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# Third-Order High-Pass Filter

2017-02-27 07:05
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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.

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