High Pass Filter Bode Plot or Frequency Response

The frequency response or bode plot of the high pass filter is totally opposite compared to the frequency response of the low pass filter.

Using the transfer function, we can plot a frequency response of the filter circuit. The magnitude curve and phase curve of the bode plot for high pass filter is as shown in the below figure.

The magnitude curve can be obtained by the magnitude of the transfer function.

$\begin{align*} | H(j \omega)|= \frac{\omega}{\sqrt{\omega^2 + (\frac{1}{RC})^2}} \end{align*}$

The phase curve can be obtained by the phase equation of the transfer function.

$\begin{align*} \theta(j\omega) = 90^\circ - \tan^-^1(\omega RC) \end{align*}$

Magnitude Plot

As shown in the magnitude curve, it will attenuate the low frequency at the slope of +20 db/decade. The region from an initial point to the cutoff frequency is known as stop band.

When it crosses the cutoff frequency, it will allow the signal to pass. And the region above the cutoff frequency point is known as a pass band.

At cutoff frequency point the output voltage amplitude is 70.7% of the input voltage.

Phase Plot

At cutoff frequency, the phase angle of the output signal is +45 degree. From the phase plot, the output response of the filter shows that it can pass to infinite frequency. But in practice, the output response does not extend to infinity.

By proper selection of components, the frequency range of filter is limited.

Ideal High Pass Filter

The ideal high pass filter blocks all the signal which has frequencies lower than the cutoff frequency. It will take an immediate transition between pass band and stop band.

The magnitude response of the ideal high pass filter is as shown in the below figure. The amplitude will remain as original amplitude for signals which have a higher frequency than the cutoff frequency. And the amplitude will completely zero for signals which have a lower frequency than the cutoff frequency. Therefore, an ideal high pass filter has a flat magnitude characteristic.

The transfer function of ideal high pass filter is as shown in the equation below:

$\begin{equation*} |H(\omega)| = \begin{cases} 1, & |\omega|>\omega_c \\ 0, & \omega|<\omega_c \end{equation*}$

The frequency response characteristics of an ideal high pass filter is as shown in below figure.

This type of ideal characteristic of a high pass filter is not possible for practical filters. But the Butterworth filter characteristic is very close to the ideal filter.

Applications of High Pass Filters

The applications of high pass filters include:

It is used in amplifiers, equalizers, and speakers to reduce the low-frequency noise.
For sharpening the image, high pass filters are used in image processing.
It is used in various control systems.

Ezoic

Magnitude Plot

Phase Plot

Ideal High Pass Filter

Applications of High Pass Filters

Published by howdy