1. How can a first-order low pass filter can be converted into a second-order low pass filter

A. By adding LC network
B. By adding an RC network
C. By adding RC || LC network
D. None of the mentioned

Answer: B

The addition of the RC network makes the stopband response have a 40dB/decade.

2. Consider the following specifications and calculate the high cut-off frequency for the circuit given?

A. 95Hz
B. 48Hz
C. 14Hz
D. 33Hz

Answer: D

The high cut-off frequency,

f_{H}= 1/[2 π√(R_{2} ×R_{3}× C_{2}× C_{3})]

= 1/[2π√(33kΩ×15kΩ×0.47µF×0.1µF)]

= 1/[2π× 4.82×(10^{-3})]= 33Hz.

3. Find the gain and phase angle of the second-order low pass filter?
Where the passband gain of the filter is 5, the frequency and the high cut-off frequency of the filter are 3000Hz and 1kHz.

A. None of the mentioned
B. Gain magnitude = -1.03dB , φ =63.32^{o}
C. Gain magnitude = -5.19dB , φ =71.56^{o}
D. Gain magnitude = -4.94dB , φ =90^{o}

Answer: C

The gain of the second order low pass filter

[V_{O} /V_{in}] =A_{F}/ √ [1+(f/f_{h})^{2}]

=5/ √[1+(3000/1000)^{4}]

=5/9.055 =0.55.

=> [V_{O} /V_{in}] = 20log(0.55) =-.519dB.

Phase angle of second order low pass filter is given as φ= tan^{-1}(f/f_{H})

=> φ =71.56^{o}.

4. A second-order low pass filter is given an input frequency of 30kHz and produces an output having a phase angle of 79^{o}. Determine the passband gain of the filter?

A. 11 dB
B. 89.11 dB
C. 46.78 dB
D. None of the mentioned

Answer: C

Phase angle of the filter,

φ = tan^{-1}(f/f_{H})

=> f_{h} =f×tan(φ)

=30kHz × tan(79) = 154.34kHz.^{
}

Therefore, the pass band gain

A_{F} = f_{H}/0.707 = 154.34kHz/0.707

A_{F}= 218.3 =20log(218.3)= 46.78dB.

5. The passband voltage gain of a second-order low pass Butterworth filter is

A. 1.586
B. 8.32
C. 0.586
D. 0.707

Answer: A

The second-order low pass filter has a passband voltage gain equal to 1.586 because of equal resistor and capacitor values. This gain is necessary to guarantee Butterworth’s response.

6. Arrange the series of steps involved in designing a filter for first-order low pass filter

Step 1: Select a value of C less than or equal to 1µF
Step 2: Choose a value of high cut-off frequency f_{H}
Step 3: Select a value of R_{1}C and R_{F} depending on the desired passband gain
Step 4: Calculate the value of R

A. Steps- 2->4->3->1
B. Steps- 4->1->3->2
C. Steps- 2->1->4->3
D. Steps- 1->3->4->2

Answer: B

The series of steps involved in designing a filter for a first-order low pass filter is

Step 1: Calculate the value of R

Step 2: Select a value of C less than or equal to 1µF

Step 3: Select a value of R_{1}C and R_{F} depending on the desired passband gain

Step 4: Choose a value of high cut-off frequency f_{H}

The mentioned option is the sequence of steps followed for designing a low pass filter.

7. Frequency scaling is done using

A. Standard capacitor
B. Varying capacitor
C. Standard resistance
D. None of the mentioned

Answer: A

In frequency scaling, standard capacitors are chosen, because for the non-standard value of the resistor, a potentiometer is used.

8. How are the higher-order filters formed?

A. By increasing resistors and capacitors in low pass filter
B. By decreasing resistors and capacitors in low pass filter
C. By interchanging resistors and capacitors in low pass filter
D. All of the mentioned

Answer: C

High pass filters are often formed by interchanging frequency determining resistors and capacitors in low pass filters. For example, a first-order high pass filter is formed from a first-order low pass filter by interchanging components Rand C.

9. In a first-order high pass filter, frequencies higher than low cut-off frequencies are called
A. Stopband frequency
B. Passband frequency
C. Centre band frequency
D. None of the mentioned

Answer: B

The low cut-off frequency, f_{L} is 0.707 times the passband gain voltage. Therefore, frequencies above f_{L} are passband frequencies.

3. Compute the voltage gain for the following circuit with an input frequency 1.5kHz.