.1 To double the corner frequency in the low-pass and high pass two-pole filters

Question

.1 To double the corner frequency in the low-pass and high pass two-pole filters, how would

you change the values of the resistors and capacitors?

.2 Compare the one pole RC filters used in an active setup versus the passive setup? What are the advantages of using it in an active state?

.3 Comment on the response of the Butterworth filters (high and low pass) to step input.

.4 Determine the rise time, defined as the time for the waveform to rise from 10% to 90% its

final value for the response to square wave. Comment on the results from the four filter used

Any kind of help is appreciated.

Explanation / Answer

1. Multiply them root 2 times

2.An active filter is a type of analog electronic filter that uses active components such as an amplifier. Amplifiers included in a filter design can be used to improve the performance and predictability of a filter, while avoiding the need for inductors (which are typically expensive compared to other components). An amplifier prevents the load impedance of the following stage from affecting the characteristics of the filter. An active filter can have complex poles and zeros without using a bulky or expensive inductor. The shape of the response, the Q (quality factor), and the tuned frequency can often be set with inexpensive variable resistors. In some active filter circuits, one parameter can be adjusted without affecting the others Using active elements has some limitations. Basic filter design equations neglect the finite bandwidth of amplifiers. Available active devices have limited bandwidth, so they are often impractical at high frequencies.

3.The frequency response of the Butterworth filter is maximally flat (i.e. has no ripples) in the passband and rolls off towards zero in the stopband. When viewed on a logarithmic Bode plot the response slopes off linearly towards negative infinity. A first-order filter's response rolls off at ?6 dB per octave (?20 dB per decade) (all first-order lowpass filters have the same normalized frequency response). A second-order filter decreases at ?12 dB per octave, a third-order at ?18 dB and so on. Butterworth filters have a monotonically changing magnitude function with ?, unlike other filter types that have non-monotonic ripple in the passband and/or the stopband.The Butterworth filter has a slower roll-off, and thus will require a higher order to implement a particular stopband specification, but Butterworth filters have a more linear phase response in the pass-band.

4.rise time= 0.35/ f3dB

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