1Which of the following elements are used to construct a passive filter?
A.Transistors and Capacitors
B.Resistors, Capacitors, and Op-Amps
C.Op-Amps and Inductors
D.Resistors, Inductors, and Capacitors
Correct Answer: Resistors, Inductors, and Capacitors
Explanation:
Passive filters are constructed using only passive components: Resistors (), Inductors (), and Capacitors (). They do not require an external power source.
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2In a symmetrical T-network, the characteristic impedance is given by which formula, where is the total series arm impedance and is the shunt arm impedance?
A.
B.
C.
D.
Correct Answer:
Explanation:
The characteristic impedance of a T-section is defined as .
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3What is the relationship between the characteristic impedance of a T-network () and a -network () composed of the same series and shunt impedances?
A.
B.
C.
D.
Correct Answer:
Explanation:
For the same prototype section, the geometric mean of the characteristic impedances relates to the product of the arm impedances: .
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4In a pure reactive network, the propagation constant . What condition defines the passband?
A. and
B. and
C. and
D.
Correct Answer: and
Explanation:
In the passband, there should be no attenuation. Therefore, the attenuation constant must be zero, while the phase constant changes with frequency.
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5What defines a Constant-K filter?
A.The ratio of series to shunt impedance is constant.
B.The sum of series and shunt impedances is constant.
C.The difference between series and shunt impedances is constant.
D.The product of series () and shunt () impedances is a frequency-independent constant ().
Correct Answer: The product of series () and shunt () impedances is a frequency-independent constant ().
Explanation:
A Constant-K filter is a prototype filter where (or ), where is a real constant independent of frequency.
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6For a Constant-K Low Pass Filter using T-section, the series arm consists of __ and the shunt arm consists of __.
A.Inductors; Capacitors
B.Inductors; Resistors
C.Resistors; Capacitors
D.Capacitors; Inductors
Correct Answer: Inductors; Capacitors
Explanation:
A low pass T-section filter has inductors in the series arms (to block high frequencies) and a capacitor in the shunt arm (to bypass high frequencies to ground).
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7Calculate the cut-off frequency () of a Constant-K Low Pass Filter given and .
A.
B.
C.
D.
Correct Answer:
Explanation:
For a Constant-K Low Pass Filter, the cut-off frequency is derived from , which gives .
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8In the design of a Constant-K High Pass Filter, what are the design equations for and given cut-off frequency and design impedance ?
A.
B.
C.
D.
Correct Answer:
Explanation:
For a Constant-K High Pass Filter: and .
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9What is the primary disadvantage of a simple Constant-K filter?
A.It uses active components.
B.It cannot be designed for high frequencies.
C.It has zero phase shift in the passband.
D.The attenuation in the stopband rises very slowly (gradual cut-off) and varies with frequency.
Correct Answer: The attenuation in the stopband rises very slowly (gradual cut-off) and varies with frequency.
Explanation:
Constant-K filters have a gradual transition from passband to stopband and their characteristic impedance varies widely within the passband, causing mismatch problems.
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10Which filter type is used to overcome the slow attenuation rate of Constant-K filters?
A.RL Filter
B.RC Filter
C.m-derived filter
D.All-pass filter
Correct Answer: m-derived filter
Explanation:
m-derived filters are modified versions of Constant-K filters designed to provide a very sharp cut-off (infinite attenuation) at a specific frequency .
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11In an m-derived low pass filter, the resonant frequency (frequency of infinite attenuation) is related to the cut-off frequency by:
A.
B.
C.
D.
Correct Answer:
Explanation:
For a low pass filter, the attenuation pole must occur in the stopband, so must be greater than the cut-off frequency .
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12The value of 'm' in an m-derived filter lies in the range:
A.
B.
C.
D.
Correct Answer:
Explanation:
The parameter 'm' is a derivation constant derived from the ratio of cut-off frequency to infinite attenuation frequency, strictly falling between 0 and 1.
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13What is the formula for 'm' in an m-derived Low Pass Filter?
A.
B.
C.
D.
Correct Answer:
Explanation:
For a low pass filter, .
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14In a Series m-derived Low Pass T-section, what component is added to the shunt arm?
A.A resistor
B.A capacitor in parallel with the shunt inductor
C.An inductor in parallel with the shunt capacitor
D.An inductor in series with the shunt capacitor
Correct Answer: An inductor in series with the shunt capacitor
Explanation:
In a series m-derived LPF T-section, the shunt arm becomes a series LC resonant circuit (tuned to ), requiring an inductor in series with the capacitor.
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15What is the characteristic impedance of a Series m-derived T-section compared to the prototype Constant-K section?
A.It is equal to the prototype at all frequencies.
B.It is completely different.
C.It is equal to the prototype .
D.It is zero.
Correct Answer: It is equal to the prototype at all frequencies.
Explanation:
Series m-derived filters are designed such that their characteristic impedance () remains identical to that of the prototype Constant-K section, allowing them to be cascaded.
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16Why are Composite Filters used?
A.To create oscillators.
B.To combine the advantages of Constant-K (passband), m-derived (sharp cut-off), and half-sections (impedance matching).
C.To save components.
D.To reduce the gain of the circuit.
Correct Answer: To combine the advantages of Constant-K (passband), m-derived (sharp cut-off), and half-sections (impedance matching).
Explanation:
No single filter section provides ideal characteristics. Composite filters cascade different sections to achieve flat impedance, sharp attenuation, and high stopband loss.
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17In a composite filter, what is the purpose of the terminating half-sections?
A.To provide sharp cut-off.
B.To double the voltage.
C.To make the image impedance constant () over the passband for matching.
D.To block DC.
Correct Answer: To make the image impedance constant () over the passband for matching.
Explanation:
Terminating half-sections, usually with , are used to provide a characteristic impedance that is nearly constant and resistive over the entire passband.
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18What specific value of 'm' is typically used for the terminating half-sections to ensure flat characteristic impedance?
A.
B.
C.
D.
Correct Answer:
Explanation:
Ideally, provides the flattest characteristic impedance curve in the passband, ensuring good matching with a constant resistive load.
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19Which of the following is a major advantage of Active Filters over Passive Filters?
A.They require no power supply.
B.They can handle high voltage and current.
C.They eliminate the need for bulky inductors.
D.They are inherently stable.
Correct Answer: They eliminate the need for bulky inductors.
Explanation:
Active filters use Op-Amps with resistors and capacitors to simulate inductive effects, eliminating the need for physical inductors which are bulky and expensive, especially at low frequencies.
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20Active filters are generally restricted to which frequency range?
A.Radio frequencies
B.Microwave frequencies (> 1 GHz)
C.Audio and low radio frequencies
D.X-ray frequencies
Correct Answer: Audio and low radio frequencies
Explanation:
Active filters are limited by the Bandwidth (Gain-Bandwidth Product) of the Op-Amps used, making them suitable mostly for audio and lower RF ranges.
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21Which component is NOT used in a standard Active Filter design?
A.Inductor
B.Op-Amp
C.Resistor
D.Capacitor
Correct Answer: Inductor
Explanation:
The primary design goal of active filters is to avoid the use of inductors.
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22What is the voltage gain capability of an Active Filter?
A.Always exactly 1 (Buffer)
B.Always 0
C.Always less than 1 (Attenuator)
D.Can be greater than 1 (Amplification)
Correct Answer: Can be greater than 1 (Amplification)
Explanation:
Because they contain active elements (Op-Amps), active filters can provide passband gain, unlike passive filters which always introduce some insertion loss.
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23A First-Order Active Low Pass Filter provides a roll-off rate of:
A.-40 dB/decade
B.-60 dB/decade
C.-20 dB/decade
D.-80 dB/decade
Correct Answer: -20 dB/decade
Explanation:
The order of the filter determines the roll-off. A first-order filter rolls off at -20 dB/decade (-6 dB/octave).
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24In a standard non-inverting First-Order Active Low Pass Filter, where is the capacitor placed?
A.In series with the output.
B.In the feedback loop of the Op-Amp.
C.In series with the input signal.
D.In parallel with the input resistor to ground (shunt arm) at the non-inverting terminal.
Correct Answer: In parallel with the input resistor to ground (shunt arm) at the non-inverting terminal.
Explanation:
For a non-inverting LPF, an RC circuit is placed at the non-inverting input. The resistor is in series with the source, and the capacitor is connected from the non-inverting input to ground.
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25The cut-off frequency for a First-Order Active Low Pass Filter with input resistor and shunt capacitor is:
A.
B.
C.
D.
Correct Answer:
Explanation:
The standard formula for the cut-off frequency of a simple RC network used in first-order active filters is .
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26In a First-Order Active High Pass Filter, the positions of the resistor and capacitor at the non-inverting input are:
A.Both in series.
B.Both in parallel.
C.Swapped compared to the Low Pass Filter.
D.Ideally the same as the Low Pass Filter.
Correct Answer: Swapped compared to the Low Pass Filter.
Explanation:
To convert a 1st order LPF to a HPF, the positions of the R and C in the frequency-selective network are interchanged. C is in series, R is to ground.
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27The passband gain () of a non-inverting active filter is determined by:
A.The feedback resistor () and input resistor () of the Op-Amp.
B.The input voltage amplitude.
C.The RC time constant.
D.The frequency of the signal.
Correct Answer: The feedback resistor () and input resistor () of the Op-Amp.
Explanation:
For a non-inverting configuration, the gain is determined by the feedback network: .
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28What is the phase shift at the cut-off frequency for a First-Order Active Low Pass Filter?
A.-90 degrees
B.-45 degrees
C.0 degrees
D.+45 degrees
Correct Answer: -45 degrees
Explanation:
At the cut-off frequency (), the real and imaginary parts of the denominator in the transfer function are equal, resulting in a phase shift of -45 degrees.
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29Which of the following is a limitation of Passive Filters compared to Active Filters?
A.High noise.
B.Loading effect: The source and load impedances affect the filter characteristics.
C.Limited bandwidth.
D.They require a power supply.
Correct Answer: Loading effect: The source and load impedances affect the filter characteristics.
Explanation:
Passive filters are sensitive to impedance matching. Active filters typically have high input impedance and low output impedance, isolating the filter characteristics from the load.
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30If you need to design a filter with a cut-off frequency of 50Hz, which type is preferred and why?
A.Passive, because inductors are small at 50Hz.
B.Active, because it uses more power.
C.Passive, because it has gain.
D.Active, because passive inductors required for 50Hz would be extremely large.
Correct Answer: Active, because passive inductors required for 50Hz would be extremely large.
Explanation:
At low frequencies (like 50Hz), the inductance required () is very large, making physical inductors heavy, expensive, and lossy. Active filters are preferred.
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31In a T-section network, if is the open-circuit impedance and is the short-circuit impedance, then is:
A.
B.
C.
D.
Correct Answer:
Explanation:
The characteristic impedance of any symmetrical network is the geometric mean of the open-circuit and short-circuit impedances measured at the input.
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32A Band Pass Filter allows frequencies:
A.Outside a specific range.
B.Below a certain cut-off.
C.Above a certain cut-off.
D.Within a specific range ( to ).
Correct Answer: Within a specific range ( to ).
Explanation:
A Band Pass Filter passes frequencies between a lower cut-off () and an upper cut-off () and attenuates others.
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33A Band Stop (Notch) Filter is formed by:
A.Cascading a LPF and a HPF with overlapping passbands.
B.Connecting a LPF and HPF in parallel.
C.Series combination of LPF and HPF where cut-off frequencies do not overlap in a specific way.
D.A single capacitor.
Correct Answer: Connecting a LPF and HPF in parallel.
Explanation:
While there are many topologies, conceptually, connecting a Low Pass (allows low) and High Pass (allows high) in parallel creates a stop band in the middle, provided the LPF cutoff < HPF cutoff.
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34What is the stopband attenuation rate of a Second-Order Active Filter?
A.-60 dB/decade
B.-10 dB/decade
C.-40 dB/decade
D.-20 dB/decade
Correct Answer: -40 dB/decade
Explanation:
The roll-off rate is dB/decade, where is the order. For , it is -40 dB/decade.
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35Which parameter determines the selectivity or sharpness of an Active Band Pass Filter?
A.Input Voltage
B.Gain
C.Supply Voltage
D.Q-factor (Quality Factor)
Correct Answer: Q-factor (Quality Factor)
Explanation:
The Q-factor determines the sharpness of the resonance. A high Q indicates a narrow bandwidth and high selectivity.
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36Design a Constant-K Low Pass Filter (T-section) with and Hz. The value of is approximately:
A.95.5 mH
B.600 mH
C.318 mH
D.191 mH
Correct Answer: 191 mH
Explanation:
For LPF T-section, total series H or 191 mH.
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37In the design of the filter in the previous question, what is the value of the shunt Capacitor ?
A.0.53 F
B.0.26 F
C.10 F
D.1.06 F
Correct Answer: 0.53 F
Explanation:
F.
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38The 'Butterworth' response in active filters is characterized by:
A.Ripples in the stopband.
B.Fastest roll-off.
C.Maximally flat response in the passband.
D.Ripples in the passband.
Correct Answer: Maximally flat response in the passband.
Explanation:
Butterworth filters are designed to have a frequency response which is as flat as mathematically possible in the passband.
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39The 'Chebyshev' filter response is known for:
A.Flat passband.
B.Linear phase response.
C.Slowest roll-off.
D.Ripples in the passband but sharper roll-off than Butterworth.
Correct Answer: Ripples in the passband but sharper roll-off than Butterworth.
Explanation:
Chebyshev filters sacrifice passband flatness (allowing ripples) to achieve a steeper roll-off (transition) compared to Butterworth filters.
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40In a Shunt m-derived T-section, the series arms consist of:
A.Parallel LC circuits
B.Resistors
C.Single Inductors (for LPF)
D.Series LC circuits
Correct Answer: Single Inductors (for LPF)
Explanation:
In a Shunt m-derived T-section, the 'm' variation is applied to the shunt arm (making it a series resonant circuit). The series arms remain simple inductors, though their value is modified by 'm'.
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41For a symmetrical -network, the characteristic impedance is:
A.
B.
C.
D.
Correct Answer:
Explanation:
This formula is equivalent to . The math simplifies to the option shown.
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42What happens to the characteristic impedance of a Constant-K LPF at the cut-off frequency ?
A.It remains .
B.It becomes infinite.
C.It becomes zero or imaginary.
D.It becomes negative.
Correct Answer: It becomes zero or imaginary.
Explanation:
At cut-off, the filter transitions from passband to stopband. Theoretically, for a lossless filter, goes to zero (for ) or infinity (for T) or becomes purely imaginary in the stopband.
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43Which filter is characterized by the equation ?
A.Passive High Pass Filter (RC)
B.Inductive Filter
C.Active High Pass Filter
D.Passive Low Pass Filter (RC)
Correct Answer: Passive Low Pass Filter (RC)
Explanation:
This is the transfer function of a simple passive RC series circuit taken across the capacitor, which acts as a Low Pass Filter.
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44To convert a low-pass Constant-K filter prototype to a high-pass filter, one must:
A.Halve the values of L and C.
B.Add resistors in series.
C.Double the values of L and C.
D.Replace L with C and C with L.
Correct Answer: Replace L with C and C with L.
Explanation:
This is the standard transformation. Series inductors become series capacitors, and shunt capacitors become shunt inductors.
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45In a composite filter design, the order of cascading sections is usually:
A.Half-Section Constant K m-derived Half-Section
B.Constant K m-derived Constant K
C.Random
D.m-derived Half-Section
Correct Answer: Half-Section Constant K m-derived Half-Section
Explanation:
Terminating half-sections are placed at the input and output for impedance matching. The internal sections (Constant K and m-derived) provide the filtering and attenuation characteristics.
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46If an active filter circuit oscillates, the most likely cause is:
A.The capacitors are too large.
B.Positive feedback is present causing instability.
C.Negative feedback is too high.
D.The input signal is too small.
Correct Answer: Positive feedback is present causing instability.
Explanation:
Filters require negative feedback for stability. Unintentional positive feedback turns the amplifier into an oscillator.
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47The Bandwidth of a filter is defined as:
A.
B.
C.
D.
Correct Answer:
Explanation:
Bandwidth is the difference between the upper cut-off frequency () and the lower cut-off frequency ().
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48What is the formula for the design impedance in terms of L and C for a prototype filter?
A.
B.
C.
D.
Correct Answer:
Explanation:
For a constant-K filter, the nominal characteristic impedance is (Conceptually for LPF/HPF components).
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49In a First-Order Active HPF, if and , calculate the cut-off frequency.
A.1.59 kHz
B.15.9 kHz
C.1.59 Hz
D.159 Hz
Correct Answer: 1.59 kHz
Explanation:
Hz = 1.59 kHz.
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50Why is the Slew Rate of the Op-Amp important in Active Filter design?
A.It determines the input impedance.
B.It determines the DC gain.
C.It sets the lower cut-off frequency.
D.It limits the maximum frequency and amplitude the filter can handle without distortion.
Correct Answer: It limits the maximum frequency and amplitude the filter can handle without distortion.
Explanation:
The Slew Rate defines the maximum rate of change of the output voltage. If the signal frequency/amplitude requires a change faster than the slew rate, the signal will be distorted.