ideas about envelope detector

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envelope detector how the the envelope detector works in time and frequency domain the envelope detector condition

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  • Understand all the needed ideas about envelope

    detector in time and frequency domain

    By : Oussama Gassab

    Contact : [email protected]

  • (( ))

    282

  • 1- to understand how the envelope detector demodulate the

    signal (( how it extract the original signal s(t) from the

    modulated signal x(t) )) and why the condition 1

    RC 0

    must be achieved , we have to analyze the concepts in frequency

    domain

    When look to the phenomena of envelope detector in time

    domain we will see only the detection of the envelope ,

    when the capacitor is charged and discharged, and all the

    other amazing concepts cannot be seen

    Because when we try to construct and prove the relation

    1

    RC 0 we will only say that the period of the charging

    capacitor must be very large than the period of the frequency 0

    so 0 0 1

    RC 0

    But when we try to prove 1

    RC we will not have clear

    vision in time domain .

    To take very clear understand we have to observe the

    phenomena in both time and frequency domains.

    Since the AM signal is in the

    form

    = 1 + 0

    The diode is On for the

    positive wave of 0 and

    is Off in the negative wave

    So the diode will follow the following graph

  • The Fourier series of this signal

    =1

    2+

    2

    (1)

    2 + 1

    +

    =0

    cos(2 + 1)0

    So the current i(t) is

    = where = 1 + 0 so

    = 1 + 1

    20 +

    2

    1

    2 + 1 0

    +

    =0

    cos(2 + 1)0

    We have

    0 cos 2 + 1 0 =1

    2 cos 2 + 2 0 + cos(2)0

    With small simplification we got :

    = 1 + 1

    +

    1

    20

    2

    1

    42 1 20

    +

    =1

    We have obtained the Fourier series of the current through the

    diode

    When we drew the spectrum () of the current , we will

    observe

    If the spectrum of s(t) is given by

    0 t

    d(t)

    1

  • Than the spectrum of () is given by

    The resistor and the capacitor circuit

    construct low pass filter with transfer

    function

    =

    1+ the cutoff frequency is

    1

    and

    Rits graph as shown

    below . when the current passes

    through this low pass filter

    We will obtain the original signal as

  • Shown below

    So to retain our signal that must 1

    RC must be between 0

    and and since 0 that is mean 1

    RC must satisfy the

    condition 1

    RC 0

    As an remark we have always to understand any phenomena in

    both time and frequency domains in order to get complete

    understanding about this phenomena