In a RC high-pass filter, as ω approaches infinity, the magnitude of the transfer function approaches which value?

In a RC high-pass filter, as ω approaches infinity, the magnitude of the transfer function approaches which value?

• A. 1
• B. 0.5
• C. 0
• D. Infinity

Answer: (A)

High-pass RC filters pass high-frequency signals with almost no attenuation. The magnitude of its transfer function is |H(jω)| = ωRC / sqrt(1 + (ωRC)^2). When ω becomes very large, the term (ωRC)^2 dominates, so sqrt(1 + (ωRC)^2) ≈ ωRC, and the ratio tends to 1. So the magnitude approaches 1, meaning the output follows the input in amplitude at high frequencies. This contrasts with low frequencies, where the magnitude tends to 0, and the cutoff occurs at ωc = 1/RC.

High-pass RC filters pass high-frequency signals with almost no attenuation. The magnitude of its transfer function is |H(jω)| = ωRC / sqrt(1 + (ωRC)^2). When ω becomes very large, the term (ωRC)^2 dominates, so sqrt(1 + (ωRC)^2) ≈ ωRC, and the ratio tends to 1. So the magnitude approaches 1, meaning the output follows the input in amplitude at high frequencies. This contrasts with low frequencies, where the magnitude tends to 0, and the cutoff occurs at ωc = 1/RC.