Question 1

Audio DAC choice in CD players: Is a sigma-delta (ΔΣ) D/A converter the most likely DAC architecture used in a consumer CD player?

Accepted Answer

Introduction / Context: Consumer audio playback emphasizes high resolution, excellent linearity, and low noise at moderate bandwidths. Sigma-delta (ΔΣ) DACs excel here by oversampling and noise-shaping quantization noise out of the audible band, followed by digital filtering and simple analog reconstruction filters. The question checks whether this common industry practice is recognized. Given Data / Assumptions: Audio sample rates around 44.1 kHz and multiples (oversampling). Emphasis on dynamic range and low distortion over extreme speed. Mass-market integration and cost sensitivity. Concept / Approach: ΔΣ DACs convert a high-rate, low-bit-depth bitstream into analog using a simple analog filter, achieving high effective resolution through oversampling and noise-shaping. Their architecture suits audio CD playback (16-bit/44.1 kHz) and modern high-resolution formats, enabling excellent performance with economical analog filtering compared to multibit R-2R ladders that demand precise trimming and steep analog filters. Step-by-Step Solution: Optical pickup reads pits → digital PCM stream.Digital filtering/oversampling shapes noise out of band.ΔΣ DAC reconstructs analog with a gentle analog filter stage. Verification / Alternative check: Audio DAC datasheets for consumer CD and DVD players over the past decades predominantly feature sigma-delta architectures due to their cost-performance advantage. Why Other Options Are Wrong: “Incorrect”: Contradicts widespread industry usage.“Only for 24-bit” / “only portable”: Architecture applies broadly across bit-depths and product types.Optical pickup details do not determine DAC architecture choice. Common Pitfalls: Assuming R-2R ladders dominate audio; while used in high-end niches, ΔΣ is the mainstream choice. Final Answer: Correct

Question 2

Defining DAC resolution (practical metric): One practical way to express the resolution of a DAC is the ratio of one LSB step size to the full-scale output span. Evaluate this statement.

Accepted Answer

Introduction / Context: Resolution can be stated in several complementary ways: in bits (n), in number of distinct codes (2^n), as an absolute LSB voltage/current step, or as a fraction of the full-scale range. Engineers often use the ratio LSB/FS (sometimes expressed as a percentage or parts per million) because it directly links code granularity to the converter’s usable output span. Given Data / Assumptions: Ideal n-bit DAC with a defined full-scale span (FS). Uniform step size across codes (ignoring DNL/INL for the definition). Full-scale may be specified as Vref or a scaled multiple thereof by the DAC topology. Concept / Approach: For an ideal DAC, LSB step size = FS / (2^n). Many texts define “resolution” as 1 in 2^n of full scale, i.e., LSB/FS. Some use (2^n − 1) in the denominator when mapping codes 0…(2^n − 1) over FS; the key point is that resolution can be expressed as the fractional LSB size relative to FS. This is a practical, widely used definition alongside the bit count. Step-by-Step Solution: Identify bit resolution n → total codes = 2^n.Relate step to span: LSB ≈ FS / 2^n (ideal case).State resolution as a ratio: LSB/FS = 1 / 2^n (or closely 1 / (2^n − 1)). Verification / Alternative check: Datasheets often present both n (bits) and LSB size in volts or microamps; the fractional view is inherent in percent-of-full-scale specifications. Why Other Options Are Wrong: “Incorrect”: Conflicts with standard engineering usage.Unipolar/endpoint caveats: The ratio concept applies broadly; sign and endpoint choice do not invalidate it.“Depends solely on Vref”: Vref sets absolute LSB in volts, but the ratio is determined by n and mapping, not by the specific Vref value. Common Pitfalls: Confusing resolution (granularity) with accuracy (INL/DNL, gain/offset) and noise; a small LSB does not guarantee accurate outputs. Final Answer: Correct

Question 3

Basic hardware classification – considering a simple household circuit consisting of a mechanical on/off switch in series with a light bulb, does this arrangement qualify as an analog circuit, or is it better described as a binary (two-state) contro…

Accepted Answer

Introduction / Context: Students often mix up “analog circuits” with any circuit that involves analog quantities like voltage and current. A light bulb and a mechanical switch form a very common circuit. The question is whether this particular arrangement should be classified as an analog circuit or as something else from a digital/logic standpoint. Given Data / Assumptions: The circuit is a single-pole mechanical switch in series with a lamp. No dimmer, no feedback, no proportional control—just on/off control. Supply can be DC or AC; this does not change the control mode classification. Concept / Approach: An analog circuit processes signals with continuously variable values and usually exhibits proportional relationships (for example, op-amp amplifiers, filters, sensors with linear conditioners). A simple switch enforces two discrete states: closed (current flows) or open (no current). Even though the lamp is an analog load whose brightness could vary with voltage/current, in the described configuration the system behavior presented to the user is binary. Therefore, the more accurate classification is a two-state control of an analog load, not an analog signal-processing circuit. Step-by-Step Solution: 1) Identify functional behavior: switch provides two states only.2) Check for proportionality: none—no partial conduction path or continuous control is specified.3) Recognize: absence of analog processing blocks (amplifiers, filters, linear regulators).4) Conclude: not an analog circuit in the usual sense; it is a binary control circuit. Verification / Alternative check: If a dimmer (triac phase control or PWM with driver) is added, the circuit begins to perform analog or mixed-signal control (continuous dimming average), but the original two-element on/off circuit does not. Why Other Options Are Wrong: “Correct” mislabels the binary nature. “Analog only if a dimmer is added” introduces extra hardware that was not given. AC mains or bulb wattage do not determine whether signal processing is analog. Common Pitfalls: Equating an analog load with an analog circuit; assuming any non-digital device automatically implies analog processing. Final Answer: Incorrect

Question 4

Op-amp applications – can a resistor-weighted summing operational amplifier be configured to implement a digital-to-analog converter (DAC) by converting digital input lines into a proportional analog voltage?

Accepted Answer

Introduction / Context: Digital-to-analog conversion can be realized using resistor networks and an operational amplifier. The widely taught approach is a binary-weighted or R–2R ladder network feeding a summing node at the inverting input of an op-amp. This question checks whether a summing op-amp can serve as the core of a DAC stage. Given Data / Assumptions: Binary input lines are available (e.g., D0…Dn) with known logic levels. Resistors are chosen to produce binary-weighted currents at the summing node. The op-amp operates within its linear region, with proper reference and supply rails. Concept / Approach: A summing amplifier converts input currents through its feedback network to an output voltage: Vout = -Rf * (V1/R1 + V2/R2 + ...). Using binary-weighted resistors (or an R–2R ladder that presents equivalent currents), digital “1” lines contribute fixed current portions while “0” contribute none. The op-amp sums these currents to produce a proportional analog voltage referenced to ground or a set reference level, thus implementing a DAC function. Step-by-Step Solution: 1) Choose resistor values so each higher-order bit contributes double the current of the next lower bit.2) Drive each bit from a logic source referenced to Vref.3) Use an op-amp with feedback resistor Rf to convert summed current to voltage.4) Calibrate Vout scale and offset by selecting Rf and Vref. Verification / Alternative check: Replace weighted resistors with an R–2R ladder feeding the op-amp; behavior and transfer function are equivalent but with improved matching and tolerance requirements. Why Other Options Are Wrong: Inductors are unnecessary; rail-to-rail capability depends on voltage range, not the principle; MHz operation is not a requirement for DAC functionality. Common Pitfalls: Ignoring op-amp headroom, output drive limits, and resistor tolerance which directly affect linearity (INL/DNL) and accuracy. Final Answer: Correct

Question 5

ADC architectures – compared to common alternatives (SAR, dual-slope/integrating, flash), is a voltage-to-frequency (V–F) converter ADC generally more complicated, or is it comparatively simple but slower and counter-based?

Accepted Answer

Introduction / Context: Voltage-to-frequency (V–F) conversion is a classic way to digitize signals by converting an analog voltage into a pulse train whose frequency is proportional to the input. Counting pulses over a fixed gate time provides a digital result. The question probes whether this approach is inherently more complicated than other ADC types. Given Data / Assumptions: Baseline comparators/integrators and a VCO or charge-balancing block are available. A digital counter and timing reference exist to count pulses. We compare “complexity” in terms of analog hardware and control, not raw speed. Concept / Approach: V–F ADCs are often valued for their simplicity and noise immunity over long cables: the analog front-end is modest and the measurement reduces to frequency counting. Compared with flash ADCs (which need many comparators) and even SAR ADCs (which require a precise DAC and a sequencer), a basic V–F approach can be simpler, though slower due to counting intervals. Therefore, the claim that it is “more complicated than other ADCs” is generally not accurate. Step-by-Step Solution: 1) Convert Vin to frequency f(Vin) using a simple integrator/comparator loop.2) Count pulses for a gate time Tg: N ≈ f(Vin) * Tg.3) Map N back to Vin using calibration.4) Note hardware count logic is straightforward; accuracy hinges on time base and linearity. Verification / Alternative check: Industrial sensor interfaces use V–F conversion for remote data links because the frequency signal is robust; implementations are compact compared to multi-comparator flash ADCs. Why Other Options Are Wrong: Saying “Correct” inverts the common characterization. Sigma-delta is a different architecture. A DAC is not required for a basic V–F converter ADC. Common Pitfalls: Confusing longer measurement time (for resolution) with architectural complexity; these are separate considerations. Final Answer: Incorrect

Question 6

Sigma–delta (delta–sigma) modulation – is one common form specifically designed to convert a continuous-time analog input into a 1-bit, noise-shaped bitstream for subsequent digital filtering (i.e., an A/D front end)?

Accepted Answer

Introduction / Context: Sigma–delta modulators underpin many modern high-resolution ADCs used in audio, instrumentation, and sensor interfaces. They oversample the input and shape quantization noise out of band, producing a high-rate 1-bit stream that a digital decimation filter converts into multi-bit samples. Given Data / Assumptions: Analog input is band-limited relative to the modulator clock. A 1-bit quantizer (comparator) and a feedback DAC form the core loop with an integrator. Digital filtering/decimation follows the modulator. Concept / Approach: A sigma–delta modulator integrates the error between the analog input and a 1-bit DAC's feedback, feeding the result to a 1-bit quantizer. The output bitstream contains the input information plus shaped noise (pushed to higher frequencies). Later, a digital low-pass filter and downsampler recover a precise digital representation of the analog signal in the desired bandwidth, completing the A/D path. Step-by-Step Solution: 1) Integrate the difference: accumulative loop filters the input.2) Quantize to 1 bit at high rate; emit bitstream.3) Feed back via a 1-bit DAC to close the loop.4) Apply digital decimation filter to obtain multi-bit samples. Verification / Alternative check: Audio ADCs (for example, 24-bit) and precision sensor ADCs commonly specify a sigma–delta front end followed by digital filtering, confirming the A/D purpose of this architecture. Why Other Options Are Wrong: The architecture is not limited to D/A tasks; it measures amplitude over time, not just frequency; it is applicable to many sensor types, not only thermocouples. Common Pitfalls: Confusing the 1-bit stream with low resolution—after decimation, effective resolution can be very high within the signal band. Final Answer: Correct

Question 7

Flash (parallel) ADC operation – do flash converters require an external input clock pulse for each conversion, or do they resolve input levels combinationally with optional output latching?

Accepted Answer

Introduction / Context: Flash ADCs are the fastest architecture for moderate resolutions, using many parallel comparators to encode the input level instantly. This question evaluates whether a flash ADC inherently depends on an input clock to perform a conversion. Given Data / Assumptions: N-bit flash uses 2^N - 1 comparators and a resistor ladder. The thermometer code is encoded into binary. Designs may add latches/registers for timing alignment. Concept / Approach: A pure flash front-end resolves the input level as soon as the analog comparators settle—no explicit “start conversion” clock is required for the analog decision. However, practical converters often include clocked latches or pipelines at the outputs to synchronize data to a system clock. The conversion itself is combinational; the clock is used for capturing and transferring results, not for performing the analog comparison process. Step-by-Step Solution: 1) Apply Vin to the ladder/comparators.2) Comparators switch according to Vin; thermometer code appears.3) Digital encoder maps thermometer code to binary.4) Optional latches clock the result for stable system interfacing. Verification / Alternative check: Datasheets describe “track-and-hold” and output register clocks but do not require a “start conversion” clock as in SAR or successive-approximation loops. Why Other Options Are Wrong: Claiming a conversion clock is mandatory confuses output synchronization with the analog decision mechanism. Nonoverlapping clocks or PLLs are unrelated to the basic flash principle. Common Pitfalls: Assuming all ADCs step through time-sequenced algorithms; flash is inherently parallel and instantaneous within analog settling limits. Final Answer: Incorrect

Question 8

ADC performance terms – the time required to complete one full analog-to-digital conversion cycle (from start to valid digital result) is called ________.

Accepted Answer

Introduction / Context: Manufacturers specify timing parameters to characterize how fast an ADC can deliver results. Understanding the correct terminology prevents misinterpretation of datasheets and helps in budgeting sample rates and latencies in system design. Given Data / Assumptions: We consider the interval from initiating a conversion to the time the digital output is valid. Architecture may be SAR, sigma–delta, or pipeline; term meaning remains consistent. Other timing terms exist but refer to different phenomena. Concept / Approach: The industry-standard term for the duration needed to finish a single conversion is “conversion time.” It encompasses the algorithmic or settling actions required inside the ADC. By contrast, “aperture jitter” is the uncertainty of the sampling instant; “pipeline latency” is the fixed number of clock cycles between sampling and output in pipeline/sigma–delta ADCs; “settling tolerance” and “monotonic interval” are not names for the full cycle time. Step-by-Step Solution: 1) Identify the timing interval of interest: start → valid output.2) Map to datasheet term: “conversion time.”3) Distinguish from jitter (timing uncertainty) and latency (pipeline cycles).4) Select the correct term accordingly. Verification / Alternative check: ADC datasheets list “tCONV” or similar symbols explicitly for conversion time; other parameters appear in separate timing sections. Why Other Options Are Wrong: Aperture jitter is a sampling timing noise; pipeline latency is a fixed delay not equal to the algorithm duration of single-shot devices; the other terms are not standard conversion-cycle names. Common Pitfalls: Confusing high sample rate (1 / sample period) with conversion time when pipelines introduce additional latency. Final Answer: conversion time

Question 9

Comparator usage – can a general-purpose operational amplifier be used as a voltage comparator in basic interfacing tasks, even though a dedicated comparator IC is usually preferred for speed and input structures?

Accepted Answer

Introduction / Context: Designers sometimes repurpose an op-amp as a comparator to detect whether one voltage exceeds another. While this can work for slow signals, there are caveats compared to dedicated comparators that are engineered for fast, open-loop switching with appropriate input and output stages. Given Data / Assumptions: Op-amp used open-loop or with high gain to sense a threshold crossing. Input common-mode and output swing are within device limits. Response time requirements are modest. Concept / Approach: An op-amp saturates when used open-loop as a threshold detector; the sign of (V+ − V−) determines the output state. This implements the essential comparator function. However, dedicated comparators feature faster propagation delay, input hysteresis (or allow external hysteresis), and output stages suited to logic-level interfacing (e.g., open-drain). Therefore, while it is correct that an op-amp can be used as a comparator, one must verify that speed, input ranges, and recovery from saturation meet the application’s needs. Step-by-Step Solution: 1) Set a reference on one input; apply signal to the other.2) Operate open-loop so the output rails depending on which input is higher.3) Optionally add positive feedback (hysteresis) for noise immunity.4) Buffer/level-shift output as required for logic compatibility. Verification / Alternative check: Many application notes show op-amp Schmitt triggers and zero-crossing detectors; they function well for low-to-moderate speed signals when device limits are respected. Why Other Options Are Wrong: FET inputs, dual supplies, or bandwidth constraints do not define the possibility in principle; they affect performance windows but are not prerequisites. Common Pitfalls: Ignoring input common-mode range, output saturation recovery, and lack of built-in hysteresis—leading to chatter near threshold. Final Answer: Correct

Question 10

Counter-ramp (digital ramp) ADC – to enable automatic continuous conversions, should the end-of-conversion (EOC) signal be routed to the counter clear/start so that the next ramp begins immediately?

Accepted Answer

Introduction / Context: In a counter-ramp ADC, a digital counter drives a DAC to create a staircase that rises until it matches the analog input, as detected by a comparator. Once a match is detected, the current count is latched as the result. Configuring the control lines allows either single-shot operation or continuous conversions. Given Data / Assumptions: EOC indicates that the DAC count has reached the comparison threshold. The counter has a clear or load input to reset for the next conversion. Clock source is available to step the counter. Concept / Approach: To run conversions back-to-back, the system can use EOC to automatically reset and restart the counter, initiating the next ramp without external intervention. This creates a free-running conversion loop: count up → compare → latch result → clear → repeat, yielding a steady stream of conversion results at a rate set by the clock and input magnitude dynamics. Step-by-Step Solution: 1) Clock the counter to increment the DAC output.2) Comparator asserts EOC when DAC equals/exceeds Vin.3) Latch the count as the digital output.4) Feed EOC to counter clear/start to begin the next cycle automatically. Verification / Alternative check: Logic timing diagrams of digital-ramp ADCs often show EOC used to reset the counter; continuous mode is a common teaching lab configuration. Why Other Options Are Wrong: Input being DC is not a requirement; synchronous counters are typical but not the principle; dual-slope is a different ADC architecture altogether. Common Pitfalls: Forgetting to debounce or shape EOC properly; not latching the result before clearing can lose the conversion value. Final Answer: Correct

Question 11

Channel multiplexing – when several analog sources must be digitized, can a single ADC be time-shared via an analog multiplexer that selects one input at a time for conversion?

Accepted Answer

Introduction / Context: Many embedded systems must digitize multiple sensor channels but can afford only one ADC due to cost or space. A standard approach is to time-division multiplex channels using an analog multiplexer (MUX) and a sample-and-hold or track-and-hold front end as needed for accuracy and speed. Given Data / Assumptions: ADC has adequate sampling rate to service all channels within required update times. An analog MUX selects which sensor connects to the ADC input. Settling and source impedance are compatible with ADC input requirements. Concept / Approach: Time-sharing a single ADC works by cycling through inputs: select channel i, allow settling and hold if necessary, start conversion, read result, then proceed to channel i+1. Provided the ADC's throughput meets the sum of per-channel rates and the analog front end is designed for proper settling and isolation, one ADC can serve many sources effectively. Step-by-Step Solution: 1) Use a MUX to connect one sensor at a time to the ADC input.2) Provide adequate acquisition time and buffering to meet input capacitance/impedance specs.3) Trigger conversion; read and store the result with channel ID.4) Repeat for all channels within the sampling schedule. Verification / Alternative check: Microcontrollers with built-in ADCs commonly expose multiple channels through an internal MUX; discrete designs replicate this externally with 74HC4051-class devices or instrumentation multiplexers. Why Other Options Are Wrong: Current-mode only is false; strict 1 mV ground match is unnecessarily tight (use proper grounding/guarding). A dedicated S/H per channel is optional, not always required. Common Pitfalls: Insufficient settling time, high source impedance causing gain errors, and crosstalk between channels if MUX isolation is poor. Final Answer: Correct

Question 12

Signal conversion roles – does a D/A (digital-to-analog) converter convert physical analog variables (e.g., temperature) into digital numbers, or is that the role of an A/D converter?

Accepted Answer

Introduction / Context: In mixed-signal systems, it is essential to distinguish between the directions of conversion. Sensors produce analog voltages or currents proportional to physical quantities such as temperature, pressure, or light. Understanding whether an ADC or a DAC performs the conversion to digital numbers avoids architectural mistakes. Given Data / Assumptions: D/A (DAC) converts digital codes into analog voltages or currents. A/D (ADC) converts analog signals into digital codes. Sensors typically feed ADCs; DACs typically drive actuators or setpoints. Concept / Approach: The directionality is clear: a DAC takes a digital input word and produces a corresponding analog output. An ADC takes an analog input and produces a digital representation. Therefore, converting temperature (an analog variable sensed as a voltage/current) into a digital quantity is the role of the ADC, not the DAC. The statement that a D/A converter changes temperature variations into digital quantities is incorrect. Step-by-Step Solution: 1) Identify the signal flow: sensor → analog voltage/current.2) Choose conversion direction needed: analog → digital → requires ADC.3) Recognize DAC performs the inverse: digital → analog.4) Conclude the statement is false for a DAC. Verification / Alternative check: Block diagrams in microcontroller datasheets show sensors feeding ADC inputs and DAC outputs driving actuators, VCO controls, or audio lines—supporting the directional roles. Why Other Options Are Wrong: Calling it “Correct” reverses definitions; flash is an ADC architecture and unrelated here; sensor linearization and reference choices do not change DAC vs ADC roles. Common Pitfalls: Mixing up acronyms under time pressure; assuming any converter can work both ways—it cannot without redesign; each device is directional. Final Answer: Incorrect

Question 13

Binary-weighted DAC (operational-amplifier summing type): Evaluate the statement — “In a binary-weighted digital-to-analog converter, the sum of all currents from the binary-weighted resistors flows through the operational amplifier.” Clarify where …

Accepted Answer

Introduction / Context: A binary-weighted digital-to-analog converter (DAC) commonly uses an operational amplifier as an inverting summing amplifier. Understanding the exact current paths in this topology is essential for correct intuition about linearity, settling, and output scaling. The statement claims that the summed current “flows through the operational amplifier,” which is a frequent misconception. Given Data / Assumptions: Classic inverting DAC: binary-weighted resistors feed an op-amp summing node. Ideal op-amp assumptions: infinite input impedance, virtual ground at the inverting input, and zero input current. Feedback element (usually a resistor, sometimes a capacitor for filtering) from output to the inverting node. Concept / Approach: In an ideal op-amp, the inverting input is a virtual ground that draws negligible current. Currents from the binary-weighted network meet at the summing node and must continue through the feedback path to the output node, not into the op-amp input. Therefore, the op-amp enforces node voltage (virtual ground) and provides output current via its output stage, but the input terminal itself does not carry the summed current. Step-by-Step Solution: 1) Binary-weighted sources produce currents I1, I2, … determined by input bits and resistor values.2) These currents enter the inverting summing node held near 0 V by negative feedback.3) Because op-amp input current ~ 0, KCL forces the sum(Ik) to flow through the feedback element.4) The op-amp output supplies whatever current is required through the feedback to keep the summing node at virtual ground. Verification / Alternative check: Apply Kirchhoff’s current law at the summing node: sum(currents from sources) + input current + feedback current = 0. With input current ≈ 0, feedback current equals the negative sum of source currents, confirming the path is through feedback, not into the op-amp input pin. Why Other Options Are Wrong: “Correct” misunderstands op-amp input behavior. “Correct only for noninverting DACs” is irrelevant; the noninverting configuration still avoids input current. “Correct when the op-amp has finite input bias” confuses tiny bias currents with the large signal sum; bias is negligible compared to the functional current path. Common Pitfalls: Assuming current “flows into” an op-amp input; forgetting virtual ground; ignoring that the op-amp output stage delivers the necessary feedback current to satisfy KCL. Final Answer: Incorrect

Question 14

Successive-approximation (SAR) ADC advantage: Evaluate the claim that the principal advantage of the SAR analog-to-digital conversion method is high conversion speed relative to integrating converters while maintaining good resolution and accuracy.

Accepted Answer

Introduction / Context: Analog-to-digital converters come in multiple architectures: flash, SAR, dual-slope, sigma-delta, and more. Each balances speed, resolution, power, and cost. The successive-approximation (SAR) ADC is widely used in embedded and instrumentation systems due to its favorable speed-versus-resolution trade-off. Given Data / Assumptions: SAR ADC performs a binary search using an internal DAC, comparator, and SAR register. Typical resolutions: 8–18 bits, with microsecond to sub-microsecond conversions common. Comparison set: integrating (dual-slope) and oversampling converters (slower for a given resolution) vs flash (faster but costly and low-to-moderate resolution). Concept / Approach: SAR’s binary-search strategy requires roughly N comparison steps for N-bit resolution, enabling rapid, deterministic conversion times without massive comparator arrays (like flash). It therefore delivers high speed relative to integrating converters, while maintaining good accuracy and moderate power, making it a “go-to” choice for data acquisition. Step-by-Step Solution: 1) Initialize MSB in the SAR and set the internal DAC accordingly.2) Compare DAC output with the input; keep or clear the bit based on comparator result.3) Iterate for each bit until LSB; total ~ N comparisons.4) Conversion time scales ~ linearly with bits, yielding high speed at common resolutions. Verification / Alternative check: Benchmark typical 12- to 16-bit SAR datasheets vs dual-slope ADCs used in digital multimeters; SARs are orders faster while flash remains faster but impractical at high resolution. Why Other Options Are Wrong: “Incorrect” ignores widely documented SAR performance. The flash-only comparison is misguided; SAR’s advantage is not relative to flash (which is faster) but relative to many other architectures at similar resolutions. Common Pitfalls: Assuming “highest speed overall”; flash wins in absolute speed but at high hardware cost. SAR is popular because it balances speed, resolution, and efficiency. Final Answer: Correct

Question 15

DAC resolution dependency: In a digital-to-analog converter, the analog output step size (smallest output change) is primarily determined by the number of input bits, with full-scale range also influencing absolute step magnitude. Evaluate this stat…

Accepted Answer

Introduction / Context: Resolution tells how finely a DAC can represent analog values given digital codes. Designers often size the number of bits to meet an application’s dynamic-range and quantization-noise targets, then choose a reference to set absolute volt levels. Given Data / Assumptions: N-bit DAC with reference Vref and full-scale range dependent on architecture. Ideal LSB size = full_scale / (2^N − 1) (often approximated as VFS / 2^N). Non-idealities (INL/DNL, noise) do not change the fundamental dependency. Concept / Approach: Increasing bit count halves the LSB size each added bit, improving resolution exponentially with N. While Vref sets the absolute voltage per step, the primary driver of how many distinct analog levels exist is the number of bits (2^N codes). Step-by-Step Solution: 1) Distinct codes = 2^N.2) Ideal step size ≈ VFS / 2^N.3) Add one bit → step size halves.4) Therefore, resolution scales principally with N. Verification / Alternative check: Compare a 10-bit vs 12-bit DAC at same Vref; LSB shrinks by factor 4, confirming N is the prime factor. Why Other Options Are Wrong: “Incorrect” ignores the 2^N relationship. Constraints about zero Vref or thermometer coding do not alter the bit-driven code count. Common Pitfalls: Confusing resolution (LSB size) with accuracy or linearity; non-idealities limit effective resolution but not the theoretical 2^N levels. Final Answer: Correct

Question 16

DAC dynamic behavior term: The interval between a valid digital code change at a DAC’s input and the time the analog output reaches and remains within a specified error band of its final value is called the settling time. Assess this definition.

Accepted Answer

Introduction / Context: When a DAC input code changes, the output does not jump instantly to the new voltage; it slews, rings, and experiences glitch energy before stabilizing. “Settling time” quantifies how quickly the output becomes reliably usable. Given Data / Assumptions: DAC experiences a code transition at t0. A specified error band (for example ±0.5 LSB) defines “settled.” Output includes dynamic effects: slew, overshoot, and glitches. Concept / Approach: Settling time is the elapsed time from input change to the moment the output first enters and stays within the error band. It encompasses all transient behavior, distinguishing it from simple propagation delay (which ignores final stabilization quality). Step-by-Step Solution: 1) Apply digital step at the DAC input.2) Observe the analog output waveform.3) Determine when the output is within the specified band.4) Confirm it remains within band thereafter; that interval is the settling time. Verification / Alternative check: Datasheets specify “settling time to ±X LSB,” confirming the definition across architectures (R-2R, current-steering, sigma-delta with reconstruction filters, etc.). Why Other Options Are Wrong: “Incorrect” confuses with pure propagation delay; architecture-specific qualifiers do not change the generic definition. Common Pitfalls: Ignoring the error band; assuming first crossing equals settled even if ringing pushes it back out temporarily. Final Answer: Correct

Question 17

Digital storage oscilloscope (DSO) basic functions: Complete the statement—A DSO ________, ________, and ________ analog waveforms as part of its measurement process.

Accepted Answer

Introduction / Context: A digital storage oscilloscope converts analog signals into digital samples, retains those samples in memory, and renders the result on a screen. Recognizing these core functions helps differentiate DSOs from purely analog oscilloscopes and explains features like deep memory, triggering, and post-processing. Given Data / Assumptions: Input is an analog waveform. Scope includes ADCs, memory, and a display subsystem. Trigger circuitry governs when sampling and storage occur. Concept / Approach: First, the DSO digitizes the input via an ADC at a chosen sample rate. Second, it stores the resulting digital samples in acquisition memory. Third, it displays the reconstructed waveform and measurements on the screen. Additional processing (filtering, math) is optional but not fundamental to the three verbs that define DSO operation. Step-by-Step Solution: 1) Condition/attenuate the analog input to ADC range.2) Sample and quantize → digital samples.3) Buffer the samples in memory.4) Render the data on the display with timebase and scaling. Verification / Alternative check: Instrument block diagrams show front-end conditioning, ADC, acquisition memory, and display engine as the canonical DSO pipeline. Why Other Options Are Wrong: Other triplets include irrelevant verbs (weighs, translates) or omit the essential “digitize”/“display” elements. Common Pitfalls: Confusing optional digital filtering with core functionality; assuming storage occurs only after display—acquisition precedes rendering. Final Answer: digitizes, stores, displays

Question 18

AD7524 characteristics: The AD7524 is a CMOS, 8-bit multiplying digital-to-analog converter widely available from multiple vendors. It implements its conversion core using a(n) ________.

Accepted Answer

Introduction / Context: Many integrated DACs use either binary-weighted resistors or an R/2R ladder to realize precise digital-to-analog conversion. The AD7524 family is a classic example of an 8-bit multiplying DAC using R/2R topology for compactness and matching. Given Data / Assumptions: CMOS 8-bit multiplying DAC. No internal sample-and-hold; the device outputs a current proportional to the reference. Architecture based on precision resistor network. Concept / Approach: The R/2R ladder network provides equal-valued switching currents with only two resistor values, easing matching and scaling and improving accuracy across bits compared to discrete binary weighting. The DAC output current is subsequently converted to a voltage with an external op-amp if needed. Step-by-Step Solution: 1) Decode input bits to control ladder switches.2) Route currents through the R/2R network to form a binary-weighted sum.3) Present the resulting current at the DAC output node.4) Convert to voltage using an I-to-V stage if required. Verification / Alternative check: Vendor datasheets for AD7524 explicitly describe the R/2R architecture and multiplying capability (output scales with reference). Why Other Options Are Wrong: Sample-and-hold is an ADC accessory. A standalone multiplexer is not a DAC core. A “10 µs clock” is not an architecture and the device does not require a fixed clock. Common Pitfalls: Assuming all DACs include S/H; confusing R/2R with simple resistor ladders used for audio volume controls. Final Answer: R/2R ladder network

Question 19

Digital voltmeter (DVM) output representation: A digital voltmeter converts an analog input voltage into its ________ representation for display and processing.

Accepted Answer

Introduction / Context: Digital voltmeters are measurement instruments that sample analog voltages and present numerically readable results. The internal conversion produces digital data which may be formatted as BCD for display or transmitted to interfaces, but the essential nature is digital encoding of an analog quantity. Given Data / Assumptions: Analog input voltage is measured. Instrument contains an ADC. Display logic shows numbers derived from the digital result. Concept / Approach: The ADC converts the analog voltage to a digital value. Downstream, this value can be represented in various numeric encodings (binary, BCD) and displayed as decimal digits. Therefore, the most general and accurate description is that the DVM outputs a digital representation; BCD is a specific internal/external encoding that some instruments use, but not universally. Step-by-Step Solution: 1) Condition the analog input to the ADC’s range.2) Convert the voltage using an ADC (often dual-slope or sigma-delta in DVMs).3) Produce a digital code representing the measured voltage.4) Format and display the code as decimal digits. Verification / Alternative check: DVM block diagrams show ADC → digital processing → display; service manuals often mention both binary and BCD formats internally. Why Other Options Are Wrong: “BCD-code” is specific, not universal. “Decimal” refers to human-readable formatting, not the representation type. “Alias” is unrelated to representation. Common Pitfalls: Equating display format (decimal digits) with the underlying data type; assuming all DVMs expose BCD on external ports. Final Answer: digital

Question 20

Converter identification (recovery applied): The originally referenced figure is unavailable. Applying the recovery-first policy, consider the common block diagram that includes a comparator, a DAC, a successive-approximation register, and control l…

Accepted Answer

Introduction / Context: Since the figure is missing, we reconstruct the likely intent. Many textbooks show a block diagram with four hallmark blocks: a DAC, a comparator, a successive-approximation register (SAR), and a control clock. Together, these perform a binary search to converge on the input voltage—the defining behavior of a SAR ADC. Given Data / Assumptions: Blocks present: DAC, comparator, SAR register, control logic. Operation: iterative MSB-to-LSB decision sequence. Goal: identify the converter type by functional blocks. Concept / Approach: In each bit trial, the SAR sets a tentative bit in the internal DAC and compares the DAC output against the analog input. The comparator decides to keep or clear the bit. Repeating this for all bits yields the final digital code in roughly N steps for an N-bit result—signature of SAR conversion. Step-by-Step Solution: 1) Set MSB in SAR → DAC outputs mid-scale.2) Comparator compares Vin vs Vdac → decision keeps/clears MSB.3) Proceed to next bit, repeating the compare-and-decide loop.4) After LSB, the SAR holds the conversion result; the architecture is SAR ADC. Verification / Alternative check: Contrast with dual-slope (integrator + counter timing) and tracking (up/down counter follows Vin). Only SAR shows the DAC-comparator-SAR closed loop with binary search. Why Other Options Are Wrong: Dual-slope uses integration and timed de-integration, not a DAC. Tracking uses a counter driving a DAC continuously, not a SAR register. “Dual-approximation D/A comparator” is not a standard converter type. Common Pitfalls: Confusing SAR with flash (which uses many comparators in parallel) or with ramp/tracking architectures. Final Answer: successive-approximation A/D converter

Interfacing to the Analog World Questions