TECHCENTER

First Order Band Pass Filter Transfer Function

A first order band pass filter is not possible, because it has minimum two energy saving elements (capacitor or inductor). So, the transfer function of second-order band pass filter is derived as below equations.

Second Order Band Pass Filter Transfer Function

A second-order band pass filter transfer function has been shown and derived below.

Band Pass Filter Transfer Function

Where,

Band Pass Filter Cutoff Frequency

The band pass filter is a combination of two filters. Therefore, it has two cutoff frequencies. One cutoff frequency is derived from the high pass filter and it is denoted as Fc-high. The filter allows the signal which has the frequencies more than Fc-high. The value of Fc-high is calculated from the below formula.

  The second cutoff frequency is derived from the low pass filter and it is denoted as Fc-low. The filter allows the signal which has frequencies lower than the Fc-low. The value of Fc-low is calculated from the below formula.

  The filter operates between frequencies Fc-high and Fc-low. The range between these frequencies is known as bandwidth. Therefore, the bandwidth is defined as the below equation.

The cutoff frequency of a high pass filter will define the lower value of bandwidth and the cutoff frequency of low pass filter will define the higher value of bandwidth.

Band Pass Filter Bode Plot or Frequency Response

The above figure shows the bode plot or the frequency response and phase plot of band pass filter. The filter will allow the signal which has a frequency in between the bandwidth.

The filter will attenuate the signals which have frequency lower than the cutoff frequency of high pass filter. And till the signal reaches to FL, the output is increasing at the rate of +20 DB/Decade the same as the high pass filter.

After that, the output continuous at maximum gain until it reaches the cutoff frequency of low pass filter or at the point FH. Then the output will decrease at the rate of -20 DB/Decade the same as the low pass filter.

The band pass filter is a second-order filter because it has two reactive components in the circuit diagram. Therefore, the phase difference is twice the first-order filter and it is 180˚.

Until the center frequency, the output signal leads the input by 90˚. At the center frequency, the output signal is in phase with the input. Hence, the phase difference is 0˚.

After the center frequency, the output signal lags the input by 90˚.

Ideal Band Pass Filter

An ideal band pass filter allows signal with exactly from FL similar to the step response. The signal allowing exactly at FL with the slope of 0 DB/Decade. And it abruptly attenuates the signals which have frequency more than FH.

The frequency response of the ideal band pass filter is as shown in the below figure. This type of response cannot result in an actual band pass filter.

Band Pass Filter Equation

When the signal frequency is in the range of bandwidth, the filter will allow the signal with input impedance. And the output is zero when the signal frequency is outside of the bandwidth.

For band pass filter;

Band Pass Filter Applications

The application of band pass filter is as follows,

Band pass filters are widely used in audio amplifier circuits. For example, the speaker is used to play only a desired range of frequencies and ignore the rest of the frequencies.

It is used optics like LASER, LIDARS, etc.

These filters are used in a communication system for choosing the signals with a particular bandwidth.

It is used in audio signal processing.

It is also used to optimize the signal to noise ratio and sensitivity of the receiver.