Filters are used in various fields, including telecommunications, where bandpass filters are used in speech recognition and modems in the audio frequency range (0 Hz to 20 KHz). In telephone exchanges, high-frequency (hundreds of MHz) bandpass filters are used for channel selection.
In data acquisition systems, low-pass noise filters and anti-aliasing low-pass filters are required for signal conditioning. Bandpass filters are used in power supply systems to suppress 50 Hz noise.
All pass filters are used to add delay to each frequency component of a complex signal. Since pass filters do not filter out any frequency components of complex signals, they only add a linear phase shift to each frequency component of a signal.
At higher frequencies (greater than MHz), these filters consist of passive components such as inductors, capacitors, and resistors and are called RLC filters. However, at lower frequencies (below 1 MHz), inductor values and size increase, which makes the design bulky.
In these cases, an active filter comes into action. Active filters are filter circuits that consist of an operational amplifier with a combination of passive components and provide LRC-like filtering at lower frequencies.
1: Second-order LCR low-pass filter and second-order active low-pass filter.
RC Low Pass Filter
As shown below, a low pass filter can be created by placing a resistor in series with the input signal and a capacitor in parallel with the input signal.
Fig. 2: Passive low-pass filter design
The cutoff frequency of the low-pass filter is given by
Fc = 1/2piRC
Fc – Cutoff frequency
Pi – 3.141
For example:
R – 1K; C-10nF
I was doing math and calculating the cutoff frequency of the above values.
Fc = 1/2*3.141*1K*10nF = 15.9 KHz
This means that frequencies above 15.9 kHz will be attenuated and frequencies below 15.9 kHz will be in the passband.
LR Low Pass Filter
The LR low-pass filter is composed of an inductor in series with the input signal and a resistor in parallel with the input signal and works in the same way as the RC low-pass filter; attenuates the high-frequency band of a signal and attenuates more and more as the frequency increases.
Fig. 3: Passive low-pass filter design
The LR filter circuit works on the principle of inductive reactance. This means how the resistance or impedance of the inductor behaves with the frequency passing through it. Resistance has fixed resistance. But the inductor has different resistance for different frequency signals, just like capacitors.
The inductor produces high impedance or resistance for high frequency signals and very low resistance for low frequency signals. It behaves exactly the opposite of a capacitor. Because of this, the location of the resistor is different in the RL circuit. The above circuit effectively blocks the high frequency signal and transmits the low frequency signals.
The cutoff frequency is given by
Fc = R/2PiL
If L = 210mH and R = 10K in the above circuit,
then Fc will be 7.58 KHz
This means that if a complex signal passes through the filter above, it will attenuate frequencies above 7.58 KHz and let frequencies below pass through.
RC High Pass Filter
A simple passive RC high pass filter can be designed using a capacitor in series with the input signal and a resistor in parallel with the input signal, as in the circuit below.
Fig. 4: RC high pass filter design
The capacitor is a reactive device that offers different resistances to signals with different interesting frequencies through the capacitor. A capacitor is a reactive device that offers very high resistance to a very low frequency signal or DC signal and low resistance to a very high frequency signal. As a capacitor offers high resistance or impedance to a DC or low frequency signal, it blocks its input through a capacitor.
The cutoff frequency of the RC high pass filter is given by the formula below.
Fc = 1/2PiRC
A high pass filter is commonly used in various device circuits such as microphone. Since the microphone operates on both AC and DC, it records the AC signals that enter it and operates on DC power. Therefore, it becomes necessary to use it in the microphone recording circuit.
If in the above RC high pass filter C = 10nF and R = 1K
So FC = 1/2*3.14*1K*10nF
FC = 15.923 KHz
The cutoff frequency is calculated at 15.923 kHz, which means that if a complex signal passes through the above circuit, signals with a frequency below 15.923 kHz will be blocked and frequency components above that will pass through.
LR high pass filter
An LR high pass filter can be composed by placing a resistor in series with an input source signal and an inductor in parallel with the input source signal entering the circuit.
Fig. 5: LR high pass filter design
An inductor has inductive reactance that varies with different frequency signals and offers great resistance to high-frequency signals and very low resistance to low-frequency signals. It provides high resistance to high frequency signals so that high frequency current does not pass through the inductor and the signal chooses a low resistance path and travels to the output. But the low frequency current faces very low resistance offered by the inductor, so it passes through the inductor to ground.
The formula gives the cutoff frequency.
Fc = R/2PiL
For example, in the circuit above
R = 10K; L = 470mH
Then the calculated cutoff frequency is
FC = 3.39 KHz
If a signal passes through the above circuit, the frequency components of that signal below this frequency will be attenuated and greater than this will be seen at the output.
