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First-Order Band-Pass Filter

2017-02-20 05:05
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Application of first order band pass filter to find out the output voltage gain magnitude of specific frequency. A specific range of frequency can pass through the amplifier which has a specific bandwidth of this band pass filter.
A band pass filter is a frequency selector. It allows one to select or pass only one particular band of frequencies from all other frequencies that may be present in a circuit. This type of filter has a maximum gain at a resonant frequency.

A band pass filter is the combination of high pass and low pass filter combination. It has a pass band between two cut off frequency fH and fL such that fH > fL. Any input frequency outside this pass band is attenuated. There are two types of band pass filters wide band pass and narrow band pass. If the quality factor Q < 10 and Q > 10 then it would be wide band pass and narrow band pass filter.
The relationship between Q, the 3-dB bandwidth and the center frequency fc is given by,

According to Figure 01 of band pass filter circuit, there are two sections. One is first order high pass section and other is low pass section.
For first order high pass section the output voltage equation is,For first order low pass section the output voltage equation is,
Putting the value of first order high pass section output voltage  from equation (1),

So the final voltage equation of first order band pass filter is,
The voltage gain magnitude of the band pass filter is equal to the product of the voltage gain magnitudes of the high pass and low pass filters.

Therefore the equation (2) is,Where,  = Total band pass gainf = frequency of the input signal (Hz)  = low cut off frequency (Hz) = high cut off frequency (Hz)
The above first order low pass band width filter was designed by taking following precautions,a.
Limited magnitude of input voltage was applied at the input, so that the op-amp must not be driven to saturation.
b.                 Only selected frequency can pass through the filter.
c.                         Overall gain of the first order band pass filter is the multiplication of  high pass filter gain and low pass filter gain.
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