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How can I deduce the damping characteristics formula?

Discussion in 'Electronics Homework Help' started by chrisjrollin, Aug 3, 2015.

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  1. chrisjrollin

    chrisjrollin

    5
    0
    May 3, 2015
    Dear members,

    I've got the interest arranging and deducing the formulas defining the damping characteristics of RC lag lead filter.

    This is the circuit I've designed:
    RC_Lag_Lead_Filter.png

    And this is sort of the arrangements to deduce the damping characteristics formula.
    RC_Lag_Lead_Filter_Formula_Arrangements-1.png

    And the problem is that, I'm trying to make the arrangements into the deduced form below:
    RC_Lag_Lead_Filter_Formula_Arrangements-3.png


    But this is the arrangement having the deduced form at its end and I could make as much far as possible:
    RC_Lag_Lead_Filter_Formula_Arrangements-2.png

    Is there any missing steps or wrong arrangment that I've made in the calculations above?
    I would gratefully take your advice and help to improve my knowledge.

    Thanks for your interest to my question.

    * References:
    http://old.iihr.uiowa.edu/~hml/people/kruger/Teaching/ece_55141_2012/Articles/PLLExtract.pdf
    http://mars.uta.edu/mae4310/handouts/compensator_realization.pdf
    http://www.ece.ucsb.edu/~long/ece594a/PLL_intro_594a_s05.pdf
    http://www.ti.com.cn/cn/lit/an/scha003b/scha003b.pdf
     
  2. LvW

    LvW

    604
    146
    Apr 12, 2014
    I think, you must fail if you are trying to find a second-order function for a first-order circuit.
    The first part of your calculation is, of course, correct.

    Note that on page 632 of the 1st document we have two different finctions: First-order F(s) and second-order T(jw).
     
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