Question

A first-order high-pass RC filter has cutoff frequency \(\text{f}_\text{c}=1\text{ kHz}\). If the magnitude of the transfer function is measured at \(\text{f}=500\text{ Hz}\), the gain magnitude is

• A. \(0.25 \)
• B. \(0.45 \)
• C. \(0.71 \)
• D. \(0.89 \)

Hint:

For a first-order filter: - High Pass Filter Magnitude: \( \frac{1}{\sqrt{1 + (f_c/f)^2}} \) - Low Pass Filter Magnitude: \( \frac{1}{\sqrt{1 + (f/f_c)^2}} \) Since the operating frequency ($500\text{ Hz}$) is exactly half of the cutoff frequency ($1\text{ kHz}$), it must experience significant attenuation (more than $3\text{ dB}$, meaning less than $0.707$). This immediately eliminates $0.71$ and $0.89$, allowing you to quickly choose between $0.25$ and $0.45$.

Answer 1

The Correct Option is B