Showing posts with label attenuated. Show all posts
Showing posts with label attenuated. Show all posts
Wednesday, May 25, 2011
First Order Low Pass Filter
Here an explanation of the operation of low pass filter was made, the operation principle of active low pass filter was made, of active low pass filter was made, I designed an active low pass filter & finally I have drawn the frequency response of designed active filter by using filter gain equation & plotting the frequency vs. gain curve.
An electric filter is frequency-selective circuit that passes a specified band of frequencies & blocks or attenuates signals of frequencies outside this band. Active filters can be designed using op-amps, resistors, capacitors or inductors. RC filters are used for audio or low frequency operation, where LC filters are used for high frequencies. For designing audio filters I used capacitors, because inductors are very large, costly & may dissipate more power. I chose active filters instead of passive filters because,
a. It has gain & frequency adjustment flexibility.
b. It has no loading problem.
c. It has very high input impedance & very low output impedance.
d. It is more economical than passive filters.
I designed first order low pass butter-worth filter with RC network in my present assignment. The key characteristic of butter-worth filter is it has a flat pass-band & a flat stop-band. The ideal and practical frequency response of a first order low pass filter is given below,
The above figure shows the frequency response of a 1st order low pass butter-worth filter. The ideal frequency response is shown by the dashes line while the practical response is shown by the solid line. We can see from the frequency response that, the filter allow signal with frequencies less than fH to pass through it & the signal appears at the output with predefined gain.
Ideally it attenuates the signal appearing at the input which has frequencies greater than fH & gives zero output. Ideally at fH, the frequency response curve changes sharply from AF (closed loop gain) to zero. Hence the frequencies from f to fH are called pass-band frequencies & frequencies greater than fH are called stop-band frequencies.
fH is called high cutoff frequency. Unfortunately the change is not so sharp at fH in practical low pass filters. In practical 1st order low pass butter-worth filter gain changes with 20dB/decade with frequencies greater than fH.
First-Order Band-Pass Filter
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 gain
f = 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.
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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