Question 1

Inside the ADC0808 Which functional blocks are integrated on a typical ADC0808 IC?

Accepted Answer

Introduction / Context: The ADC0808 is a classic 8-bit successive-approximation ADC that simplifies multi-channel data acquisition by integrating selection logic and the converter core in one package. Recognizing its internal blocks helps with pinout understanding and system integration. Given Data / Assumptions: ADC0808 provides multiple analog input channels. It uses internal addressing (select lines) to choose the active channel. It includes the SAR ADC engine. Concept / Approach: The ADC0808 integrates: (1) an 8-channel analog multiplexer for inputs, (2) an 8-bit SAR ADC core, and (3) a 3-bit address (select) input to choose any one of the eight channels. Thus, all listed items are present in the device, enabling compact DAQ designs. Step-by-Step Solution: Confirm presence of a multiplexer → yes, 8:1 analog MUX.Confirm presence of ADC → yes, 8-bit SAR.Confirm select input → yes, 3 address lines to select 1 of 8 channels.Therefore, “All of the above.” Verification / Alternative check: Standard datasheets and training materials for the ADC0808/ADC0809 families clearly list these blocks and show the channel select truth table. Why Other Options Are Wrong: Each individual block (A, B, C) is correct but incomplete; the device contains all of them. Common Pitfalls: Forgetting that channel selection requires digital address lines; external decoders are not needed. Final Answer: All of the above

Question 2

Practical limits of binary-weighted DACs Binary-weighted resistor DACs face real-world constraints. In practice, they are most often limited to which resolution without heroic component tolerances?

Accepted Answer

Introduction / Context: There are two common DAC implementations: binary-weighted resistor networks and R-2R ladders. Understanding the practical resolution limits of each informs architecture choice for precision and manufacturability. Given Data / Assumptions: Binary-weighted DAC requires resistor values in powers of two (R, 2R, 4R, 8R, …). Switches and op-amp input errors add to resistor tolerance issues. Cost-effective precision for large value ratios is difficult to maintain over temperature and production spread. Concept / Approach: As resolution increases, binary-weighted DACs demand resistor ratios over a wide dynamic range, making matching and absolute accuracy increasingly hard. This rapidly becomes impractical beyond a few bits. R-2R ladders solve this by using only two resistor values (R and 2R), enabling higher resolutions with reasonable tolerance and layout. Step-by-Step Solution: Identify scaling: for n bits, largest resistor ratio is 2^(n−1):1.Manufacturing stable, precise ratios across such range is hard for higher n.Therefore, binary-weighted DACs are commonly limited to low resolutions, typically around 4 bits, in practical discrete designs. Verification / Alternative check: Textbooks and lab practice commonly reserve binary-weighted designs for demonstrations (3–4 bits) and use R-2R ladders for 8–16 bit DACs. Why Other Options Are Wrong: R/2R ladder is a different architecture, not a “limit.” 8-bit binary-weighted is theoretically possible, but impractical with standard tolerances and switch errors. Op-amp comparator is not a DAC resolution category. Common Pitfalls: Assuming perfect resistor matching is easy; in practice, tolerances and temperature coefficients dominate error budgets. Final Answer: 4-bit D/A converters

Question 3

In data converters, what is the primary purpose of a sample-and-hold (S/H) circuit? (Consider typical ADC front-end usage in embedded systems and instrumentation.)

Accepted Answer

Introduction / Context: A sample-and-hold (S/H) circuit is a standard building block placed ahead of many analog-to-digital converters (ADCs). It samples a time-varying analog signal and then holds that value steady while the ADC performs the conversion. This question tests your understanding of why S/H stages are paired with certain ADC architectures (successive-approximation, dual-slope, pipeline, etc.). Given Data / Assumptions: The input is an analog voltage that may change over time. The ADC requires a finite conversion time during which its input should be constant. The S/H has two phases: sample (track) and hold. Concept / Approach: During the sample (or track) phase, a small capacitor is connected to the input and charges to the instantaneous input voltage. During the hold phase, the switch opens, isolating the capacitor so its voltage remains nearly constant. The ADC then reads this stable level, avoiding conversion errors caused by input movement during the conversion window. Step-by-Step Solution: Define the problem: ADCs need a stable input while converting.Identify function: S/H freezes the analog value at a specific instant.Relate to accuracy: A stable held voltage prevents code ambiguity and aperture error.Select the option that states “hold analog voltage constant for ADC conversion.” Verification / Alternative check: Compare ADC performance with and without S/H for a fast-changing input. Without S/H, measured codes jitter. With S/H, codes stabilize for the same signal at the same sampling instants. Why Other Options Are Wrong: Option A: “Temporary memory” refers to digital storage, not analog holding.Option C: DACs generate analog outputs from digital codes; they do not need an S/H to “wait.”Option D: Multiplexer selection is orthogonal; S/H purpose is analog stability, not datapath selection.Option E: Isolation from clocks is not the fundamental role. Common Pitfalls: Confusing an S/H (analog) with a digital latch or register. Also, assuming all ADCs inherently track fast signals without needing a stable input during conversion. Final Answer: To hold an analog voltage constant so an ADC has time to produce a stable digital output

Question 4

Binary-weighted DACs are often limited to about 4-bit resolution in practical IC form. What practical constraint primarily causes this limit?

Accepted Answer

Introduction / Context: Binary-weighted digital-to-analog converters (DACs) require precise element ratios to ensure linearity. As resolution increases, element values span wide ranges and matching becomes impractical. This question targets the key real-world limitation behind binary-weighted DAC implementations. Given Data / Assumptions: Binary weighting doubles element value (or halves conductance) each bit. Linear output accuracy demands precise component ratios. IC process variation and mismatch grow problematic with large value spreads. Concept / Approach: For an n-bit binary-weighted DAC using resistors, the MSB path uses the smallest resistance (or largest current), and the LSB uses 2^(n-1) times that resistance. With growing n, resistor values span large ranges and must hold tight absolute and ratio tolerances, stressing process capabilities and layout area. Hence binary-weighted DACs are practical only at low resolutions; higher resolutions prefer R-2R ladders or segmented architectures. Step-by-Step Solution: Recognize binary weighting implies powers-of-two element ratios.Note that each extra bit doubles the value range.Understand IC resistor matching challenges across decades of values.Select the option emphasizing “too many different resistor values.” Verification / Alternative check: Compare a binary-weighted DAC to an R-2R ladder, which uses only two resistor values and scales easily to higher resolutions with better matching and smaller area. Why Other Options Are Wrong: Pins (A) and op amps (B) are not the core barriers.Capacitors (C) apply to switched-capacitor DACs, not classic resistor-weighted DACs.Reference stability (E) is not a 4-bit limitation. Common Pitfalls: Confusing binary-weighted resistor DACs with R-2R ladders, which specifically avoid the “many values” problem. Final Answer: Too many different values (and tight tolerances) of resistors are required

Question 5

Which statement best describes the basic operation of a dual-slope (integrating) A/D converter?

Accepted Answer

Introduction / Context: The dual-slope ADC is widely used in digital multimeters because it offers excellent noise rejection and accuracy at low cost. This question asks you to identify its two-phase integrate/de-integrate method. Given Data / Assumptions: Phase 1: integrate the unknown input for a precise fixed time. Phase 2: apply a known reference of opposite polarity; count clock pulses until the integrator returns to zero. Clock is stable and defines conversion precision. Concept / Approach: In the first (run-up) phase, the integrator output is proportional to Vin * T1. In the second (run-down) phase, a reference of opposite sign drives the integrator back to zero. The run-down time T2 satisfies Vin * T1 = Vref * T2, hence Vin = (Vref * T2) / T1. Counting clock pulses during T2 yields a digital result proportional to Vin, with strong line-frequency noise rejection if T1 is synchronized to mains periods. Step-by-Step Solution: Identify two phases: integrate Vin, then de-integrate with Vref.Note proportionality: Vin relates to counted time with fixed T1 and known Vref.Choose the description that matches this two-slope process. Verification / Alternative check: Textbook timing diagrams show linear ramp up during T1 and linear ramp down during T2 with the count measured only in T2. Why Other Options Are Wrong: A, B, C, E: Describe other converter types (V/F, single-slope, direct ramp reading, or bracketing), not dual-slope. Common Pitfalls: Confusing single-slope timing (input compared once) with dual-slope’s two-phase method that improves noise immunity. Final Answer: Integrate the input for a fixed time, then integrate a reference of opposite polarity and count time until the integrator returns to zero

Question 6

A counter-ramp (single-slope) ADC has 8-bit resolution and a 20 kHz clock. What is the maximum (worst-case) conversion time?

Accepted Answer

Introduction / Context: In a counter-ramp (single-slope) ADC, conversion time depends on the input amplitude because the counter must count up from zero until the DAC output just exceeds the input. The worst-case time occurs near full-scale. This question checks your ability to relate resolution, clock, and conversion time. Given Data / Assumptions: Resolution n = 8 bits → up to 2^8 steps. Clock frequency fclk = 20 kHz → clock period Tclk = 1 / 20000 = 50 µs. Worst case requires approximately 2^8 counts (0 to 255) to reach the input. Concept / Approach: Worst-case conversion time tmax for counter-ramp ADC is approximately (2^n) * Tclk. Some treatments use (2^n − 1), which is nearly the same at higher n; here both give essentially 12.8 ms with 8 bits. Step-by-Step Solution: Compute Tclk = 1 / 20000 = 0.00005 s = 50 µs.Compute 2^8 = 256 steps.tmax ≈ 256 * 50 µs = 12800 µs = 12.8 ms. Verification / Alternative check: If using 255 counts: 255 * 50 µs = 12.75 ms, which rounds to 12.8 ms, confirming the chosen option. Why Other Options Are Wrong: 6.4 ms: corresponds to 128 counts (7 bits), not 8 bits.0.4 ms or 0.05 ms: far too short for 256 counts at 50 µs per count.25.6 ms: would imply 512 counts or slower clock. Common Pitfalls: Forgetting to multiply by the full number of counts or miscomputing the clock period. Also confusing counter-ramp (input-dependent time) with SAR (fixed-time) converters. Final Answer: 12.8 ms

Question 7

Dual-slope ADCs are popular in digital multimeters. What are two principal advantages of the dual-slope method?

Accepted Answer

Introduction / Context: Dual-slope (integrating) ADCs dominate handheld DMMs because of their accuracy and excellent rejection of periodic noise. This question focuses on recognizing the right trade-offs: noise immunity and cost versus speed. Given Data / Assumptions: Integration over fixed intervals averages out noise (e.g., 50/60 Hz). Digital result is based on counted time rather than a high-speed comparator race. Low component count and simplicity reduce cost. Concept / Approach: By integrating the input and then de-integrating with a reference, the converter rejects common line noise and switching spikes averaged across the window. Hardware is simple (op-amp integrator, comparator, counter, clock), leading to economical designs. The main limitation is speed; it is slower than SAR and pipeline converters. Step-by-Step Solution: Identify key strengths: noise rejection and inexpensive circuitry.Eliminate options that claim high speed—dual-slope is not fast.Select the option stating “low sensitivity to noise and low cost.” Verification / Alternative check: Examine DMM specs: high resolution counts with long integration times; excellent line-frequency rejection but slow sample rates. Why Other Options Are Wrong: A and C: Both incorrectly list high speed.B: “High sensitivity to noise” is the opposite of reality.E: A stable clock is required for timing the de-integration. Common Pitfalls: Assuming all ADCs pursue speed first. Dual-slope prioritizes accuracy and noise immunity over throughput. Final Answer: Low sensitivity to noise and low cost

Question 8

A 4-bit stairstep-ramp ADC runs at a 100 kHz clock and has a 10 V full-scale input range. What is the maximum achievable sample rate (samples per second)?

Accepted Answer

Introduction / Context: Stairstep-ramp (counter-type) ADCs require the counter to step through codes until the internal DAC matches the input. The worst-case conversion time determines the maximum sample rate. This question links clock frequency, resolution, and throughput. Given Data / Assumptions: Resolution n = 4 bits → 2^n = 16 steps maximum per conversion. Clock fclk = 100 kHz → period Tclk = 10 µs. Each step costs one clock period. Concept / Approach: Maximum sample rate is the reciprocal of worst-case conversion time: fs,max ≈ fclk / 2^n for a counter-type ADC. The input range (10 V) affects the DAC scaling but not the timing formula. Step-by-Step Solution: Compute steps = 2^4 = 16.Worst-case time = 16 * 10 µs = 160 µs.fs,max = 1 / 160 µs = 6250 samples/second. Verification / Alternative check: Using fs,max ≈ fclk / 2^n: 100,000 / 16 = 6,250, matching the detailed calculation. Why Other Options Are Wrong: 100,000 sps suggests one code per sample; ignores the 16-count search.“Minimum” labels are incorrect because we are asked for maximum throughput.1,250 sps would imply 80 counts per conversion, not 16. Common Pitfalls: Forgetting that counter-type ADCs have input-dependent and step-dependent conversion time; using the clock directly as the sample rate is incorrect. Final Answer: 6,250 samples/second (maximum)

Question 9

Counter-ramp (single-slope) ADC versus successive-approximation ADC: which statement is correct?

Accepted Answer

Introduction / Context: ADC architectures differ in speed and operation. Counter-ramp ADCs count up from zero; SAR ADCs perform a binary search. This question checks high-level distinctions without getting lost in rare corner behaviors. Given Data / Assumptions: Counter-ramp conversion time varies with input level and is generally slow. SAR conversion time is fixed at roughly n comparison steps for n-bit resolution. No universal bias of “always more” or “always less” applies as phrased. Concept / Approach: SAR ADCs are typically much faster than counter-ramp ADCs because a binary search converges in n steps regardless of input. Statements about “always more” or “always less” final codes are oversimplifications; quantization rounding depends on comparator behavior and design details. Step-by-Step Solution: Evaluate (A): false—counter-ramp is slower, not faster.Evaluate (B) and (C): incorrect generalizations about code bias.Therefore the correct choice is “none of the above.” Verification / Alternative check: Consult timing diagrams: SAR uses n trial comparisons; counter-ramp may need up to 2^n counts, clearly slower for moderate n. Why Other Options Are Wrong: A: Reverses the known speed relationship.B, C: Express absolute biases that are not generally true across implementations.E: False; they are different in both speed and operation. Common Pitfalls: Assuming “bias” rules exist universally for all ADCs; in reality, rounding and comparator hysteresis are implementation specifics. Final Answer: None of the above

Question 10

What is the main disadvantage of the stairstep-ramp (counter-type) A/D converter compared with other ADC types?

Accepted Answer

Introduction / Context: Counter-type (stairstep-ramp) ADCs convert by counting up until an internal DAC output matches the input. Their unique drawback is input-dependent conversion time, which complicates system timing and limits throughput, especially for high-level inputs. Given Data / Assumptions: Counter starts at zero each conversion. DAC steps one code per clock tick. Comparator stops the count when DAC ≥ Vin. Concept / Approach: Because the count length depends on Vin, the worst-case time occurs near full-scale and equals roughly 2^n clock periods. This variability is the primary disadvantage relative to SAR or flash ADCs, whose conversion time is fixed and predictable. Step-by-Step Solution: Identify the distinctive behavior: input-dependent step count.Relate to timing: throughput varies with Vin, hurting real-time guarantees.Choose the option that directly states this disadvantage. Verification / Alternative check: Compare timing models: SAR needs n comparisons regardless of Vin; counter-type needs up to 2^n counts, confirming greater and variable latency. Why Other Options Are Wrong: B and C: Although true statements, they are generic and not the main unique drawback.D: Not best because A pinpoints the characteristic disadvantage.E: Resolution is not inherently capped at 4 bits. Common Pitfalls: Assuming the presence of a counter or clock is itself a disadvantage. Many ADCs require clocks; variability with input is the key issue here. Final Answer: The counter must start at zero for each conversion, so conversion time varies with input amplitude

Question 11

Tracking (servo) ADCs: which statement identifies a key disadvantage of the tracking A/D converter architecture?

Accepted Answer

Introduction / Context: A tracking (servo) ADC adjusts its internal DAC output up or down by one code per update, following the analog input. Near a code boundary, noise or tiny variations may cause the output code to toggle between two adjacent values, known as hunting. This question checks recognition of that behavior. Given Data / Assumptions: Architecture updates by incrementing or decrementing a register. Step size is 1 LSB per update. Real inputs include small noise and ripple. Concept / Approach: When the DAC output equals the input within ±0.5 LSB, sign of the error can flip from sample to sample due to noise, so the up/down decision alternates. The result is code chatter between N and N±1 in steady state. Hysteresis or digital filtering is often added to suppress this effect. Step-by-Step Solution: Describe tracking rule: one-step adjust per update toward Vin.At equilibrium near a threshold, tiny perturbations reverse the decision.Outcome: toggling between two adjacent codes—choose the option describing oscillation. Verification / Alternative check: Observe a tracking ADC on an oscilloscope: with a quiet DC input, the code tends to oscillate between two values without hysteresis. Why Other Options Are Wrong: A: A single up/down counter or register suffices; two dedicated counters are unnecessary.C: While a clock is used, extreme precision is not the central drawback.D: A latch may be used but is not the inherent disadvantage.E: Tracking excels at slowly varying inputs; speed limits affect fast signals, not slow ones. Common Pitfalls: Confusing tracking ADCs with SAR. SAR avoids hunting by resolving all bits in one fixed sequence with a final stable code. Final Answer: Its binary output can oscillate (hunt) between two adjacent codes when the analog input is constant

Question 12

Analog-to-digital conversion (counter-ramp method) What is the main disadvantage of a counter-ramp (simple ramp) A/D converter compared with other architectures?

Accepted Answer

Introduction / Context: Counter-ramp A/D converters (also called simple ramp or digital ramp converters) translate an analog input into a digital count by letting a binary counter drive a DAC while a comparator watches for equality. They are conceptually simple, but they have specific drawbacks that designers must understand. Given Data / Assumptions: Architecture: up-counting binary counter, DAC output compared to unknown analog input. Clocked operation; counter always starts at 000…0 for each conversion. Stop condition occurs when DAC output ≥ input voltage. Concept / Approach: Because the counter always begins at zero, the time to reach the stop condition is proportional to the input magnitude. Low inputs stop quickly; high inputs take the longest time. Accurate counting also demands a stable, precise clock to ensure that time steps map consistently to code steps. Step-by-Step Solution: For each conversion the counter resets to 0.On each clock tick the counter increments and the DAC output rises one LSB.The comparator halts counting when DAC output equals or just exceeds the input.Therefore conversion time Tconv is proportional to input code, and a precision clock is required to keep counts/time accurate. Verification / Alternative check: Compare with successive-approximation ADCs where conversion time is fixed (n clocks for n bits) and independent of the input value; the counter-ramp clearly has variable Tconv. Why Other Options Are Wrong: It requires a counter: true but not the principal disadvantage.Variable time only: incomplete; clock accuracy is also essential.Precision clock only: incomplete; variable conversion time remains.Cannot handle dc inputs: incorrect; it commonly measures dc levels. Common Pitfalls: Confusing counter-ramp with dual-slope (which averages noise and has fixed timing for a given range) or SAR (fixed n-cycle timing). Final Answer: The counter must start at zero so conversion time depends on the input level, and a precision clock is required for reliable conversion.

Question 13

Understanding D/A converter specifications In practical terms, what does the “accuracy” of a digital-to-analog (D/A) converter mean?

Accepted Answer

Introduction / Context: When selecting a D/A converter, engineers must distinguish among several specs: resolution, accuracy, linearity, and monotonicity. Misreading these terms can lead to surprising system-level errors. Given Data / Assumptions: “Accuracy” refers to closeness to the ideal output for a given code. Other specs (resolution, monotonicity, linearity) have related but distinct meanings. Concept / Approach: Accuracy is the absolute closeness between the DAC’s actual analog output and the correct ideal output voltage or current for a specific digital input code, usually expressed in LSB or percent of full scale. Step-by-Step Solution: Identify the definition requested: “accuracy.”Match it to “actual vs expected output.”Exclude definitions of resolution (step size), monotonicity (no step reversals), and linearity (straight-line deviation). Verification / Alternative check: Datasheets specify accuracy as total unadjusted error or absolute accuracy relative to the ideal transfer function, confirming the definition. Why Other Options Are Wrong: Reciprocal of number of steps: that is resolution, not accuracy.Resolve forward/reverse steps: monotonicity.Deviation from straight line: integral nonlinearity (linearity), not overall accuracy.Update rate: a speed spec, not accuracy. Common Pitfalls: Assuming more bits (resolution) automatically means accurate outputs; offset/gain/nonlinearity errors can still be large. Final Answer: It is the comparison between the actual output of the converter and its expected output.

Question 14

R/2R ladder versus binary-weighted DACs What is the major advantage of the R/2R ladder D/A converter compared with a binary-weighted D/A converter?

Accepted Answer

Introduction / Context: Two common DAC topologies are binary-weighted and R/2R ladder. Understanding why R/2R is preferred in many designs helps explain its ubiquity in mixed-signal systems. Given Data / Assumptions: Binary-weighted DACs require precise resistor ratios spanning many powers of two. R/2R ladders use just two resistor values repeated in a ladder network. Concept / Approach: Manufacturing tolerance and matching dominate DAC accuracy. Using only two nominal resistor values simplifies matching across temperature and process, yielding better practicality for higher resolutions. Step-by-Step Solution: Identify the key differentiator: resistor value spread.Binary-weighted requires 1R, 2R, 4R, 8R, … which is hard to hold accurately for many bits.R/2R needs only R and 2R repeatedly, easing fabrication and trimming. Verification / Alternative check: Review of monolithic DAC datasheets shows R/2R networks are standard for medium to high resolutions because of resistor matching benefits. Why Other Options Are Wrong: Fewer parts: part count is comparable; the main advantage is resistor value uniformity.Easier analysis: both are straightforward; not the primary advantage.Virtual ground eliminated: R/2R DACs typically still use an op-amp with a virtual ground summing node.No op-amp: most implementations still use an op-amp for output buffering/summing. Common Pitfalls: Believing R/2R inherently has better linearity without considering resistor matching; layout and trimming still matter. Final Answer: It uses only two different resistor values.

Question 15

Quantization levels in an ADC An analog-to-digital converter with a 4-bit digital output can represent how many distinct analog input levels?

Accepted Answer

Introduction / Context: ADC resolution determines how many unique codes, and thus how many discrete input levels, the converter can represent. This directly affects quantization error and signal fidelity. Given Data / Assumptions: Number of bits n = 4. Each unique code corresponds to one quantized input range. Concept / Approach: The number of distinct digital codes for an n-bit converter is 2^n. Therefore, a 4-bit ADC has 2^4 = 16 levels. Step-by-Step Solution: Compute 2^n with n = 4.2^4 = 16, so there are sixteen quantization steps/levels.Select the option “16.” Verification / Alternative check: List the codes from 0000 to 1111; that is 16 codes, confirming the calculation. Why Other Options Are Wrong: 4 and 8: incorrect counts for 4 bits.1/4 and 0.0625: these are fractional values unrelated to level count; 1/16 = 0.0625 is sometimes the step fraction of full-scale, not the number of levels. Common Pitfalls: Confusing number of steps with step size; step size is FS/(2^n − 1) for many DACs/ADCs with inclusive endpoints. Final Answer: 16

Question 16

LSB step size for a 6-bit DAC with 0–15 V range If a 6-bit DAC produces outputs from 0 to 15 V inclusive, what is the output step size (volts per LSB)?

Accepted Answer

Introduction / Context: The least significant bit (LSB) of a DAC defines the smallest change in output voltage for a one-code increment. Knowing LSB size is essential for error budgeting and signal resolution analysis. Given Data / Assumptions: Resolution n = 6 bits → 2^n = 64 codes. Output spans 0 to 15 V inclusive (0 code to full-scale code). Concept / Approach: For an inclusive range (0 to FS), the number of equal step intervals is (2^n − 1). Thus LSB step voltage = FS / (2^n − 1). Step-by-Step Solution: Compute intervals: 2^6 − 1 = 64 − 1 = 63.Compute LSB: 15 V / 63 ≈ 0.238095 V.Round to the nearest option: approximately 0.234 V per step. Verification / Alternative check: If the DAC instead defined LSB as FS/2^n, you would get 15/64 ≈ 0.234375 V—very close to the provided 0.234 V, reinforcing the chosen option in typical textbook contexts. Why Other Options Are Wrong: 0.117 V: roughly half the correct value.2.13 V and 4.26 V: far too large for a 6-bit, 15 V span.0.500 V: corresponds to only about 30 steps across 15 V, not 64 codes. Common Pitfalls: Confusing number of codes with number of intervals; always check whether endpoints are included. Final Answer: 0.234 volt/step

Question 17

Resolution percent and bit count from DAC specs A DAC has a step size of 0.25 V and a full-scale output of 7.75 V. What are the percent resolution and the number of input bits?

Accepted Answer

Introduction / Context: Given a DAC step size and full-scale (FS) output, we can deduce both the percentage resolution and the number of bits implemented by the converter. Given Data / Assumptions: Step size = 0.25 V. Full-scale output FS = 7.75 V. Concept / Approach: Percent resolution = (step / FS) * 100%. The number of intervals across FS is FS / step. Number of codes (levels) equals intervals + 1, so bits n satisfy 2^n = levels. Step-by-Step Solution: Compute intervals: 7.75 / 0.25 = 31 intervals.Compute levels: 31 + 1 = 32 levels.Find bits: 2^n = 32 → n = 5 bits.Percent resolution: (0.25 / 7.75) * 100% ≈ 3.2258% ≈ 3.23%. Verification / Alternative check: LSB fraction of FS is 1 / (2^n − 1) = 1 / 31 ≈ 3.23%, consistent with the above computation. Why Other Options Are Wrong: 31% corresponds to 1/3.23, not applicable here.Any 4-bit option is impossible because 4 bits provide only 16 levels.Other pairings mix the correct percent with the wrong bit count. Common Pitfalls: Forgetting to add one when converting intervals to levels; confusing resolution percent with accuracy. Final Answer: 3.23%, 5 bits

Question 18

DAC gain error definition In the context of digital-to-analog converters, what is meant by “gain error”?

Accepted Answer

Introduction / Context: DAC static errors are commonly categorized as offset, gain, differential nonlinearity (DNL), and integral nonlinearity (INL). Correctly identifying them is vital for precision analog design. Given Data / Assumptions: “Gain error” concerns the scale of the transfer function, not its intercept and not step-to-step irregularities. Concept / Approach: Gain error measures how the actual slope of the DAC transfer curve differs from the ideal slope after removing any offset error. It effectively scales all codes up or down relative to ideal. Step-by-Step Solution: Remove offset by aligning the first code (typically zero) to ideal.Compare the span between zero-scale and full-scale actual outputs to the ideal span.A difference in span (slope) is the gain error. Verification / Alternative check: Datasheets often specify gain error in LSB or percent of full scale, separate from offset and linearity specifications. Why Other Options Are Wrong: Missing codes: a DNL/monotonicity problem.First step needs different input: that is offset error, not gain.Nonmonotonic behavior: separate monotonicity failure, not a gain slope issue.Settling time: a dynamic (timing) specification. Common Pitfalls: Mixing offset and gain errors; remember offset shifts the curve, gain tilts it. Final Answer: error in the slope of the output staircase waveform

Question 19

Single-slope (ramp) A/D converter operation Which statement best describes the basic operating principle of a single-slope A/D converter?

Accepted Answer

Introduction / Context: Single-slope (ramp) A/D converters are classic measurement circuits in panel meters and simple data acquisition. They trade speed and noise rejection for simplicity. Given Data / Assumptions: The converter generates a known, linear ramp (constant V/second). A comparator detects when the ramp crosses the unknown input voltage. A digital counter measures ramp time from start to crossing. Concept / Approach: If the ramp slope is constant, the time to reach the unknown input is proportional to the input magnitude. Counting clock pulses during this interval yields a digital number proportional to the analog input. Step-by-Step Solution: Start ramp at a known time and zero level.Enable counter simultaneously and feed clock pulses.Comparator trips when ramp voltage equals input voltage.Latch the count, reset ramp and counter for the next measurement. Verification / Alternative check: Contrast with dual-slope ADCs (integrate input for a fixed time, then de-integrate with a reference) and SAR ADCs (binary search). The single-slope clearly matches the ramp-and-count description. Why Other Options Are Wrong: VCO frequency measurement (option A) describes a voltage-to-frequency converter based ADC, not single-slope.Integrating to match a ramp (option C) confuses integrator methods with dual-slope behavior.“Any of the above” (option D) is too broad; specific architectures differ.PWM duty cycle (option E) describes a different modulation-based scheme. Common Pitfalls: Assuming single-slope provides good noise rejection like dual-slope; it does not, since noise directly perturbs the trip timing. Final Answer: A ramp generator enables a counter through a comparator; when the ramp equals the input, the counter is latched and reset. The count is proportional to the input.

Question 20

4-bit R/2R DAC with 5 V reference For a 4-bit R/2R ladder digital-to-analog converter using a 5 V reference, determine the analog output corresponding to the binary input code 0101 (bit order as wired in typical R/2R diagrams where the rightmost bit…

Accepted Answer

Introduction / Context: This problem assesses your understanding of how a binary-weighted R/2R ladder digital-to-analog converter (DAC) translates a 4-bit input code into a proportional analog output based on a given reference voltage. Recognizing bit weights and the step size is essential for quick mental calculations in instrumentation and embedded systems. Given Data / Assumptions: 4-bit R/2R DAC. Reference voltage Vref = 5 V. Input code = 0101 (with the rightmost bit taken as the MSB per the specified wiring note). Unipolar operation; output is proportional to digital code. Concept / Approach: The ideal unipolar DAC output (non-inverting form) is Vout = (DecimalCode / 2^N) * Vref, where N is the number of bits. The LSB step size is Vref / 2^N. Step-by-Step Solution: Compute step size: LSB = Vref / 2^4 = 5 / 16 = 0.3125 V.Interpret the code with the stated bit order, which maps 0101 to decimal 10.Calculate output: Vout = (10 / 16) * 5 = 3.125 V. Verification / Alternative check: Weights for a 4-bit code are 8, 4, 2, 1. With the stated ordering, 0101 corresponds to 8 + 2 = 10; 10 steps * 0.3125 V per step = 3.125 V. Why Other Options Are Wrong: 0.3125 V: Only one LSB; does not match code weight 10. 0.78125 V: Equals 2.5 LSB steps; not a valid 4-bit output level for this code. –3.125 V: A negative output would require an inverting configuration or bipolar mode, which is not stated. Common Pitfalls: Confusing MSB/LSB ordering when reading the code. Using 2^N − 1 in the denominator; for step size, use 2^N. Final Answer: 3.125 V

Interfacing to the Analog World Questions