Q: Half-wave rectifier (ideal diode): Given an input of v(t) = 20 sin(ωt) volts, determine the average (DC) value and the root-mean-square (rms) value of the output voltage.

Introduction / Context: Half-wave rectifiers pass only one half-cycle of a sinusoid. For an ideal diode, the negative half is completely blocked, leading to standard formulae for the average (DC) and rms output values. This problem reinforces those results for a specific amplitude. Given Data / Assumptions: Input: v(t) = V_m sin(ωt) with V_m = 20 V. Ideal diode (no drop), pure half-wave rectification. Output taken across the load directly. Concept / Approach: For an ideal half-wave rectifier: V_avg = V_m/π and V_rms = V_m/2. These come from integrating the rectified waveform over a full period, remembering that the second half of the cycle is zero. Step-by-Step Solution: V_avg = V_m / π = 20 / π ≈ 6.366 V → ≈ 6.37 V.V_rms = V_m / 2 = 20 / 2 = 10 V. Verification / Alternative check: Compute rms from definition: V_rms^2 = (1/2π) ∫0→π (V_m sinθ)^2 dθ = V_m^2/4 → V_rms = V_m/2, confirming 10 V. Why Other Options Are Wrong: Options listing 5 V for average or rms contradict standard half-wave results. Average of 10 V implies full-wave or different amplitude. Values like 14.14 V correspond to V_m/√2 of an unrectified sine, not a half-wave output. Common Pitfalls: Forgetting the average is over the full period, not just the conducting half. Confusing full-wave with half-wave formulae. Final Answer: V_avg ≈ 6.37 V and V_rms = 10 V

Q: Negative feedback and noise: Determine whether the statement “Negative feedback reduces noise originating at the amplifier input” is correct in the context of linear feedback amplifiers.

Introduction / Context: Negative feedback is used to stabilize gain, extend bandwidth, and reduce distortion in amplifiers. Its effect on noise depends on where the noise originates. This item probes whether feedback specifically suppresses input-source noise. Given Data / Assumptions: Linear voltage-series feedback topology typical of audio and instrumentation amplifiers. “Noise originating at the amplifier input” means noise coming from the signal source or input resistor, added in series with the intended signal. Concept / Approach: Negative feedback divides the closed-loop gain by approximately (1 + loop gain). Both the desired signal and any input-referred noise from the source are amplified by the same closed-loop gain; thus the output signal-to-noise ratio due to input noise is not inherently improved by feedback. Feedback can reduce the contribution of internal amplifier noise (e.g., output-referred disturbances) by the factor of the loop gain, but it does not preferentially suppress noise that is indistinguishable from the input signal. Step-by-Step Solution: Model output = A_cl * (signal + input_noise) + reduced internal noise / (1 + loop gain).Because signal and input_noise are both scaled by A_cl, their ratio is unchanged.Therefore the statement that negative feedback reduces input-originated noise is false. Verification / Alternative check: Closed-loop noise analysis shows source noise remains unchanged in input-referred form; only amplifier-generated noise is suppressed by feedback. Why Other Options Are Wrong: Options asserting “True” ignore that feedback treats input signal and source noise equally. Topology-dependent statements do not change this fundamental point. Common Pitfalls: Confusing reduction of internal noise and distortion with reduction of source noise. Final Answer: False

Q: Oscillator selection by frequency range: Which oscillator topology is most suitable for generating signals in the megahertz (MHz) range?

Introduction / Context: Different oscillator types employ different frequency-selective networks. RC oscillators are generally preferred for audio to low-RF, while LC oscillators excel at radio frequencies. The question asks which topology is suitable in the MHz range without invoking crystals. Given Data / Assumptions: Target frequency in the MHz range (say 1–30 MHz). Standard, free-running analog oscillator topologies. Concept / Approach: RC phase-shift and Wien bridge oscillators rely on RC networks whose component values become inconvenient and lossy at high frequencies. LC resonant circuits (inductors and capacitors) provide higher Q and ease of tuning at MHz; Hartley (and Colpitts) are classical RF oscillators designed for this regime. Step-by-Step Solution: Identify MHz regime → prefer LC resonance for adequate Q.Hartley uses tapped inductor (or two inductors) + capacitor → well suited for MHz.Therefore, the most appropriate choice is the Hartley oscillator. Verification / Alternative check: Practical radios and RF signal generators widely use Hartley/Colpitts at HF/VHF; RC oscillators are usually limited to < 1 MHz (Wien bridge often in audio-LF range). Why Other Options Are Wrong: RC phase-shift and Wien bridge: typically low-frequency; component parasitics limit MHz use. “Both (a) and (c)” is incorrect since RC phase-shift is not ideal for MHz. Crystals are excellent in MHz but overly restrictive to a single option not offered in the set-up; the question compares common generic topologies. Common Pitfalls: Assuming any RC oscillator can be scaled indefinitely; parasitics and required gain become impractical at high frequency. Final Answer: Hartley oscillator (LC)

Q: Conduction angle recognition: In Class C operation of a transistor power amplifier, the collector current flows for what portion of the input signal cycle?

Introduction / Context: Amplifier classes are categorized by conduction angle—how long the active device conducts current during one cycle of a sinusoidal input. Class C is commonly used in RF transmitters with tuned loads to obtain high efficiency at the cost of linearity. Given Data / Assumptions: Sinusoidal drive applied to a biased transistor stage. Standard class definitions: A (360°), B (180°), AB (>180° but <360°), C (<180°). Concept / Approach: In Class C, the bias point is set below cutoff so the device conducts only around the peaks of the input waveform, for a conduction angle strictly less than 180°. A resonant load network reconstructs a sinusoidal output from these narrow current pulses. Step-by-Step Solution: Identify class definition → Class C conduction angle < 180°.Therefore, the correct statement is that current exists for less than half of the cycle. Verification / Alternative check: Typical Class C conduction ranges between 60° and 120°, depending on the desired efficiency and distortion acceptable before the tank circuit filters harmonics. Why Other Options Are Wrong: 360° corresponds to Class A. 180° corresponds to ideal Class B. More than 180° corresponds to Class AB. “Exactly 120°” is not a definition, only an example. Common Pitfalls: Confusing the conduction angle definition with the harmonic content at the output of a tuned circuit. Final Answer: less than 180° of the input wave

Q: Assertion–Reason on large-signal analysis: For large signal variations an amplifier circuit must often be analysed graphically because the transistor output characteristics are nonlinear. Evaluate the statements.

Introduction / Context: Amplifier analysis can be categorized as small-signal (around a bias point) or large-signal (where the device traverses a wide portion of its characteristics). This question examines why graphical methods such as load-line analysis are used for large-signal cases. Given Data / Assumptions: Transistor output characteristics are inherently nonlinear outside a very small region. Large excursions drive the operating point across curved portions of the characteristics. Concept / Approach: Small-signal linearization uses slopes at the bias point and works only for small variations. For large signals, linear approximations break down; therefore, plotting the DC load line and using the family of I–V curves (graphical method) captures the device behavior across the entire swing, including cutoff and saturation. Step-by-Step Solution: Assess Assertion (A): Large-signal analysis often requires graphical treatment → True.Assess Reason (R): Transistor characteristics are nonlinear → True.Causality: Nonlinearity is precisely why linear small-signal equations fail, thus R explains A. Verification / Alternative check: Practical amplifier design for power stages routinely employs load-line plots and transfer curves to predict clipping, saturation, and distortion—confirming the reasoning. Why Other Options Are Wrong: Any option denying A or R conflicts with standard device physics and design practice. Common Pitfalls: Attempting to use small-signal parameters (re, h-parameters) for large excursions; these are valid only near the quiescent point. Final Answer: Both A and R are correct and R is correct explanation for A

Q: Consider the active filter shown (an operational-amplifier based network). Evaluate the following claims about the filter: (1) it is an active low-pass filter, (2) it is second order, and (3) its magnitude slope changes by 40 dB per decade beyond cu…

Introduction / Context: Active filters employ operational amplifiers with resistors and capacitors to realize frequency-selective responses without using inductors. A classic low-pass topology (such as Sallen–Key or multiple-feedback) provides a second-order transfer function, giving a −40 dB/decade roll-off in the stopband. This question checks your ability to match qualitative statements to a standard active low-pass response. Given Data / Assumptions: The depicted circuit is a common op-amp active filter topology. Component choices yield a low-pass response (DC gain finite, high-frequency attenuation). Order is determined by the highest power of s in the denominator (two reactive elements ⇒ second order). Concept / Approach: A second-order low-pass filter has transfer function magnitude that is flat near DC (passband), transitions around the natural frequency or cutoff, and then attenuates with a slope of 40 dB/decade (12 dB/octave) as frequency increases past the corner. Whether implemented by Sallen–Key or multiple-feedback, two capacitors (or two independent energy storage elements) confirm the second order. Step-by-Step Solution: Identify passband behavior: unity or set gain at low frequency ⇒ low-pass.Count energy storage elements: two reactive components ⇒ second order.Apply asymptotic Bode slope: second order ⇒ −40 dB/decade beyond the cutoff. Verification / Alternative check: Plot a Bode magnitude sketch: 0 dB slope in passband, then −40 dB/decade after ωc, confirming (1), (2), (3). Why Other Options Are Wrong: Any option omitting one of the three statements contradicts the standard second-order low-pass characteristics. Common Pitfalls: Confusing second-order low-pass (−40 dB/dec) with first-order (−20 dB/dec); misidentifying a high-pass due to capacitor placement without analyzing the transfer function. Final Answer: 1, 2 and 3

Q: In a common-emitter (CE) amplifier, the quiescent collector current I_C and collector-to-emitter voltage V_CE are defined as the values measured under which signal condition?

Introduction / Context: The quiescent (Q-point) defines the DC operating state of a transistor amplifier in the absence of any applied time-varying signal. It is the reference around which the signal swings occur, ensuring linear amplification with minimal distortion if properly placed on the load line. Given Data / Assumptions: CE amplifier with some biasing network setting base current. No input AC applied when defining quiescent values. Supply voltage and resistors fix the nominal operating point. Concept / Approach: By definition, the quiescent state is the steady DC condition: I_C = I_CQ and V_CE = V_CEQ with the input signal set to zero. Small signals then cause symmetric excursions about this point. Using 'very low amplitude' is not the formal definition; it may approximate the quiescent behavior but is not exact. Negative half-cycle only is irrelevant to defining a DC state. Step-by-Step Solution: Set AC source = 0 (short for AC analysis; no time-varying input).Solve DC bias network for base current, then collector current I_CQ.Compute V_CEQ from supply and voltage drops across resistors and transistor.This pair (I_CQ, V_CEQ) is the Q-point. Verification / Alternative check: Load-line method: intersection of transistor characteristic (at chosen base bias) and the collector resistor line gives the quiescent values. Why Other Options Are Wrong: 'Very low signal' is not a definition; it is an approximation. 'Negative half-cycle' has no role in DC definition. 'Either (a) or (b)' dilutes the precise definition. Common Pitfalls: Trying to define the Q-point during signal swing; mixing small-signal incremental analysis with the DC operating point. Final Answer: When the AC input signal is zero (no signal condition)

Q: Large input with symmetrical clipping at both peaks: What is the approximate output waveform shape of an amplifier when a large AC input causes equal clipping on both positive and negative peaks?

Introduction / Context: When an amplifier is overdriven, its output voltage cannot exceed the supply headroom and device limits. The tops and bottoms of the waveform flatten—this is clipping. Understanding the limiting waveform helps predict harmonic content and power dissipation in power electronics and audio systems. Given Data / Assumptions: AC input amplitude is large enough to drive the stage into saturation and cutoff on alternate half-cycles. Clipping is symmetrical (both peaks clipped by roughly the same amount). The stage is otherwise linear in its central region. Concept / Approach: With equal positive and negative clipping, the output transitions quickly between two plateau levels set by the rails and spends little time in the linear mid-region. As the drive increases further, the flat segments dominate. The limiting shape approaches a square wave whose amplitude equals the saturation headroom limits of the stage. Step-by-Step Solution: Start with a sinusoid at moderate level → undistorted sine.Increase drive → tops/bottoms flatten because of rail limits.At strong overdrive, waveform spends most of the period at +Vsat and −Vsat with fast transitions, i.e., a square wave. Verification / Alternative check: Fourier analysis: severe symmetrical clipping produces strong odd harmonics, which is characteristic of square waves, confirming the qualitative prediction. Why Other Options Are Wrong: Sine wave: only when not clipped. Triangular wave: arises from slew-rate limiting, not rail clipping. Other listed shapes do not match symmetrical hard-limiting behavior. Common Pitfalls: Confusing slew-rate limiting (triangle) with clipping (flat tops). Assuming asymmetrical biasing; the prompt states both peaks clip. Final Answer: Square wave.

Q: Negative feedback stabilisation: An amplifier with open-loop gain A = −1000 and feedback factor β = −0.1 experiences a 20% change in A due to temperature. What is the approximate percentage change in the closed-loop gain?

Introduction / Context: One of the most powerful benefits of negative feedback is gain desensitisation: the closed-loop gain varies far less than the open-loop gain. This problem quantifies that effect for a realistic loop gain. Given Data / Assumptions: Open-loop gain A = −1000. Feedback factor β = −0.1. Open-loop gain change ΔA/A = 20% = 0.20 (due to temperature). Concept / Approach: Closed-loop gain for negative feedback: Af = A / (1 + Aβ). Sensitivity S of Af to A is S = (ΔAf/Af) / (ΔA/A) = 1 / (1 + Aβ). Hence the percentage change in closed-loop gain equals (ΔA/A) * 1/(1 + Aβ). Step-by-Step Solution: Compute loop gain: Aβ = (−1000) * (−0.1) = +100.Sensitivity: S = 1 / (1 + 100) = 1/101 ≈ 0.00990.Closed-loop percentage change: 0.20 * 0.00990 ≈ 0.0198 ≈ 1.98% of 1 → 0.198% ≈ 0.2%. Verification / Alternative check: Direct computation: Af nominal = −1000/101 ≈ −9.901. If A increases 20% to −1200, Af = −1200/ (1 − 1200*0.1) = −1200/ (−119) ≈ 10.084 in magnitude; change relative ≈ (10.084 − 9.901)/9.901 ≈ 1.85% → ~0.19, consistent with 0.2% rounding. Why Other Options Are Wrong: 5% or 10% would imply very small loop gain. 0.01% would require loop gain ≈ 20,000. 2% is one order larger than the predicted desensitised change. Common Pitfalls: Using Af ≈ 1/β without checking sign and magnitude; while numerically close here, the sensitivity must still be computed with (1 + Aβ). Final Answer: 0.2%.

Q: Protecting diodes in a rectifier with a capacitor-input filter: Which component is typically inserted to limit the inrush and peak currents and thereby protect the rectifier diodes?

Introduction / Context: Capacitor-input (C-filter) rectifiers draw very high current pulses when the input sine peaks exceed the capacitor voltage. These brief but large surge currents stress rectifier diodes and transformer windings. Designers add impedance to limit surge and extend diode life. Given Data / Assumptions: Single-phase rectifier feeding a large reservoir capacitor. Goal: reduce peak repetitive current and initial inrush at power-up. Concept / Approach: A small series resistance in the AC path limits di/dt and peak current during the short conduction angle. This “surge resistor” (sometimes NTC inrush limiter) is the simplest, most common, and predictable solution. Although a choke (inductor) can also limit current, a true choke-input filter changes the operating mode and requires a sufficiently large inductance to maintain continuous current; it is not what is “necessary” for a capacitor-input filter dedicated only to diode protection. Step-by-Step Solution: Place a modest series resistor in the secondary (or primary) path.Select value to cap Ipeak below diode rating while keeping ripple/voltage drop acceptable.Optionally, use an NTC thermistor which is high resistance cold (limiting inrush) and low resistance hot (reducing losses). Verification / Alternative check: Simulate with and without a series resistor: peak current waveform amplitude reduces substantially, diode junction temperature and transformer copper loss also reduce. Why Other Options Are Wrong: Series inductor: can work, but not typically required for a capacitor-input design devoted solely to diode protection; it transforms the filter style. Surge capacitor across secondary: increases current spikes; not protective. Both (a) and (b): overstates what is necessary; a resistor alone suffices in common designs. Common Pitfalls: Placing a capacitor across the transformer in hopes of “smoothing” actually raises reactive currents. Final Answer: Surge (series) resistor.

Question 1

Power amplifier classes: For a given supply and proper loading, which amplifier class can deliver the maximum average load power under linear operation—Class A, Class AB, Class B, or Class C?

Accepted Answer

Introduction / Context: Power amplifier classes (A, AB, B, C) are defined by the conduction angle of the output device and strongly influence efficiency and the maximum undistorted power delivered to the load. This question checks recognition of which conventional linear class (excluding switching Class D) can deliver the most average load power for a given supply voltage and load. Given Data / Assumptions: Amplifier operates in its intended linear region (not clipping). Supply voltage and load impedance are fixed and identical for each class. Comparison among traditional linear classes A, AB, B, C. Concept / Approach: Class A conducts 360°, is very linear but wastes headroom; its theoretical efficiency is 25% to 50% depending on configuration, so the maximum deliverable power is limited. Class B conducts 180° per device in a push-pull stage, allowing the output to swing nearly the full supply across the load with no standing current, achieving a theoretical efficiency of ~78.5% and the largest undistorted output swing among the linear classes. Class AB is a compromise between A and B with some conduction overlap; its maximum power is close to but slightly less than ideal Class B. Class C conducts less than 180°, is non-linear and intended for tuned RF loads; average power at audio/untuned loads is not maximized. Step-by-Step Solution: Identify which class allows the largest output swing with minimum DC loss → Class B push-pull.Compare efficiencies (indicative of deliverable power): Class A < Class AB < Class B; Class C is non-linear for tuned RF only.Hence, for a given supply and load, Class B delivers the highest average load power among linear classes. Verification / Alternative check: Textbook results show Pout,max ∝ V2/R with the largest coefficient for Class B due to near-rail voltage swing and zero quiescent loss at ideal conditions, confirming the selection. Why Other Options Are Wrong: Class A: limited by large quiescent dissipation. Class AB: improved over A but not as high as ideal B. Class C: suited to resonant RF; not a general maximum-power linear stage. Class D: a switching class not listed in the original comparison; excluded by the linear-operation context. Common Pitfalls: Confusing highest efficiency with highest fidelity—Class B is efficient but requires crossover-distortion management. Final Answer: Class B

Question 2

Half-wave rectifier (ideal diode): Given an input of v(t) = 20 sin(ωt) volts, determine the average (DC) value and the root-mean-square (rms) value of the output voltage.

Accepted Answer

Introduction / Context: Half-wave rectifiers pass only one half-cycle of a sinusoid. For an ideal diode, the negative half is completely blocked, leading to standard formulae for the average (DC) and rms output values. This problem reinforces those results for a specific amplitude. Given Data / Assumptions: Input: v(t) = V_m sin(ωt) with V_m = 20 V. Ideal diode (no drop), pure half-wave rectification. Output taken across the load directly. Concept / Approach: For an ideal half-wave rectifier: V_avg = V_m/π and V_rms = V_m/2. These come from integrating the rectified waveform over a full period, remembering that the second half of the cycle is zero. Step-by-Step Solution: V_avg = V_m / π = 20 / π ≈ 6.366 V → ≈ 6.37 V.V_rms = V_m / 2 = 20 / 2 = 10 V. Verification / Alternative check: Compute rms from definition: V_rms^2 = (1/2π) ∫0→π (V_m sinθ)^2 dθ = V_m^2/4 → V_rms = V_m/2, confirming 10 V. Why Other Options Are Wrong: Options listing 5 V for average or rms contradict standard half-wave results. Average of 10 V implies full-wave or different amplitude. Values like 14.14 V correspond to V_m/√2 of an unrectified sine, not a half-wave output. Common Pitfalls: Forgetting the average is over the full period, not just the conducting half. Confusing full-wave with half-wave formulae. Final Answer: V_avg ≈ 6.37 V and V_rms = 10 V

Question 3

Negative feedback and noise: Determine whether the statement “Negative feedback reduces noise originating at the amplifier input” is correct in the context of linear feedback amplifiers.

Accepted Answer

Introduction / Context: Negative feedback is used to stabilize gain, extend bandwidth, and reduce distortion in amplifiers. Its effect on noise depends on where the noise originates. This item probes whether feedback specifically suppresses input-source noise. Given Data / Assumptions: Linear voltage-series feedback topology typical of audio and instrumentation amplifiers. “Noise originating at the amplifier input” means noise coming from the signal source or input resistor, added in series with the intended signal. Concept / Approach: Negative feedback divides the closed-loop gain by approximately (1 + loop gain). Both the desired signal and any input-referred noise from the source are amplified by the same closed-loop gain; thus the output signal-to-noise ratio due to input noise is not inherently improved by feedback. Feedback can reduce the contribution of internal amplifier noise (e.g., output-referred disturbances) by the factor of the loop gain, but it does not preferentially suppress noise that is indistinguishable from the input signal. Step-by-Step Solution: Model output = A_cl * (signal + input_noise) + reduced internal noise / (1 + loop gain).Because signal and input_noise are both scaled by A_cl, their ratio is unchanged.Therefore the statement that negative feedback reduces input-originated noise is false. Verification / Alternative check: Closed-loop noise analysis shows source noise remains unchanged in input-referred form; only amplifier-generated noise is suppressed by feedback. Why Other Options Are Wrong: Options asserting “True” ignore that feedback treats input signal and source noise equally. Topology-dependent statements do not change this fundamental point. Common Pitfalls: Confusing reduction of internal noise and distortion with reduction of source noise. Final Answer: False

Question 4

Oscillator selection by frequency range: Which oscillator topology is most suitable for generating signals in the megahertz (MHz) range?

Accepted Answer

Introduction / Context: Different oscillator types employ different frequency-selective networks. RC oscillators are generally preferred for audio to low-RF, while LC oscillators excel at radio frequencies. The question asks which topology is suitable in the MHz range without invoking crystals. Given Data / Assumptions: Target frequency in the MHz range (say 1–30 MHz). Standard, free-running analog oscillator topologies. Concept / Approach: RC phase-shift and Wien bridge oscillators rely on RC networks whose component values become inconvenient and lossy at high frequencies. LC resonant circuits (inductors and capacitors) provide higher Q and ease of tuning at MHz; Hartley (and Colpitts) are classical RF oscillators designed for this regime. Step-by-Step Solution: Identify MHz regime → prefer LC resonance for adequate Q.Hartley uses tapped inductor (or two inductors) + capacitor → well suited for MHz.Therefore, the most appropriate choice is the Hartley oscillator. Verification / Alternative check: Practical radios and RF signal generators widely use Hartley/Colpitts at HF/VHF; RC oscillators are usually limited to < 1 MHz (Wien bridge often in audio-LF range). Why Other Options Are Wrong: RC phase-shift and Wien bridge: typically low-frequency; component parasitics limit MHz use. “Both (a) and (c)” is incorrect since RC phase-shift is not ideal for MHz. Crystals are excellent in MHz but overly restrictive to a single option not offered in the set-up; the question compares common generic topologies. Common Pitfalls: Assuming any RC oscillator can be scaled indefinitely; parasitics and required gain become impractical at high frequency. Final Answer: Hartley oscillator (LC)

Question 5

Conduction angle recognition: In Class C operation of a transistor power amplifier, the collector current flows for what portion of the input signal cycle?

Accepted Answer

Introduction / Context: Amplifier classes are categorized by conduction angle—how long the active device conducts current during one cycle of a sinusoidal input. Class C is commonly used in RF transmitters with tuned loads to obtain high efficiency at the cost of linearity. Given Data / Assumptions: Sinusoidal drive applied to a biased transistor stage. Standard class definitions: A (360°), B (180°), AB (>180° but <360°), C (<180°). Concept / Approach: In Class C, the bias point is set below cutoff so the device conducts only around the peaks of the input waveform, for a conduction angle strictly less than 180°. A resonant load network reconstructs a sinusoidal output from these narrow current pulses. Step-by-Step Solution: Identify class definition → Class C conduction angle < 180°.Therefore, the correct statement is that current exists for less than half of the cycle. Verification / Alternative check: Typical Class C conduction ranges between 60° and 120°, depending on the desired efficiency and distortion acceptable before the tank circuit filters harmonics. Why Other Options Are Wrong: 360° corresponds to Class A. 180° corresponds to ideal Class B. More than 180° corresponds to Class AB. “Exactly 120°” is not a definition, only an example. Common Pitfalls: Confusing the conduction angle definition with the harmonic content at the output of a tuned circuit. Final Answer: less than 180° of the input wave

Question 6

Assertion–Reason on large-signal analysis: For large signal variations an amplifier circuit must often be analysed graphically because the transistor output characteristics are nonlinear. Evaluate the statements.

Accepted Answer

Introduction / Context: Amplifier analysis can be categorized as small-signal (around a bias point) or large-signal (where the device traverses a wide portion of its characteristics). This question examines why graphical methods such as load-line analysis are used for large-signal cases. Given Data / Assumptions: Transistor output characteristics are inherently nonlinear outside a very small region. Large excursions drive the operating point across curved portions of the characteristics. Concept / Approach: Small-signal linearization uses slopes at the bias point and works only for small variations. For large signals, linear approximations break down; therefore, plotting the DC load line and using the family of I–V curves (graphical method) captures the device behavior across the entire swing, including cutoff and saturation. Step-by-Step Solution: Assess Assertion (A): Large-signal analysis often requires graphical treatment → True.Assess Reason (R): Transistor characteristics are nonlinear → True.Causality: Nonlinearity is precisely why linear small-signal equations fail, thus R explains A. Verification / Alternative check: Practical amplifier design for power stages routinely employs load-line plots and transfer curves to predict clipping, saturation, and distortion—confirming the reasoning. Why Other Options Are Wrong: Any option denying A or R conflicts with standard device physics and design practice. Common Pitfalls: Attempting to use small-signal parameters (re, h-parameters) for large excursions; these are valid only near the quiescent point. Final Answer: Both A and R are correct and R is correct explanation for A

Question 7

DC amplifiers in analog electronics often exhibit a tendency toward instability due to drift, offsets, and very low-frequency effects. Evaluate the statement and choose the most accurate characterization.

Accepted Answer

Introduction / Context: Direct-coupled (DC) amplifiers are widely used whenever the signal includes very low frequencies or a constant (zero-hertz) component, such as in sensor conditioning, instrumentation, and operational amplifier stages. A common practical observation is that DC amplifiers have a tendency to be unstable unless carefully designed. This question asks you to judge that statement from an electronics design perspective and explain why it is generally considered correct. Given Data / Assumptions: Amplifiers under discussion pass down to 0 Hz (no coupling capacitor), so offsets and low-frequency noise matter. Device parameters (input offset voltage, input bias current) are non-ideal and temperature-dependent. Long-term drift and 1/f (flicker) noise become significant near DC. Concept / Approach: The apparent 'instability' of DC amplifiers is not just about oscillation. It includes output wandering due to input offset, temperature drift, bias current, resistor tolerance, and power-supply variation. Small DC errors, when multiplied by high closed-loop gains, can drive outputs toward saturation, where the stage can no longer respond linearly. Compensation networks must ensure adequate phase margin over a bandwidth that includes very low frequencies, while trimming and auto-zeroing minimize offset and drift. Step-by-Step Solution: Identify DC error sources: input offset voltage, input bias/offset current, resistor mismatch.Recognize temperature and time dependence: offsets and bias currents vary with temperature and age.Understand loop behavior: at low frequencies the loop gain may be very large, magnifying small DC errors.Result: output drift or saturation unless proper offset trimming, chopping/auto-zero, and compensation are used. Verification / Alternative check: Compare a capacitor-coupled AC amplifier (which blocks DC) with a DC-coupled stage. The AC stage avoids DC drift at its output; the DC stage must actively manage it via design techniques. Why Other Options Are Wrong: 'False': contradicts common practice and datasheet guidance; designers routinely mitigate DC drift.'Only with feedback': instability issues exist with or without feedback; feedback can help but also requires compensation.'Only at high frequencies': DC issues are fundamentally low-frequency problems.'Depends entirely on load': load matters, but core drift/offset and loop-gain causes are internal. Common Pitfalls: Ignoring input bias currents through large resistances, neglecting temperature coefficients, and assuming that high open-loop gain always improves stability at DC. Final Answer: True

Question 8

Consider the active filter shown (an operational-amplifier based network). Evaluate the following claims about the filter: (1) it is an active low-pass filter, (2) it is second order, and (3) its magnitude slope changes by 40 dB per decade beyond cu…

Accepted Answer

Introduction / Context: Active filters employ operational amplifiers with resistors and capacitors to realize frequency-selective responses without using inductors. A classic low-pass topology (such as Sallen–Key or multiple-feedback) provides a second-order transfer function, giving a −40 dB/decade roll-off in the stopband. This question checks your ability to match qualitative statements to a standard active low-pass response. Given Data / Assumptions: The depicted circuit is a common op-amp active filter topology. Component choices yield a low-pass response (DC gain finite, high-frequency attenuation). Order is determined by the highest power of s in the denominator (two reactive elements ⇒ second order). Concept / Approach: A second-order low-pass filter has transfer function magnitude that is flat near DC (passband), transitions around the natural frequency or cutoff, and then attenuates with a slope of 40 dB/decade (12 dB/octave) as frequency increases past the corner. Whether implemented by Sallen–Key or multiple-feedback, two capacitors (or two independent energy storage elements) confirm the second order. Step-by-Step Solution: Identify passband behavior: unity or set gain at low frequency ⇒ low-pass.Count energy storage elements: two reactive components ⇒ second order.Apply asymptotic Bode slope: second order ⇒ −40 dB/decade beyond the cutoff. Verification / Alternative check: Plot a Bode magnitude sketch: 0 dB slope in passband, then −40 dB/decade after ωc, confirming (1), (2), (3). Why Other Options Are Wrong: Any option omitting one of the three statements contradicts the standard second-order low-pass characteristics. Common Pitfalls: Confusing second-order low-pass (−40 dB/dec) with first-order (−20 dB/dec); misidentifying a high-pass due to capacitor placement without analyzing the transfer function. Final Answer: 1, 2 and 3

Question 9

A forward source of 9 V is applied to a silicon diode in series with a 1 kΩ load resistor. The measured voltage across the load resistor is 0 V. What does this observation most strongly indicate about the diode or circuit condition?

Accepted Answer

Introduction / Context: In a simple series circuit (source → diode → resistor → return), the load resistor drop equals I * R. If the voltmeter across the resistor reads 0 V under an applied forward voltage, then the series current must be zero. The diagnostic task is to identify which fault is consistent with zero current and zero resistor drop. Given Data / Assumptions: Supply voltage nominally +9 V forward-biasing the diode in series with a 1 kΩ resistor. Measured V_R across the resistor = 0 V. Ideal meter with negligible burden; wiring otherwise correct. Concept / Approach: Ohm's law requires a nonzero voltage drop across the resistor if current flows. Therefore, V_R = 0 implies I = 0 A. In a series path, I = 0 indicates an open circuit somewhere in the chain. If the diode were shorted, the current would be approximately 9 V / 1 kΩ = 9 mA and the resistor drop would be about 9 V, not 0 V. Hence, a shorted diode is inconsistent with the observation. An open diode, however, completely stops current, producing zero resistor drop and leaving nearly all the source voltage across the open device. Step-by-Step Solution: Observation: V_R = 0 ⇒ I = V_R / R = 0 / 1000 = 0 A.Series path with I = 0 ⇒ an open exists.Open diode is consistent; shorted diode is inconsistent (would give V_R ≈ 9 V).Therefore, most likely fault: diode is open-circuited. Verification / Alternative check: Meter the diode with a DMM: forward junction should show ~0.6–0.7 V; infinite both ways indicates open. Why Other Options Are Wrong: Short-circuited diode ⇒ large current and ~9 V across R (not 0 V).Open 1 kΩ resistor would normally present the entire 9 V across the open component, not 0 V across the resistor element itself in a typical measurement scenario.'Either short or open' is too non-diagnostic given the zero-volt reading. Common Pitfalls: Assuming a shorted diode implies zero volts everywhere; forgetting that in series circuits a short increases current and resistor drop, not decreases it. Final Answer: The diode is open-circuited

Question 10

To prevent any direct-current (DC) return path between a signal source and a load while still allowing the alternating-current (AC) signal to pass, which coupling element should be inserted between the source and load?

Accepted Answer

Introduction / Context: In analog circuits we often need to block DC bias from reaching a following stage, meter, or load, while passing the AC information. The standard technique is capacitive coupling, which provides high impedance at DC and low impedance over the desired AC band, thereby eliminating DC return while preserving signal content. Given Data / Assumptions: Goal: block DC (0 Hz), pass AC band of interest. Source and load impedances are finite and the coupling capacitor value can be chosen. We ignore transformer coupling here to keep the solution component-minimal and broadband around low audio/RF as needed. Concept / Approach: A capacitor's reactance Xc = 1 / (2 * π * f * C) is infinite at f = 0, so it perfectly blocks DC. At sufficiently high frequency, Xc becomes small and the capacitor behaves like a short for AC. Choosing C such that the high-pass cutoff f_c = 1 / (2 * π * R_total * C) lies well below the lowest signal frequency ensures negligible amplitude distortion. Step-by-Step Solution: Specify the lowest frequency f_min you need to pass.Estimate R_total seen by the capacitor (source resistance + load resistance as appropriate).Choose C so that f_c = 1 / (2 * π * R_total * C) ≤ f_min / 10.Insert capacitor in series; include a bleed resistor if necessary to set reference bias. Verification / Alternative check: Simulate a small-signal AC sweep; confirm flat response above f_c and DC isolation at 0 Hz. Why Other Options Are Wrong: Resistor: provides a DC path and drops DC per divider action, not full isolation.Inductor: passes DC (low reactance at 0 Hz is not correct—an ideal inductor has zero DC resistance, so it actually allows DC) and blocks high frequencies (opposite of the requirement).Transformer: can block DC but imposes bandwidth, impedance, and size constraints; the question asks what is 'necessary' and simplest—capacitive coupling. Common Pitfalls: Picking too small a capacitor causing low-frequency roll-off; forgetting biasing at the load side when AC-coupling into transistor/op-amp inputs. Final Answer: A capacitor between source and load

Question 11

In a self-bias (emitter-bias) BJT amplifier stage, what is the primary advantage provided by the self-bias network with respect to the operating point (Q-point)?

Accepted Answer

Introduction / Context: Biasing a BJT for linear amplification requires choosing a Q-point that remains reasonably constant despite part-to-part variation and temperature changes. The self-bias (also called emitter-bias with emitter resistor and feedback) is a classic topology to stabilize that operating point using negative feedback from the emitter resistor. Given Data / Assumptions: BJT in common-emitter configuration with an emitter resistor providing DC feedback. Base bias provided by a resistive divider or current source referenced to the emitter line. Thermal effects increase collector current unless countered by feedback. Concept / Approach: As collector current increases (due to temperature or beta variation), the emitter current rises, increasing the voltage across the emitter resistor. This raises the emitter potential, reduces base-emitter voltage V_BE, and thereby counteracts the increase in current. The negative feedback stabilizes both I_C and V_CE, keeping the transistor within the desired linear region. Step-by-Step Solution: Assume I_C rises due to temperature.I_E ≈ I_C increases ⇒ V_E = I_E * R_E increases.V_BE = V_B − V_E drops, reducing conduction.New equilibrium Q-point established near the original value. Verification / Alternative check: Small-signal analysis shows DC feedback factor proportional to R_E; larger R_E increases stability but reduces gain unless bypassed for AC. Why Other Options Are Wrong: Large voltage gain is not guaranteed (R_E without bypass reduces gain).High input impedance depends on bias network and transistor; it is not guaranteed by self-bias alone.Forcing high base current is not an objective; in fact, the network seeks stable, not excessive, current.Collector resistors are still required for voltage gain and load line setting. Common Pitfalls: Confusing AC bypass (which restores gain) with DC stabilization; forgetting that temperature rise increases I_C unless counteracted. Final Answer: It provides a stable Q point over device and temperature variations

Question 12

In a common-emitter (CE) amplifier, the quiescent collector current I_C and collector-to-emitter voltage V_CE are defined as the values measured under which signal condition?

Accepted Answer

Introduction / Context: The quiescent (Q-point) defines the DC operating state of a transistor amplifier in the absence of any applied time-varying signal. It is the reference around which the signal swings occur, ensuring linear amplification with minimal distortion if properly placed on the load line. Given Data / Assumptions: CE amplifier with some biasing network setting base current. No input AC applied when defining quiescent values. Supply voltage and resistors fix the nominal operating point. Concept / Approach: By definition, the quiescent state is the steady DC condition: I_C = I_CQ and V_CE = V_CEQ with the input signal set to zero. Small signals then cause symmetric excursions about this point. Using 'very low amplitude' is not the formal definition; it may approximate the quiescent behavior but is not exact. Negative half-cycle only is irrelevant to defining a DC state. Step-by-Step Solution: Set AC source = 0 (short for AC analysis; no time-varying input).Solve DC bias network for base current, then collector current I_CQ.Compute V_CEQ from supply and voltage drops across resistors and transistor.This pair (I_CQ, V_CEQ) is the Q-point. Verification / Alternative check: Load-line method: intersection of transistor characteristic (at chosen base bias) and the collector resistor line gives the quiescent values. Why Other Options Are Wrong: 'Very low signal' is not a definition; it is an approximation. 'Negative half-cycle' has no role in DC definition. 'Either (a) or (b)' dilutes the precise definition. Common Pitfalls: Trying to define the Q-point during signal swing; mixing small-signal incremental analysis with the DC operating point. Final Answer: When the AC input signal is zero (no signal condition)

Question 13

BJT polarity swap: When a pnp transistor in a circuit is replaced by an npn transistor for analysis, how should previously calculated polarities and directions be adapted to analyse the new circuit correctly?

Accepted Answer

Introduction / Context: Transistor circuits built with pnp and npn devices are duals of each other. The small-signal and large-signal equations are identical in form if the reference polarities and current directions are consistently reversed. This question checks the core idea behind converting a solved pnp biasing/problem into the corresponding npn case without redoing every derivation from scratch. Given Data / Assumptions: The original circuit used a pnp transistor and was fully analysed. The new circuit uses an npn transistor in the same topology. Device models follow conventional sign conventions: for npn, base–emitter forward bias is approximately +0.7 V; for pnp it is approximately −0.7 V with reversed polarities and current directions. Concept / Approach: An npn behaves like a pnp with all terminal voltages and currents inverted with respect to the chosen reference. If a pnp analysis gave certain node voltages and branch currents, the npn solution can be inferred by reversing the assumed polarities (voltage drops) and the assumed current directions while keeping magnitudes consistent. This is an application of network duality and sign convention consistency, not a change of the underlying transistor laws. Step-by-Step Solution: Identify reference polarities used in the pnp solution.For the npn version, flip the supply rails and bias polarities (VBE becomes positive instead of negative, etc.).Reverse every branch current direction used previously; magnitudes remain the same for an otherwise identical bias network.Translate results: voltages and currents are the negatives (with respect to the original references) of the pnp case. Verification / Alternative check: Re-derive one KVL around the input loop and one KCL at the collector node. You will recover the same magnitude relations with flipped signs, confirming that polarity and direction reversals are sufficient. Why Other Options Are Wrong: Repeating all calculations wastes effort; symmetry allows reuse. Flipping only voltages or only currents violates KCL/KVL consistency. Flipping supply rails alone is incomplete without reversing reference directions. Common Pitfalls: Keeping the same VBE sign between pnp and npn. Forgetting to reverse the sign of node voltages referenced to ground. Final Answer: Replace all previously calculated voltages and currents by their reverse polarities and directions.

Question 14

Large input with symmetrical clipping at both peaks: What is the approximate output waveform shape of an amplifier when a large AC input causes equal clipping on both positive and negative peaks?

Accepted Answer

Introduction / Context: When an amplifier is overdriven, its output voltage cannot exceed the supply headroom and device limits. The tops and bottoms of the waveform flatten—this is clipping. Understanding the limiting waveform helps predict harmonic content and power dissipation in power electronics and audio systems. Given Data / Assumptions: AC input amplitude is large enough to drive the stage into saturation and cutoff on alternate half-cycles. Clipping is symmetrical (both peaks clipped by roughly the same amount). The stage is otherwise linear in its central region. Concept / Approach: With equal positive and negative clipping, the output transitions quickly between two plateau levels set by the rails and spends little time in the linear mid-region. As the drive increases further, the flat segments dominate. The limiting shape approaches a square wave whose amplitude equals the saturation headroom limits of the stage. Step-by-Step Solution: Start with a sinusoid at moderate level → undistorted sine.Increase drive → tops/bottoms flatten because of rail limits.At strong overdrive, waveform spends most of the period at +Vsat and −Vsat with fast transitions, i.e., a square wave. Verification / Alternative check: Fourier analysis: severe symmetrical clipping produces strong odd harmonics, which is characteristic of square waves, confirming the qualitative prediction. Why Other Options Are Wrong: Sine wave: only when not clipped. Triangular wave: arises from slew-rate limiting, not rail clipping. Other listed shapes do not match symmetrical hard-limiting behavior. Common Pitfalls: Confusing slew-rate limiting (triangle) with clipping (flat tops). Assuming asymmetrical biasing; the prompt states both peaks clip. Final Answer: Square wave.

Question 15

Negative feedback stabilisation: An amplifier with open-loop gain A = −1000 and feedback factor β = −0.1 experiences a 20% change in A due to temperature. What is the approximate percentage change in the closed-loop gain?

Accepted Answer

Introduction / Context: One of the most powerful benefits of negative feedback is gain desensitisation: the closed-loop gain varies far less than the open-loop gain. This problem quantifies that effect for a realistic loop gain. Given Data / Assumptions: Open-loop gain A = −1000. Feedback factor β = −0.1. Open-loop gain change ΔA/A = 20% = 0.20 (due to temperature). Concept / Approach: Closed-loop gain for negative feedback: Af = A / (1 + Aβ). Sensitivity S of Af to A is S = (ΔAf/Af) / (ΔA/A) = 1 / (1 + Aβ). Hence the percentage change in closed-loop gain equals (ΔA/A) * 1/(1 + Aβ). Step-by-Step Solution: Compute loop gain: Aβ = (−1000) * (−0.1) = +100.Sensitivity: S = 1 / (1 + 100) = 1/101 ≈ 0.00990.Closed-loop percentage change: 0.20 * 0.00990 ≈ 0.0198 ≈ 1.98% of 1 → 0.198% ≈ 0.2%. Verification / Alternative check: Direct computation: Af nominal = −1000/101 ≈ −9.901. If A increases 20% to −1200, Af = −1200/ (1 − 1200*0.1) = −1200/ (−119) ≈ 10.084 in magnitude; change relative ≈ (10.084 − 9.901)/9.901 ≈ 1.85% → ~0.19, consistent with 0.2% rounding. Why Other Options Are Wrong: 5% or 10% would imply very small loop gain. 0.01% would require loop gain ≈ 20,000. 2% is one order larger than the predicted desensitised change. Common Pitfalls: Using Af ≈ 1/β without checking sign and magnitude; while numerically close here, the sensitivity must still be computed with (1 + Aβ). Final Answer: 0.2%.

Question 16

Protecting diodes in a rectifier with a capacitor-input filter: Which component is typically inserted to limit the inrush and peak currents and thereby protect the rectifier diodes?

Accepted Answer

Introduction / Context: Capacitor-input (C-filter) rectifiers draw very high current pulses when the input sine peaks exceed the capacitor voltage. These brief but large surge currents stress rectifier diodes and transformer windings. Designers add impedance to limit surge and extend diode life. Given Data / Assumptions: Single-phase rectifier feeding a large reservoir capacitor. Goal: reduce peak repetitive current and initial inrush at power-up. Concept / Approach: A small series resistance in the AC path limits di/dt and peak current during the short conduction angle. This “surge resistor” (sometimes NTC inrush limiter) is the simplest, most common, and predictable solution. Although a choke (inductor) can also limit current, a true choke-input filter changes the operating mode and requires a sufficiently large inductance to maintain continuous current; it is not what is “necessary” for a capacitor-input filter dedicated only to diode protection. Step-by-Step Solution: Place a modest series resistor in the secondary (or primary) path.Select value to cap Ipeak below diode rating while keeping ripple/voltage drop acceptable.Optionally, use an NTC thermistor which is high resistance cold (limiting inrush) and low resistance hot (reducing losses). Verification / Alternative check: Simulate with and without a series resistor: peak current waveform amplitude reduces substantially, diode junction temperature and transformer copper loss also reduce. Why Other Options Are Wrong: Series inductor: can work, but not typically required for a capacitor-input design devoted solely to diode protection; it transforms the filter style. Surge capacitor across secondary: increases current spikes; not protective. Both (a) and (b): overstates what is necessary; a resistor alone suffices in common designs. Common Pitfalls: Placing a capacitor across the transformer in hopes of “smoothing” actually raises reactive currents. Final Answer: Surge (series) resistor.

Question 17

Half-wave rectifier with capacitor-input filter: If the input to the ideal diode rectifier is v(t) = Vm sin(ωt), what is the required Peak Inverse Voltage (PIV) rating of the diode?

Accepted Answer

Introduction / Context: PIV (Peak Inverse Voltage) is the maximum reverse voltage that a rectifier diode must withstand. Choosing an adequate PIV is crucial for reliability, especially in capacitor-input filters where the reservoir capacitor holds a voltage between conduction intervals. Given Data / Assumptions: Half-wave rectifier. Capacitor-input (reservoir) filter holds approximately Vm at the output between peaks. Ideal diode and negligible transformer resistance for peak estimation. Concept / Approach: At the instant just after the capacitor has charged to Vm, the input becomes negative. The diode is then reverse-biased by the instantaneous source voltage in series with the stored capacitor voltage. With the source at approximately −Vm and the capacitor still ~ +Vm, the diode sees a reverse voltage close to Vm + Vm = 2 Vm. Step-by-Step Solution: At the negative peak: vs ≈ −Vm.Capacitor voltage: vc ≈ +Vm (little discharge between peaks under light load).Reverse voltage across diode: VR,max ≈ vc − vs ≈ Vm − (−Vm) = 2 Vm. Verification / Alternative check: Classic rectifier design tables list: Half-wave with capacitor-input → PIV ≈ 2 Vm; Full-wave bridge with capacitor-input → PIV ≈ Vm per diode, confirming the result. Why Other Options Are Wrong: Vm: valid for some bridge configurations, not for half-wave with a reservoir capacitor. 3 Vm or 4 Vm: overly conservative for the idealised case; increases cost without benefit. Vm/2: far too low and unsafe. Common Pitfalls: Ignoring the stored capacitor voltage when computing reverse stress. Final Answer: 2 Vm.

Question 18

Full-wave rectifiers: Is the efficiency of a full-wave rectifier using a centre-tapped transformer twice that of a full-wave bridge rectifier?

Accepted Answer

Introduction / Context: Efficiency in rectifiers is the ratio of DC output power to AC input power. Both the full-wave centre-tapped (two-diode) rectifier and the full-wave bridge (four-diode) rectifier deliver DC from both half-cycles, but their device counts and conduction paths differ. This question tests a common misconception about their efficiencies. Given Data / Assumptions: Ideal or near-ideal diodes (forward drops do not dominate). Same load resistance and transformer secondary RMS voltage scaled appropriately. Concept / Approach: Under comparable conditions, both topologies produce the same DC component and ripple frequency at the load, and their theoretical conversion efficiencies are essentially the same (approximately 81.2% for ideal full-wave rectification). The centre-tapped version has one diode drop per conducting half-cycle, whereas the bridge has two; this affects regulation and peak output slightly but does not double the efficiency. Step-by-Step Solution: Compute η = Pdc/Pac for an ideal full-wave → ~0.812 irrespective of configuration.Recognise that any extra diode drop in a bridge slightly reduces the average DC output but does not change the order of efficiency drastically, certainly not by a factor of two. Verification / Alternative check: Standard power-electronics texts list identical theoretical efficiencies for both full-wave rectifiers, with practical differences arising from diode drops and transformer utilisation factor (TUF), not from a twofold change in efficiency. Why Other Options Are Wrong: Claiming “True” confuses TUF and peak voltage with efficiency. “True if ideal diodes” is incorrect; ideality equalises them further. Statements about three-phase are unrelated. Common Pitfalls: Mixing up transformer utilisation factor (centre-tapped is poorer) with efficiency. Final Answer: False.

Question 19

An ideal comparator receives a pure sinusoidal input of 8 V peak-to-peak with zero DC offset. Assuming a zero-volt reference (threshold), determine the resulting output duty cycle of the comparator signal.

Accepted Answer

Introduction / Context: Comparators are fundamental building blocks in analog and mixed-signal electronics. An ideal comparator compares an input voltage against a reference and outputs a saturated high or low level depending on the sign of the instantaneous difference. This question examines how a zero-DC sinusoidal input influences the duty cycle at the output when the reference (threshold) is set at 0 V. Given Data / Assumptions: Input is a sine wave with amplitude 4 V (8 V peak-to-peak) and no DC component. Reference threshold is 0 V (the inverting or non-inverting input tied to ground, as in many textbook comparators). Comparator is ideal: infinite gain, zero propagation delay, and rail-to-rail saturated output levels. Concept / Approach: The duty cycle is the fraction of the period during which the output is high. For an ideal comparator with zero threshold, the output is high whenever the input is greater than 0 V and low whenever the input is less than 0 V. With a pure sine wave centered at 0 V, the time spent above and below zero in each cycle is exactly equal. Step-by-Step Solution: Let v_in(t) = 4 * sin(ωt). The comparator outputs HIGH when v_in(t) > 0 and LOW when v_in(t) < 0.Over one period T, sin(ωt) > 0 for exactly T/2 and < 0 for exactly T/2.Therefore, duty cycle D = (time HIGH) / T = (T/2) / T = 1/2. Verification / Alternative check: Zero crossings occur at ωt = 0, π, 2π, … . Between 0 and π, the sine is positive; between π and 2π, it is negative. The intervals are equal, confirming 50% duty. Why Other Options Are Wrong: 1/3, 1/6, 1/12: These would require a DC offset shifting the zero-crossing angles or a non-sinusoidal input. With zero DC, symmetry forces 50% duty.'None of these': Incorrect because 1/2 is achievable and correct. Common Pitfalls: Confusing comparators with Schmitt triggers (which add hysteresis). Hysteresis or DC offset would change the duty cycle; a pure zero-centered sine with zero threshold yields 50%. Final Answer: 1/2

Question 20

According to the Barkhausen criterion for sustained oscillations, the total phase shift of the loop gain around an oscillator loop must be equal to which angle?

Accepted Answer

Introduction / Context: Oscillators generate periodic waveforms without an external input signal by satisfying specific feedback conditions. The Barkhausen criterion captures the essence of these conditions in terms of loop gain magnitude and phase. This question asks you to identify the required total phase shift around the loop for sustained oscillation. Given Data / Assumptions: Linear time-invariant small-signal model near the intended oscillation frequency. Loop gain L(jω) = A(jω) * β(jω), where A is the amplifier transfer and β is the feedback network transfer. Frequency is such that the oscillator is designed to start and sustain oscillations. Concept / Approach: The Barkhausen criterion states two key conditions at the oscillation frequency ω0: (1) magnitude condition |L(jω0)| = 1 and (2) phase condition ∠L(jω0) = 0° modulo 360°. The '0° modulo 360°' requirement ensures that the fed-back signal reinforces (is in phase with) the original, enabling self-excitation without an external drive. Step-by-Step Solution: Write L(jω) = A(jω) β(jω). For reinforcement, the returning signal must have the same phase as the original.Hence the total loop phase shift ∠A + ∠β must equal 0° + 360°k (k is an integer). The smallest positive equivalent is 360°.Simultaneously, |Aβ| must equal 1 at ω0 to avoid decay (<1) or divergence (>1). Verification / Alternative check: Common RC phase-shift oscillators produce 180° in the RC network and 180° in the inverting amplifier, totaling 360°. Why Other Options Are Wrong: 90°, 45°: These do not produce constructive reinforcement around the loop.270°: Often seen in part of the loop, but the total must be 0° mod 360°.180°: Alone implies inversion; without an additional 180° from elsewhere, feedback is negative, not regenerative. Common Pitfalls: Assuming 180° is sufficient; forgetting that the net phase after one loop must be an integer multiple of 360°. Final Answer: 360°

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