What is the transfer function representation of a high pass filter?

What is the transfer function representation of a high pass filter?

• A. 1/(1 + jw)
• B. jw/(1 + jw)
• C. 1/(1 + j/w)
• D. jw/(1 + j/w)

Answer: (B)

The transfer function of a high-pass filter describes how the filter responds to different frequencies of input signals. A high-pass filter allows high-frequency signals to pass through while attenuating low-frequency signals. The correct answer, which presents the transfer function as \( \frac{jw}{1+jw} \), reflects this behavior. In this function, \( jw \) represents the frequency-dependent gain that increases with higher frequencies. As the frequency \(w\) increases, the term \(jw\) dominates the denominator, leading to a transfer function that approaches 1. This means that high frequencies are passed with minimal attenuation. In contrast, at lower frequencies, the behavior of the function changes. The term \(1 + jw\) in the denominator suggests that as the frequency decreases, the impact of the \(1\) term becomes significant, resulting in a lower output relative to the input, thus demonstrating the filter's ability to reject low frequencies. This behavior aligns with the typical characteristics of a high-pass filter, making the transfer function \( \frac{jw}{1+jw} \) an accurate representation. The other forms do not represent the standard response of a high-pass filter effectively, particularly when considering the physical implications of frequency response and gain.

The transfer function of a high-pass filter describes how the filter responds to different frequencies of input signals. A high-pass filter allows high-frequency signals to pass through while attenuating low-frequency signals.

The correct answer, which presents the transfer function as ( \frac{jw}{1+jw} ), reflects this behavior. In this function, ( jw ) represents the frequency-dependent gain that increases with higher frequencies. As the frequency (w) increases, the term (jw) dominates the denominator, leading to a transfer function that approaches 1. This means that high frequencies are passed with minimal attenuation.

In contrast, at lower frequencies, the behavior of the function changes. The term (1 + jw) in the denominator suggests that as the frequency decreases, the impact of the (1) term becomes significant, resulting in a lower output relative to the input, thus demonstrating the filter's ability to reject low frequencies.

This behavior aligns with the typical characteristics of a high-pass filter, making the transfer function ( \frac{jw}{1+jw} ) an accurate representation. The other forms do not represent the standard response of a high-pass filter effectively, particularly when considering the physical implications of frequency response and gain.