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OCTC and SCTC methods to analyze pole/zero locations in 1st order circuits

Discussion in 'Electronic Basics' started by firebird, Feb 5, 2007.

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  1. firebird

    firebird Guest

    Suppose a simple first order circuit has the following form:

    K*(1+s*Tau_z)
    -----------------
    (1+s*Tau_p)

    Where Tau_z and Tau_p are the zero and pole time constants,
    respectively. To find these, I've read somewhere that a shortcut
    method is to use the open circuit time constant method (OCTC) and the
    short circuit time constant method, if the circuit follows a voltage
    divider topology. Basically, to find the zero time constant, you can
    open the input and short the output to ground, and find the thevenin
    resistance w.r.t the relevant capacitor (Then, Tau_p = C * Rth). To
    find the pole time constant, we can short the input to ground and open
    the output.

    Why do these tests work? I think I understand the idea of time
    constants as approximate locations of zeros and poles (the locations
    where a capacitor's impedance equals the Rth around it)...but why do
    we open the input for the zero and short the input for the pole? Can
    anyone shed light on this issue?

    Thanks!
     
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