First Order Active Low Pass Filter with Amplification

The original filter design lacks sufficient voltage gain, prompting the need for the modifications illustrated below.

Ezoic

At lower frequencies, the input signals flow directly through the amplifying circuit. When the frequency of the input frequency increases, it is bypassed and made to pass through the capacitor C. This increases the amplitude of the output signal by passband gain.

In a non-inverting amplifier circuit configuration, the measurement of the voltage gain for the filter is given as a ratio of the feedback resistor ( R₂ ) divided by its corresponding input resistor ( R₃ ) value.

$DC= 1 +\frac{R_{2}}{R_{3}}$

First Order Low Active Pass Filter Inverted Configuration

The inverting low pass filter is designed using IC741, an Op-Amp with 8 pin configuration. In inverting mode, the output of the Op-Amp is 180 degrees out of phase with the input signal. Initially, the Op-Amp has to be supplied with DC power. The amount of DC power will depend on how large the signal will be amplified at the output.

The output is AC signal which has peak-peak value. In this example, we are going to design the circuit for a gain of 10, hence the supply voltage of 12VDC is supplied to V⁺, pin 7 of the Op-Amp and -12VDC is supplied to V^– pin 4 of the Op-Amp. This is termed inverted Op-Amp configuration and the output signal will be inverted than the input signal.

Inverting -amplifier- configuration — Inverting amplifier configuration

First Order Low Active Pass Filter Non-Inverted Configuration

In this configuration also IC741 Op-Amp is used. But, here the input signal and output signal will be in phase with each other. RC which forms the low pass filter part is the first half of the circuit.

Then the signal is passed through the Op-Amp, where the signal gets amplified by a voltage gain that is proportional to resistors R2 and R1. In this configuration the external impedance makes no effect on the reactance of the capacitor, thus the stability improved.

Non-inverting -configuration — Non-inverting configuration

First Order Low Pass Filter Voltage Gain

The frequency components are used to obtain the voltage gain of the filter.

$Voltage\ Gain\ (A_{v}) =\frac{V_{out}}{V_{in}} = \frac{A_{F}}{\sqrt{1+\left(\frac{f}{f_{c}}\right)^{2}}}$

where,

V_in is the input voltage
V_out is the output voltage
A_f is the passband gain of the filter (1+R₂/R₁)
f is the frequency of the input signal in Hertz
f_c is the cutoff frequency in Hertz

When the frequency is increased, then the gain is decreased by 20 dB. The operation of an active low pass filter can be checked from the above equation of frequency gain. Let f be the operating frequency and f_c be the cutoff frequency.

Ezoic

At low frequency

$\begin{align*} \frac{V_{out}}{V_{in}} = A_{f} \end{align*}$

When operating frequency is equal to cut off frequency

$\begin{align*} \frac{A_{f}}{\sqrt{2}} =0.707 A_{f} \end{align*}$

And at high frequency

$\begin{align*} \frac{V_{out}}{V_{in}} < A_{f}\end{align*}$

From the above equations, it is seen that at low frequencies the gain of the circuit is equal to the maximum value of gain. Whereas at high frequencies condition, the gain of the circuit is very much lesser than the maximum gain Af. When the operating frequency is equal to cut off frequency, the gain is equal to 0.707 Af. In these filter circuits, the quantitative value (magnitude) of the passband gain is expressed in decibels or dB which is a function of the voltage gain.

$A_{v} (dB) = 20 log_{10}\left [ V_{out}/V_{in} \right ]$

Frequency Response Curve

First Order Low Active Pass Filter Inverted Configuration

First Order Low Active Pass Filter Non-Inverted Configuration

First Order Low Pass Filter Voltage Gain

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