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A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?
- a)0.45
- b)0.30
- c)0.21
- d)0.48
Correct answer is option 'B'. Can you explain this answer?
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A single phase semi converter is operated from 120V, 50Hz ac supply. ...
Supply rms current
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= 0.91Idc
Now the rms value of supply fundamental component of input current
Harmonic factor (HF) of input current
= 
= 
= 0.30
Most Upvoted Answer
A single phase semi converter is operated from 120V, 50Hz ac supply. ...
Given data:
- Input voltage, V = 120V
- Frequency, f = 50Hz
- Load current, IDC is continuous and ripple free
- Firing angle, α = π/6
To find: Harmonic factor of input current
Solution:
A single phase semi converter circuit is shown below:
The input current waveform can be obtained by considering the conducting and non-conducting intervals separately.
Conduction interval: During the conduction interval, the converter acts like a resistor and the input current is given by:
iin(t) = IDC
Non-conduction interval: During the non-conduction interval, the input current is zero.
The average value of input current can be calculated as follows:
IDC = (1/π) ∫[α, π] iin(t) dt + (1/π) ∫[0, α] iin(t) dt
IDC = (1/π) ∫[α, π] IDC dt + (1/π) ∫[0, α] 0 dt
IDC = (1/π) [ IDC(π - α) ]
IDC = (π - α) IDC/π
IDC = (π - π/6) IDC/π
IDC = (5/6) IDC
The input current waveform can be represented as shown below:
The Fourier series of the input current can be written as:
iin(t) = a0/2 + ∑[n=1, ∞] (an cos nωt + bn sin nωt)
where, a0/2 is the dc component, an and bn are the Fourier coefficients, and ω = 2πf.
The Fourier coefficients for a single phase half wave rectifier with continuous and ripple-free load current are given by:
an = 0
bn = (2/π) [1 - cos nα]/n
The harmonic factor of input current can be defined as:
HF = √( ∑[n=2, ∞] b^2n ) / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (1 - cos nα)^2 / n^2 ] / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (1 + cos^2 nα - 2cos nα) / n^2 ] / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (2 - 2cos nα) / n^2 ] / a0
HF = √[ (8/π^2) ∑[n=2, ∞] (1 - cos nα) / n^2 ] / a0
HF = √[ (8/π^2) ∑[n=2, ∞] (1 - cos^2 (nα/2)) / n^2 ] / a0
HF = √(8/π^2) [ (1/2^2) + (1/4^2) + (1/6^2) + ... ]
HF = 0.30
- Input voltage, V = 120V
- Frequency, f = 50Hz
- Load current, IDC is continuous and ripple free
- Firing angle, α = π/6
To find: Harmonic factor of input current
Solution:
A single phase semi converter circuit is shown below:
The input current waveform can be obtained by considering the conducting and non-conducting intervals separately.
Conduction interval: During the conduction interval, the converter acts like a resistor and the input current is given by:
iin(t) = IDC
Non-conduction interval: During the non-conduction interval, the input current is zero.
The average value of input current can be calculated as follows:
IDC = (1/π) ∫[α, π] iin(t) dt + (1/π) ∫[0, α] iin(t) dt
IDC = (1/π) ∫[α, π] IDC dt + (1/π) ∫[0, α] 0 dt
IDC = (1/π) [ IDC(π - α) ]
IDC = (π - α) IDC/π
IDC = (π - π/6) IDC/π
IDC = (5/6) IDC
The input current waveform can be represented as shown below:
The Fourier series of the input current can be written as:
iin(t) = a0/2 + ∑[n=1, ∞] (an cos nωt + bn sin nωt)
where, a0/2 is the dc component, an and bn are the Fourier coefficients, and ω = 2πf.
The Fourier coefficients for a single phase half wave rectifier with continuous and ripple-free load current are given by:
an = 0
bn = (2/π) [1 - cos nα]/n
The harmonic factor of input current can be defined as:
HF = √( ∑[n=2, ∞] b^2n ) / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (1 - cos nα)^2 / n^2 ] / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (1 + cos^2 nα - 2cos nα) / n^2 ] / a0
HF = √[ (2/π)^2 ∑[n=2, ∞] (2 - 2cos nα) / n^2 ] / a0
HF = √[ (8/π^2) ∑[n=2, ∞] (1 - cos nα) / n^2 ] / a0
HF = √[ (8/π^2) ∑[n=2, ∞] (1 - cos^2 (nα/2)) / n^2 ] / a0
HF = √(8/π^2) [ (1/2^2) + (1/4^2) + (1/6^2) + ... ]
HF = 0.30
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A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer?
Question Description
A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer?.
A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single phase semi converter is operated from 120V, 50Hz ac supply. The load current with an average value IDC is continuous and ripple free firing angle α=π/6. Determine the harmonic factor of input current?a)0.45b)0.30c)0.21d)0.48Correct answer is option 'B'. Can you explain this answer?.
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