Filters MCQ Quiz in বাংলা - Objective Question with Answer for Filters - বিনামূল্যে ডাউনলোড করুন [PDF]

Critical Frequency:

At 3 dB power of the amplifier becomes half of its total power

It is often known as the “Cut-off frequency”, and it is also known as the “Corner frequency” or “break frequency”

It is defined as the frequency at which the ratio of output to input has a magnitude of 0.707 of the maximum amplitude.

When converted in decibels it is equal to – 3 dB.

\(Magnitude = 20\log \left( {\frac{{output}}{{input}}} \right)\)

The cut-off frequency is a characteristic of the filtering devices, such as RC circuits.

After this cut-off frequency point, the amount of attenuation due to the filter begins to increase rapidly.

Band Pass Filter :

A circuit which pass signal between two frequencies and reject other frequency component.

FDM :

An analog multiplexing technique in which numerous signals are transmitted on a single communication channel. 

To separate the channels in FDM is done by Bandpass filter.

In other modulation scheme only one channel so no need of channel separation.

Hence correct option is "4"

The advantages of an active filters:

• More reliability
• Can eliminates harmonics easily
• Smaller size
• Has better resonance stability
• Voltage regulation is also possible
• No loading effect
• Gain can be introduced

Active filters have better resonance stability 

⇒ Quality factor is high ⇒ better selectivity of channels.

Hence Active filters can be easily tunable.

Butterworth Filter:

• The frequency response of the Butterworth filter is almost flat having no ripples in the passband and rolls off towards zero in the stopband.
• The Bode plot response slopes off linearly towards negative infinity.
• A first-order filter's response rolls off at −6 dB per octave (−20 dB per decade). A second-order filter decreases at −12 dB per octave, a third-order filter decreases at −18 dB, and so on.
• Butterworth filters have a monotonically changing magnitude function with ω. While other filter types have non-monotonic ripples in the passband and/or in the stopband.

Features of other filters are briefly mentioned below:

Elliptic:

• The frequency response in the passband is ripple and is a ripple in the stopband also.
• The transition between passband and stopband is the fastest and is having the worst group delay.

Bessel:

• There is no ripple in the passband and the in stopband the response is monotonically decreasing the slowest decrease of all filters.
• The transition between passband and stopband is slow and the group delay is maximally flat.

Chebyshev type-2:

• There is no ripple in the passband and ripples are present in the stopband.
• The transition between passband and stopband is fast and the group delay is moderately poor depending upon the allowable decibel ripple.

Chebyshev type-1:

• The frequency response of the Chebyshev type -1 is a ripple in the passband and monotonically decreasing in the stopband.
• The transition between passband and stopband is fast and the group delay is moderately poor depending upon the allowable decibel ripple.

The correct answer is option '2'.

Concept:

Pi filter

• A Pi filter is a type of filter that consists of a shunt capacitor at the input side, and an L–section filter follows it.
• Output from the rectifier is given to the capacitor.
• The pulse present in the DC output voltage is filtered by the capacitor connected at the input side, then by the L-section inductor coil, and then by another shunt capacitor.
• It is also known as a capacitive input filter.
• It is mainly used to filter ripples from DC voltage.
• It is more efficient than other filters in removing the ripples as it consists of more than one capacitor on the input side.

Working

• The first capacitor that is present at input side provides small reactance toward a.c. component of rectifier o/p as it makes nearly infinite reactance to D.C component.
• In this way first capacitor filters most part of a.c component of rectifier o/p and d.c component is passes toward L-section or at the choke coil 'L'.
• The choke coil L provides nearly zero reactance to the d.c component and high reactance path to a.c component. In this way it passes d.c component and blocks a.c component.
• The second capacitor blocks the a.c component that is not filtered by first capacitor. In this way o/p as d.c is presented across the load.

Output characteristics

Since the Inductor 'L' or choke coil is made of turns of coils and makes the filter bulkier and costly, we uses a resistor in place of it to reduce the cost and weight.

• Passive elements are the elements that don't generate power, but store, release or dissipate it
• Resistor, Inductor, Capacitor are a type of passive elements
• Passive filters are formed by using a combination of passive elements only
• Active Filters contain passive elements as well as active components such as operational amplifiers, transistors or FET’s within their circuit design.

An active filter using R and L is shown in the figure below:

Ideal filter

An ideal filter is one that has zero attenuation in the pass band and infinite attenuation in the stop band.

The characteristic of an ideal filter is shown below:

Here, f_c1 and f_c2 are known as the lower and upper cut-off frequencies respectively.

An ideal filter will pass the frequencies lying between fc1 and fc2 and block the frequencies lying outside fc1 and fc2

Finite Impulse Response Filter (FIR):

• In signal processing, a finite impulse response filter is a filter whose impulse response is of finite duration, because it settles to zero in finite time. 
• FIR filters can be discrete-time or continuous-time, and digital or analog.

​Properties of an FIR Filter:

• FIR filters are non-recursive in nature.
• Requires no feedback.
• They are inherently stable.
• They can easily be designed to be linear phases by making the coefficient sequence symmetric.

Explanation:

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels.It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor).

Notch filters are a highly selective, high-Q, form of the band stop filter which can be used to reject a single or very small band of frequencies rather than a whole bandwidth of different frequencies.

Important Points

• Notch filters by design have a very narrow and very deep stop band around their center frequency with the width of the notch being described by its selectivity Q in exactly the same way as resonance frequency peaks in RLC circuits.
• The most common notch filter design is the twin-T notch filter network.
• Variable notch filters are also used by musicians in sound equipment such as graphic equalizers, synthesizers and electronic crossovers to deal with narrow peaks in the acoustic response of the music

We can find the transfer function by applying the superposition theorem.

The input is taken at inverting and non-inverting terminal separately

When V_i is applied at non-inverting terminal:

\({v^ + } = \left( {\frac{{\frac{1}{{SC}}}}{{R + \frac{1}{{SC}}}}} \right){V_i}\) 

\({V_{01}} = \left( {1 + \frac{R}{R}} \right)\left( {\frac{1}{{SRC + 1}}} \right){v_i}\) 

When V_i is applied at inverting terminal:

\({V_{02}} = - \frac{R}{R}{V_i}\) 

\({V_0} = {V_{01}} + {V_{02}}\) 

\( = {V_i}\left( {\frac{2}{{1 + SRC}} - 1} \right)\) 

\(= {V_i}\left( {\frac{{2 - 1 - SRC}}{{1 + SRC}}} \right)\) 

\(\frac{{{V_0}}}{{{V_i}}} = \left( {\frac{{1 - SRC}}{{1 + SRC}}} \right)\) 

Putting s = jω, we get

\(\frac{{{V_0}}}{{{V_i}}} = \frac{{1 - j\omega \;RC}}{{1 + j\omega \;RC}}\) 

\(\left| {\frac{{{V_0}}}{{{V_i}}}} \right| = \frac{{\sqrt {1 + {\omega ^2}{R^2}{C^2}} }}{{\sqrt {1 + {\omega ^2}{R^2}{C^2}} }}\) 

= 1

∴ The circuit is an all-pass filter

|V₀| = |V_i|

∴ The magnitude of output does not depend on the circuit element (Capacitance, resistance).

∴ option (2) and (3) are correct.