Second Order Active Low Pass Filter Voltage Gain

The gain of the second-order filter is a product of gain of ‘n’ stages that are cascaded together. For example, if two first-order filters are cascaded, the gain of the filter will be as follows.

$\begin{align*} A_{v}= A_{v1}\times A_{v2} \end{align*}$

$\begin{align*} A_{v}= 10\times 30 = 300\end{align*}$

If the gain of both stages are given in dB, then the total gain is calculated by adding both gains

$\begin{align*} A_{v} (dB) = A_{v1} + A_{v2} \end{align*}$

Second Order Active Low Pass Filter Cutoff Frequency

The cut-off frequency equation is given as

$\begin{align*} f_{c}=\frac{1}{2\pi\sqrt{R_{3}R_{4}C_{1}C_{2}}} \end{align*}$

When R3 = R4 = R and C1=C2=C then the cut-off frequency will be given as

$f_{c}=\frac{1}{2\pi RC}$

The gain at the cut-off frequency for the first stage of filter is -3dB. For second order filter, combining the gain of two first order filters, the total gain will be -6dB.

Second Order Active Low Pass Filter Design And Example

Assume Rs1 = Rs2 = 15KΩ and capacitor C1 = C2 = 100nF. The gain resistors are R1=1KΩ, R2= 9KΩ, R3 = 6KΩ, and R4 =3KΩ. Design a second-order active low pass filter with these specifications.

The cut-off frequency is given as

$\begin{align*} f_{c}=\frac{1}{2\pi RC} \end{align*}$

(1) $\begin{align*} f_{c}=\frac{1}{2\pi \times 15\times 10^{3}\times 100\times 10^{-9}} \end{align*}$

$\begin{align*} f_{c}=106.10Hz\end{align*}$

The gain of first stage amplifier is

$\begin{align*} A_{1} = 1 +(R_{2}/R_{1}) \end{align*}$

$\begin{align*} A_{1} = 1 + \frac{9\times 10^{3}}{1\times 10^{3}} \end{align*}$

$\begin{align*} A_{1} =10 \end{align*}$

The gain of second stage amplifier is

$\begin{align*} A_{2} = 1 +(R_{4}/R_{3}) \end{align*}$

$\begin{align*} A_{2} = 1 + \frac{6\times 10^{3}}{3\times 10^{3}} \end{align*}$

$\begin{align*} A_{2} =3 \end{align*}$

Total Gain of the filter

$\begin{align*} A_{v} = 10\times 3 \end{align*}$

$\begin{align*} A_{v} =30 \end{align*}$

The total gain in dB

(2) $\begin{align*} A_{v} = 20 log(30) \end{align*}$

(3) $\begin{align*} A_{v} = 30dB \end{align*}$

The gain at cut-off frequency is

(4) $\begin{align*} \ Gain \ at f_{c} = 30dB -6dB = 24dB \end{align*}$

Active Low Pass Filter Applications

These filters are used predominantly in electronics application like in speakers and subwoofers. They act as filter in speakers and as inputs for subwoofers. They play a major role in design of audio amplfiers and equalizers also. When you use analog to digital converters, these filters are used as anti-aliasing filters to control the signals. When it comes to acoustics and sound, the filter is used to stop the high frequency signals from transmitting sound to prevent echoes.

Active Filtering in Automotive Audio Applications

Operational amplifiers are one of the automotive audio circuits ‘ most popular construction blocks. To boost audio efficiency, many developers choose to integrate Op-Amps into their automotive audio circuits. Active filters eliminate the possibility of undesired interference with the audio signal. Filtering is essential for helping to ensure high-quality sound for the audio system of a car.

A filter with an Op-Amp or active filter, while amplifying the audio signal, retains the frequency response. Another popular use of Op-Amp filters in an automotive audio system is to distinct frequency ranges across the entire vehicle for individual speakers. However, the energy needed to drive a big subwoofer, particularly at greater volumes, could harm a greater frequency speaker. HPF and LPF can be used to set cutoff frequencies to provide the right speakers with frequencies.

Active Low Pass Filters For Biomedical Applications

For low voltage and low energy, ECG Monitoring System apps, active CMOS LPF with two-stage operational amplifier topology is used. This Miller-compensated two-stage amplifier can be used in low-power, low-voltage high CMRR applications such as Biomedical tools and tiny battery-operated devices such as a cardiac pacemaker, electrocardiogram (ECG) where low-power consumption is of primary concern.

Second Order Active Low Pass Filter Cutoff Frequency

Second Order Active Low Pass Filter Design And Example

Active Low Pass Filter Applications

Active Filtering in Automotive Audio Applications

Active Low Pass Filters For Biomedical Applications

Published by howdy