Analog Filters: Butterworth, Chebyshev, and Active Filters Quiz Quiz

Explore the essentials of analog filters with this quiz covering Butterworth filters, Chebyshev filters, and the principles behind active filter designs. Challenge your understanding of frequency response characteristics, filter orders, and design applications within analog electronic circuits.

1. Butterworth Filter Roll-Off

   Which of the following best describes the magnitude response of a 4th order Butterworth low-pass filter near the cutoff frequency?

   1. It amplifies signals above the cutoff frequency.
   2. It passes high frequencies unattenuated.
   3. It rolls off at -80 dB per decade past the cutoff frequency.
   4. It exhibits ripples in the passband and a steep roll-off.

   Explanation: A 4th order Butterworth low-pass filter has a roll-off rate of -80 dB per decade (20 dB per decade per order). The correct option reflects this characteristic. Chebyshev filters, not Butterworth, exhibit ripples in the passband and a steeper roll-off; thus, that distractor is incorrect. The other options incorrectly state the filter either passes or amplifies high frequencies, which is not true for a low-pass filter.

2. Chebyshev Filter Distinctive Feature

   When designing an analog Chebyshev filter, what property differentiates it from a Butterworth filter with the same order?

   1. It completely eliminates phase distortion.
   2. It has a maximally flat passband response.
   3. It features equiripple behavior in the passband.
   4. It offers a logarithmic roll-off rate.

   Explanation: Chebyshev filters are known for having ripples of equal height (equiripple) in the passband to achieve a steeper roll-off compared to Butterworth filters. The maximally flat passband belongs to the Butterworth type, not Chebyshev. No analog filter can entirely remove phase distortion, making that distractor incorrect. Roll-off in these filters is not logarithmic, so the last choice is inappropriate.

3. Active Filter Topology Selection

   In designing a second-order active low-pass filter with operational amplifiers, which topology is commonly used to achieve high input impedance and ease of design?

   1. Differential amplifier circuit
   2. Sallen-Key configuration
   3. Common-base arrangement
   4. T-network passive filter

   Explanation: The Sallen-Key configuration is widely used for active filter designs because it provides high input impedance and a straightforward design process when using operational amplifiers. The common-base arrangement is a transistor amplifier configuration, not typically used for this purpose. Differential amplifier circuits are designed for signal amplification with respect to common-mode rejection, not for simple low-pass filtering. A T-network passive filter does not involve active components like op-amps.

4. Filter Order and Steepness

   Given two filters of the same type and cutoff frequency, how does increasing the order of the filter affect its frequency response near the cutoff?

   1. The bandwidth increases without changing attenuation.
   2. The transition from passband to stopband becomes steeper.
   3. The filter allows higher frequencies to pass unchecked.
   4. Increasing order only affects phase, not amplitude response.

   Explanation: Raising the order of a filter steepens the roll-off, making the transition between passband and stopband sharper. The bandwidth does not increase; instead, the attenuation becomes more rapid beyond the cutoff. Higher frequencies are actually more heavily attenuated, not less. While the phase response does change with order, saying that amplitude is unaffected is incorrect, as the amplitude response is altered significantly.

5. Application of Active Filters

   Which scenario best illustrates a practical advantage of using active filters rather than passive filters in analog circuits?

   1. Needing voltage gain while also filtering a signal.
   2. Creating filters that operate without phase shift.
   3. Avoiding power consumption by using only resistors.
   4. Designing circuits only with inductors and capacitors.

   Explanation: Active filters, unlike passive ones, can provide voltage gain in addition to filtering, which is a major advantage in signal processing applications. Circuits that use only inductors and capacitors refer to passive filters, not active, so that distractor is off-topic. Pure resistor filters cannot avoid power consumption, and all real filters introduce some phase shift, so the remaining options are less appropriate.