Edge-frequency estimate: If a pulse has a 10 µs rise time and 10 µs fall time, what is the highest significant frequency contained in the waveform?

Introduction / Context:
Rise time is linked to the bandwidth of a system or equivalently to the highest significant frequency content in a pulse. A widely used rule-of-thumb relates the bandwidth to the rise time for first-order systems and many practical pulses.

Given Data / Assumptions:

• Rise time Tr = 10 µs (and similar fall time).
• We are estimating the significant highest frequency component.
• Assume approximately first-order edge shaping.

Concept / Approach:
The common approximation is BW ≈ 0.35 / Tr, where Tr is the 10%–90% rise time (seconds) and BW is the -3 dB bandwidth (Hz). This corresponds to the frequency content needed to support that edge sharpness.

Step-by-Step Solution:
Tr = 10 µs = 10 × 10^-6 sBW ≈ 0.35 / Tr = 0.35 / 10e-6BW ≈ 35,000 Hz = 35 kHz

Verification / Alternative check:
For a 1 µs rise time, the estimate would be ~350 kHz; scaling Tr by 10 increases the rise time and reduces the bandwidth by 10, hence 35 kHz for 10 µs fits the rule.

Why Other Options Are Wrong:

• 3.5 kHz or 10 kHz: Too low for a 10 µs edge.
• 100 kHz: Too high; would correspond to shorter rise times around 3.5 µs.

Common Pitfalls:
Confusing the 0.35 constant (rise time rule) with the 0.707 factor from -3 dB magnitude, or mis-converting microseconds to seconds. Always express Tr in seconds before applying the formula.

Final Answer:
35 kHz