS value of the load voltage by delaying the firing of antiparallel SCRs in each half-cycle. To avoid DC components and ensure symmetrical waveforms, firing angles are typically chosen to be the same in both polarities. Given Data / Assumptions: Single-phase full-wave regulator with two antiparallel thyristors. Goal is to control RMS voltage without introducing DC offset. Normal symmetrical firing strategy. Concept / Approach: If the firing angles differ between the positive and negative half-cycles, the average value of the load voltage becomes nonzero (introducing a DC component). This can saturate transformers, increase EMI, and stress devices. Hence, equal firing angles are maintained for symmetry and minimal DC offset. Step-by-Step Solution: Define α+ for the positive half-cycle and α− for the negative half-cycle.Set α+ = α− → symmetrical conduction windows → zero average (no DC component).Therefore, standard operation keeps equal firing angles in both half-cycles. Verification / Alternative check: Textbook waveforms for full-wave AC regulators show mirrored conduction intervals about the zero axis when α is the same in both halves. Why Other Options Are Wrong: False or 90° difference: would deliberately introduce asymmetry and unwanted DC. Unity power factor or purely resistive caveats are unnecessary; symmetry is desired across many load types, though current waveforms vary with load. Common Pitfalls: Assuming different α helps power factor; it generally harms waveform quality. Final Answer: True

Question 18

Equalizing networks for series-connected thyristors Why is an equalizing network required when thyristors are connected in series for high-voltage applications?

Accepted Answer

Introduction / Context: To withstand high voltages, multiple thyristors are often connected in series. However, device parameter tolerances cause unequal blocking voltage distribution, risking over-voltage on a single device. Equalizing networks mitigate this risk. Given Data / Assumptions: Series string of SCRs used for high DC or AC blocking. Devices exhibit tolerances in leakage current, junction capacitances, and recovery behavior. We consider both steady-state and transient conditions. Concept / Approach: Static equalizing resistors help share DC (steady-state) blocking voltage by equalizing leakage currents. Dynamic equalizing capacitors (often with resistors) help share transient voltages during switching, countering dv/dt differences and recovery disparities. Step-by-Step Solution: Problem: Without equalization, the device with lowest leakage or different capacitance may block a disproportionate voltage.Remedy: Add parallel resistors across each SCR for static sharing and RC snubbers for dynamic sharing.Outcome: Each device sees approximately its designed portion of the total voltage, improving reliability. Verification / Alternative check: Waveform measurements across devices with and without equalizing networks show reduced voltage imbalance and lower over-voltage spikes when networks are used. Why Other Options Are Wrong: Proper firing is controlled by gate drive timing and magnitude, not by equalizing networks. Current division pertains to parallel connections; series strings need voltage, not current equalization. “None” ignores the well-established engineering practice. Common Pitfalls: Using only resistors and neglecting dynamic sharing; both static and dynamic effects matter. Assuming perfectly matched devices; real components vary. Final Answer: ensure proper voltage division

Question 19

Multiphase choppers in power electronics Where are multiphase (interleaved) choppers primarily employed to improve performance such as reduced ripple and shared device stress?

Accepted Answer

Introduction / Context: Multiphase (interleaved) choppers are DC–DC converters that split total power among two or more identical phases. This architecture is common in traction drives, HVDC auxiliaries, DC microgrids, and server/VLSI supplies when power levels are significant. The question checks where such choppers are mainly used from a practical engineering standpoint. Given Data / Assumptions: Multiple converter legs operate with phase-shifted gating. Goal is to reduce input/output ripple and distribute current/thermal stress. Application context is general power conversion (not a specific numeric case). Concept / Approach: By interleaving N phases, the effective ripple frequency seen at the input and output is multiplied, so for a given filter size ripple drops markedly. Also, average current per device is reduced by about 1/N, easing conduction and thermal stress. These benefits are most valuable where power is large and single-device stress or filter size would otherwise be excessive. Step-by-Step Solution: Identify main advantages: reduced ripple, better thermal distribution, fault tolerance.Map advantages to application class: these matter most as power increases.Conclude primary usage: high power circuit environments benefit the most. Verification / Alternative check: Industry designs (traction DC links, telecom rectifiers, large point-of-load modules) routinely interleave phases precisely to meet stringent ripple and thermal constraints at high power. Why Other Options Are Wrong: Low or merely medium power can use single-phase topologies with simpler magnetics; benefits are smaller. Saying “both low and high” dilutes the fact that primary motivation is high power. Common Pitfalls: Assuming interleaving is only for small-voltage CPUs; the concept scales and is crucial at high power for magnetics and thermal management. Final Answer: high power circuit

Question 20

Three-phase full converter with highly inductive load A 3-phase full converter feeds a highly inductive (continuous current) load with an average load current of 150 A. What is the peak current through each thyristor device?

Accepted Answer

Introduction / Context: In a three-phase full-controlled bridge (six-pulse) converter with a highly inductive load, current is nearly constant and continuous. Each thyristor conducts for 120 electrical degrees carrying the same magnitude as the DC load current during its conduction interval. This question tests understanding of device current in continuous conduction. Given Data / Assumptions: Converter: 3-phase full bridge, six SCRs. Load: highly inductive, thus current ripple is small and continuous. Average load current I_load,avg = 150 A. Concept / Approach: With continuous current, the DC link current equals the instantaneous device current whenever a device conducts. Each SCR pair conducts 120°, and current commutates from one device to the next without significant overlap (idealized). Therefore, the instantaneous (and hence peak) current in any conducting thyristor equals the DC load current. Step-by-Step Solution: Recognize continuous conduction: i_dc approximately constant.During its 120° interval, each SCR carries i_device = i_dc.Given i_dc ≈ 150 A → i_peak,thyristor = 150 A. Verification / Alternative check: Circuit waveforms from standard analyses show flat device current pulses of width 120° at the DC current level for high inductance loads. Why Other Options Are Wrong: 75 A or 50 A imply sharing between parallel devices in one arm, which does not occur; 300 A suggests both devices in series carry doubled current, which is incorrect. Common Pitfalls: Confusing RMS with peak; in this idealized case, peak equals the DC level because the waveform is nearly flat during conduction. Final Answer: 150 A

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