Ac circuit analysis - band pass filters using laplace

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Reference no: EM131931545

AC Circuit Analysis

Problems

Low Pass Filter

Question 1:

A low pass filter has cut-off frequency of fc = 3000 Hz.
a. Design a RC circuit to realize this filter. Consider C = 1μF . Draw the circuit and analyze its operation.
b. Design a RL circuit to realize this filer. Consider L = 150mH. Draw the circuit and analyze its operation.

Question 2:

A low pass filter has cut-off frequency of fc = 60 Hz.
a. Design a RC circuit to realize this filter. Consider C = 10μF . Draw the circuit and analyze its operation.
b. Design a RL circuit to realize this filer. Consider L = 10mH. Draw the circuit and analyze its operation.

Question 3:

In a RL LPF, the circuit parameters are R = 2 Ω and L = 0.05 mH. Find the cutoff frequency of the filter. Determine the output voltage amplitude and phase when a Vin = 10V input is tuned at the following frequencies ω = 4000,40,000, 400,000 (rad/sec).

Question 4:

In a RC LPF, the circuit parameters are R = 2 Ω and C = 10μF. Find the cutoff frequency of the filter. Determine the output voltage amplitude and phase when a Vin = 10V input is tuned at the cutoff frequency and a decade above and a decade below the cutoff.

Low Pass Filter Using Laplace

Question 5:

Design a unity gain LPF with cutoff frequency of ωc = 15k rad/sec . Find its transfer function.

Question 6:

Design a unity gain LPF to cut the frequencies higher than the heartbeat of 1Hz. The frequency of 1Hz should fully pass to the output. Find the transfer function of the filter.

Question 7:

Determine the filter type of the following systems, and determine their cutoff frequency.
a. G(s) = 200/s+200
b. G(s) = 1/1e-3s+1
c. G(s) = 400/ 2e-4s+2

Question 8. In problem 7, find the poles and zeros of the transfer functions, identify the correlation between the poles and the cutoff frequency and the filter types.

Question 9. Determine and sketch the frequency response of the transfer functions in problem 7.

High Pass Filter

Question 10

A high pass filter has cut-off frequency of fc = 3000 Hz.

a. Design a RC circuit to realize this filter. Consider C = 1μF . Draw the circuit and analyze its operation.

b. Design a RL circuit to realize this filer. Consider L = 150mH. Draw the circuit and analyze its operation.

Question 11.

A high pass filter has cut-off frequency of fc = 60 Hz.
a. Design a RC circuit to realize this filter. Consider C = 10μF . Draw the circuit and analyze its operation.

b. Design a RL circuit to realize this filer. Consider L = 10mH. Draw the circuit and analyze its operation.

Question 12.

In a RL HPF, the circuit parameters are R = 2 Ω and L = 0.05 mH. Find the cutoff frequency of the filter. Determine the output voltage amplitude and phase when a Vin = 10V input is tuned at the following frequencies ω = 4000,40,000, 400,000 (rad/sec).

Question 13.

In a RC HPF, the circuit parameters are R = 2 Ω and C = 10μF. Find the cutoff frequency of the filter. Determine the output voltage amplitude and phase when a Vin = 10V input is tuned at the cutoff frequency and a decade above and a decade below the cutoff.

High Pass Filter Using Laplace

Question 14.

Design a unity gain HPF with cutoff frequency of ωc = 15k rad/sec . Find its transfer function.

Question 15.

Design a unity gain HPF to cut the frequencies lower than 60Hz. The frequency of 60Hz should fully pass to the output. Find the transfer function of the filter.

Question 16.

Determine the filter type of the following systems, and determine their cutoff frequency.
a. G(s) = 200s/s+200
b. G(s) = s/1e-3s+1
c. G(s) = 400s/2e-4s+2

Question 17.

In problem 16, find the poles and zeros of the transfer functions, identify the correlation between the poles and the cutoff frequency and the filter types.

Question 18.

Determine and sketch the frequency response of the transfer functions in problem 17.

Series and Parallel LC circuits

Question 19.

Tune a LC series circuit at the 60Hz. Find a reasonable value (in existing range) for L and C. Analyze the operation of this circuit as a bridge between the input and output (of a filter). Analyze the operation of this circuit in parallel to the output (of a filter).

Question 20.

Tune a LC parallel circuit at the 60Hz. Find a reasonable value (in existing range) for L and C. Analyze the operation of this circuit as a bridge between the input and output (of a filter). Analyze the operation of this circuit in parallel to the output (of a filter).

Band Pass Filters

Question 21.

Design a BPF to show a bandwidth of 100 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 22.

Design a BPF to show a bandwidth of 10 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 23.

Design a BPF to show a bandwidth of 1 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 24.

Design a BPF to show a bandwidth of 0.5 Hz, and cutoff frequency of 60 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 25.

Damping of a BPF is designed to be ζ = 0.5. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 26.

Damping of a BPF is designed to be ζ = 0.1. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 27.

Damping of a BPF is designed to be ζ = 0.05. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Band Pass Filters using Laplace

Question 28.

Find transfer function of a BPF with bandwidth of 100 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 29.

Find transfer function of a BPF with bandwidth of 10 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 30.

Find transfer function of a BPF with bandwidth of 1 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 31.

Find transfer function of a BPF with bandwidth of 0.5 Hz, and cutoff frequency of 60 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 32.

Determine the filter type, cutoff frequency, resonant frequency, quality factor, damping factor, and bandwidth of the following transfer functions:
a. G(s) = 20s/s² +20s+10000
b. G(s) = 200s/s² +200s+9000
c. G(s) = 0.1s/s²+0.1s+(120Π)²
d. G(s) = 0.01s/s²+0.01s+(2Π)²

Question 33.

Realize the transfer functions of problem 33 in LC series.

Question 34.

Realize the transfer functions of problem 32 in LC parallel.

Question 35.

Damping of a BPF is designed to be ζ = 0.5. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 36.

Damping of a BPF is designed to be ζ = 0.1. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 37.

Damping of a BPF is designed to be ζ = 0.05. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 38.

Find the transfer function of a BPF with cutoff frequencies of fc1 = 100Hz, fc2 = 500Hz.

Question 39.

Find the transfer function of a BPF with cutoff frequencies of ωc1 = 58Hz, fc2 = 60Hz.

Question 40.

Find the transfer function of a BPF with cutoff frequencies of ωc1 = 1000 rad/sec , ωc2 = 5000 rad/sec.

Band Reject Filters

Question 41.

Design a BRF to show a bandwidth of 100 Hz, and cutoff frequency of 400 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 42.

Design a BRF to show a bandwidth of 10 Hz, and cutoff frequency of 400 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 43.

Design a BRF to show a bandwidth of 1 Hz, and cutoff frequency of400 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 44.

Design a BRF to show a bandwidth of 0.5 Hz, and cutoff frequency of 60 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components.

Question 45.

Damping of a BRF is designed to be ζ = 0.5. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 46.

Damping of a BRF is designed to be ζ = 0.1. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 47.

Damping of a BRF is designed to be ζ = 0.05. What is the Q of the circuit. Design the filter if the resonant frequency is 100 Hz. Sketch the frequency response.

Band Pass Filters using Laplace

Question 48.

Find transfer function of a BRF with bandwidth of 100 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 49.

Find transfer function of a BRF with bandwidth of 10 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 50.

Find transfer function of a BRF with bandwidth of 1 Hz, and cutoff frequency of 5000 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 51.

Find transfer function of a BRF with bandwidth of 0.5 Hz, and cutoff frequency of 60 Hz. Find the transfer function in two cases of using a LC series and a LC parallel. Use existing range components. Determine the poles and zeros of the circuit and estimate the cutoff frequency from the values of the poles.

Question 52.

Determine the filter type, cutoff frequency, resonant frequency, quality factor, damping factor, and bandwidth of the following transfer functions:
a. G(s) = s²+10000/s²+20s+10000

b. G(s) = s²+9000/s²+200s+9000
c. G(s) = s²+(120Π)²/s²+0.1s+(120Π)²
d. G(s) = s²+(2Π)2/s²+0.01s+(2Π)²

Question 53.

Realize the transfer functions of problem 52 in LC series.

Question 54.

Realize the transfer functions of problem 52 in LC parallel.

Question 55.

Damping of a BRF is designed to be ζ = 0.5. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 56.

Damping of a BRF is designed to be ζ = 0.1. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 57.

Damping of a BRF is designed to be ζ = 0.05. What is the Q of the circuit. Find the transfer function if the resonant frequency is 100 Hz. Sketch the frequency response.

Question 58.

Find the transfer function of a BRF with cutoff frequencies of fc1 = 100Hz, fc2 = 500Hz.

Question 59.

Find the transfer function of a BRF with cutoff frequencies of ωc1 = 58Hz, fc2 = 60Hz.

Question 60.

Find the transfer function of a BRF with cutoff frequencies of ωc1 = 1000 rad/sec , ωc2 = 5000 rad/sec.

Higher Order Filter

Question 61.

A LPF has cutoff frequency of ωc = 100 rad/sec . The filter is repeated 3 times. Find the new cutoff frequency. Sketch a RL and a RC filter separately to realize the 3rd order filter. Sketch the frequency response of the 1st order and 3rd order.

Question 62.

A 3rd order LPF has to have a cutoff frequency of ωc = 100 rad/sec. Find the cutoff frequency of the first order circuit. Sketch a RL and a RC filter separately to realize the 3rd order filter. Sketch the frequency response of the 1st order and 3rd order.

Question 63.

A HPF has cutoff frequency of ωc = 100 sec . The filter is repeated 3 times. Find the new cutoff frequency. Sketch a RL and a RC filter separately to realize the 3rd order filter. Sketch the frequency response of the 1st order and 3rd order.

Question 64.

A 3rd order HPF has to have a cutoff frequency of ωc = 100 rad/sec. Find the cutoff frequency of the first order circuit. Sketch a RL and a RC filter separately to realize the 3rd order filter. Sketch the frequency response of the 1st order and 3rd order.

Higher Order Filter Using Laplace

Question 65.

Determine the type, order, cutoff frequency, bandwidth, and quality factor of the following filters (whichever applies).
a. G(s) = 10³/(s+10)³
b. G(s) = s⁴/(s+1000)⁴
c. G(s) = 400s²/(s²+20s+10000)²
d. G(s) = (s²+(120Π)²)³/(s²+0.1s+(120Π)²)³

Reference no: EM131931545

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