e6midtermsolutionsW10

# e6midtermsolutionsW10 - Engineering 6 Winter 2010 Midterm...

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In the single phasor form, the ( ) t j j e Ae ω ϕ part is a complex number that moves counter-clockwise in a circle of radius A in the complex plane as t varies (all the other quantities are constants). The real part of this "rotating phasor" at any given time t is the value of x(t) at that time t. In the dual phasor form, there are two phasor-like terms. The first one is a complex number that moves counter-clockwise in a circle of radius A/2 in the complex plane as t varies. The second term is a complex number that moves clockwise in a circle of radius A/2. At any given time t, the imaginary part of the first complex number is equal and opposite to the imaginary part of the second complex number. So when the two terms are added together, the imaginary parts cancel and one is left with a real value, which is the value of x(t) at that time t (and is the same value you would get using the single phasor version). For further explanation and sketches, see the "Phasors 1" and "Phasors 2" video clips. (In the first case, the
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e6midtermsolutionsW10 - Engineering 6 Winter 2010 Midterm...

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