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Corner frequency & Cut-Off Frequency of a Low Pass Filter:

The transition of a low pass filter is always swift and smooth from the pass-band to stopband. Also, a cut-off frequency is not any parameter to measure the goodness or badness in a range of frequency. The cut-off frequency is more accurately referred to as the -3dB frequency, i.e., it is the frequency at which the magnitude response is 3dB lower than the value at 0 Hz.

What is Pass-band?

“Pass-band is the particular range of frequencies which a filter pass through inside it.”
For low pass filters, the frequencies that move towards the end of the pass-band cannot have any significant gain or attention.

What is Stopband?

“A filter always carries filters within a given band, and rejects the frequencies which are below the given range. This particular range is known as a Stopband”.
As the limitations are there for low pass filters, the stopband attenuates at a particular frequency, which moves near the cut-off frequency closer to 0 Hz.

The transfer function of a Low pass Filter:

What is a Transfer Function?

“Transfer function is a complex number that has both magnitude and phase. In the case of filters, transfer function helps to introduce a phase difference between input and output.”
Since low pass filter allows low-frequency AC signals to pass through it, the output gets attenuated. We use different active and passive components to make a filter, which eventually has other characteristics. The transfer function tells us how one input is related to an output depending on the component’s characteristics. The transfer function can easily be determined from a graph of the output signal at various frequencies. We can also calculate the transfer function using Kirchoff’s Laws to derive the filter’s differential equation.

As more signal passes through it, the filter will apply a phase shift to the output signal for the input signal. Hence, the transfer function of a filter is a complex function of frequency. It also contains all the vital information we need to determine the magnitude of the output signal and its phase.