Pulse Edges — Standard definitions of rise time (tr) and fall time (tf) Fill in the standard reference levels used to define a pulse’s rise and fall times: tr is measured from ________ to ________; tf is measured from ________ to ________.

Introduction / Context:
Rise and fall times provide standardized measures of how quickly a digital signal transitions. The industry-standard convention uses percentage thresholds of the final amplitude to avoid ambiguity caused by ringing and overshoot.

Given Data / Assumptions:

• We assume a monotonic transition between well-defined LOW and HIGH levels.
• Measurement thresholds are taken as fractions of the steady-state amplitude.
• Oscilloscope rise/fall measurements typically default to these standard percentages.

Concept / Approach:
By convention, rise time tr is the time required for a waveform to transition from 10% to 90% of its final amplitude; fall time tf is measured from 90% down to 10%. This symmetric convention captures the main transition interval and minimizes sensitivity to endpoint aberrations.

Step-by-Step Solution:
Identify rise time reference → lower threshold 10% to upper threshold 90%.Identify fall time reference → upper threshold 90% to lower threshold 10%.Map to choices → “10%, 90%, 90%, 10%.”

Verification / Alternative check:
Oscilloscope manuals and digital design texts consistently define tr and tf using 10–90% thresholds. Some RF specs use 20–80% for bandwidth correlation, but that is a different (non-default) standard.

Why Other Options Are Wrong:

• b: Reverses rise/fall definitions.
• c: 20–80% is a nonstandard alternative, not the common digital default.
• d: 70.7% is a special amplitude (1/√2) used for bandwidth, not edge timing.

Common Pitfalls:
Measuring from 0% to 100% leads to inconsistent results due to overshoot, undershoot, and noise at endpoints.

Final Answer:
10%, 90%, 90%, 10%