Third-order Lowpass Butterworth Filter
Third-order Lowpass Butterworth Filter
Third-order lowpass Butterworth filter can design by cascading the first-order and second-order Butterworth filter.
The below figure shows the circuit diagram of the third-order lowpass Butterworth filter.
In this figure, the first part shows the first-order lowpass Butterworth filter, and the second part shows the second-order lowpass Butterworth filter.
But in this condition, the voltage gain of the first part is optional and it can be set at any value. Therefore, the first op-amp is not taking part in voltage gain. Hence, the figure for the third-order low pass filter can be expressed as below figure also;
The voltage gain of a second-order filter affects the flatness of frequency response. If the gain of the second-order filter is kept at 1.586, the gain will down 3db for each part. So, the overall gain will down 6dB at the cutoff frequency.
Increasing the voltage gain in the second-order filter compensates for any cumulative voltage loss.
In the third-order Butterworth filter, the rate of a roll-off period is -60dB/decade. And the frequency response of this filter is nearer to the ideal Butterworth filter compared to the first and second-order filters. The frequency response of this filter is as shown in the below figure.
Fourth-order Lowpass Butterworth Filter
Fourth-order Butterworth filter is established by the cascade connection of two second-order low pass Butterworth filters. The circuit diagram of the fourth-order lowpass Butterworth filter is as shown in the below figure.
If the gain of both filters is set at 1.586, the voltage gain will be down 6 dB at the cutoff frequency. We can get a more flat response by choosing different values of voltage gain for both stages. According to the advanced research, we get maximum flat response, if we use the voltage gain 1.152 for the first stage and 2.235 for the second stage.
The illustrated figure below displays the frequency response for a fourth-order lowpass Butterworth filter.
