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The output value e1 and e2 of two full bridge inverter are added using output transformer. In order to eliminate the 3rd harmonic from output voltage, the phase angle between e1 and e2 should be ______ degree.
Correct answer is '60'. Can you explain this answer?
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The output value e1and e2of two full bridge inverter are added using o...
It is possible when
3θ = π
θ = π/3
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The output value e1and e2of two full bridge inverter are added using o...
Explanation:
The full bridge inverter produces an output voltage with a fundamental frequency and harmonics of 3rd, 5th, 7th, etc. If the output voltage of two full bridge inverters is added using an output transformer, then the harmonics of the output voltage will also get added. Thus, it is necessary to eliminate the 3rd harmonic from the output voltage.
Phase Angle:
The 3rd harmonic can be eliminated if the phase angle between e1 and e2 is 60 degrees. This is because the 3rd harmonic is an odd multiple of the fundamental frequency and has a phase angle of 180 degrees. When e1 and e2 are added with a phase angle of 60 degrees, the 3rd harmonic of e1 cancels the 3rd harmonic of e2, resulting in the elimination of the 3rd harmonic from the output voltage.
Mathematical Explanation:
The output voltage of a full bridge inverter can be represented as:
V = Vm sin(wt) + Vm/3 sin(3wt) + Vm/5 sin(5wt) + ...
If two full bridge inverters are connected in series with a phase angle of 60 degrees, then the output voltage can be represented as:
Vout = V1 + V2
where,
V1 = Vm sin(wt)
V2 = Vm sin(wt+60)
Substituting the values, we get:
Vout = Vm sin(wt) + Vm sin(wt+60)
Using the trigonometric identity,
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
we can write,
Vout = Vm [sin(wt)cos(60) + cos(wt)sin(60)]
Vout = Vm sin(wt+30)
Thus, the output voltage has a phase angle of 30 degrees. As the 3rd harmonic has a phase angle of 180 degrees, it gets cancelled out and eliminated from the output voltage.
Conclusion:
Hence, the phase angle between e1 and e2 should be 60 degrees to eliminate the 3rd harmonic from the output voltage.
The full bridge inverter produces an output voltage with a fundamental frequency and harmonics of 3rd, 5th, 7th, etc. If the output voltage of two full bridge inverters is added using an output transformer, then the harmonics of the output voltage will also get added. Thus, it is necessary to eliminate the 3rd harmonic from the output voltage.
Phase Angle:
The 3rd harmonic can be eliminated if the phase angle between e1 and e2 is 60 degrees. This is because the 3rd harmonic is an odd multiple of the fundamental frequency and has a phase angle of 180 degrees. When e1 and e2 are added with a phase angle of 60 degrees, the 3rd harmonic of e1 cancels the 3rd harmonic of e2, resulting in the elimination of the 3rd harmonic from the output voltage.
Mathematical Explanation:
The output voltage of a full bridge inverter can be represented as:
V = Vm sin(wt) + Vm/3 sin(3wt) + Vm/5 sin(5wt) + ...
If two full bridge inverters are connected in series with a phase angle of 60 degrees, then the output voltage can be represented as:
Vout = V1 + V2
where,
V1 = Vm sin(wt)
V2 = Vm sin(wt+60)
Substituting the values, we get:
Vout = Vm sin(wt) + Vm sin(wt+60)
Using the trigonometric identity,
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
we can write,
Vout = Vm [sin(wt)cos(60) + cos(wt)sin(60)]
Vout = Vm sin(wt+30)
Thus, the output voltage has a phase angle of 30 degrees. As the 3rd harmonic has a phase angle of 180 degrees, it gets cancelled out and eliminated from the output voltage.
Conclusion:
Hence, the phase angle between e1 and e2 should be 60 degrees to eliminate the 3rd harmonic from the output voltage.
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The output value e1and e2of two full bridge inverter are added using output transformer. In order to eliminate the 3rdharmonic from output voltage, the phase angle between e1and e2should be ______ degree.Correct answer is '60'. Can you explain this answer?
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