FE Electrical & Computer Practice Question Solution included after investigation
CASE E-024 · FE

The 1 kHz Filter That Only Passed 70.7%

A 'passband' tone reached the cutoff and lost nearly 30% of its amplitude.

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Case E-024 engineering failure visual
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1

Inspect

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2

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Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

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Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A first-order RC low-pass is specified with fc = 1.0 kHz. A 1.0 kHz, 2.00 V peak sensor tone is expected to pass almost unchanged, but the measured output is about 1.41 V peak. Diagnose the missing amplitude and choose a higher cutoff that keeps at least 90% of the 1 kHz amplitude.

Signal Processing Electrical & Computer Design Verification Root Cause Analysis Safe Correction
E-024
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What was measured

A 2.00 V peak input became about 1.414 V peak at 1 kHz.

What was missed

The cutoff frequency is already the -3 dB point.

Corrected model

Use the magnitude response to place fc according to allowed attenuation.

QUICK ANSWER

For a first-order RC low-pass, the cutoff frequency is the -3 dB point. At f = fc, |H| = 1/sqrt(2) ≈ 0.707, so a 2.00 V peak input becomes about 1.414 V peak.

ENGINEERING TAKEAWAY

Treat cutoff as the -3 dB point, not a zero-loss boundary. Use |H| = 1/sqrt(1+(f/fc)^2) and choose fc from the allowed amplitude loss.

CASE QUESTIONS

Questions this case should settle.

What is the gain of a first-order low-pass at cutoff?

About 0.707, or -3 dB.

Why is cutoff called the half-power point?

Because power is proportional to amplitude squared, so 0.707² is about 0.5.

How do I reduce attenuation at a frequency of interest?

Place the cutoff sufficiently above that frequency based on the allowed magnitude loss.

NEXT FE PRACTICE QUESTION

The Digital Filter That Lagged a Perfect Step

Signal Processing · 5–10 min

Continue Practice →
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