Digital-to-analog ladder basics: In a five-step R/2R ladder network, the smallest resistor value is 1 kΩ. What is the largest resistor value used in the ladder (ignoring end resistors or op-amp components)?

Introduction / Context:The R/2R ladder is a classic digital-to-analog converter (DAC) network that uses only two resistor values: R and 2R. This uniformity simplifies matching and linearity, regardless of the number of bits (steps). Recognizing that only R and 2R appear allows quick identification of the largest value once the smallest is given.

Given Data / Assumptions:

• An R/2R ladder with five steps (a 5-bit ladder).
• The smallest resistor value present is 1 kΩ.
• Only ideal passive resistors R and 2R are considered.

Concept / Approach:By construction, an R/2R ladder uses two values: R and its double 2R. If the smallest value is 1 kΩ, that must correspond to R. Therefore, the largest value used is 2R = 2 * 1 kΩ = 2 kΩ. The number of stages does not introduce additional resistor magnitudes beyond these two.

Step-by-Step Solution:

Verification / Alternative check:Inspect standard R/2R schematics: all horizontal rungs are R, all vertical legs are 2R. Only these two values occur, independent of bit count, confirming the result.

Why Other Options Are Wrong:

• 10 kΩ, 20 kΩ: Not used in a pure R/2R ladder unless scaled globally.
• indeterminable: The ladder definition itself determines the values; it is determinable.

Common Pitfalls:

• Assuming more values appear as the number of steps increases.

Final Answer:2 kΩ