# How to Design Active Band Pass Filter - Cascaded HPF and LPF Band Pass Filter

Electronics filters are used to allow or block signals with certain range of frequencies. Noise suppression filters, EMI suppression filters, filters in communication systems are example of usage of electronics filters. Electronics filters can be passive or active filters. Filters that uses passive components like resistors, capacitors and inductors are called passive filters. Active filters uses operational amplifiers along with capacitor and resistors for filtering operation. No inductors are used in active filters. Filters are also classified as low pass filters, high pass filters, band pass filters, band reject filters or band stop filters.

Last tutorial How to design Active Filters- Low Pass Filter & High Pass Filter showed how to design active LPF and HPF. Here active band pass filter is explained with different methods of realizing a band pass filter. Design example are provided along with online band pass filter calculator.

A band pass filter is an electronics filter which allows signal(s) of certain desired range of  frequencies to pass and blocks other frequencies.

There are couples of methods to realize a band pass filters which are:

- Cascaded HPF and LPF Band Pass Filter

- Multi-Feedback Band Pass Filter

- State Variable Band Pass Filter

### Cascaded HPF and LPF Band Pass Filter

One way of creating a band pass filter is to cascade a HPF(High Pass Filter) and LPF(Low Pass Filter). The order of cascading filters does not matter, that is, either LPF can placed first and HPF latter or vice versa.

#### Second order Cascaded HPF/LPF Band Pass Filter

The following shows circuit diagram of 2nd order active Band Pass Filter by cascading a 2nd order active HPF with a 2nd order active LPF.

In the above circuit diagram, both the low pass filter and high pass filter are using Sallen-Key topology. The rolloff rate is -40dB/decade. The frequency response graph of the bandpass filter is shown below.

The lower cutoff frequency fc1 is due to high pass filter and is given by the following equation,

$f_{c1}= \frac{1}{2 \pi \sqrt{R_{A1} R_{B1} C_{A1} C_{B1}} }$

Similarly, the higher cutoff frequency fc2 is due to low pass filter and is given by the following equation,

$f_{c2}= \frac{1}{2 \pi \sqrt{R_{A2} R_{B2} C_{A2} C_{B2}} }$

The center frequency fo which is inside the passband is given by the geometric mean of lower and higher cutoff frequency as follows,

$f_{0}= \sqrt{f_{c1} f_{c2} }$

### Online Cascaded HPF and LPF Band Pass Filter

Inputs:

Theoretical Results:

Design Example:

Let the lower and upper cutoff frequencies be fc1=1KHz, fc2=4KHz. Let the choose C=CA1=CB1=CA2=CB2=0.001uF. Also let the passband gain Ap=1.58 and choose R2=R4=10KOhm then using the above calculator we have,

fo=2KHz,  RA1=RB =159.24 KOhm, RA2=RB2 =39.81 KOhm and R1=R3=5.80 KOhm.

The following shows circuit schematic of the cascaded band pass filter using LM324 op-amp with component values.

The following shows the frequency response of the above second order BPF.

The following video shows how to plot frequency response graph of the designed band pass filter in Proteus electronics circuit simulation software.

The following video shows simulation of the designed band pass filter to check the filter response to signal generated by function generator in Proteus Software with display of the output signal on the oscilloscope.

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