Here Sallen-Key second order unity gain active low pass filter with Butterworth response is designed and tested. The filter is build on a breadboard and its frequency response and waveform are are shown. Here an active second filter is used which means operational amplifier is used. Here LM358 operational amplifier was selected. Other op-amp such as TL072, TL074 etc can be used as well.

**Recommended prerequisites**

- Active 1st Order Low Pass Filter Design on Breadboard
- First order Active HPF Design and Test
- Active 2nd order HPF with LM358
- Active 2nd order LPF on breadboard

### Video demonstration

Watch the following video demonstration of how SallenKey second order Unity gain Low Pass Filter works.

In the video, it can be seen that the amplitude of the filtered output signal from the filter decreases as the frequency is increased because the low pass filter will attenuate high frequency signal. The video also shows that the amplitude of the output signal before 1KHz is equal to the amplitude of the input driving signal. That is the output signal amplitude is not greater than the magnitude of the input signal. This is because the filter is a unity gain filter with voltage gain of 1.### Sallen Key Unity Gain LPF on breadboard

The following shows the Sallen key unity gain low pass filter build on a breadboard.

### Sallen Key Unity Gain LPF Circuit Diagram

Following is the circuit diagram of Sallen key unity gain low pass filter.

For unity gain filter the passband voltage gain is unity, that is \( A_v=1 \) . In unity gain sallen key filter equal resistors(R) are used but the capacitors are different. For this filter the Quality factor Q is given by,

\( Q=0.5\sqrt{\frac{C_2}{C_1}} \)

Here we are designing filter with Butterworth response. In this case Q has value of 0.707. By selecting C1 equal to 10nF we can obtain the capacitor C2 which is 20nF.

The pole frequency of the 2nd order filter is given by,

\( f_p = \frac{1}{2 \pi \sqrt{R_1 R_2 C_1 C_2}} \)

But here we are using equal resistors R1=R2=R so the above equation is,

\( f_p = \frac{1}{2 \pi R \sqrt{C_1 C_2}} \)

The cutoff frequency(fc) is related to the pole frequency(fp) as follows,

\( f_c = K_c f_p \)

where \(Kc\) is a proportionality constant

For Butterworth filter, \(Kc=1\) and so for Butterworth filter, pole frequency is the same as the cutoff frequency. Hence by selecting cutoff frequency and knowing the value of C2 and C1 we can calculate the resistor R value. In this case the value of R turns out to be approximately 11kohm.

We can calculate all this values using the Sallen-Key 2nd order unity gain LPF calculator.

### Waveform and Frequency Response

The following shows the frequency response of simulation of the above filter circuit in electronics design software.

The frequency response graph of actual build Sallen-Key 2nd Order Unity Gain LPF circuit on the breadboard driven by actual signal is shown below.

Waveform Graph

At 500Hz which is below the cutoff frequency the output and input signal amplitude are almost equal. This is shown in the following waveform graph.

At input signal frequency of 1kHz the input and output signal waveform is shown shown below. As you can see the output signal amplitude is decreased relative to the input but not by so much.