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 1^st 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 f_H 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 f_H & gives zero output. Ideally at f_H, the frequency response curve changes sharply from A_F (closed loop gain) to zero.  Hence the frequencies from f to f_H are called pass-band frequencies & frequencies greater than f_H are called stop-band frequencies.

f_H is called high cutoff frequency. Unfortunately the change is not so sharp at f_H in practical low pass filters. In practical 1^st order low pass butter-worth filter gain changes with 20dB/decade with frequencies greater than f_H.

Third-Order High-Pass Filter

       This report focuses on active third-order high-pass filter design using operational amplifiers. High-pass filters are commonly used to implement high frequency in a system. Design of Third-order filters is the main topic of consideration. To illustrate an actual circuit implementation, separated into two types of filters first-order and second-order.

       A third-order high pass filter is formed by connecting in series first and second order high pass section and so on. As the order of the filter increased, the actual stop-band response of the filter approaches its ideal stop-band characteristic. The overall gain of the filter is fixed because all the frequency determining resistors and capacitor are equal.

         A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others. High Pass Filter (HPF), sometimes called a low-cut filter, is a filter that high frequencies can be transmitted well and frequencies lower than the cutoff frequency are attenuated or reduced.  The actual amount of attenuation for a particular frequency varies from filter to filter.

        A third-order high pass filter is formed by connecting in series first and second order high pass section and so on. In the stop-band the gain of the filter changes at the rate of 20 dB/decade for first-order filter and at 40 dB/decade for second-order filter. This means that, as the order of the filter is increased, the actual stop-band response of the filter approaches its ideal stop band characteristic.

         Higher order filter are formed simply by using the first and second order filter. A third-order high pass filter is formed by connecting in series first and second order high pass section and so on. Although there is no limit to the order of the filter that can be formed, as the order of the filter increase, so does its size.

         Also, its accuracy declines, in that the difference between the actual stop-band response and the theoretical stop-band response increase with an increase in the order of the filter.  Note that in the third order filter the voltage gain of the first order section is one, and that of the second order section is two. This gain values are necessary to guarantee butter-worth response and must remain the same regardless of the filter’s cutoff frequency. Furthermore, the overall gain of the filter is fixed because all the frequency determining resistors and capacitor are equal.

 

             Generally, the minimum-order filter required depends on the application specifications.     Although a higher-order filter than necessary gives a better stop-band response, the higher-order type filter is more complex, occupies more space, and is more expensive. As the order of the filter increased, the actual stop-band response of the filter approaches its ideal stop-band characteristic.