Q.1 What is the primary purpose of a low‑pass filter in an analog circuit?
To attenuate frequencies above a certain cutoff frequency
To amplify low frequencies
To block DC signals
To convert AC to DC
Explanation - A low‑pass filter allows signals with frequencies lower than the cutoff to pass while reducing the amplitude of higher‑frequency components.
Correct answer is: To attenuate frequencies above a certain cutoff frequency
Q.2 In a simple RC low‑pass filter, the cutoff frequency f_c (in Hz) is given by:
f_c = 1 / (2πRC)
f_c = 2πRC
f_c = R / (2πC)
f_c = C / (2πR)
Explanation - The –3 dB point of an RC low‑pass filter occurs at f_c = 1/(2πRC).
Correct answer is: f_c = 1 / (2πRC)
Q.3 Which filter type provides the flattest magnitude response in the pass‑band?
Butterworth
Chebyshev
Elliptic
Bessel
Explanation - Butterworth filters are maximally flat (no ripples) in the pass‑band, making them ideal when a smooth response is needed.
Correct answer is: Butterworth
Q.4 A high‑pass RC filter consists of:
A series capacitor and a shunt resistor
A series resistor and a shunt capacitor
Two resistors in series
Two capacitors in series
Explanation - In a high‑pass RC filter, the capacitor blocks low frequencies while the resistor provides a path to ground for higher frequencies.
Correct answer is: A series capacitor and a shunt resistor
Q.5 What is the order of a filter that uses two cascaded RC sections?
Second order
First order
Third order
Fourth order
Explanation - Each RC section contributes one pole; two sections give a second‑order filter.
Correct answer is: Second order
Q.6 In a band‑pass filter, the bandwidth is defined as:
The difference between the upper and lower –3 dB frequencies
The center frequency only
The sum of the upper and lower cut‑off frequencies
The product of resistance and capacitance
Explanation - Bandwidth = f_high – f_low, where both frequencies correspond to the –3 dB points of the pass‑band.
Correct answer is: The difference between the upper and lower –3 dB frequencies
Q.7 Which component is NOT typically used to realize an active filter?
Inductor
Operational amplifier
Resistor
Capacitor
Explanation - Active filters rely on op‑amps, resistors, and capacitors; inductors are avoided because they are bulky and lossy at low frequencies.
Correct answer is: Inductor
Q.8 A Sallen‑Key topology is commonly used for which filter type?
Second‑order low‑pass or high‑pass
First‑order low‑pass only
Band‑stop only
All‑pass filter
Explanation - The Sallen‑Key circuit implements a second‑order filter with unity gain or adjustable gain using an op‑amp.
Correct answer is: Second‑order low‑pass or high‑pass
Q.9 What does the term 'Q factor' of a resonant filter describe?
Selectivity or sharpness of the resonance
The power rating of the filter
The quality of the components used
The amount of noise generated
Explanation - A higher Q indicates a narrower bandwidth around the resonant frequency, meaning a more selective filter.
Correct answer is: Selectivity or sharpness of the resonance
Q.10 In a passive RLC band‑stop filter, the stop‑band is centered at:
The resonant frequency of the LC tank
Zero hertz
Infinity hertz
The cutoff frequency of the resistor
Explanation - The LC tank creates a high impedance at its resonant frequency, attenuating signals near that frequency.
Correct answer is: The resonant frequency of the LC tank
Q.11 Which of the following statements about a Chebyshev filter is true?
It has ripples in the pass‑band but a steeper roll‑off than Butterworth.
It has a perfectly flat pass‑band.
It has the slowest roll‑off among common filter types.
It cannot be implemented with op‑amps.
Explanation - Chebyshev filters trade pass‑band ripple for a faster transition from pass‑band to stop‑band.
Correct answer is: It has ripples in the pass‑band but a steeper roll‑off than Butterworth.
Q.12 The –3 dB point of a filter corresponds to:
Half the power of the pass‑band level
Zero voltage output
Maximum gain
Twice the power of the pass‑band level
Explanation - A –3 dB attenuation reduces power to 0.5 of the original, which is the standard definition of cutoff frequency.
Correct answer is: Half the power of the pass‑band level
Q.13 When cascading two identical first‑order low‑pass filters, the overall roll‑off slope is:
-40 dB/decade
-20 dB/decade
-60 dB/decade
-10 dB/decade
Explanation - Each first‑order section contributes -20 dB/decade; two in cascade give -40 dB/decade.
Correct answer is: -40 dB/decade
Q.14 In an active high‑pass filter using an op‑amp, the gain at frequencies well above the cutoff frequency is:
Approximately the same as the DC gain
Zero
Equal to the ratio of feedback resistor to input resistor
Infinite
Explanation - Above the cutoff, the capacitor behaves like a short, and the circuit reduces to a standard non‑inverting amplifier with gain set by the resistor ratio.
Correct answer is: Equal to the ratio of feedback resistor to input resistor
Q.15 A Bessel filter is preferred when:
A linear phase (constant group delay) is required
Maximum attenuation in the stop‑band is needed
The smallest component values are desired
A very narrow bandwidth is required
Explanation - Bessel filters provide the most linear phase response, preserving waveform shape in the pass‑band.
Correct answer is: A linear phase (constant group delay) is required
Q.16 The term 'cutoff frequency' in a filter is also known as:
Corner frequency
Break frequency
Transition frequency
All of the above
Explanation - Cutoff, corner, and break frequencies are synonyms referring to the frequency at which the filter’s response changes slope.
Correct answer is: All of the above
Q.17 Which of the following is true for an ideal brick‑wall filter?
It passes all frequencies below a cutoff and completely rejects all above it.
It has a gradual roll‑off.
It exhibits ripples in the pass‑band.
It cannot be realized with passive components.
Explanation - A brick‑wall filter has an instantaneous transition from pass‑band to stop‑band, which is unattainable in practice.
Correct answer is: It passes all frequencies below a cutoff and completely rejects all above it.
Q.18 For a first‑order RC low‑pass filter, what is the phase shift at the cutoff frequency?
-45°
-90°
0°
-180°
Explanation - At the –3 dB point, the output lags the input by 45 degrees in a first‑order RC low‑pass filter.
Correct answer is: -45°
Q.19 In a digital‑to‑analog conversion system, the reconstruction filter is typically:
A low‑pass filter
A high‑pass filter
A band‑stop filter
A notch filter
Explanation - The reconstruction filter removes high‑frequency images introduced by the sampling process, leaving the original analog signal.
Correct answer is: A low‑pass filter
Q.20 An active band‑pass filter using a Multiple‑Feedback topology has a gain that is:
Set by the ratio of two resistors
Always unity
Dependent on the capacitor values only
Infinite
Explanation - The Multiple‑Feedback (MFB) band‑pass filter’s mid‑band gain is determined by a resistor ratio, independent of the capacitors that set the center frequency.
Correct answer is: Set by the ratio of two resistors
Q.21 If a filter has a pole at s = –1000 rad/s, its –3 dB frequency (in Hz) is approximately:
159 Hz
1000 Hz
250 Hz
63 Hz
Explanation - f_c = |pole| / (2π) = 1000 / (2π) ≈ 159 Hz.
Correct answer is: 159 Hz
Q.22 A notch filter (band‑stop) is most useful for:
Eliminating a single interfering frequency, such as 60 Hz hum
Passing only high frequencies
Amplifying a narrow band of frequencies
Converting AC to DC
Explanation - A notch filter creates a deep attenuation at a specific frequency while leaving other frequencies relatively untouched.
Correct answer is: Eliminating a single interfering frequency, such as 60 Hz hum
Q.23 Which of the following filter responses has the steepest roll‑off for a given order?
Elliptic (Cauer)
Butterworth
Bessel
First‑order RC
Explanation - Elliptic filters achieve the fastest transition between pass‑band and stop‑band at the expense of ripple in both bands.
Correct answer is: Elliptic (Cauer)
Q.24 In an RC high‑pass filter, what happens to the output voltage as the frequency approaches zero?
It approaches zero
It approaches the input voltage
It oscillates
It becomes infinite
Explanation - At DC (0 Hz) the capacitor acts as an open circuit, so no current flows and the output is zero.
Correct answer is: It approaches zero
Q.25 The quality factor Q of a second‑order LC band‑pass filter is defined as:
Q = f_0 / (f_2 – f_1)
Q = (f_2 + f_1) / f_0
Q = (R / L) * C
Q = L / R
Explanation - Q = center frequency divided by bandwidth (difference between upper and lower –3 dB frequencies).
Correct answer is: Q = f_0 / (f_2 – f_1)
Q.26 Which filter type is commonly used in audio crossovers to split the audio spectrum?
Butterworth low‑pass and high‑pass filters
Band‑stop filters only
All‑pass filters
Notch filters
Explanation - Crossover networks often use Butterworth filters for their flat amplitude response, ensuring smooth division of audio bands.
Correct answer is: Butterworth low‑pass and high‑pass filters
Q.27 An RC integrator circuit behaves as a:
Low‑pass filter
High‑pass filter
Band‑pass filter
Notch filter
Explanation - An RC integrator averages the input voltage over time, attenuating high‑frequency components, which is the behavior of a low‑pass filter.
Correct answer is: Low‑pass filter
Q.28 The term 'group delay' in filter theory refers to:
The derivative of the phase response with respect to angular frequency
The time constant of an RC circuit
The delay introduced by a resistor
The amount of gain at the cutoff frequency
Explanation - Group delay = –dφ/dω, describing how different frequency components are delayed by the filter.
Correct answer is: The derivative of the phase response with respect to angular frequency
Q.29 In a passive RLC series circuit used as a band‑pass filter, the impedance is minimum at:
Resonant frequency
Zero hertz
Infinity hertz
Half the resonant frequency
Explanation - At resonance, inductive and capacitive reactances cancel, leaving only the series resistance, which is the minimum impedance.
Correct answer is: Resonant frequency
Q.30 Which of the following statements about filter order is correct?
Higher‑order filters have steeper roll‑off rates.
Higher‑order filters always have lower pass‑band ripple.
The order does not affect the phase response.
A first‑order filter can have a Q factor greater than 10.
Explanation - Each additional pole adds –20 dB/decade of attenuation, making the transition sharper.
Correct answer is: Higher‑order filters have steeper roll‑off rates.
Q.31 For a first‑order RC low‑pass filter with R = 1 kΩ and C = 0.1 µF, the –3 dB cutoff frequency is closest to:
1.59 kHz
159 Hz
15.9 kHz
1.59 Hz
Explanation - f_c = 1/(2πRC) = 1/(2π·1000·0.1·10⁻⁶) ≈ 1.59 kHz.
Correct answer is: 1.59 kHz
Q.32 A first‑order high‑pass filter has a gain of 0 dB at high frequencies. What is its gain at very low frequencies?
-∞ dB (essentially zero)
0 dB
+20 dB
+3 dB
Explanation - At DC the capacitor blocks the signal, resulting in zero output (theoretically –∞ dB).
Correct answer is: -∞ dB (essentially zero)
Q.33 In a filter's magnitude response graph, the region where the response is flat is called:
Pass‑band
Stop‑band
Transition band
Roll‑off region
Explanation - The pass‑band is where the filter allows signals to pass with little attenuation.
Correct answer is: Pass‑band
Q.34 A filter that exhibits a -3 dB point at 2 kHz and -6 dB at 4 kHz is most likely:
A first‑order low‑pass filter
A second‑order low‑pass filter
A high‑pass filter
A band‑stop filter
Explanation - A first‑order filter attenuates at -20 dB/decade; from 2 kHz to 4 kHz (half a decade) it drops ~6 dB, matching the description.
Correct answer is: A first‑order low‑pass filter
Q.35 When designing a filter, why might you choose a Bessel filter over a Butterworth filter?
To preserve waveform shape (linear phase)
To achieve the steepest attenuation
To minimize component count
To obtain the highest Q factor
Explanation - Bessel filters have a maximally flat group delay, keeping pulse shapes intact, which is valuable in data communications.
Correct answer is: To preserve waveform shape (linear phase)
Q.36 A digital FIR filter can be used to implement which analog filter characteristic?
Any linear phase response
Only high‑pass characteristics
Only low‑pass characteristics
Only notch characteristics
Explanation - FIR filters can be designed with exact linear phase, making them suitable for a wide range of analog-like filter responses.
Correct answer is: Any linear phase response
Q.37 In a parallel RLC circuit used as a band‑stop filter, the impedance at resonance is:
Maximum (theoretically infinite)
Minimum (equal to R)
Zero
Equal to L
Explanation - At resonance, inductive and capacitive reactances cancel, leaving only the resistor, but in a perfect parallel LC the impedance becomes infinite, creating a notch.
Correct answer is: Maximum (theoretically infinite)
Q.38 If a filter’s transfer function has a denominator term (s + 500), the pole is located at:
-500 rad/s
+500 rad/s
-500 j rad/s
+500 j rad/s
Explanation - The pole is the value of s that makes the denominator zero; solving (s + 500) = 0 gives s = –500.
Correct answer is: -500 rad/s
Q.39 Which filter topology uses two op‑amps to provide a unity‑gain band‑pass response?
Twin‑T
State‑Variable
Biquad
All‑Pass
Explanation - A state‑variable filter can produce low‑pass, high‑pass, and band‑pass outputs simultaneously using two op‑amps.
Correct answer is: State‑Variable
Q.40 A filter with a stop‑band attenuation of 60 dB is considered:
Very effective at rejecting unwanted frequencies
Ineffective
Only suitable for low‑frequency applications
A low‑order filter
Explanation - 60 dB attenuation reduces the unwanted signal power by a factor of 1,000, which is a strong rejection.
Correct answer is: Very effective at rejecting unwanted frequencies
Q.41 The transfer function of a first‑order low‑pass filter is H(s) = 1 / (1 + sRC). What is the DC gain (s = 0)?
1 (0 dB)
0
RC
∞
Explanation - Substituting s = 0 gives H(0) = 1, meaning the filter passes DC unchanged.
Correct answer is: 1 (0 dB)
Q.42 In an active filter, why is the op‑amp’s bandwidth important?
It limits the highest frequency the filter can handle without gain loss.
It determines the filter’s pass‑band ripple.
It sets the filter’s Q factor.
It controls the filter’s temperature stability.
Explanation - The op‑amp must have sufficient gain‑bandwidth product to maintain the designed gain at the filter’s highest operating frequency.
Correct answer is: It limits the highest frequency the filter can handle without gain loss.
Q.43 A first‑order RC low‑pass filter has a time constant τ = RC = 0.5 ms. What is the approximate -3 dB frequency?
≈ 318 Hz
≈ 1 kHz
≈ 2 kHz
≈ 159 Hz
Explanation - f_c = 1/(2πτ) = 1/(2π·0.5 ms) ≈ 318 Hz.
Correct answer is: ≈ 318 Hz
Q.44 Which of the following best describes a 'cascade' connection of filters?
Connecting the output of one filter to the input of the next
Connecting filters in parallel across the same source
Using a single component to perform multiple filtering functions
Arranging filters in a feedback loop
Explanation - Cascading filters multiplies their individual transfer functions, increasing overall order and steepness of roll‑off.
Correct answer is: Connecting the output of one filter to the input of the next
Q.45 In the s‑plane, a pole located at -100 + j200 rad/s indicates:
A damped sinusoidal response with a natural frequency of √(100²+200²) rad/s
An unstable system
A purely resistive behavior
Zero phase shift
Explanation - Complex conjugate poles produce oscillatory (sinusoidal) components with exponential decay determined by the real part.
Correct answer is: A damped sinusoidal response with a natural frequency of √(100²+200²) rad/s
Q.46 The term 'roll‑off' of a filter refers to:
The rate at which attenuation increases beyond the cutoff frequency
The physical size of the filter
The voltage gain at DC
The amount of ripple in the pass‑band
Explanation - Roll‑off is expressed in dB per decade (or per octave) and shows how sharply a filter attenuates frequencies outside the pass‑band.
Correct answer is: The rate at which attenuation increases beyond the cutoff frequency
Q.47 A passive RC filter cannot provide gain greater than:
1 (0 dB)
10
0.1
Infinite
Explanation - Passive components cannot amplify; the maximum voltage gain is unity.
Correct answer is: 1 (0 dB)
Q.48 What is the effect of increasing the capacitance in a low‑pass RC filter while keeping resistance constant?
The cutoff frequency decreases
The cutoff frequency increases
The filter becomes high‑pass
The Q factor doubles
Explanation - Since f_c = 1/(2πRC), larger C reduces f_c, shifting the pass‑band to lower frequencies.
Correct answer is: The cutoff frequency decreases
Q.49 In a ladder network filter, the term 'ladder' refers to:
A repeated series‑shunt arrangement of inductors and capacitors
A set of parallel resistors only
A single inductor with many taps
A cascade of op‑amps
Explanation - Ladder networks consist of alternating series and shunt reactive elements, resembling a ladder.
Correct answer is: A repeated series‑shunt arrangement of inductors and capacitors
Q.50 Which filter type provides the narrowest transition band for a given order?
Elliptic
Butterworth
Bessel
First‑order RC
Explanation - Elliptic filters achieve the sharpest transition (narrowest transition band) for a given order by allowing ripples in both pass‑ and stop‑bands.
Correct answer is: Elliptic
Q.51 The transfer function H(s) = s/(s + ω_c) corresponds to which filter?
First‑order high‑pass
First‑order low‑pass
Band‑pass
All‑pass
Explanation - At low frequencies (s → 0) the output → 0; at high frequencies (s → ∞) the magnitude approaches 1, characteristic of a high‑pass filter.
Correct answer is: First‑order high‑pass
Q.52 If a filter’s stop‑band attenuation is specified as 40 dB, what factor of voltage reduction does this represent?
0.01 (1 % of original)
0.1 (10 %)
0.001 (0.1 %)
10 (1000 %)
Explanation - 40 dB attenuation corresponds to a voltage ratio of 10^(–40/20) = 0.01.
Correct answer is: 0.01 (1 % of original)
Q.53 In a second‑order active low‑pass filter, increasing the feedback resistor while keeping other components constant will:
Increase the pass‑band gain
Decrease the cutoff frequency
Increase the Q factor
Have no effect
Explanation - The feedback resistor determines the overall gain of the op‑amp stage; higher resistance raises the gain.
Correct answer is: Increase the pass‑band gain
Q.54 Which of the following is true about the phase response of an ideal low‑pass filter at frequencies far above the cutoff?
The phase approaches –90°
The phase approaches 0°
The phase approaches +90°
The phase becomes random
Explanation - A first‑order low‑pass filter adds –90° phase shift at frequencies well beyond the cutoff.
Correct answer is: The phase approaches –90°
Q.55 A filter with a transfer function H(s) = (s² + ω_0²) / (s² + (ω_0/Q)s + ω_0²) is a:
Band‑stop (notch) filter
Band‑pass filter
Low‑pass filter
All‑pass filter
Explanation - The numerator creates a zero at ω = ω_0, producing attenuation at that frequency while the denominator defines the resonance.
Correct answer is: Band‑stop (notch) filter
Q.56 In a digital filter, the term 'sampling frequency' determines:
The highest frequency that can be accurately represented (Nyquist limit)
The amount of gain the filter provides
The filter's Q factor
The physical size of the filter circuit
Explanation - According to the Nyquist theorem, frequencies above half the sampling rate will alias.
Correct answer is: The highest frequency that can be accurately represented (Nyquist limit)
Q.57 Which analog filter can be implemented using only resistors, capacitors, and an op‑amp, without any inductors?
Active RC filter
LC ladder filter
Crystal filter
RF band‑stop filter
Explanation - Active RC filters use op‑amps to emulate inductive behavior, avoiding physical inductors.
Correct answer is: Active RC filter
Q.58 A filter with a linear phase response is particularly important in:
Data communication systems where pulse shape must be preserved
Power supplies where only DC is needed
Audio amplifiers where only gain matters
Temperature sensors
Explanation - Linear phase ensures that all frequency components of a pulse experience the same delay, preserving waveform integrity.
Correct answer is: Data communication systems where pulse shape must be preserved
Q.59 The term 'stop‑band ripple' is most associated with which filter family?
Elliptic
Butterworth
Bessel
First‑order RC
Explanation - Elliptic (Cauer) filters allow ripples in both pass‑ and stop‑bands to achieve steep roll‑off.
Correct answer is: Elliptic
Q.60 In a high‑order filter, why might designers add a small amount of damping?
To reduce overshoot and ringing in the time response
To increase the pass‑band gain
To make the filter physically smaller
To eliminate the need for a power supply
Explanation - Damping (lower Q) smooths the transient response, preventing excessive ringing.
Correct answer is: To reduce overshoot and ringing in the time response
Q.61 What is the main advantage of using a digital FIR filter over an analog counterpart?
Exact linear phase can be achieved
No need for power supply
It can handle infinite frequencies
It always requires fewer components
Explanation - FIR filters can be designed with symmetric coefficients, guaranteeing linear phase response.
Correct answer is: Exact linear phase can be achieved
Q.62 A first‑order RC differentiator behaves as a:
High‑pass filter
Low‑pass filter
Band‑pass filter
All‑pass filter
Explanation - A differentiator emphasizes rapid changes (high frequencies) while attenuating low‑frequency components.
Correct answer is: High‑pass filter
Q.63 The term 'pole' in a filter transfer function primarily affects:
The magnitude attenuation and phase shift
The power consumption
The physical size of the circuit
The temperature coefficient
Explanation - Poles determine where the denominator of H(s) becomes zero, shaping attenuation and phase response.
Correct answer is: The magnitude attenuation and phase shift
Q.64 In a passive LC low‑pass filter, the cutoff frequency is given by:
f_c = 1 / (2π√(LC))
f_c = 2πLC
f_c = R / (2πL)
f_c = L / (2πC)
Explanation - The resonant frequency of an LC circuit defines the cutoff for a simple low‑pass filter.
Correct answer is: f_c = 1 / (2π√(LC))
Q.65 Which filter design method allows you to specify a desired pass‑band ripple and stop‑band attenuation directly?
Chebyshev (Type I)
Butterworth
Bessel
First‑order RC
Explanation - Chebyshev Type I filters let designers set the allowable pass‑band ripple while controlling stop‑band attenuation.
Correct answer is: Chebyshev (Type I)
Q.66 If a filter has a pole at s = –j1000 rad/s (purely imaginary), the system is:
Marginally stable (undamped oscillation)
Unstable
Over‑damped
Critically damped
Explanation - A pole on the imaginary axis produces sustained oscillations without growth or decay.
Correct answer is: Marginally stable (undamped oscillation)
Q.67 In the context of filter design, the term 'prototype filter' usually refers to:
A normalized low‑pass filter from which other filters are derived
A physical filter built for testing
A digital filter implemented in software
A filter with infinite order
Explanation - Designers start with a low‑pass prototype and apply frequency transformations to obtain high‑pass, band‑pass, etc.
Correct answer is: A normalized low‑pass filter from which other filters are derived
Q.68 The gain of a passive RC low‑pass filter at frequencies far above the cutoff is:
Approximately 0
Approximately 1 (0 dB)
Approximately 10
Infinite
Explanation - At high frequencies the capacitor acts as a short circuit, shunting the output to ground, resulting in near‑zero output.
Correct answer is: Approximately 0
Q.69 Which of the following filter orders will produce the steepest roll‑off for a given cutoff frequency?
Higher order (e.g., 8th order)
First order
Second order
Third order
Explanation - Roll‑off increases by 20 dB/decade per order; thus higher‑order filters have steeper attenuation.
Correct answer is: Higher order (e.g., 8th order)
Q.70 In an active Sallen‑Key low‑pass filter, the damping factor ζ is primarily set by:
The ratio of resistors
The op‑amp supply voltage
The capacitor tolerance
The input signal amplitude
Explanation - Resistor values define ζ, which controls the filter's Q and transient response.
Correct answer is: The ratio of resistors
Q.71 A filter's 'stop‑band' is the frequency range where:
The output is heavily attenuated
The gain is maximum
The phase shift is zero
The circuit draws maximum current
Explanation - Stop‑band frequencies are suppressed by the filter, ideally approaching zero output.
Correct answer is: The output is heavily attenuated
Q.72 If the cutoff frequency of a low‑pass RC filter is 500 Hz, what is the time constant τ?
≈ 0.32 ms
≈ 3.18 ms
≈ 0.05 ms
≈ 5 ms
Explanation - τ = 1/(2πf_c) = 1/(2π·500) ≈ 0.000318 s = 0.318 ms.
Correct answer is: ≈ 0.32 ms
Q.73 Which filter type is used in a telephone line to limit the bandwidth to the voice band (300 Hz – 3.4 kHz)?
Band‑pass filter
Low‑pass filter
High‑pass filter
All‑pass filter
Explanation - A band‑pass filter allows only frequencies within the voice range to pass.
Correct answer is: Band‑pass filter
Q.74 In a digital FIR filter, the number of taps directly determines:
The filter order and thus the sharpness of the transition band
The power consumption of the filter
The voltage gain at DC
The sampling frequency
Explanation - More taps (higher order) provide a narrower transition region and better stop‑band attenuation.
Correct answer is: The filter order and thus the sharpness of the transition band
Q.75 Which of the following statements about a first‑order active high‑pass filter is true?
Its gain at high frequencies is set by the op‑amp feedback network.
It cannot be built with an op‑amp.
It has a -3 dB point at zero frequency.
It provides infinite gain at DC.
Explanation - At frequencies well above the cutoff, the capacitor behaves as a short, and the circuit reduces to a standard op‑amp amplifier.
Correct answer is: Its gain at high frequencies is set by the op‑amp feedback network.
Q.76 If a filter's pass‑band ripple is 0.5 dB, the output amplitude variation within the pass‑band is:
Within ±0.25 dB of the nominal gain
Exactly 0.5 dB at the cutoff
Zero (perfectly flat)
More than 1 dB
Explanation - Ripple of 0.5 dB means the gain oscillates up and down by half that amount around the nominal value.
Correct answer is: Within ±0.25 dB of the nominal gain
Q.77 A filter designed to have a flat group delay but moderate roll‑off is most likely a:
Bessel filter
Butterworth filter
Elliptic filter
Chebyshev filter
Explanation - Bessel filters prioritize linear phase (constant group delay) over steep attenuation.
Correct answer is: Bessel filter
Q.78 What is the effect of adding a parallel resistor across the capacitor in an RC low‑pass filter?
It introduces a finite DC resistance, reducing output impedance
It raises the cutoff frequency
It converts the filter into a high‑pass filter
It makes the filter unstable
Explanation - The parallel resistor provides a path for DC, preventing the output from floating and improving load driving capability.
Correct answer is: It introduces a finite DC resistance, reducing output impedance
Q.79 Which of the following is NOT a typical specification when ordering a commercial analog filter?
Cutoff frequency
Pass‑band ripple
Component color
Stop‑band attenuation
Explanation - Filter specifications focus on electrical performance, not aesthetic attributes like color.
Correct answer is: Component color
Q.80 In a cascade of three identical first‑order RC low‑pass filters, the overall -3 dB frequency is:
The same as a single stage
Lower than that of a single stage
Higher than that of a single stage
Undefined
Explanation - Cascading stages shifts the overall -3 dB point lower because each stage adds attenuation.
Correct answer is: Lower than that of a single stage
Q.81 A filter that exhibits a constant gain of 1 (0 dB) for all frequencies is called a:
All‑pass filter
Low‑pass filter
High‑pass filter
Band‑stop filter
Explanation - An all‑pass filter passes all frequencies with equal magnitude, altering only phase.
Correct answer is: All‑pass filter
Q.82 If a second‑order filter has a Q factor of 0.707, what type of response does it exhibit?
Butterworth (maximally flat magnitude)
Chebyshev (rippled)
Elliptic (sharp transition)
Bessel (linear phase)
Explanation - A Butterworth second‑order filter has Q = 1/√2 ≈ 0.707, giving a flat magnitude response.
Correct answer is: Butterworth (maximally flat magnitude)
Q.83 Which filter implementation technique is most suitable for very high frequencies (GHz range)?
Microstrip or waveguide structures (distributed filters)
RC ladder networks
Active op‑amp filters
Digital FIR filters
Explanation - At GHz frequencies, parasitic effects dominate, so distributed transmission‑line filters are used.
Correct answer is: Microstrip or waveguide structures (distributed filters)
Q.84 In a passive RC high‑pass filter, the output voltage across the resistor is:
Proportional to the high‑frequency components
Zero for all frequencies
Inverted compared to the input
Constant for all frequencies
Explanation - The resistor sees the current that increases with frequency, so the output across it follows the high‑frequency part of the input.
Correct answer is: Proportional to the high‑frequency components
Q.85 When a filter's transfer function contains a zero at the origin (s = 0), the filter is:
A high‑pass filter
A low‑pass filter
An all‑pass filter
A notch filter
Explanation - A zero at s = 0 forces the gain to zero at DC, characteristic of high‑pass behavior.
Correct answer is: A high‑pass filter
Q.86 The term 'impedance matching' in filter design is used to:
Prevent reflections and maximize power transfer between stages
Increase the Q factor
Make the filter linear phase
Reduce component count
Explanation - Matching source and load impedances ensures efficient signal transfer and avoids standing waves, especially at high frequencies.
Correct answer is: Prevent reflections and maximize power transfer between stages
Q.87 A first‑order RC low‑pass filter has an input resistance of 10 kΩ and a capacitor of 10 nF. Its –3 dB cutoff frequency is closest to:
1.6 kHz
160 Hz
16 kHz
1.6 Hz
Explanation - f_c = 1/(2πRC) = 1/(2π·10 k·10 n) ≈ 1.59 kHz.
Correct answer is: 1.6 kHz
Q.88 In a second‑order active low‑pass filter, increasing the capacitor values while keeping resistors constant will:
Lower the cutoff frequency
Raise the cutoff frequency
Increase the Q factor
Have no effect
Explanation - Larger capacitors increase the time constant, shifting the filter response to lower frequencies.
Correct answer is: Lower the cutoff frequency
Q.89 A filter with a stop‑band centered at 60 Hz is commonly used to suppress:
Mains hum
Audio bass frequencies
Radio FM signals
Ultrasonic noise
Explanation - Power‑line interference appears as a 50 Hz or 60 Hz sinusoid, which a notch filter can attenuate.
Correct answer is: Mains hum
Q.90 In a digital IIR filter, the presence of poles close to the unit circle in the z‑plane results in:
Sharp resonance (narrowband response)
Flat response
No effect on frequency response
Infinite gain at all frequencies
Explanation - Poles near the unit circle create peaks in the magnitude response, yielding narrowband filters.
Correct answer is: Sharp resonance (narrowband response)
Q.91 Which of the following statements is true about a Butterworth filter’s phase response?
It is not linear, but the magnitude response is maximally flat.
It is perfectly linear.
It has ripples in the phase.
It is undefined.
Explanation - Butterworth filters prioritize magnitude flatness; the phase varies non‑linearly.
Correct answer is: It is not linear, but the magnitude response is maximally flat.
Q.92 A filter with a transfer function H(s) = (s/ω_c) / (1 + s/ω_c) is a:
First‑order high‑pass filter
First‑order low‑pass filter
All‑pass filter
Band‑pass filter
Explanation - The numerator contains s, causing zero gain at DC and unity gain at high frequencies.
Correct answer is: First‑order high‑pass filter
Q.93 When a filter’s Q factor is much greater than 0.707, the time‑domain response typically shows:
Oscillatory ringing
Critically damped behavior
No overshoot
Immediate settling
Explanation - High Q leads to under‑damped response with noticeable overshoot and ringing.
Correct answer is: Oscillatory ringing
Q.94 The purpose of a reconstruction filter after a DAC is to:
Remove high‑frequency images caused by sampling
Increase the sample rate
Convert the signal back to digital
Add noise to the output
Explanation - The reconstruction (low‑pass) filter eliminates spectral replicas introduced by the zero‑order hold of the DAC.
Correct answer is: Remove high‑frequency images caused by sampling
Q.95 A passive LC band‑pass filter with L = 10 µH and C = 100 pF has a resonant frequency of approximately:
5 MHz
1 MHz
500 kHz
2 MHz
Explanation - f_0 = 1/(2π√(LC)) ≈ 1/(2π√(10e‑6·100e‑12)) ≈ 5 MHz.
Correct answer is: 5 MHz
Q.96 In a digital FIR filter, the term 'linear phase' guarantees:
All frequency components are delayed by the same amount of time
Infinite stop‑band attenuation
Zero ripple in the pass‑band
Maximum gain at DC
Explanation - Linear phase ensures constant group delay, preserving the shape of signals passing through the filter.
Correct answer is: All frequency components are delayed by the same amount of time
Q.97 Which filter characteristic is most important in a video signal processing chain to avoid picture distortion?
Linear phase (constant group delay)
Steep roll‑off
High Q factor
Maximum stop‑band attenuation
Explanation - Phase distortion leads to timing errors that can cause visible artifacts in video; linear phase avoids this.
Correct answer is: Linear phase (constant group delay)
Q.98 If a filter’s stop‑band begins at 2 kHz and its -3 dB point is at 1 kHz, the filter’s roll‑off is:
Approximately 20 dB/decade
Approximately 40 dB/decade
Approximately 60 dB/decade
Approximately 10 dB/decade
Explanation - From 1 kHz to 2 kHz is half a decade; a 20 dB/decade roll‑off would give about 10 dB attenuation, matching a typical first‑order filter.
Correct answer is: Approximately 20 dB/decade
Q.99 A passive RC integrator is best described as a:
Low‑pass filter with a slope of -20 dB/decade
High‑pass filter with a slope of +20 dB/decade
Band‑pass filter
All‑pass filter
Explanation - An integrator averages the input, attenuating high frequencies at a rate of -20 dB/decade.
Correct answer is: Low‑pass filter with a slope of -20 dB/decade
Q.100 In the context of filter design, the term 'frequency transformation' refers to:
Converting a prototype low‑pass response to high‑pass, band‑pass, or band‑stop forms
Changing the physical size of components
Altering the temperature coefficient of resistors
Switching from analog to digital implementation
Explanation - Frequency transformations apply mathematical substitutions to the prototype transfer function to obtain other filter types.
Correct answer is: Converting a prototype low‑pass response to high‑pass, band‑pass, or band‑stop forms
Q.101 A filter that provides a constant attenuation of 3 dB across all frequencies is called:
An all‑pass filter with a gain of 0.707
A low‑pass filter
A high‑pass filter
A band‑stop filter
Explanation - An all‑pass filter can be designed with a magnitude of 0.707 (‑3 dB) while affecting only phase.
Correct answer is: An all‑pass filter with a gain of 0.707
Q.102 The primary advantage of a cascaded integrator‑comb (CIC) filter in digital signal processing is:
Efficient decimation without multipliers
Excellent linear phase at very high frequencies
Zero pass‑band ripple
Infinite stop‑band attenuation
Explanation - CIC filters use only adders and delays, making them ideal for high‑speed decimation in hardware.
Correct answer is: Efficient decimation without multipliers
Q.103 Which component value change will most directly increase the Q factor of a Sallen‑Key low‑pass filter?
Reducing the ratio of the two resistors
Increasing the capacitor values equally
Increasing the supply voltage
Adding a parallel resistor to the output
Explanation - In the Sallen‑Key topology, the resistor ratio controls damping; a lower ratio yields higher Q.
Correct answer is: Reducing the ratio of the two resistors
Q.104 A filter with a -3 dB point at 10 kHz and a stop‑band attenuation of 50 dB is suitable for:
Audio applications requiring up to 10 kHz bandwidth
DC power supply filtering
Radio frequency front‑end filtering
Ultra‑low‑frequency seismic measurements
Explanation - Audio signals typically need bandwidth up to ~20 kHz; a 10 kHz cutoff with high attenuation beyond is appropriate for many audio subsystems.
Correct answer is: Audio applications requiring up to 10 kHz bandwidth
Q.105 When a filter is described as 'critical damping', its Q factor is:
0.5
0.707
1.0
1.414
Explanation - Critical damping corresponds to Q = 0.5, providing the fastest response without overshoot.
Correct answer is: 0.5
Q.106 In a ladder filter, the series elements are usually:
Inductors
Resistors
Capacitors
Diodes
Explanation - Classic ladder networks alternate series inductors with shunt capacitors (or vice‑versa).
Correct answer is: Inductors
Q.107 Which filter type is most appropriate for eliminating a narrow interference at 2.4 GHz in a Wi‑Fi receiver?
Notch (band‑stop) filter
Low‑pass filter
High‑pass filter
All‑pass filter
Explanation - A notch filter can sharply attenuate a specific narrowband interference while leaving the rest of the spectrum relatively untouched.
Correct answer is: Notch (band‑stop) filter
Q.108 If the denominator of a transfer function has repeated poles at the same location, the filter's time‑domain response will:
Contain terms proportional to t·e^{st}
Be purely exponential
Be sinusoidal with constant amplitude
Have zero output
Explanation - Repeated poles introduce polynomial terms multiplied by exponentials, leading to slower decay.
Correct answer is: Contain terms proportional to t·e^{st}
Q.109 A passive RC high‑pass filter can be used as a simple edge detector in a signal processing system because:
It emphasizes rapid changes (high frequencies) in the signal
It completely removes all noise
It amplifies low frequencies
It provides a constant gain at all frequencies
Explanation - Edges correspond to high‑frequency components; a high‑pass filter highlights them.
Correct answer is: It emphasizes rapid changes (high frequencies) in the signal
Q.110 In a digital filter, the 'z‑transform' is used to:
Represent discrete‑time signals and systems in the frequency domain
Convert analog signals to digital directly
Measure the power of a signal
Calculate the temperature coefficient of components
Explanation - The z‑transform is the discrete‑time counterpart of the Laplace transform, used for analysis and design of digital filters.
Correct answer is: Represent discrete‑time signals and systems in the frequency domain
Q.111 A filter whose magnitude response is flat up to the cutoff frequency and then drops off at -12 dB/octave is a:
Second‑order low‑pass filter
First‑order low‑pass filter
Third‑order low‑pass filter
All‑pass filter
Explanation - -12 dB/octave corresponds to -40 dB/decade, which is the roll‑off of a second‑order filter.
Correct answer is: Second‑order low‑pass filter
Q.112 What is the primary reason for using a buffer (voltage follower) after a passive filter stage?
To prevent loading effects and preserve the filter’s response
To increase the filter’s Q factor
To shift the cutoff frequency upward
To provide gain
Explanation - A buffer presents high input impedance and low output impedance, isolating the filter from subsequent stages.
Correct answer is: To prevent loading effects and preserve the filter’s response
Q.113 In a digital IIR filter, the presence of poles inside the unit circle ensures:
Stability of the filter
Infinite gain at DC
Zero phase shift
Maximum stop‑band attenuation
Explanation - Poles inside the unit circle result in bounded output for bounded input, satisfying BIBO stability.
Correct answer is: Stability of the filter
Q.114 If a filter’s pass‑band gain is 2 (6 dB) and its stop‑band attenuation is 30 dB, the overall dynamic range of the filter is:
36 dB
24 dB
6 dB
30 dB
Explanation - Dynamic range ≈ stop‑band attenuation + pass‑band gain = 30 dB + 6 dB = 36 dB.
Correct answer is: 36 dB
Q.115 A filter with a transfer function that includes a factor (s^2 + ω_0^2) in the denominator but not in the numerator is a:
Low‑pass filter
High‑pass filter
All‑pass filter
Band‑stop filter
Explanation - The denominator pole pair creates attenuation above ω_0; lacking a zero at ω_0, the response is low‑pass.
Correct answer is: Low‑pass filter
Q.116 Which of the following best describes the effect of component tolerances on a filter’s cutoff frequency?
They cause the actual cutoff frequency to deviate from the design value.
They have no effect on the cutoff frequency.
They only affect the stop‑band attenuation.
They double the filter order.
Explanation - Variations in R and C shift the RC time constant, moving the cutoff frequency.
Correct answer is: They cause the actual cutoff frequency to deviate from the design value.
Q.117 A filter that provides equal attenuation of 20 dB across its entire stop‑band is said to have:
Flat stop‑band response
Rippled stop‑band
Variable Q factor
Zero group delay
Explanation - Uniform attenuation across the stop‑band indicates a flat response in that region.
Correct answer is: Flat stop‑band response
Q.118 In an active high‑pass filter, if the coupling capacitor is increased, the cutoff frequency will:
Decrease
Increase
Remain unchanged
Become infinite
Explanation - Increasing the capacitor raises the RC time constant, lowering the cutoff frequency.
Correct answer is: Decrease
Q.119 A filter designed to have a -3 dB point at 100 kHz and a roll‑off of -60 dB/decade is most likely:
Third‑order low‑pass filter
First‑order low‑pass filter
Second‑order low‑pass filter
All‑pass filter
Explanation - -60 dB/decade corresponds to -20 dB/decade per pole, thus three poles (third order).
Correct answer is: Third‑order low‑pass filter
Q.120 When a filter is implemented with a Gm‑C (transconductance‑capacitor) topology, it is typically used in:
Integrated‑circuit (IC) analog filters for high frequencies
Power‑line filtering
Audio equalizers
Mechanical vibration isolation
Explanation - Gm‑C filters replace inductors with transconductance amplifiers, suitable for IC fabrication at RF.
Correct answer is: Integrated‑circuit (IC) analog filters for high frequencies
Q.121 A filter with a pass‑band ripple of 0 dB and a stop‑band ripple of 0 dB is:
An ideal brick‑wall filter (theoretical only)
A Butterworth filter
A Chebyshev filter
An elliptic filter
Explanation - Real filters always exhibit some ripple or finite roll‑off; a perfect brick‑wall filter is a theoretical construct.
Correct answer is: An ideal brick‑wall filter (theoretical only)
Q.122 Which filter design technique uses the concept of equiripple behavior in both pass‑ and stop‑bands?
Elliptic (Cauer) filter
Butterworth filter
Bessel filter
First‑order RC filter
Explanation - Elliptic filters are defined by equal ripple (equiripple) in both pass‑ and stop‑band.
Correct answer is: Elliptic (Cauer) filter
Q.123 A digital filter that requires no multipliers and uses only adders and delay elements is known as:
CIC (Cascaded Integrator‑Comb) filter
FIR filter
IIR filter
FFT filter
Explanation - CIC filters are multiplier‑free and widely used for decimation and interpolation.
Correct answer is: CIC (Cascaded Integrator‑Comb) filter
Q.124 In a band‑pass filter, the product of the lower and upper –3 dB frequencies equals:
The square of the center frequency (f_0^2)
The cutoff frequency
The Q factor
Zero
Explanation - For symmetrical band‑pass filters, f_low × f_high = f_0^2.
Correct answer is: The square of the center frequency (f_0^2)
Q.125 When designing an analog filter, the term 'pole‑zero cancellation' refers to:
Placing a zero at the same location as a pole to simplify the transfer function
Removing all poles from the circuit
Increasing the filter order indefinitely
Using a digital filter to emulate an analog one
Explanation - Pole‑zero cancellation can reduce unwanted effects but must be used carefully to avoid sensitivity to component variations.
Correct answer is: Placing a zero at the same location as a pole to simplify the transfer function
Q.126 A filter that exhibits a -6 dB attenuation at its cutoff frequency is:
A first‑order filter (by definition)
A second‑order filter
An all‑pass filter
A notch filter
Explanation - The -3 dB point is the standard definition for first‑order filters; however, some textbooks define -6 dB for cascaded first‑order sections. To avoid confusion, the correct answer for the conventional definition is -3 dB. Since the question asks for -6 dB, the intended answer is a second‑order filter (two cascaded first‑order sections) which yields -6 dB at the combined cutoff. Adjusting: The correct answer is "A second‑order filter".
Correct answer is: A first‑order filter (by definition)