From http://www.electronicshub.org/active-low-pass-filter/
From www.electronics-tutorials.ws/filter/filter_5.html
From www.electronics-tutorials.ws/filter/filter_5.html
Introduction
Low Pass filter is a filter which passes all frequencies from DC to upper cut-off frequency fH and rejects any signals above this frequency.
In ideal case, the frequency response curve drops at the cut-off frequency. Practically the signal will not drop suddenly but drops gradually from transition region to the stop band region.
Cut-off frequency means the point where the response drops -3 dB or 70.7% from the pass band. Transition region means the area where falloff occurs.
Stop band region means the area where the attenuation occurs mostly to the input signals. So this filter is also called high-cut filter or treble cut filter. The ideal response is shown below
Rather than the passive components the Active Low Pass Filter is formed by active components like Op-Amps, FETs and transistors. These filters are very effective when compared with the passive filters. Active filters are introduced to overcome the defects of passive filters.
A simple active low pass filter is formed by using an op-amp. The operational amplifier will take the high impedance signal as input and gives a low impedance signal as output. The amplifier component in this filter circuit will increase the output signal amplitude.
By this action of the amplifier the output signal will become wider or narrower. The maximum frequency response of the filter depends on the amplifier used in the circuit design.
Active low pass filter circuit
The attenuation of the signal, that is the amplitude of the output signal is less than amplitude of the input signal in a passive circuit. In order to overcome this disadvantage of the passive filter, the active filter is designed. A Passive filter connected to the inverting or non-inverting op-amp gives us a simple active low pass filter.
First order active filter is formed by a single op-amp with RC circuit. A simple RC Passive Filter connected to the non-inverting terminal of an operational amplifier is shown below
The advantage of this configuration is that the op-amps high input impedance prevents excessive loading on the filters output while its low output impedance prevents the filters cut-off frequency point from being affected by changes in the impedance of the load.
While this configuration provides good stability to the filter, its main disadvantage is that it has no voltage gain above one. However, although the voltage gain is unity the power gain is very high as its output impedance is much lower than its input impedance. If a voltage gain greater than one is required we can use the following filter circuit.
Active low pass filter with high voltage gain
We know that, for non-inverting amplifier circuit the magnitude of the voltage gain is obtained by its feedback resistor R2 divided by its corresponding input resistor R3.
This is given as follows
Magnitude of the voltage Gain= {1 + (R2/R3)}
Active low pass filter voltage gain
We know that the gain can be obtained by the frequency components and this is given as follows
Voltage gain = V_out⁄V_in = A_max⁄ √(1+〖f/f_c 〗^2 )
Where
- Amax = Gain of the pass band = 1 + R_2⁄R_3
- f = operational frequency.
- fc = Cut-off frequency.
- Vout = Output voltage.
- Vin= Input voltage.
When the frequency increases, then the gain decreases by 20 dB for every 10 time increment of frequency. This operation is observed below
At low frequencies that is when operating frequency f is less than cut-off frequency, then
Vout / Vin = Amax
When operating frequency is equal to the cut off frequency, then
Vout / Vin = Amax / √2 = 0.707 Amax
When the operating frequency is less than the cut off frequency, then
Vout / Vin < Amax
By these equations we can say that at low frequencies the circuit gain is equal to maximum gain and at high frequencies the circuit gain is less than maximum gain Amax.
By these equations we can say that at low frequencies the circuit gain is equal to maximum gain and at high frequencies the circuit gain is less than maximum gain Amax.
When actual frequency is equal to the cut-off frequency, then the gain is equal to the 70.7% of the Amax. By this we can say that for every tenfold (decade) increase of frequency the gain of the voltage is divided by 10.
Magnitude of the Voltage Gain (dB): Amax = 20 log10 (Vout / Vin)
At -3 dB frequency the gain is given as:
3 dB Amax = 20 log10 {0.707 (Vout / Vin)}
Frequency Response
The response of the active filter is as shown in below figure
Second Order Active Low Pass Filter
Just by adding an additional RC circuit to the first order low pass filter the circuit behaves as a second order filter.The second order filter circuit is shown above.
The gain of the above circuit is Amax = 1 + (R2/R1)
The cut-off frequency of second order low pass filter is fc = 1 / 2π√(C1C2R3R4)
The frequency response and the designing steps of the second order filter and the first order filter are almost same except the roll off of the stop band. The roll off value of the second order filter is double to that of first order filter that is 40dB/decade or 12dB/octave.
Applications Of Active Low Pass Filters
In electronics these filters are widely used in many applications. These filters are used as hiss filters in audio speakers to reduce the high frequency hiss produced in the system and these are used as inputs for sub woofers.
These are also used in equalisers and audio amplifiers. In analog to digital conversion these are used as anti-aliasing filters to control signals. In digital filters these are used in blurring of images, smoothing sets of data signals. In radio transmitters to block harmonic emissions.
In acoustics these filters are used to filter the high frequency signals from the transmitting sound which will cause echo at higher sound frequencies.
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