Find conversion effiiencies of half and full-wave converters

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Reference no: EM13272126

In an AC-DC power adapter, one of the following two conversions is used: half-wave recti?er and full-wave recti?er. The half wave recti?er can be described mathematically as a system with input x(t) and output y(t) such that

y(t) = {x(t), if x(t) ≥ 0, {0, if x(t) < 0,

whereas the full-wave recti?er can be de?ned as a system with input x(t) and output z(t) such that

z(t) = |x(t)|,

where | · | stands for absolute value.
After rectifying, only the DC component is kept, and other components are eventually ?ltered out. The conversion e?ciency can be described by
η =(|a0|2)/(A2/2)
where A2/2 is the input power, and a0 is the output DC component amplitude.
Suppose the input is

x(t) = Acos(2πf0t)

where f0 = 60 Hz, and A = 110.
b) Find the spectrum of the output y(t) of a half-wave recti?er with input x(t).
d) Find the spectrum of the output z(t) of a full-wave recti?er with input x(t).
e) Find the conversion e?ciencies of the half- and full-wave converters.

Reference no: EM13272126

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